Fuel-E cient Platooning of Heavy Duty Vehicles through Road Topography Preview Information

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1 Fuel-E cient Platooning of Heavy Duty Vehicles through Road Topography Preview Information LUKAS BÜHLER Master s Degree Project Stockholm, Sweden August 213 XR-EE-RT 213:2

2 Fuel-E cient Platooning of Heavy Duty Vehicles through Road Topography Preview Information LUKAS BÜHLER Master s Thesis at the Automatic Control Laboratory of KTH, Stockholm Supervisors: Assad Alam, Jonas Mårtensson Examiner: Prof. Karl Henrik Johansson Examiner at ETH: Prof. Manfred Morari XR-EE-RT 213:2

3 I Abstract Road freight transport is a growing business and serves as a centerpiece of modern economics. Traffic congestions due to the increasing amount of vehicles, growing environmental problems due to CO 2 emissions and rising fuel prizes create a vast demand for solutions to these global issues. Look ahead cruise control and vehicle platooning can be part of a future transport concept. By using GPS localization and considering road topography data (map data), a Look Ahead Cruise Controller LAC optimizes the velocity profile of a single vehicle when facing steep up- or downhills in order to save fuel. Platooning describes the concept of driving vehicles in a convoy with short intermediate distance to reduce the aerodynamic drag and achieve considerable fuel consumption reductions for all vehicles in the platoon. However, research on platooning with road topography preview information is a novel topic. In this thesis, look ahead cruise control and platooning are analyzed and results are combined in order to develop a platoon look ahead controller (PLAC). The PLAC features low computational complexity due to a simple parametric optimization method and reaches simulated energy consumption reductions of up to 2% for a vehicle in the platoon compared to its single drive on the same road. When velocity limits are considered, the fuel saving potential is even higher. It can be shown that the reached energy consumption with a PLAC lies slightly (1.3%-1.9%) over a minimum energy consumption needed to traverse the road section. Results reveal that in practical situations, a platoon should be maintained whenever possible. Errors in parameters of the vehicle, road parameters and localization errors are analyzed in terms of their influence on the energy consumption. Strategies are presented to reduce the influence of parameter errors on the fuel consumption and especially reduce the chance of a separate of the platoon.

4 II Preface With this thesis, I complete my studies for a Master of Science in Electrical Engineering and Information Technology at ETH Zurich. As an exchange student, I wrote this thesis at KTH in Stockholm. However, the thesis will be part of my ETH diploma. I believe that the reduction of the consumption of fossil fuels and the lowering of CO 2 emissions to the environment will become main global issues in the upcoming centuries. In the freight transport sector, there is clearly a large potential for improvement where platooning can be part of a future transport concept. The importance of this issue, the technical challenges and the close relation to reality were my personal motivation. I enjoyed working on this topic and writing my thesis and I hope to have contributed thereby to future transport concepts. Acknowledgement I would like to express my deepest gratitude to Prof. Karl Henrik Johansson at KTH, who was my main advisor and examiner. He made it possible for me to write my thesis within his group. I highly valuate his good inputs and his communication on eye-level with students. With Assad Alam and Jonas Mårtensson, I had the privilege to have two very committed supervisors. I would like to thank both of them for the inspiring meetings we had and the valuable tips and inputs I received. A special thank goes to Prof. Manfred Morari at ETH, who made it possible for me to write my master thesis in Sweden. Many thanks go to my parents for supporting me during all of my education and studies. Without you, I would not have reached this success in my life. And last but not least, I am very grateful to my beloved girlfriend Caroline, who gave me the support I needed during all my years of studying. Lukas Bühler Stockholm, August 213

5 Contents Abstract Preface I II Nomenclature 1 1 Introduction Problem Formulation Thesis Outline Model and Definitions Equation of motion Engine Force Brake Force Aerodynamic Drag Force Roll Resistance Force Gravity Force Engine Model Model simplification Engine fueling Definitions and Assumptions Definition of road gradients Definition of expressions Definition of road section use cases Assumptions Fuel and energy consumption measurement Look Ahead Cruise Control for a single HDV Optimal control Intuitive explanation of optimal control solution Velocity limits Parametric optimization for finding energy optimal velocity profile Requirements for a look ahead controller for a vehicle in a platoon Cruise Controller as a reference Simulation results of LAC vs. CC and discussion Energy saving comparison and dimension estimation 23 III

6 CONTENTS IV 4.1 Fuel and energy consumption Roll Resistance Energy Potential Energy Kinetic Energy Brake Energy Aerodynamic Drag Energy Total energy losses Variance reduction due to the use of an LAC Fuel efficiency due to brake usage reduction Fuel efficiency due to platooning Comparison between fuel saving strategies Platooning with road topography preview information Acceleration agreement among a platoon Shifting the velocity profile in order to maintain the platoon Platoon Look Ahead Controller Intermediate distance Velocity limits and brake usage minimization Simulation and Discussion of the PLAC HDV order in a platoon Platoon splitup investigation Energy consumption comparison between different controllers Parameter Error Influence and Control Actions Vehicle Parameter Error Causes of Vehicle Parameter Errors Estimation error in minimum acceleration Estimation error in maximum acceleration Control actions on platoon velocity profile on VPE Preventing a Vehicle Parameter Error Road Parameter Error RPE without velocity limit constrains RPE with velocity constrains Conclusion and Outlook Conclusion Outlook and Future Work References Appendix II IV A IV A.1 Master Thesis Definition V A.2 Declaration of Originality VII A.3 Variables and Parameters VIII A.4 Cruise Controller vs. LAC for a single HDV IX

7 CONTENTS V A.4.1 No velocity limits IX A.4.2 Upper velocity limit of 9km/h XI A.5 PLAC XIII A.6 Road Parameter Error Simulations XIV

8 Nomenclature Acronyms and Abbreviations ACC CC ETH HDV ITS KTH LAC MPC PLAC RPE VPE Adaptive Cruise Controller Cruise Controller Federal Institute of Technology Zurich Heavy Duty Vehicle Intelligent Transportation Systems Royal Institute of Technology Stockholm Look Ahead Cruise Controller Model Predictive Control Platoon Look Ahead Controller Road Parameter Error Vehicle Parameter Error 1

9 Chapter 1 Introduction The road transport sector for goods has grown rapidly over the past centuries tonnekilometers were driven by freight transports on roads of the EU-27 states in 21 [9] The increasing density of vehicles on roads causes traffic congestions and expensive renewals of the infrastructure are carried out in many places. Beneath the road capacity problem, the increasing traffic accounts for resource shortage and environmental problems. Global warming is growing to a major environmental problem worldwide, caused by the CO 2 exhaust and other greenhouse gasses. Road freight transport, which is carried out mainly through fossil fuel combustion, is responsible for a significant part of the problem. The road transport sector accounts for 71% of all CO 2 emissions from transports within Europe [1]. Aside of environmental problems, fossil fuels are a diminishing energy source. Fuel prices have increased during the past years and account for around one third of the life cycle cost for a Heavy Duty Vehicle (HDV) [17]. Both from an economical and environmental point of view, effort is required in order to reduce the usage of fossil fuels for road transports. During the past centuries, significant improvements in the efficiency of HDVs were achieved through technological progress. The focus mainly lied on the increase in efficiency of the motor and drive train, but not on intelligent traffic control. Modern transport concepts for road transportation as part of Intelligent Transportation Systems (ITS) are being developed. One main objective is the fuel usage reduction of HDVs and the avoidance of traffic congestions. Optimization in terms of avoiding empty drives, better utilization of vehicles and fuel-efficient driving is demanded. New communication standards [1] have been defined in order to implement Vehicle-to-Vehicle V2V and Vehicleto-Infrastructure V2I communication, which will be important for a future ITS. The concept of driving vehicles in a convoy (platooning) can be part of a solution to the above mentioned problems of road congestion, CO 2 emission and limited fuel resources. By driving in platoons, the road capacity can be increased and the fuel consumption can be reduced [7]. Figure 1.1 shows a vehicle platoon on a highway with short intermediate distance among the vehicles. The aerodynamic drag (airdrag) forces, which are responsible for a major part of the energy losses of a vehicle, can thereby be reduced significantly. Studies on 1

10 CHAPTER 1. INTRODUCTION Swedish highways show that the fuel consumption of a following vehicle can be reduced by up to 4-7% by using the Adaptive Cruise Controller ACC with a short intermediate distance [3]. This controller measures the distance to the HDV in front and holds a predefined distance. A framework for a future HDV platooning concept is presented in [2] by using decentralized LQR control. Figure 1.1. Demonstration of HDV platooning on a highway1 A typical HDV is not able to hold a constant velocity over steep uphill or downhill slopes on a highway due to the limited engine power. On uphill slopes, the vehicle decelerates while applying full throttle. Whereas on downhill slopes, the vehicle accelerates while applying zero throttle. This fact was addressed in several scientific papers in order to find control strategies to minimize the fuel consumption of a single vehicle by using the knowledge about the road topography in front of the vehicle, hereinafter referred to as look ahead cruise control LAC. Fuel optimal control by keeping an over all constant travel time with road topography preview information for a single HDV has been studied in [11], [12], [13] and [14]. Fuel minimizing velocity profiles for a single HDV on a set of simple road profiles are shown in [12]. The optimal control input for an affine engine model consists of sections of zero fueling, sections of full fueling and sections where the fueling is selected in order to keep the velocity constant [13]. The optimal velocity profile to traverse a downhill section is described by a fuel cut-off before the slope, so that the speed is reduced until the start of the slope. The vehicle accelerates during the downhill and reaches a higher speed than the initial speed. After the slope, it decelerates to its initial velocity where steady fueling is taken up again. Similar for an uphill section, full fueling is applied before the uphill so that the vehicle accelerates until the start of the slope. Even with maximum fueling during the uphill, the vehicle decelerates and the speed is reduced until the end of the slope. After the slope, it gains speed so that it reaches its set velocity after the uphill. Platooning requires a coordinated control of the vehicles due to their deviating acceleration when it comes to steep hills on a highway. 1 Source: Courtesy of Scania CV AB 2

11 CHAPTER 1. INTRODUCTION 1.1 Problem Formulation The problem addressed in this thesis is fuel-efficient control of a platoon for a given road topography. Therefore, a platoon of N heterogeneous vehicles as shown in Figure 1.2 is considered. The slope of the road, α(s), in front of the platoon is assumed to be known and the vehicles are assumed to be equipped with wireless communication, which makes local centralized control possible. N N v N v N-1 v 2 1 v 1 α Figure 1.2. HDVs driving in a platoon experience a decreased air drag force and can therefore reduce their fuel consumption considerably. Over downhill or uphill sections, the individual vehicles might not be able to maintain a constant velocity, which requires a control strategy for the whole platoon in order to traverse the slope with the objective of fuel consumption minimization. On the level road in front of a steep road section, the platoon is in steady state with a set velocity and constant spacing between the vehicles. Strategies and control should be investigated in order to minimize the fuel consumption of the whole platoon for the given road topography by maintaining a given average speed (constant travel time) after the slope. Control actions are completed when the platoon is back in steady state on level road. It is of particular importance that the control solution is of low computational complexity, which makes the implementation on the vehicle feasible. Therefore, the interest lies not only on optimal control in terms of fuel reduction, but also on simple control strategies in order to implement fuel-efficient drive. In a final step, the influence of erroneous assumptions about parameters (vehicle, map data, localization error) should be investigated and strategies in terms of control should be found. 1.2 Thesis Outline In chapter 2, the used model for HDVs is presented and simplifications are explained. Look ahead cruise control for a single vehicle is addressed in Chapter 3. The optimal control inputs for a single vehicle are derived and parametric optimization is presented as a solution in order to implement an optimal controller with low computational complexity. Due to the fact that the optimal control problem grows significantly in complexity when considering not only a single vehicle, but a platoon, energy flows and fuel saving potentials in a vehicle platoon is analyzed in Chapter 4. This leads to the design of a PLAC in Chapter 5, which combines the highest energy saving possibilities and achieves energy consumptions, which lie only slightly above the calculated minimum energy consumption. In Chapter 6, the influence of errors is investigated and conclusions are drawn in order to prevent severe effects on the 3

12 CHAPTER 1. INTRODUCTION fuel consumption. Chapter 7 summarizes and discusses the obtained results and gives an outlook on future work. 4

13 Chapter 2 Model and Definitions This Chapter presents the model of an HDV used for calculations and simulations. The model assumes a vehicle reduced to its ability of longitudinal movement. This means the vehicle is considered without any sideway steering action. The equation of motion was derived in [2]. This equation of motion provides a general model of a vehicle without any restrictions to a specific type of HDV. An engine model for the 12 liter Scania DT1211 L2 diesel combustion engine was presented in [16]. This model was used as a reference to derive a general engine model. This engine model should apply to various vehicle engines. Input to the system is therefore not a throttle input, but the torque requested from the engine. All variables and parameters are described in appendix A Equation of motion The equation of motion describes the acceleration of the vehicle v depending on the forces acting on the vehicle. It was derived in [2]. v = 1 m t (F engine (ω e, P ) F brake F airdrag (v, d) F roll (α) F gravity (α)) (2.1) The acting forces are illustrated in Figure Engine Force The engine force is produced through the torque of the engine T e acting on the power train which drives the wheels of the vehicle. The engine torque mainly depends on the applied throttle position P [, 1] and the current engine speed ω e. Over the shifting gear with ratio i t, efficiency η t, the gear of the final drive with ratio i f and efficiency η f, the torque is applied to the wheels with radius r w. The wheels then apply a force F engine acting on the vehicle. F engine = i ti f η t η f r w T e (ω e, P ) (2.2) 5

14 CHAPTER 2. MODEL AND DEFINITIONS Figure 2.1. Forces acting on the HDV Brake Force The brake force is considered as a direct input to the system to slow the vehicle down Aerodynamic Drag Force The aerodynamic drag force is produced by the airflow around the vehicle. It depends on the coefficient for the aerodynamic drag c d (d), the density of the air ρ a, the area exposed to the airflow A a and the velocity of the vehicle v. It should be remarked that the aerodynamic force is proportional to v 2. For an HDV with a mass m = 4kg on a flat road α = with a speed of v = 85km/h, the aerodynamic drag force is responsible for around 65% of the repulsive forces acting on the vehicle. F airdrag = 1 2 c D(d)A a ρ a v 2 (2.3) The aerodynamic drag force of a vehicle is reduced if it drives in a platoon due to the vehicles surrounding it. This reduction of the aerodynamic drag coefficient was found in empirical tests in a wind tunnel and is described in [3]. 6

15 CHAPTER 2. MODEL AND DEFINITIONS Figure 2.2 shows the model for the reduction of the air drag coefficient. It is assumed that the distance to the vehicle ahead (lead vehicle) d l and the distance to the follower vehicle d f is known and the total c D reduction is calculated as a function of the distances as shown in equation 2.4. c Dreduction (d l, d f ) = c Dreduction-l (d l ) + c Dreduction-f (d f ) (2.4) The empirical air drag reduction was approximated with a 3rd order least squares polynomial fit. For all simulations, the approximated polynomial fit was used and the calculation of the c D reduction was done according to equation Reduction due to following vehicle (d f ) Reduction due to 1 leading vehicle (d l ) Reduction due to 2 leading vehicle (d l ) 6 c D reduction [%] Distance d l, d f [m] Figure 2.2. c D reduction due to a vehicle in the back (follower vehicle) and one or two vehicles in the front (lead vehicles) Roll Resistance Force The roll resistance force acts on the HDV due to friction losses in the tires and wheels. It depends on the roll resistance constant c r, the mass of the vehicle m, the gravity constant g and the road angle α. F roll (α) = c r mg cos(α) (2.5) Gravity Force As soon as the road is not flat, α, the gravitational force influences the vehicle strongly, especially vehicles with a high mass m. F gravity (α) = mg sin(α) (2.6) 7

16 CHAPTER 2. MODEL AND DEFINITIONS In order to unite rotational movements and longitudinal movements, a total inertial mass m t is used in the equation of motion. It is calculated as follows: m t = m + J w r 2 w + i2 t i 2 f η tη f J e r 2 w (2.7) Distance reference A given road profile defines road gradients as a function of distance in front of a vehicle. The equation of motion is therefore adapted from time reference to distance reference in order to simplify calculations. The infinitesimal horizontal distance element ds is assumed. v = dv dt = dv ds ds dt = dv ds v (2.8) (2.9) dv ds = 1 (F engine F brake F airdrag F roll (α) F gravity (α)) (2.1) v m t = 1 ( it i f η t η f T e (ω e, P ) F brake 1 ) v m t r w 2 c D(d)A a ρ a v 2 c r mg cos(α) mg sin(α) (2.11) 2.2 Engine Model The engine torque model derived in [16] was used. The engine torque, T e, depends on the engine speed, ω e, and the fueling, γ: T e (ω e, γ) = { ae ω e + b e γ + c e, γ > a d ω e + b d, γ = (2.12) The fueling is approximated by γ = P ˆγ max with the throttle input P [, 1] and the approximation for the upper bound of the fueling: ˆγ max (ω e ) = a γ ω 2 e + b γ ω e + c γ (2.13) The parameters a γ,b γ and c γ are characteristic engine coefficients. The engine speed ω e is coupled with the velocity of the vehicle, v, over the gear ratios and the wheel radius: ω e = iti f r w v Model simplification The above shown engine model represents the 12 liter Scania DT1211 L2 diesel combustion engine as presented in [16]. Other engines have different parameters and therefore different engine characteristics. In order to get a general applicable engine model, the above mentioned model was analyzed and characteristics were simplified. 8

17 CHAPTER 2. MODEL AND DEFINITIONS Figure 2.3 shows the range of the engine torque T e depending on the velocity for the highest gear. The green area shows the engine torque T e which can be reached by variation of the throttle position P [, 1] at different vehicle velocities with the highest gear. In order to simplify this model, a lower and upper limit for the engine torque T e was defined which can be reached over the whole relevant speed range with this engine. The new input of the system is the engine torque T e [T min, T max ]. This leads to the following motion of equation with the engine torque T e [T min, T max ] as input: dv ds = 1 ( it i f η t η f T e F brake 1 ) v m t r w 2 c D(d)A a ρ a v 2 c r mg cos(α) mg sin(α) (2.14) (2.15) T max T e [Nm] 1 5 T min v [km/h] Figure 2.3. Engine torque range depending on the vehicle velocity Engine fueling The fueling for a given engine torque T e and an engine speed ω e can be calculated for the 12 liter Scania DT1211 L2 diesel combustion engine as shown in (2.16). γ(ω e ) = 1 b e (T e a e ω e c e ) (2.16) Figure 2.4 shows the fueling of an HDV driving with the highest gear. The fueling depends on the velocity and the applied torque. It can be seen that the dependency on the velocity is negligible compared to the dependency on the torque. This function also changes with the engine. To use a general model for the fueling, the engine torque T e can be integrated over 9

18 CHAPTER 2. MODEL AND DEFINITIONS 25 Fueling γ [mg/stroke] T e [Nm] v [km/h] Figure 2.4. Fueling function the distance to get a correct appraisal of the consumed fuel. The following affine engine fueling model is assumed: γ = k T T e + c T (2.17) 1

19 CHAPTER 2. MODEL AND DEFINITIONS 2.3 Definitions and Assumptions Definition of road gradients HDVs are typically not able to hold their velocity constant on various road gradients of highways. On steep uphill segments, a fully loaded HDV is decelerating even if full engine torque is applied. On steep downhill segments, an HDV is accelerating even if minimum engine torque is applied without using the brake. Therefore, the following definition of road gradients can be stated: small gradient T e such that dv ds = steep gradient T e such that dv ds = T max T e T min (2.18) T max T e T min (2.19) Definition of expressions Coasting: Reducing the engine fueling to the minimum, so that the engine applies a braking force on the vehicle Definition of road section use cases A real road can be considered as a sequence of road sections with constant inclinations. The test road profiles were constructed to be easy enough to be used for the derivation of fuelefficient velocity profiles and still capture the properties of real roads. Use cases 6 and 7 were designed in order to investigate the influence of an asymmetrical road profile, especially when velocity limits are considered. 11

20 CHAPTER 2. MODEL AND DEFINITIONS Figure 2.5. Road profiles 12

21 CHAPTER 2. MODEL AND DEFINITIONS Assumptions Equal Power Trains: All vehicles are assumed to have the same powertrain and therefore the same torque range T e [T min, T max ]. Velocity Range: HDVs are assumed to drive in a limited velocity range of 7-1km/h. This range contains the upper speed limits on european highways (8km/h or 9km/h) and provides a reasonable range for variation. This gives also reason to the engine model simplifications (affine engine model) done in Section 2.2. Gearshifts: Constant Travel Time: Inter-Vehicle Distance: Velocity Limit Constraint: Gearshifts require a more complex engine and fueling model. Due to the limited velocity range, no gearshifts are considered. One exception are lower velocity limits. The vehicle is then assumed to shift gear immediately without any temporary loss of engine torque. A constant travel time or an average velocity respectively is assumed as constraint to be fulfilled after traversing the slope. This assumption is important since otherwise the velocity would drop to zero for the optimization criteria. The average velocity should be maintained as soon as possible after the steep slope. This requirement comes due to the fact that the controller of the platoon acts in a wider context together with other more global acting controllers. Other platoons depend on the schedule of the controlled platoon. Investigations about the minimum distance between two vehicles in terms of safety and crash avoidance were done in [4]. If no time delay in the communication between two vehicles is assumed and two vehicles have the same velocity, it is reasonable to define a minimum distance d min which is independent of their velocity. This minimum distance depends on vehicle parameters like the weight or the tires but remains constant while driving. Therefore, the distance between two vehicles has to fulfill the following constraint: d d min Upper velocity limit constraints are required due to speed limits on roads. If an upper velocity limit is considered, it makes sense to also consider a lower velocity limit. Otherwise the velocity is likely to exceed the velocity range where the engine simplification is reasonable. 13

22 CHAPTER 2. MODEL AND DEFINITIONS Fuel and energy consumption measurement One of the main subjects of this thesis is the fuel consumption minimization for an HDV on a given road profile. Therefore, the fuel and energy consumption of a vehicle is often given in simulation results. It will be shown in Section that the fuel consumption is closely related to the energy consumption of a vehicle and that the minimum of the fuel consumption is equal to the minimum energy consumption. The calculation of the fuel and energy consumption is done according to (2.2) and (2.21). Fuel: F = Energy: E = sb s a i t γds (2.2) sb s a F airdrag + F roll + F brake ds (2.21) The distance s a describes the point where the first control action in front of a steep road section starts, i.e. the point at which the first vehicle starts accelerating or decelerating. s b describes the point where the last control action is completed in order to get the last vehicle back to a constant velocity. 14

23 Chapter 3 Look Ahead Cruise Control for a single HDV A typical HDV is unable to maintain a constant velocity on uphill or downhill sections of a normal highway. On steep uphill slopes, the engine can not provide enough power to maintain the velocity and the vehicle decelerates. On steep downhill sections, a heavy vehicle might accelerate even if no fueling is applied to the engine (Section 2.3.1). This behavior of an HDV gives rise to the question of finding an optimized velocity profile which minimizes the fuel consumption. The problem of fuel consumption minimization for a single vehicle on a given road segment with a given travel time was addressed in several scientific works. Optimal velocity profiles for simple road topographies can be found analytically [12]. Fuel optimal control with road topography preview information for a single HDV has been studied in [11], [12], [13] and [14], hereinafter referred to as Look Ahead Cruise Control (LAC). In all cases of finding an optimal velocity profile for a given road topography, it is assumed that the travel time T t will be maintained with every strategy. In other words, the average velocity v av is constant over the investigated section of the road. 3.1 Optimal control The problem of minimizing the fuel consumption of an HDV by controlling the velocity on a given road topography with a given travel time has been analyzed in [12] and [13]. Below, the optimal control inputs to the system are derived in brief. The method was adopted from [13]. An affine engine fueling model as presented in this thesis (2.17) was used for the derivation of optimal control solutions. The vehicle is assumed to drive in the highest gear and the gear ratio i t is therefore assumed to be constant. The optimal control problem can be formulated as fuel consumption minimization over the distance s f which is equivalent to the minimization of the integration of the input T e over the distance by(2.17). A constant travel 15

24 CHAPTER 3. LOOK AHEAD CRUISE CONTROL FOR A SINGLE HDV time T t will be maintained: min s.t. sf sf γds min sf T e ds (3.1) 1 v ds = T t (3.2) With the states x = [v, T t ] T and the state equations for the dynamics of the velocity and the travel time: dv ds = 1 ( it i f η t η f T e 1 ) m t v r w 2 c DA a ρ a v 2 c r mg cos(α) mg sin(α) = f v (3.3) dt t ds = 1 v = f T (3.4) Pontryagin s minimum princeple is used in order to find the optimal input torque T e (s). The Hamiltonian can be stated as follows: H = T e + λ v f v + λ T f T (3.5) The adjoint state variables, λ v and λ T are calculated according to (3.6). dλ ds = xh(x(s), T e (s), λ(s), s) (3.6) dλ v ds = λ ( ) v it i f η t η f m t v 2 T e c r mg cos(α) mg sin(α) + 1 r w 2 c DA a ρ a + λ T v 2 (3.7) dλ T ds = (3.8) The optimal input T e (s) minimizes the Hamiltonian: T e (s) = argmin T e {H (x(s), T e (s), λ(s))} (3.9) It can be seen that the Hamiltonian is linear in T e, which means that the optimal control will consist of sections of minimum engine torque, maximum engine torque and sections where =. The latter sections are called singular arcs. dh dt e dh = i ti f η t η f λ v + 1 = (3.1) dt e m t r w v During singular arcs λ v is given by λ v = rwmt i ti f η tη f v and it must hold that d ds ( dh dt e ) =. ( ) d dh = d ( ) it i f η t η f λ v (3.11) ds dt e ds m t r w v = i ( ti f η t η f 1 dλ v m t r w v ds λ ) v v 2 f v (3.12) = i ( ) ti f η t η f 1 c d A a ρ a λ v v + λ T v 3 = (3.13) m t r w mt 16

25 CHAPTER 3. LOOK AHEAD CRUISE CONTROL FOR A SINGLE HDV By solving (3.1) for λ v and inserting into (3.13), the following equation must apply for singular arcs: ( 1 c d A a ρ a + i ) ti f η t η f λ T v 3 = (3.14) r w m t Due to the fact that λ T is a constant, the velocity must be constant during singular arcs. This means that the system is stationary. The optimal input during singular arcs can therefore be defined as the torque which keeps the velocity constant. The optimal control input T e (s) will therefore consist of the following input torques: T e (s) = [T min, T stat, T max ] with T stat = T e s.t. dv ds = (3.15) This result simplifies the complexity of finding the optimal control input for a given road profile. As described in [13], the optimal control solution will consist of the following pattern: Constant engine torque T e = T stat for flat road and small gradients Maximum engine torque T e = T max in and in the neighborhood of steep uphill slopes. Minimum engine torque T e = T min in and in the neighborhood of steep downhill slopes. The problem of finding an optimal speed trajectory was therefore reduced to a parametric optimization problem of finding the positions for switching between optimal control inputs [12]. This result is of particular significance since it highly reduces the complexity of the problem. 3.2 Intuitive explanation of optimal control solution The above stated conclusions about fuel optimal control can also be obtained intuitively. The energy losses of a vehicle consist to a major part of losses due to the air drag force. As it will be shown in Chapter 4, only the energy losses due to the air drag and the brake usage can be controlled. All other energy losses are independent of the driven velocity profile. Due to the fact that the air drag force is proportional to the square of the velocity F airdrag v 2, the strategy of maintaining a constant velocity on a road with small gradients is apparent. In case of a road profile with steep slopes, the argumentation for full and zero fueling can be comprehended by the illustration shown in Figure 3.1. The green to red lines show the range of fuel cutoff to maximum fueling. If maximum fueling is applied during the uphill, the deceleration of the vehicle is much lower compared to the situation where minimum fueling is applied. Therefore, the distance before and after the uphill where maximum fueling has to be applied is longer. In total, the variation of the velocity is higher and therefore also the aerodynamic drag energy. Similar, the downhill velocity profile can be analyzed. When minimum fueling is applied during the downhill, the variation of the velocity is lower and therefore also the aerodynamic drag energy. 17

26 CHAPTER 3. LOOK AHEAD CRUISE CONTROL FOR A SINGLE HDV The objective of finding the optimal control solution for an uphill(downhill) as shown in Figure 3.1 is reduced to the question of finding the position in distance where the torque is increased(decreased) to maximum(minimum) engine torque. Figure 3.1. The effect of fuel minimum fueling (green line) to maximum fueling (red line) during a steep uphill or downhill. The variation of the velocity profile is minimized by applying maximum fueling during the uphill and minimum fueling during the downhill. During the black velocity segments, the fueling is maximized on the uphill and minimized on the downhill. 3.3 Velocity limits Optimal control of a vehicle on a track with velocity limits was addressed in [13]. The velocity limit constraints cause the optimal control problem to be more complicated. The solution is described in the following way: The start of the deceleration on a downhill should be selected so, that the upper speed limit is reached exactly at the end of the slope. This will minimize brake usage and therefore minimize the total energy consumption. The same reasoning can be done for uphill slopes. The upper speed limit is exactly reached at the beginning of an uphill section. It can be seen in the next section about parametric optimization (3.4), that exactly the described solution will be found by optimizing the parameters. Therefore, no special attention has to be set to speed limitations in terms of finding the solution. 3.4 Parametric optimization for finding energy optimal velocity profile As shown in the previous sections, the problem of finding the optimal control solution for the engine torque in order to minimize the fuel consumption can be reduced to a parametric optimization. The switching points between the three possible optimal control inputs have to be found. For interconnected road sections of steep gradients without any small gradients in between, this parameter optimization is reduced to two parameters. Figure 3.2 shows a downhill profile with an upper velocity limit of 9km/h. A start parameter d s defines the distance to the slope in which the engine torque is reduced to the minimum. During the downhill, the only 18

27 CHAPTER 3. LOOK AHEAD CRUISE CONTROL FOR A SINGLE HDV possible input is minimum engine torque due to the fact that no input torque can maintain the velocity of the vehicle. After the slope, a final distance parameter d f is defined which is selected such that the average speed of the vehicle (constant travel time T t ) is maintained with the selected d s. Therefore, d s is used in order to find the minimum Energy. Altitude [m] v [km/h] Engine Torque [Nm] d s 5 1 d 15 f Figure 3.2. Parameter optimization for finding the optimal velocity profile (blue) for a 4t HDV on a downhill section of -3% over 5m. An upper velocity limit of 9km/h was assumed. The parameters d s and d f were found, which minimize the energy consumption within the constraint of a constant travel time. The gray lines show non-optimal profiles with shorter and longer start distance d s. For the sake of clarity, no lower speed limit was defined. The energy consumption for different values of the start distance d s is plotted in Figure 3.3 for the above shown situation. For every possible start distance, d f was selected such that the average velocity remains. The start distance d s was found by the golden section search method [8]. It can be seen that the energy consumption of the vehicle which is proportional to the integration of the engine torque over the distance, finds a minimum at a start distance d s of 27.5m. The HDV runs into the upper speed limit before the end of the slope if d s is selected shorter. The fact that the vehicle has to brake in this case causes a steep increase of the energy consumption for shorter start distances. If the start distance is selected longer, the final distance during which the velocity is held at the upper speed limit increases. This occurs due to the fact that the average velocity has to be maintained. Therefore, the variance of the velocity profile increases and the energy consumption rises. 19

28 CHAPTER 3. LOOK AHEAD CRUISE CONTROL FOR A SINGLE HDV x Energy [J] Start distance ds [m] Figure 3.3. Energy consumption depending on the start distance at which the vehicle starts to decelerate. Test conditions were a 5m/-3% downhill and a 4t HDV. An upper velocity limit of 9km/h was assumed. The high increase in energy consumption for short start distances is caused by brake usage during the downhill. 3.5 Requirements for a look ahead controller for a vehicle in a platoon A look ahead cruise controller for a platoon acts as one controller in a hierarchy of controllers for global path planing down to the control of a single vehicle. Therefore, additional basic requirements for an LAC used in platoons arise. In contrast to previously done work about look ahead systems, especially [16], a platoon LAC needs to fulfill the requirement of a constant average velocity as soon as possible after a section with steep gradients. This is important since globally acting controllers rely on the fulfillment of a timeline of one platoon. In addition, a platoon which was split for any reason will be maintained again at the end of a slope if every vehicle fulfills this requirement. 3.6 Cruise Controller as a reference In order to assess the performance of an LAC and later on the performance of a look ahead controller for platoons, the cruise controller CC for a single HDV is used as a reference. The objective of a CC is to hold the velocity to the set speed. On level road and small gradients, the CC adjusts the engine torque in order to hold a constant velocity. On steep gradients, a CC is not able to hold a constant velocity within the control input and the vehicle starts to accelerate or decelerate. A real cruise controller of an HDV does not fulfill the requirement of a constant travel time when it comes to steep gradients in the road profile. On a downhill section, the vehicle gains speed so that the average velocity will increase and vice versa on an uphill section. 2

29 CHAPTER 3. LOOK AHEAD CRUISE CONTROL FOR A SINGLE HDV In order to compare the performance of a new controller, a non-look-ahead controller, which maintains an average velocity, was desired. Therefore, the cruise controller was extended with a compensation of the average velocity. Hereinafter, whenever a CC is used, it compensates the average speed so that it can be compared to a new controller which holds an average velocity. Figure 3.4 shows the resulting velocity profile of a CC acting on a vehicle traversing a downhill section. At a distance of 5m, the CC is not able to hold the velocity anymore and reduces the engine torque to the minimum. Nevertheless, the velocity increases during the downhill. At a distance of approximately 15m, the velocity reaches the set speed. Due to the fact that the average velocity was too high up to this point, the CC starts do decelerate in order to fulfill the requirement of a constant average velocity as soon as possible. On an uphill road profile, the CC would on contrast to the downhill profile accelerate after the slope in order to fulfill the requirement of a constant average velocity as soon as possible. Altitude [m] v [km/h] Engine Torque [Nm] Figure t HDV with cruise controller on a 5m/-3% downhill section. After a distance of 15m, the controller compensates for the missed average velocity. 21

30 CHAPTER 3. LOOK AHEAD CRUISE CONTROL FOR A SINGLE HDV 3.7 Simulation results of LAC vs. CC and discussion Simulations with an LAC and a CC with post compensation for the missed average velocity were performed with all presented road profile use cases (section 2.3.3). The simulations were performed without speed limits and with an upper speed limit of 9km/h. The results are shown in table 3.1 and 3.2. Use Case: Energy Saving with LAC comp. to CC.48%.8%.54%.87%.23%.46%.94% Table 3.1. Energy saving with LAC compared to CC for all road profile use cases. All simulations were performed with a 4t HDV. Detailed results can be found in Appendix A.4.1. Use Case: Energy Saving with LAC comp. to CC 15.9%.43% 4.3% 5.49% 9.99% 13.8% 11.6% Table 3.2. Energy saving with LAC compared to CC for all road profile use cases. All simulations were performed with a 4t HDV and an upper velocity limit of 9km/h. Detailed results can be found in Appendix A.4.2. It can be seen that a look ahead controller saves up to 1% energy if no velocity limits are considered. As soon as the upper speed limit is introduced, the savings reach up to 16%. This result shows that a look ahead system is of particular advantage when speed limits force vehicles to brake. The above mentioned results should for the moment serve to familiarize with the dimension of the energy saving potential. In Chapter 4, a detailed analysis of the energy saving possibilities will be given. 22

31 Chapter 4 Energy saving comparison and dimension estimation The driven velocity profile of a single HDV can be optimized in order to minimize the energy consumption as shown in the last Chapter. The resulting velocity profile depends on various parameters of the vehicle. Especially the mass of a vehicle has a major influence on the driven optimal velocity profile. In a platoon, several vehicles of different masses travel together in order to save fuel due to the reduced aerodynamic losses. On a road with small gradients where every vehicle is able to maintain a constant velocity, the optimal solution in terms of energy consumption is obvious. By driving a constant velocity and minimizing the distance between the vehicles to the minimum allowed distance [4], this optimal solution is implemented. The air drag force acting on every vehicle will be minimal and will stay constant. Driving a constant velocity is the optimal solution for every vehicle as shown in the previous Chapter. However, when steep road gradients are considered, this solution does not hold anymore. The individual optimal velocity profiles for every vehicle diviate from each other, especially due to the mass differences of the vehicles. And if the vehicles drive different velocity profiles, the distance between each other will vary. Therefore, the air drag force will be higher than the minimum air drag force with minimum distance between the vehicles. Finding an optimal control solution for a platoon driving on a road with steep gradients which minimizes the total energy consumption of all vehicles is of much higher complexity than the previously shown optimal control solution for a single HDV. The results for the optimal control input found for a single HDV (3.15) do not apply anymore to vehicles traveling in a platoon. This makes the finding of an optimal control solution through parametric optimization computationally extremely intensive due to the increased number of parameters. Using dynamic programming is conceivable, but of high computational complexity. The aim of this thesis was to find a controller which is able to drive a vehicle platoon over a given road profile in a fuel-efficient way. This Chapter shows a new approach in order to identify cause and effect of energy flows in a vehicle traveling in a platoon. It sets the premise for the energy saving potential. 23

32 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION 4.1 Fuel and energy consumption The fuel consumption is a linear function of the generated engine torque T e as shown in Section and with assumed constant gear i t = const also linearly depending on the engine force F engine. In order to calculate the consumed fuel, the fueling γ is integrated over the driven distance s f : F = = sf sf i t γds (4.1) i t k T T e + i t c T ds (4.2) sf = i t k T T e ds + i t c T s f (4.3) (4.4) The minimization objective of the fuel can be stated as a minimization of the integration of the engine torque. Due to the proportionality between engine torque and engine force with assumed constant gear, it can also be seen as the minimization of the generated mechanical engine energy. Common constraint is a constant travel time T t. min (F) min T e s.t. sf T e ( sf T e ds ) ( sf ) min F engine ds = min (E engine ) (4.5) F engine F engine 1 v ds = T t (4.6) For all integrations, the infinitesimal distances as shown in Figure 4.1 will be used. A detailed description of this forces can be found in Section 2.1. Figure 4.1. Forces and infinitesimal distance elements In order to compare the energy consumption of HDV s driving different velocity profiles on the same topographic street profile, the general road profile shown in Figure 4.2 is used. The track has horizontal length s and road profile length s. The road angle α is assumed to 24

33 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION be known for the whole road profile. Therefore, the over all height difference between the start point and the endpoint h is also known. In addition, the initial velocity v i and the final velocity v f are assumed to be known. Figure 4.2. General road profile The energy consumption of a vehicle driving over the shown road profile can be calculated by the integration of its engine force over the driven distance as shown in (4.7). The integration can be separated into an integration over every acting force. This corresponds then to the aerodynamic drag energy, the roll resistance energy, the gravitational energy (or potential energy), the acceleration energy (or kinetic energy) and the brake energy as shown in (4.1). E engine = = = F engine ds (4.7) F airdrag + F roll + F gravity + F acceleration + F brake ds (4.8) F airdrag ds + F roll ds + F gravity ds + F acceleration ds + F brake ds (4.9) = E airdrag + E roll + E gravity + E acceleration + E brake (4.1) In order to analyze the influence of the driven velocity profile to the energy consumption of the vehicle, the following properties of the driven velocity will be used, here shown with respect to the time: Empirical mean value: The mean value is the measure of the average. With respect to the time, the mean value of the velocity represents the average velocity. vds mean t (v) = = 1 vdt = v t (4.11) dt T Empirical variance: The variance of the velocity represents the average squared distance between the velocity and the average velocity. It provides a measurement of the variation of the velocity profile. var t (v) = mean t ([v v t ] 2) (4.12) Empirical skewness: The skewness is a measure of the lack of symmetry of the velocity profile around the average 25

34 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION velocity. skew t (v) = mean t(v 3 ) 3var t (v)v t v t 3 var t (v) 3 2 (4.13) The energies mentioned in (4.1) can be calculated knowing the properties of the road profile shown in Figure 4.2 and the empirical properties of the driven velocity profile. This is done in the following sections Roll Resistance Energy E roll = = = = F roll ds (4.14) 1 F roll ds cos(α) (4.15) 1 c r mg cos(α) ds cos(α) (4.16) c r mgds (4.17) = c r mg s (4.18) The roll resistance energy does not depend on the driven velocity over the track. It is proportional to the horizontal length of the track s and to the mass of the vehicle m Potential Energy E gravity = = = = F gravity ds (4.19) 1 F gravity ds cos(α) (4.2) 1 mg sin(α) ds cos(α) (4.21) mg dh (4.22) = mg h (4.23) The gravitational energy is independent of the driven velocity profile. It is proportional to the hight difference between the start and the end point h and to the mass of the vehicle m. 26

35 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION Kinetic Energy E acceleration = F acceleration ds (4.24) = F accelerations s (4.25) = mean s (m v) s (4.26) vds = m mean s ( v) s 1 vvdt 2 mean s ( v) = = = f v2 i ) ds ds s (4.27) = 1 2 m(v2 f v 2 i ) (4.28) The energy needed for accelerating and decelerating a vehicle over a track does not depend on the velocity profile driven between the start and the end point, but does depend on the initial velocity v i and the final velocity v f. It is proportional to the mass of the vehicle Brake Energy The brake force is a direct input to the system. Therefore, the brake energy losses can simply be calculated by the integration of this force. E brake = F brake ds (4.29) Aerodynamic Drag Energy E airdrag = F airdrag ds (4.3) = F airdrags s (4.31) ( ) 1 = mean s 2 c DA a ρ a v 2 s (4.32) = 1 2 c DA a ρ a s mean s (v 2 ) (4.33) The mean aerodynamic drag force acting on the vehicle depends on the mean of v 2 with respect to the distance. It is assumed that the average velocity between the start and the end point of the drive is constant because of the requirement of a constant travel time. This means, that the mean value of the velocity with respect to the time is known and constant for all HDVs traveling over the track: mean t (v) = v t = const (4.34) The mean value of v 2 with respect to the distance can be expressed with respect to the time in order to insert the above mentioned average velocity: mean s (v 2 ) = v 2 ds v 3 dt v 3 dt dt = = = mean t(v 3 ) ds vdt dt vdt mean t (v) (4.35) 27

36 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION The mean value of v 3 is not given. Therefore, the following formula inserting the skewness skew(v) will be used. mean t (v 3 ) = skew t (v)var t (v) vart (v)mean t (v) + mean t (v) 3 (4.36) By inserting (4.36) into (4.35), the following expression for the air drag energy with the empirical properties of the velocity can be found. E airdrag = 1 2 c DA a ρ a s mean s (v 2 ) (4.37) = 1 ( ) 2 c DA a ρ a s skewt (v)var t (v) var t (v) + mean t (v) 2 (4.38) mean t (v) The velocity profiles for the given road profile use cases in Section were analyzed in terms of their mean value, variance and skewness. The following relation of this values was found: skew t (v) < var t (v) << mean t (v) (4.39) This relationship is mainly a result of the symmetry of the velocity around the mean value. It was found that the calculation of the mean aerodynamic drag force can be simplified and approximated as follows. It is later shown in Section 4.2 that this simplification is reasonable for the driven velocity profiles. E airdrag 1 2 c DA a ρ a s ( 3var t (v) + v t 2 ) (4.4) Total energy losses The energy losses due to the aerodynamic forces, the roll resistance, the gravity, the vehicle acceleration and the brake force on a given track with initial velocity v i and final velocity v f can finally be written as: E airdrag 1 2 c DA a ρ a s ( 3var t (v) + v t 2 ) (4.41) E roll = c r mg s (4.42) E gravity = mg h (4.43) E acceleration = 1 2 m(v2 f vi 2 ) (4.44) E brake = F brake ds (4.45) The result shows that the roll energy E roll, the gravitation energy E gravity and the acceleration energy E acceleration are independent of the driven velocity profile and therefore independent of the control strategy between the start and end point. The only energies which depends on the driven speed profile are the energy to overcome the aerodynamic drag force E airdrag 28

37 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION and the brake energy E brake. Those energies depend on the applied control strategy and are therefore subject to be minimized. With a controller taking the road topography into account, the velocity can be kept closer to the set speed v, which results in a smaller variance of the speed var t (v). Driving in a platoon reduces the air drag coefficient c D. It can be seen that with both methods, the mean aerodynamic drag force F airdrags can be reduced. For platoons consisting of vehicles with different masses, the driving strategy deviates for most of the vehicles from their single fuel optimal strategy taking the road topography into account. Therefore, the dimensions of the expected savings are assessed below. The energy needed to accelerate the vehicle E acceleration and the energy needed to overcome a potential difference E gravity can be considered as stored energy. The energy needed to accelerate the vehicle will flow back when the vehicle is decelerated. If the speed at the end of a track is equal to the speed at the start of the track v f = v i, the acceleration energy is zero E acceleration =. The same applies if the potential difference between the start and the end of the track is zero h =. In this case, the energy needed to overcome gravitational forces is zero E gravity =. Due to the fact that the gravitational energy and the potential energy are stored, the losses consist of the aerodynamic drag energy, the roll energy and the brake energy. E lost = E airdrag + E roll + E brake (4.46) 4.2 Variance reduction due to the use of an LAC As shown in Chapter 3, the LAC reduces the variation of the velocity and prevents the vehicle from hitting speed limits which would cause the vehicle to brake. Keeping the velocity closer to the set speed and therefore reducing the variation of the velocity should hereinafter be addressed closer in order to assess its effects on the consumed energy. In order to gain a feeling for the dimension of the variance, Figure 4.3 compares three different velocity profiles and their variance of the velocity. The track simulated is a downhill with 3% slope from 5m to 1m (Use Case 1). The blue line shows the velocity of a vehicle with a look ahead controller LAC. The red line shows the velocity of a vehicle with a normal Cruise Controller CC which compensates the average velocity after the hill. The green profile shows a hypothetical vehicle which is able to maintain its velocity during the downhill. 29

38 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION v [km/h] տ Var t (v) =.42 m2 s 2 Skew t (v) =. տ ւ Var t (v) = 2.34 m2 s 2 Skew t (v) =.9 Var t (v) = m2 s 2 Skew t (v) = Figure 4.3. Comparison of properties of the velocity for different velocity profiles on a downhill between 5m and 1m (Use Case 1) The energy consumption of a vehicle was measured for all use cases (1 to 7) defined in Section for an LAC and a CC. By knowing the parameters of the vehicle, the road profile and the empirical mean and variance of the velocity, the energy consumption can be assessed according to (4.46) with the simplified description of the air drag energy (4.4). Figure 4.4 shows the resulting linear dependency of the consumed energy on the variance of the velocity profile (red line). The energy consumption measured in the simulation is displayed with red points. It can be seen that the simplification made in (4.4) is reasonable for the simulated situation. +1.4% UC7 CC Energy consumption [%] +1.2% +1.% +.8% +.6% +.4% +.2% +% UC6 LAC UC5 LAC UC3 UC2 LAC UC1 LAC LAC UC4 LAC UC1 UC7 CC LAC UC5 CC UC6 CC UC3 CC UC2 CC UC4 CC Calculated energy consumption with linear dependency on var(v) Energy consumption measured in Simulation Var(v) [m 2 /s 2 ] Figure 4.4. Energy consumption depending on the variance of the velocity compared to an assumed vehicle with constant velocity (zero variance). The points show the measured energy consumption in the simulation of a 4t HDV. 3

39 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION The results in Figure 4.4 show the energy saving potential of a vehicle driven by a controller which reduces the variation in the velocity profile as it is the case with a normal LAC when no velocity limits are considered. The measured energy saving of up to 1% as described in Section 3.7 can now be said to come mainly from a reduction in the variance of the velocity. The dimension of the energy saving due to a reduction in the variation of the velocity profile lie in a minor single-digit percentage. 4.3 Fuel efficiency due to brake usage reduction If upper speed limits are considered, a vehicle is forced to brake if it exceeds the limit. In addition to the energy losses by the aerodynamic drag and the roll resistance, the HDV looses energy due to the usage of the brake. Figure 4.5 shows two HDVs driving on a downhill road profile. An upper speed limit of 9km/h is assumed. The vehicle with Cruise Controller CC runs into the speed limit during the downhill segment and has to use the brake to maintain its velocity while the vehicle with an LAC decelerates before the downhill so that it does not reach the speed limit. The vehicle with LAC is therefore able to reduce the energy consumption by 11.6 % compared to the vehicle with CC. Altitude [m] Velocity [km/h] HDV with CC HDV with LAC Brake Force [kn] Figure 4.5. Comparison of two vehicles traveling on a downhill segment with an upper speed limit of 9km/h. The first vehicle with a Cruise Controller CC reaches the speed limit and has to brake, while the vehicle with look ahead controller is able to stay below the speed limit. This causes the vehicle with LAC to save 11.6 % fuel compared to the vehicle with CC. The energy saving due to the brake usage depends highly on many parameters like the ve- 31

40 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION hicle mass, the length and slope of a steep hill or the velocity limit. Therefore, no general conclusion about the fuel saving potential by reducing the brake usage can be drawn. But the example in Figure 4.5 shows that the dimension of fuel saving due to brake energy reduction can be major compared to the savings achieved by reducing the variance of the velocity profile as shown in Section 4.2. Due to the fact that an LAC keeps the velocity over all closer to the set speed and therefore reduces the variance of the velocity profile, the brake usage is also reduced. A vehicle with CC generally runs into speed limitations earlier than a vehicle with LAC. If lower speed limits are considered, a vehicle with LAC is also less likely to run into this speed limit. The energy saving potential at the lower velocity limit is not exactly determinable due to the simplified engine model. Lower velocity limits during uphill slopes can only be maintained by shifting gears, which results in a temporary loss of engine torque. This scenario is not covered with the current engine model. 4.4 Fuel efficiency due to platooning A vehicle driving in a platoon experiences a reduced aerodynamic drag force and therefore reduced energy losses. This can be described with a reduction of the aerodynamic force coefficient c D which becomes in case of platooning dependent on the distances to the vehicle in front and the vehicle in the back. Figure 4.6 shows the energy consumption increase of a 4t vehicle driving in a platoon depending on the distance between the vehicles. It can be seen that the energy consumption rapidly increases as the distance between the vehicle increases. The energy saving potential through platooning is significant. +2% Energy consumption [%] +15% +1% +5% +% Distance between vehicles [m] Figure 4.6. Energy consumption deepening on the distance between the vehicles in a platoon shown for a vehicle with a mass of 4t. 32

41 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION 4.5 Comparison between fuel saving strategies For an HDV driving on a road with steep slopes, three different ways to save fuel have been found and described: Reduction of the aerodynamic drag force mainly due to the reduction of the variance in the velocity profile. Reduciton of the brake energy due to the avoidance of hitting speed limits. Reduction of the aerodynamic drag force due to platooning. Platooning and the reduction of the variation of the speed profile both influence the aerodynamic drag energy. An additional sink of energy is the usage of the brake. Brake energy is only lost if speed limits are considered and hit by a vehicle. If speed limits are hit and the brake is used, a vehicle easily experiences a 1% increased energy consumption over the length of control action compared to a vehicle with a different velocity profile which does not hit the speed limit. The magnitude of fuel saving due to brake usage reduction is obviously much higher than the magnitude of fuel saving due to the reduction of the variance of a velocity profile. Therefore, hitting speed limits should be avoided with priority. A visualization of the acting forces which are responsible for energy losses and their reduction potential through a controller are shown in Figure 4.7. Figure 4.7. Visualization of the average forces acting on an HDV with a mass m = 4kg and reduction possibilities on a downhill section of 3% over 5m. The roll force can not be influenced by any control strategy. By using a look ahead controller, the variance reduction of the velocity profile causes a reduction of the mean air drag force (3rd bar). A variance reduction of 3 m2 was considered. By platooning, the vehicle experiences a reduced air drag force as shown s 2 with the 4th bar. A c D-reduction of 4% is shown. The mean brake force depends highly on the driven velocity profile, however, a large reduction potential is given through the use of a look ahead controller. 33

42 CHAPTER 4. ENERGY SAVING COMPARISON AND DIMENSION ESTIMATION It can be seen that the mean roll force is given and independent of the driven velocity profile. The mean air drag force can be reduced slightly by the use of a look ahead controller. If vehicle platooning is applied, a major reduction of the mean air drag force can be achieved. The brake force depends highly on the driven velocity profile and speed limits. Generally, the use of a look ahead controller offers a high reduction potential of the mean brake force. Look ahead cruise control for a single vehicle finds its optimal velocity profile. This velocity profile is individual for every vehicle and depends mainly on the mass of the vehicle. In contrast, the strategy of platooning tries to minimize the distance between two vehicles. This requires that the two vehicles drive the same velocity profile. Platooning shows to reduce the mean air drag force considerably, which results in a significant energy consumption reduction while look ahead control for single vehicles reduces brake usage and decreases the variation of the velocity profile. The brake usage reduction has a large fuel saving potential. It can finally be stated that control strategies trying to minimize the energy consumption of a vehicle should clearly focus on keeping short distances between the vehicles and avoiding brake usage. Only second priority has the reduction of the variance in the velocity profile. If possible, the vehicles should drive the same velocity profile so that the distance between the vehicles can be shortened to the minimum. 34

43 Chapter 5 Platooning with road topography preview information Platooning by using the ACC on roads with predominantly small gradients has been shown to be a method to highly reduce the fuel consumption of a vehicle due to the reduced air drag force [3]. For single vehicles, optimal control solutions were found and described as look ahead controller in order to minimize the fuel consumption for a given road topography and especially minimize brake usage when velocity constraints are considered [11]. As described in Chapter 4, the computational complexity of finding optimal control strategies for platoons with road topography preview information is significantly growing compared to the optimal control problem for a single HDV. Therefore, causes and effects of different control strategies on the energy consumption are analyzed to find not necessary optimal, but very fuel-efficient control strategies for platoons with road topography preview information. The focus of a control strategy for platoons should clearly be the minimization of distances between vehicles and the reduction of brake usage as shown in Section 4.5. A basic requirement in order to constantly minimize distances between two vehicles is that they drive the same velocity. This can be seen in the following equation describing the dependency of the distance change on the velocities of two vehicles d = v 1 v 2, (5.1) where v 1 and v 2 denotes the velocity of the lead and the follower vehicle and d the intermediate distance. By traversing steep road sections, a vehicle is not be able to hold a constant velocity and will accelerate or decelerate. Due to the fact that a platoon consists of different vehicles with deviating parameters, the acceleration range of the vehicles vary. In order to keep a constant distance, the question arises whether two vehicles can change their velocity in the same way so that the distance does not change. This would require a common acceleration or deceleration of two vehicles. 35

44 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION 5.1 Acceleration agreement among a platoon An analysis of the dynamics of a vehicle was done with different vehicle and road parameters. As it was already shown in [2], the mass and the road gradient have the most significant effect on the dynamics of a vehicle. Figure 5.1 shows the acceleration range of a vehicle with T e [T min, T max ] and no brake usage. It can be seen that the road inclination causes mainly a shift of the acceleration range while the mass of the vehicle mainly shortens the acceleration range of a vehicle. By reducing c d (reduced airdrag) through a short inter-vehicle distance by 5%, the acceleration range is shifted. Uphill: α=3% Level Road: α=% Downhill: α= 3% Light Vehicle m=1kg 1 Light Vehicle m=1kg Acceleration [m/s 2 ].5 Light Vehicle m=1kg reduced airdrag Heavy Vehicle m=4kg reduced airdrag Heavy Vehicle m=4kg reduced airdrag Heavy Vehicle m=4kg reduced airdrag reduced airdrag reduced airdrag.5 Figure 5.1. Acceleration range of a vehicle on different road slopes with input engine torque T e [T min, T max] without braking F brake =. For the acceleration range with reduced air drag force, a c d reduction of 5% was considered, which represents an inter-vehicle distance of 5m. It can be seen that for every section of the road, an intersecting set for the acceleration can be found. This means that vehicles driving on the same road section can agree on a common acceleration and therefore drive the same velocity profile relative to the road. The optimal control solution for a single vehicle describes sections with maximum engine torque, minimum engine torque and sections where the engine torque is selected so that the velocity remains stationary (section 3.1). This strategy causes the acceleration of a vehicle to either be zero or to be at the upper or lower limit of the acceleration range. On a steep uphill section, the acceleration will be at the upper limit of the acceleration range, but still below zero. While accelerating before a steep uphill section, the maximum engine torque is applied and the acceleration hence lies at the upper limit of the acceleration range. On steep downhill sections, the acceleration will be at the lower limit of the acceleration range, but above zero. Before a downhill section while decelerating, the acceleration will lie at the lower limit of the acceleration range. 36

45 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION From the intersecting set of accelerations among a platoon, a similar strategy can be found by finding a vehicle which defines the acceleration in the current road section, hereinafter referred to as the weakest vehicle. The possible set of acceleration is shown in Figure 5.1 by red dashed lines. On uphill sections, the common acceleration will be selected according to the highest possible acceleration among the intersecting set of accelerations. On level road and small road gradients, three accelerations are possible. On longer road sections with small gradients, a constant velocity will be held with zero acceleration. Before an uphill section, the velocity is increased by choosing the maximum acceleration among the intersecting set of accelerations. In order to decelerate in front of a downhill section, the acceleration will be selected according to the smallest possible acceleration among the set. During downhill sections, the minimum possible acceleration among the intersecting set of accelerations is selected. Therefore, the following limited set of accelerations depending on the road inclination, the velocity and the distance between the vehicles of the platoon can be defined. The acceleration ranges of all vehicles A 1 (α, v, d)...a N (α, v, d) can be derived from the equation of motion. a(α, v, d) = [a min (α, v, d),, a max (α, v, d)] (5.2) with a min (α, v, d) = max[min(a 1 (α, v, d)), min(a 2 (α, v, d)),..., min(a N (α, v, d))] (5.3) a max (α, v, d) = min[max(a 1 (α, v, d)), max(a 2 (α, v, d)),..., max(a N (α, v, d))] (5.4) By applying this strategy, all vehicles in a platoon find a common acceleration in every section of the road profile. This results in common velocity profile for all vehicles where the velocity is described depending on the position of the vehicle v(s). 5.2 Shifting the velocity profile in order to maintain the platoon The Adaptive Cruise Controller (ACC) of a vehicle is often used by drivers in order to hold a constant distance to the vehicle in front. In other words, it shifts the velocity profile of the vehicle in front in distance. This strategy of platooning works well for a platoon traveling on a road with small gradients as shown in [2]. Using the ACC for platooning on steep road sections does not work anymore as it is shown in Figure 5.2. The left illustration shows a platoon crossing an uphill section with activated ACC for all vehicles but the first. The first vehicle using the Cruise Controller CC will decelerate on the uphill segment and accelerate to the set speed after the segment. A follower vehicle using the ACC will maintain a constant distance (red bar) to the 1st vehicle. Therefore, it starts to decelerate already in front of the uphill. At the time the first vehicle reaches the level road after the uphill and accelerates, the 2nd vehicle is still in the uphill and unable to accelerate. It is not able to maintain the distance so that the distance between the vehicles will be increased after the uphill. With every vehicle, this problem gets more severe so that the platoon configuration can not be maintained. This result shows that a shift of the velocity profile in distance as it is realized by the ACC is not a fuel efficient solution to the problem of driving a platoon over a road profile with steep slopes. The right illustration in Figure 5.2 shows a velocity profile which is shifted in time instead of distance. It illustrates the solution proposed in the previous Section (5.1) with a velocity profile based on the current position of the vehicle v(s). This will result in a slightly varying 37

46 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION Figure 5.2. Shift of velocity profile in distance (left illustration) as it is done by an ACC and in time (right illustration), Assumption: identical vehicles distance between the vehicles during the slope. After the slope and the acceleration period of the vehicles, the distance is maintained and the platoon configuration keeps existing. 5.3 Platoon Look Ahead Controller The above mentioned results show that it is possible to find a common velocity profile which can be followed by every vehicle. This profile will define a velocity depending on the current position of the vehicle v(s) and will cause minor changes in the distance between two vehicles. Due to the fact that the distance between the vehicles remains close to the minimum distance [4], the air drag forces acting on the vehicles will be reduced significantly, which was one of the main objectives of a new controller. It will be shown in Section that also the brake usage can be minimized by this strategy. With the limited set of accelerations defined in (5.2), a parametric optimization similar to the parametric optimization for a single vehicle can be performed. For an interconnected section of steep road gradients, a start distance d s and final distance d f can be found as it is described for a single vehicle in section 3.4. The following equations of motion for the velocity and the distance between the vehicles deepening on the position s can be found. The first equation describes the dynamics of the velocity of a vehicle and the second equation describes the dynamics of the distance between this vehicle and its follower vehicle. dv ds = 1 a(α(s), v(s), d(s)) v(s) (5.5) dd ds = 1 (v(s) v(s d(s))) v(s) (5.6) Similar to the parametric optimization method for finding a velocity profile for a single vehicle, a velocity profile for a platoon can be found by the above mentioned equations of motion. A final distance d f is used as a parameter to fulfill the constraint of a constant average speed 38

47 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION after a steep road section. The start distance d s will be used in order to find the minimum energy for the platoon, which can be calculated as follows: E = N k=1 ( sf ) F k,airdrag (d(s), v(s)) + F k,brake (s)ds + Ns f F k,roll (5.7) The resulting energy consumption is iteratively minimized similar to the method described for parametric optimization (section 3.4) and the start distance d s where the platoon should start to accelerate/decelerate will be found. The described parametric optimization method in order to find a common velocity profile for a platoon will hereinafter be referred as PLAC Intermediate distance One of the major objectives of the PLAC is the minimization of the distance between two vehicles in order to reduce the air drag forces. An initial short distance between two vehicles is aimed to be kept short by driving similar velocity profiles. Due to the shift in time between the velocity profiles driven by two vehicles, the distance will slightly change. An estimation of this distance is given below. Figure 5.3. In time shifted velocity profile of two HDVs traveling in a plaoon. Two vehicles traveling in a platoon with distance d(s) are shown in Figure 5.3. The velocity profile for the front vehicle (solid line) and the second vehicle (dashed line) are shown. They are shifted in time according by the time shift t d given from the initial velocity and the initial distance: t d = d v (5.8) The distance at any time can easy be calculated by integrating the difference of the velocities of the two vehicles as equation (5.1) shows. Due to the small change of the velocity in time, an even simpler approach can show how the distance developes. Therefore, the two vehicles are assumed to reach the same final velocity v f. The distance between the two vehicles after they reached the final distance can be assessed as follows. 39

48 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION d f = d + t d (v f v ) (5.9) = d + d v (v f v ) (5.1) = d v f v (5.11) Due to the slow change of the velocity in time and the short time shift between the profiles t d, the two vehicles can for the distance estimation always be assumed to have the same final velocity. Therefore, the distance at every point becomes a function of the current velocity: d(s) d v(s) v (5.12) This estimation of the current distance between two vehicles shows that it can be kept small if the deviation from the initial velocity is small. With this result, a practical implementation of decentralized control is conceivable by a lead vehicle which defines the the velocity profile based on the knowledge about the acceleration range of all vehicles. The following vehicles simply hold a distance according to their current velocity Velocity limits and brake usage minimization A major objective of a PLAC is to reduce the brake usage due to its high influence on the energy losses. If a vehicle on a downhill slope runs into an upper velocity limits, the brake will be used to prevent further acceleration. As mentioned above, the acceleration of the platoon is selected according to the acceleration of the weakest vehicle, which is often the vehicle with the highest mass. If the weakest vehicle therefore defines an acceleration which will cause the velocity profile to end up in a speed limit at the end of a downhill, all vehicles of a platoon have to brake..6 A B C Acceleration [m/s 2 ].4.2 Vehicle 3 Vehicle 2 Vehicle 1 A B C Figure 5.4. A platoon with three HDVs on a downhill section with speed limits. By following the minimum acceleration of the weakest vehicle (A), the platoon would hit the speed limit before the end of the slope and all vehicles would have to brake (C). Instead, they could agree on a common acceleration where they hit the speed limit at the end of the slope (B). 4

49 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION Figure 5.4 shows a platoon with three vehicles driving on a downhill profile. An upper (and lower) speed limit is assumed. If the platoon would follow the minimum acceleration (A) of the weakest vehicle (vehicle 2), it would run into the upper speed limit before the end of the slope. All vehicles would have to brake in order to maintain their velocity (C). Instead of this strategy, the platoon could follow a constant acceleration (B), so that it reaches the speed limit at the last point of the downhill section. In this case, only the weak vehicle (vehicle 2) would have to brake. Therefore, driving a profile with the accelerations (A) and (C) for the whole platoon is obviously less energy-efficient than driving acceleration (B). The question remains whether an earlier split-up of the platoon could be more fuel-efficient so that only the weak vehicle follows acceleration (A) and (C). Altitude [m] Splitting Strategy: Altitude [m] Maintaining Platoon Strategy: Velocity [km/h] st Vehicle (m=4kg) 2nd Vehicle (m=2kg) Velocity [km/h] st Vehicle (m=4kg) 2nd Vehicle (m=2kg) Brake Force [kn] 1 5 Brake Force [kn] Dist. bet. HDVs [m] Dist. bet. HDVs [m] Figure 5.5. Comparison of a platoon with N = 2 vehicles driving two different strategies on a downhill profile. The left Figure shows the platoon splitting up with the heavy vehicle in front hitting the speed limit on the downhill. The left Figure shows the maintained platoon where the heavy vehicle in front continuously brakes during the downhill in order to maintain a short distance and reach the speed limit at the end of the downhill slope. This strategy results in a reduced energy consumption of.3% for the lead vehicle and.6% for the follower vehicle. Figure 5.5 compares this two strategies for a platoon with two vehicles, a heavy vehicle with m=4kg in front and a follower light vehicle with m=2kg. The left simulation shows the platoon splitting up at a distance of 5m. The heavy vehicle reaches a higher acceleration on the downhill and runs finally into the speed limit where it has to brake. The light vehicle with a smaller acceleration is able to coast down the hill without reaching the speed limit and therefore without braking. Driving this strategy increases the distance between the vehicles considerably. 41

50 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION The right simulation shows the same platoon configuration following the strategy of maintaining the platoon and driving the same velocity profile. Both vehicles follow a path where they reach the upper speed limit at the end of the slope. Therefore, the heavy vehicle will continuously brake over the whole downhill profile in order to maintain the platoon configuration. The distance between the vehicle can be maintained short. Table 5.1 compares the energy consumption of the vehicles with both strategies. It shows that the aearodynamic drag energy is reduced considerably for both vehicles with the strategy of maintaining the platoon and therefore reducing the distance between the vehicles. The brake energy of the first vehicle is increased slightly because of the reduced aerodynamic drag forces during the downhill and the follower vehicle. Over all, the strategy of maintaining the platoon configuration saves.3% energy for the first vehicle and.6% energy for the follower vehicle. 1st Vehicle: Airdrag Energy: Brake Energy: Roll Energy: Total Energy: Splitting Strategy: 2839kJ 664kJ 4465kJ 7968kJ 1.5% +2.5% +.% -.3% Maintaining Platoon Strategy: 2798kJ 681kJ 4465kJ 7944kJ 2nd Vehicle: Airdrag Energy: Brake Energy: Roll Energy: Total Energy: Splitting Strategy: 176kJ kj 274kJ 3834kJ 1.3% +.% +.% -.6% Maintaining Platoon Strategy: 1737kJ kj 274kJ 3811kJ Table 5.1. Energy consumption of two HDV simulated on a downhill slope with splitting strategy and maintaining platoon strategy. The result confirms that the strategy of maintaining a platoon can also be applied to drive energy-efficient on downhill sections with speed limits. If the platoon would drive into the speed limit, the acceleration during the downhill should be selected so that the platoon hits the speed limit at the end of the downhill slope. 42

51 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION 5.4 Simulation and Discussion of the PLAC This section presents the results obtained with the PLAC. In a first simulation, two vehicles of different masses were simulated on a downhill section of 5m/-3%. The second simulation addresses a split-up scenario and determines the theoretical number of vehicles which are needed in extremal conditions until a split-up a platoon is worth doing in terms of energy consumption. At the end, the energy of a platoon controlled by a PLAC is compared to the energy consumption achieved by other controllers HDV order in a platoon Figure 5.6 compares two vehicles following each other with a PLAC. The driven velocity profile slightly changes due to the fact that the heavy vehicle, which defines the acceleration, experiences different air drag reductions. Its acceleration range changes slightly. It can be seen that the individual energy consumptions of the vehicles change significant depending on their position in the platoon. However, the total energy for the whole platoon remains nearly the same. A minor change comes due to the difference in the variation of the velocity profile. Light vehicle ahead: Heavy vehicle ahead: Altitude [m] Altitude [m] Velocity [km/h] st Vehicle (m=2kg) 2nd Vehicle (m=4kg) Velocity [km/h] st Vehicle (m=4kg) 2nd Vehicle (m=2kg) Distance between vehicles [m] Distance between vehicles [m] Light Vehicle: Heavy Vehicle: Total: 477kJ 576kJ 1476kJ 22% +18.4%.% 3718kJ 6756kJ 1474kJ Figure 5.6. Downhill road section driven with LAC and PLAC with different vehicle order 43

52 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION Platoon splitup investigation The platoon look ahead controller is defined so that all vehicles in a platoon drive the same velocity profile, which results in a short distance between the vehicles and hence a decreased air drag force. The velocity profile is given by the acceleration range of the weakest vehicle in a platoon, which is generally the vehicle with the highest mass. If a platoon is considered with vehicles with highly deviating acceleration ranges, situations are conceivable where a split-up of the platoon into two sub-platoons is more energy-efficient. A weak vehicle might impose a velocity profile on other vehicles, even though they would better drive their own strategy. Figure 5.7 shows a platoon heading towards a road topography with steep gradients. The PLAC finds a common velocity profile for all vehicles and lets them follow the velocity profile over the topography. If the parameters of the vehicles in a platoon highly deviate (especially the mass), it is conceivable that a split-up between the k th and the k + 1 th vehicle is more energy-efficient. Figure 5.7. Platoon with vehicles of highly deviating acceleration range heading a steep road section. Is a split-up more energy-efficient than maintaining the platoon with a PLAC strategy? In order to assess the performance of a PLAC strategy with a common velocity profile compared to a strategy with a platoon split up into two sub-platoons, simulations were performed with a highly non-homogeneous platoon. A heavy vehicle with a mass of 4t followed by n light vehicles with a mass of 12t were simulated on a downhill of -3% over 5m. In a first simulation, the heavy vehicle in front split up from the follower vehicles and drove its own velocity profile. This simulation is shown in Figure 5.8 on the left side. The distance between this vehicle and the follower vehicles is therefore increased to up to 2m. The light vehicles are able to drive a velocity profile with much lower variance and are therefore able to save energy. This strategy is compared to the strategy implemented by a PLAC shown on the right side. The heavy vehicle defines the velocity profile and the light vehicles are therefore forced to drive a velocity profile with highly increased variance compared to the velocity profile they could have driven. The two strategies are compared in terms of the energy consumption of all vehicles. Figure 5.9 shows the resulting change in the energy consumption for the strategy of maintaining the platoon compared to the split-up strategy as a reference. It can be seen, that the first vehicle uses around 2% less energy when driving with a common PLAC which maintains the platoon. This result comes through the short distance to its follower vehicle when not splitting up. The second vehicle saves around 3.6% energy by using the PLAC strategy due to the fact that it has a preceding vehicle in a short distance and thus a more reduced air drag force. But from the 4th vehicle on, the energy consumption is higher with the use of a PLAC. This result comes due to the fact that the variation of the velocity profile is smaller for the split-up 44

53 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION Altitude [m] Altitude [m] Velocity [km/h] st Vehicle (m=4kg) all following Vehicles (m=12kg) Velocity [km/h] st Vehicle (m=4kg) all following Vehicles (m=12kg) Distb bet. HDV [m] Distb bet. HDV [m] Figure 5.8. Platoon split-up (left) vs. maintaining the platoon. A extreme situation of one weak vehicle 4t and N 1 vehicles with 12t is assumed..5 Energy Consumption [%] st 2nd 3rd 4th 5th 6th 7th 8th 9th 1th 11th 12th 13th 14th 15th Vehicle in platoon Figure 5.9. Energy consumption comparison for every vehicle between the PLAC strategy of maintaining a platoon and the split-up strategy as a reference. Vehicles 1 to 3 save fuel due to the PLAC strategy, while vehicles 4 to N would save more fuel with the split-up strategy. 45

54 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION strategy, while the distance between the light vehicles remains. Finally, the simulation gave that the brake even point between the two strategies lies at N=38 follower light vehicles. This means that a platoon has to be extremely non-homogenous until a split-up strategy is worth driving Energy consumption comparison between different controllers In order to assess the performance of the designed PLAC, it was compared to several other controller strategies in terms of energy consumption. A cruise controller CC for a single vehicle and an LAC for a single vehicle were used as a reference. In order to be able to compare the performance of a PLAC to other possible look ahead controller strategies for platoons, a minimum energy consumption could be found. Comparison to minimum A minimum energy needed by a platoon to traverse a road section with steep gradients can be calculated from the evaluated energy saving possibilities in Chapter 4, namely the reduction of the variance, the minimization of the distance and the brake energy reduction. The minimum of each of those three energies can be combined in order to find a lower limit in the energy for a platoon which is needed to cross the road section. Therefore, each vehicle is assumed to cross the road section with its best velocity profile in terms of variance reduction, but with assumed vehicles around to always experience minimum air drag forces. Acceleration [m/s 2 ] reduced airdrag Figure 5.1. Set of acceleration for a single vehicle in order to get its velocity profile with the smallest variation. In a first step, the velocity profile which minimizes the variation in the velocity for every vehicle is found v k (s). Therefore, the acceleration of a vehicle is selected from a set of acceleration shown in Figure 5.1. This set contains the minimum accelerations with and without reduced air drag (inter vehicle distance reduced to minimum d = d min ) and the maximum acceleration with and without reduced air drag. For small road gradients, zero acceleration is also contained. From this set of acceleration, it is simple to find the velocity profile which minimizes the brake usage and has the smallest variance with second priority. In a second step, the air drag energy and the brake energy is calculated for this profile. The air drag energy is simple to calculate from the driven velocity profile and the minimum 46

55 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION distance assumed by the integration of the air drag force F airdrag = 1 2 c D(d min )A a ρ a v(s) 2. The brake force and the roll force can be measured in simulation. The minimum energy a platoon needs to cross a road section with steep gradients is calculated as follows: E min = N k=1 ( sf ) F k,airdrag (d min, vk(s)) + Fk,brake(s) + F k,roll (s)ds (5.13) Results The energy consumption of the PLAC was compared in simulation to the energy consumption of a CC, an LAC and the above mentioned minimum energy. Test condition was a platoon with the following vehicles: [2t, 3t, 4t, 3t, 2t] The minimum distance between the vehicles was d min = 4.5m. For the CC and LAC, a single drive of all vehicles was assumed and the total energy was calculated. Test road sections were use cases 1 to 6. The velocity profiles driven for the platoon controlled by the PLAC for use cases 1 to 3 can be found in A.5. Figure 5.11 shows the resulting energy consumption for all controllers and the minimum energy consumption. It can be seen that the platoon driving with PLAC reaches a remarkable energy consumption reduction of up to around 2% compared to a single drive of all vehicles with LAC or CC. The LAC saves less than 1% energy compared to the CC as it was expected from earlier results in Section 4.2. The minimum energy consumption for the whole platoon lies around 1.3% to 1.9% lower than the energy consumption by using the PLAC. Figure 5.12 shows the energy consumption results for the same platoon and road section as above, but with introduced velocity limits. A lower velocity limit of 79km/h and an upper velocity limit of 91km/h was considered. The result shows major fuel savings achieved with the LAC compared to the CC for single drive of all vehicles due to reduced brake usage. The fuel consumption with the PLAC remains close to the calculated minimum energy needed to drive over the given road section. The performed simulations with and without velocity limits show that driving every vehicle individually over a hill with an LAC saves up to 1% energy compared to a CC if no velocity limits are considered. As soon as velocity limits are introduced, the energy saving potential is much higher. If vehicles are driven in a platoon with a minimum distance of d=4.5m, the reduction in the air drag forces causes the whole platoon to save up to around 2% energy compared to a single drive of all vehicles with CC. As soon as velocity limits are considered, the energy saving can be even higher. If the energy consumption is compared to the calculated minimum energy which is needed to traverse the steep road section, it can be seen that the PLAC has an energy consumption which lies 1.3% - 1.9% above this minimum. This means that even with a more advanced controller than the PLAC, no major energy savings can be achieved compared to the PLAC. 47

56 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION Use Case % +28% Use Case % +25.8% Energy [%] 1 Minimum +1.8% PLAC LAC CC Energy [%] 1 Minimum +1.3% PLAC LAC CC Use Case % +26.4% Use Case % +26.5% Energy [%] 1 Minimum +1.9% PLAC LAC CC Energy [%] 1 Minimum +1.9% PLAC LAC CC Use Case % +26.4% Use Case % +26.6% Energy [%] 1 Minimum +1.3% PLAC LAC CC Energy [%] 1 Minimum +1.9% PLAC LAC CC Figure Energy consumption comparison between the PLAC, the CC and the LAC. Reference is the minimum energy consumption needed to traverse the road section. No speed limits were defined for the simulations. Use case 7 is not shown since the platoon exceeds the range of 7km/h to 1km/h. 48

57 CHAPTER 5. PLATOONING WITH ROAD TOPOGRAPHY PREVIEW INFORMATION Use Case % +33.5% Use Case % +26.6% Energy [%] 1 Minimum +1.6% PLAC LAC CC Energy [%] 1 Minimum +1.3% PLAC LAC CC Use Case % +28.7% Use Case % +35.1% Energy [%] 1 Minimum +1.6% PLAC LAC CC Energy [%] 1 Minimum +1.3% PLAC LAC CC Use Case % +34.4% Use Case % +37.4% Energy [%] 1 Minimum +1.7% PLAC LAC CC Energy [%] 1 Minimum +1.4% PLAC LAC CC Use Case % +31.5% Energy [%] 1 Minimum +1.7% PLAC LAC CC Figure Energy consumption comparison with a lower speed limit of 79km/h and an upper speed limit of 91km/h. 49

58 Chapter 6 Parameter Error Influence and Control Actions Errors and wrong assumptions of parameters can cause an increase in energy consumption for the platoon or even situations where the vehicles are not able to follow an originally planned velocity profile forcing the platoon to separate. Those errors can be devided into two groups: Vehicle Parameter Errors (VPE) and Road Parameter Errors (RPE). The following Chapter will analyze causes and effects of those errors and provide strategies in order to minimize the effect on occurance. 6.1 Vehicle Parameter Error Errors in parameters of the vehicle can cause the vehicle to have a deviant acceleration range from the calculated acceleration range. The velocity profile for the whole platoon will be calculated based on the weakest vehicle in every section of the road as shown in Section 5.3. If a vehicle parameter error occurred for the weakest vehicle, it might not be able to drive with the predicted acceleration. Or if a vehicle parameter error occurred for another vehicle, it might be the weakest vehicle instead of the predicted weakest vehicle. Figure 6.1. A platoon on a downhill section (left) and an uphill section (right). The vehicle with a parameter error is not able to drive with the same acceleration as the other vehicles. Figure 6.1 illustrates the situation of a VPE on a downhill and an uphill section. An error in the estimation of the acceleration range of an HDV occurred and the vehicle can not follow 5

59 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS the planned velocity profile. On the downhill where minimal acceleration is demanded, the vehicle acceleration is higher than expected and on the uphill where maximal acceleration is demanded, the vehicle acceleration is lower than expected. Vehicle parameter errors can be seen as errors which have an influence on the acceleration range of the vehicle. Therefore, the following cases can be distinguished: Estimation error in the minimum acceleration of an HDV Estimation error in the maximum acceleration of an HDV Acceleration [m/s 2 ] Vehicle Acceler ation Range Overestimated minimum Acceleration Underestimated minimum Acceleration Acceleration [m/s 2 ] Vehicle Acceler ation Range Overestimated maximum Acceleration Underestimated maximum Acceleration Figure 6.2. The four cases of wrong estimations about the acceleration range of a vehicle. The real acceleration range (with T e [T min, T max]) of a vehicle is printed with a green pad and the assumed minimum and maximum acceleration is shown with a red line. An over- and underestimation of this acceleration limits can occur. The velocity profile calculated for the whole platoon is based on the minimum and maximum acceleration of a weakest vehicle in every section of the road. Figure 6.2 shows the acceleration range of a vehicle and the assumed minimum and maximum acceleration (red line) of a vehicle. If a vehicle parameter error occurs, the assumption about the acceleration limits might be wrong so that an under- or overestimation of the acceleration limit occurs. The effect of those four situations will be examined in the following sections Causes of Vehicle Parameter Errors A VPE occurs if wrong assumptions about parameters of the vehicle or its environment exist. Examples of this kind of error are a erroneous estimation of the vehicle mass, wrong assumptions about the aerodynamic drag force or about the roll resistant force. An error in the estimation of the mass is likely to occur due to several potential error sources in the parameter estimation method. The aerodynamic drag force is influenced by outer conditions like winds. Therefore, errors can occur in the assumption about the acting aerodynamic force. The roll resistance force is influenced by outer conditions like the street surface or water on the street. The dimension of this parameter errors are to identify in a later step during the process of implementation. 51

60 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS The common influence of all parameter errors is a change in the acceleration range of a vehicle. Figure 6.3 shows a deviation in the above mentioned parameters of -1% to +1% and measures the influence on the minimum (at minimum engine torque T e = T min ) and maximum (at maximum engine torque T e = T max ) acceleration of the vehicle. Especially through an estimation error in the vehicle mass, a considerable error in the assumption about the vehicle acceleration can occur. Maximum Acceleration: max Acceleration deviation 1% % 1% max Acceleration deviation 1% % 1% max Acceleration deviation 1% % 1% 1% % 1% Mass deviation 1% % 1% Airdrag force deviation 1% % 1% Roll force deviation Minimum Acceleration: min Acceleration deviation 1% % 1% min Acceleration deviation 1% % 1% min Acceleration deviation 1% % 1% 1% % 1% Mass deviation 1% % 1% Airdrag force deviation 1% % 1% Roll force deviation Figure 6.3. Influence of a wrong assumption about the vehicle mass m, the aerodynamic drag force F airdrag and the roll resistance force F roll on the maximum and the minimum acceleration of the vehicle with a mass of 25kg with a set speed of v = 85km/h on a level road. (Acceleration deviation given in relation to the acceleration range of the HDV) 52

61 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Estimation error in minimum acceleration On steep downhill slopes and on desired deceleration sections on level road, the acceleration of the whole platoon is selected according to the minimum acceleration of the weakest vehicle. Due to the fact that the minimum acceleration of this HDV is estimated, it is influenced by errors. In this section, the influence of an error in the estimation of the minimum acceleration is investigated..8 Back Front Acceleration [m/s 2 ] Vehicle 5 2 kg Vehicle 4 3 kg Vehicle 3 4 kg Vehicle 2 3 kg Vehicle 1 2 kg Overestimated minimum Acceleration Underestimated minimum Acceleration Figure 6.4. Acceleration ranges (with T e [T min, T max] and highest gear number) for a platoon with 5 HDVs on a 5m downhill with α = 3%. The red line shows the common minimum acceleration of the platoon. Figure 6.4 shows the acceleration ranges of five HDVs driving in a platoon during a downhill segment with a gradient of α = 3%. The acceleration of the whole platoon is selected according to the minimum acceleration of the 3 rd vehicle. An under- or overestimation of the minimum acceleration has a direct influence on the driven velocity profile of the whole platoon. Underestimation of the minimum Acceleration An underestimation of the minimum acceleration occurs if the minimum acceleration of the vehicle is higher than expected. This becomes a problem on downhill road sections where a vehicle accelerates faster than predicted (Figure 6.5 left) or on small gradient road sections where a deceleration is desired and a vehicle can not follow the deceleration (figure 6.5 right). In case of an underestimation of the minimum acceleration, the affected vehicle has no other option than to brake. By braking, it is able to extend its acceleration range into the section of the desired acceleration. If it would continue driving its minimum acceleration without braking, a crash with the front vehicle would occur. 53

62 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Figure 6.5. Underestimation of the acceleration of the weakest vehicle on level road (left) and on steep road (right) Overestimation of the minimum Acceleration If the minimum acceleration is overestimated, the whole platoon is able to follow the selected acceleration. In this case, even the weakest vehicle has to fuel the engine slightly so that it is able to follow the selected acceleration. The resulting effect on the whole platoon is that it drives a velocity profile with a higher variance than needed. This results in a slightly higher energy consumption. Effect of an estimation error of the minimum acceleration on the energy consumption The effect of an estimation error on the minimum acceleration of a weak vehicle in a platoon was simulated with the platoon shown in Figure 6.4 on a 5m/-3% downhill profile. Figure 6.6 shows the drive properties of the 3 rd vehicle with a mass of 4t, which represents the weakest vehicle. The acceleration range of this vehicle was over- and underestimated by 12% with respect to its whole acceleration range. It can be seen that the HDV with an estimated acceleration equal to the actual acceleration reduces the engine torque to the minimum and coasts without brake usage. In case of an underestimation of the minimum acceleration, the vehicle has to brake in order to follow the calculated velocity profile. If the minimum acceleration is overestimated, the vehicle starts decelerating earlier than needed but with slight fueling. This results in a higher variance of the velocity profile. 54

63 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Altitude [m] Engine Force [N] Velocity [km/h] HDV with under estimated minimum Acceleration HDV with nominal Acceleration HDV with over estimated minimum Acceleration Brake Force [N] Figure 6.6. Drive properties of the 4t HDV (weakest vehicle) in a platoon on a 5m/-3% downhill. The drive properties are shown for an over- and underestimation of the minimum acceleration and for a correct estimation of the minimum acceleration. Platoon with N = 5 vehicles: Back [2t - 3t - 4t (weak vehicle) - 3t - 4t] Front Figure 6.7 shows the resulting energy consumption change for the whole platoon and the weakest vehicle. It can be seen that an underestimation of the minimum acceleration causes one or more vehicles to brake. Thereby, a considerable amount of energy is lost. This results in a major energy consumption increase for the whole platoon. If in contrast the minimum acceleration is overestimated, the variance in the velocity profile is rising and even the weakest vehicle is slightly fueling its engine to reach the desired acceleration. It can be seen that an overestimation of the minimum acceleration causes only a minor increase in the energy consumption of the platoon. 55

64 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS +14% +12% Weak vehicle (4t) Whole Platoon Energy consumption increase +1% +8% +6% +4% +2% +% 1% 8% 6% 4% 2% % +2% +4% +6% +8% +1% Failure in Estimation of Minimum Acceleration Figure 6.7. Energy consumption increase of a platoon and its weakest vehicle for an estimation error of the the minimum acceleration. Downhill 5m/-3%, Platoon with N = 5 vehicles: Back [2t - 3t - 4t (weak vehicle) - 3t - 4t] Front Estimation error in maximum acceleration On steep uphill slopes and on desired acceleration sections on level road, the acceleration of the whole platoon is selected according to the maximum acceleration of the weakest vehicle. Similar to the estimation of the minimum acceleration, the estimation of the maximum acceleration is influenced by errors. In this section, the influence of an error in the estimation of the maximum acceleration is investigated. Figure 6.8 shows the acceleration ranges of five HDVs driving in a platoon during an uphill segment with a gradient of α = 3%. The acceleration of the whole platoon is selected according to the maximum acceleration of the 3 rd vehicle. An under- or overestimation of the maximum acceleration has a direct influence on the driven velocity profile of the whole platoon. 56

65 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS.1 Back Front Acceleration [m/s 2 ] Vehicle 5 2 kg Vehicle 4 3 kg Vehicle 3 4 kg Vehicle 2 3 kg Vehicle 1 2 kg Overestimated maximum Acceleration Underestimated maximum Acceleration.5 Figure 6.8. Acceleration ranges (with T e [T min, T max]) for a platoon with 5 HDVs on a 5m uphill with α = 3%. The red line shows the common maximum acceleration of the platoon. Overestimation of the maximum acceleration An overestimation of the acceleration occurs if the maximum acceleration of the vehicle is smaller than expected. The vehicle can not follow the desired velocity profile and becomes slower than the other vehicles. Figure 6.9 shows an overestimated acceleration on a level road section (left) and on a steep uphill (right). Figure 6.9. Overestimation of the acceleration of the weakest vehicle on level road (left) and on steep road (right) The affected vehicle can not extend its range of acceleration to the desired acceleration. Therefore, it becomes slower than the other vehicles. This means that the follower vehicles have to adapt their velocity profile to the velocity profile of the affected vehicle, which means that the platoon can not be maintained with short distances between the vehicles. Figure 6.1 shows two options to react on a scenario as described above with a weak vehicle k which can not follow the originally planed velocity profile. Vehicle 1 is assumed to have already passed the street section with steep slopes. The vehicles between the 1 st and the k th 57

66 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Figure 6.1. Two scenarios of reaction to a vehicle k with overestimated acceleration. vehicle can follow the originally planed velocity profile and build a sub-platoon with the 1 st vehicle or increase the distance between each other so that the platoon is expanded. The resulting c D reductions for the split and expanded platoons are shown in Figure The current air drag coefficient reduction for every vehicle is marked. Due to the nonlinearity in the curves, a split-up of the platoon saves more fuel than an expansion of the platoon. This becomes clear if a large distance between the 1 st and the k th vehicle is assumed. If two sub-platoons are maintained, all vehicles apart of the vehicles at the front and at the back of the platoon have a considerably reduced air drag coefficient. If the platoon is expanded, all vehicles up to the the k th experience a higher air drag coefficient compared to the situation with two sub-platoons. 6 Platoon split up 6 Platoon expansion k 1, k+1...n 5 k+1...n 3...k c D reduction [%] k c D reduction [%] Reduction due to following vehicle Reduction due to 1 leading vehicle Reduction due to 2 leading vehicles k 2, k...n 1 k Distance d l, d f [m] k...n k Distance d l, d f [m] Figure c D reduction for vehicles driving in a split platoon compared to an extended platoon. For every vehicle, the c D reduction consists of a reduction from the follower vehicles added to a reduction for the lead vehicle. E.g: Vehicle 2 has in case of a separated platoon an air drag reduction of around 4% from the follower vehicles (blue point) plus a reduction of around 38% from the lead vehicle. This results in around 42% reduction to c D. The above mentioned situation of a vehicle with overestimated acceleration on an uphill was simulated and is shown in Figure The vehicles between the first vehicle and the weak vehicle react in a different way to this situation. In the left simulation, they change their acceleration immediately to the acceleration of the weakest vehicle. This causes the distance 58

67 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS between all vehicles in front of the weakest vehicle to increase and the platoon to expand. In the right simulation, the vehicles in front of the weakest vehicle continue on their calculated path and build a sub-platoon. The weak vehicle will be lead vehicle of a second platoon. The distance between the the two platoons increases while the distance between vehicles of the same platoon remains. One Platoon with expanding distance: Two sub-platoons: Altitude [m] st HDV HDVs between 1st and weak HDV Weak HDV and all follwoing HDVs Altitude [m] Velocity [km/h] Velocity [km/h] Leading Sub Platoon Following Sub Platoon Distance between HDVs [m] Distance between HDVs [m] Distances among leading Platoon Distance between Platoons Distances among following Platoon Figure Comparison between the split-up of a platoon into two sub-platoons and the expansion of the platoon. The platoon is assumed to consist of 2x 35t HDV. But due to a vehicle parameter error, one vehicle has a higher mass (4t) than assumed. Not all vehicles are displayed for the sake of clarity. Platoon with N = 2 vehicles: Back [4x 35t - 4t (weak vehicle) - 15x 35t] Front The energy consumption of the whole platoon is.7% lower when it is split into two subplatoons compared to the scenario with expanding distance. This energy saving is caused by the above mentioned higher c D reduction due the split-up. In addition, the variance of the velocity profile of the vehicles in front of the weakest vehicles is increased when expanding the platoon. This causes the average air drag force to be higher and the energy consumption to rise. The data about the c D reduction was derived from experimental data in the wind tunnel with a platoon with equal distances between the vehicles (cf. Section 2.1.3). If the distance between the vehicles increases, a vehicle in the platoon will become a lead vehicle. No data about this transition was available. In addition, the model about the air drag reduction in function of the distance to a lead and the distance to a follower vehicle was derived from a model with equal distances in the platoon. The savings obtained here are very small and within the error margins of the air drag reduction function. The result of.7% energy reduction is minor due to the fact that the air 59

68 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS drag reduction in the range of 5m to 2m nearly linearly decreases and could therefore be considered as negligible. One option to prevent a split-up of the platoon would be the extension of the acceleration range by a gear shift similar to the extension of the acceleration range at the minimum by braking. This scenario is beyond the scope of this thesis and requires a more complex engine model considering gear shifts. Therefore, the question whether a gearshift is worthwhile to a split-up in terms of energy consumption can not be answered here. Underestimation of the maximum Acceleration If the maximum acceleration is underestimated, the whole platoon is able to follow the selected acceleration similar to an overestimation of the minimum acceleration. In this case, even the weakest vehicle has to fuel the engine slightly below the maximum so that it is able to follow the selected acceleration. The resulting effect on the whole platoon is that it drives a velocity profile with a higher variance than needed. This results in a higher energy consumption. Effect of an estimation error of the maximum acceleration on the energy consumption The effect of an estimation error on the maximum acceleration of a weak vehicle in a platoon was simulated with the platoon shown in Figure 6.8 on a 5m/+3% uphill profile. Figure 6.13 shows the resulting drive profiles. In case of an underestimation of the maximum acceleration, all vehicles are able to follow the calculated velocity profile. The variance of this common velocity profile is higher than the variance of the profile with assumed nominal acceleration. In case of an overestimation of the maximum acceleration, the weakest vehicle and all follower vehicles have to drive on a different velocity profile than the proceeding vehicles. This causes a split-up of the platoon and therefore an increased energy consumption. Figure 6.14 shows the resulting energy consumption increase for the whole platoon and the weakest vehicle. An overestimation of the maximum acceleration causes a situation where the weakest vehicle and all follower vehicles can not follow the proceeding vehicle. This causes the platoon to split up and the energy consumption to rise considerably due to the increased aerodynamic drag force for several vehicles. In case of an underestimation of the maximum acceleration, the whole platoon drives a velocity profile with slightly increased variance. This causes a minor increase of the energy consumption of the platoon. 6

69 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS 15 Altitude [m] 1 5 Velocity [km/h] HDV with under estimated maximum Acceleration HDV with nominal Acceleration HDV with over estimated maximum Acceleration 1st sub platoon HDV with over estimated maximum Acceleration 2nd sub platoon Engine Force [N] Figure Drive properties of a platoon with underestimated maximum acceleration (green) and overestimated maximum acceleration (blue). For an overestimated maximum acceleration, the platoon is split into two sub-platoons. Platoon with N = 5 vehicles: Back [2t - 3t - 4t (weak vehicle) - 3t - 4t] Front 61

70 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS +3% +2.5% Weak vehicle (4t) Whole Platoon Energy consumption increase +2% +1.5% +1% +.5% +% 1% 8% 6% 4% 2% % +2% +4% +6% +8% +1% Failure in Estimation of Maximum Acceleration Figure Energy consumption increase of a platoon and its weakest vehicle for an estimation error of the the maximum acceleration. Uphill 5m/+3%, Platoon with N = 5 vehicles: Back [2t - 3t - 4t (weak vehicle) - 3t - 4t] Front Control actions on platoon velocity profile on VPE If a vehicle parameter error occurs and the first vehicle has not reached the steady velocity again, corrections on the path for the whole platoon can and should be done. Figure 6.15 illustrates this situation. The path was calculated according to the acceleration of the weakest vehicle, which is the red HDV. Because of a vehicle parameter error, this vehicle can not hold its predicted velocity. As soon as this error is realized, a path correction for the whole platoon is calculated and the platoon follows the new path, which describes closed loop control. The red vehicle has to brake up to the point in distance where the first vehicle changes its path to the corrected path. Due to the fact that the above mentioned problem requires a new calculation of the velocity profile for the whole platoon, this problem becomes related to a road parameter error. For a recalculation of the velocity profile, it is referred to Section 6.2 describing road parameter errors Preventing a Vehicle Parameter Error The estimation of the maximum and minimum acceleration of a platoon according to the weakest HDV is always influenced by errors due to uncertainties in the estimation of vehicle parameters. The size of energy consumption increase depends highly on the size and direction of the estimation error in the acceleration. As shown in Section 6.1.2, the energy consumption highly increases if the minimum ac- 62

71 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Figure Path corrections on vehicle parameter errors celeration is underestimated and HDVs are forced to brake. For the simulated platoon of 5 HDVs on a 5m/-3% downhill, the total energy consumption is 6% higher if the minimum acceleration is underestimated by 1% of the acceleration range. In contrast, an overestimation of the minimum acceleration causes an insignificant energy increase. An overestimation of the maximum acceleration of the weakest HDV causes a split-up of the platoon as shown in Section The two effects are an increase of the energy consumption of the platoon and an increase in the complexity of the path optimization due to the fact that a velocity profile for every sub-platoon has to be found. For the simulated platoon of 5 HDVs on a 5m/+3% uphill, the energy consumption is 1% higher if the maximum acceleration is overestimated by 1%. An underestimation of the maximum acceleration causes only a minor increase in the energy consumption. The accuracy of the parameter estimation of a vehicle is subject to be studied in future work. The uncertainty range in the estimation of the acceleration range of a vehicle is not known and not subject of this thesis. It can be stated that an underestimation of the maximum acceleration is clearly favored to an overestimation. Likewise an overestimation of the minimum acceleration is favored to an underestimation. A systematic overestimation of the minimum acceleration and an underestimation of the maximum acceleration is therefore recommended. Due to the unknown range of the estimation error of the acceleration, no recommendation about the size of this under- resp. overestimation can be given. In order to prevent the effect of vehicle parameter errors, the weak vehicle should be in front of a platoon. In general, this means that the heaviest vehicle should lead the platoon. The error is therefore recognized as soon as this vehicle reaches the steep slope and corrections for the velocity profile of the whole platoon can be executed. 63

72 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS 6.2 Road Parameter Error A road parameter error occurs if the road topography data does not correspond to the real road topography in front of the platoon. For the presented road profile use cases, there are three road parameters which can be afflicted by an error: The position, the length and the slope of a road section. Those three road parameter errors are illustrated in Figure The first case of a position error can also be seen as an error in locating the platoon with GPS data, which is likely to occur. Its the distance between the platoon and the steep slope which is uncertain. The other two errors are always map data errors where the length or the inclination of the road does not correspond to the map data. It can be said that the latter two errors are much less severe if iterative map updates are done. Map data about a specific road section will gain precision as more vehicles deliver data. In addition, the length and slope of a road section is measurable and tend not to change significantly over time, while GPS localization can be afflicted by larger errors. Shift Error: GPS Localization- or Map Data Error Section Length Error: Map Data Error Section Gradient Error: Map Data Error Figure Examples of road parameter errors: distance shift of profile, section length error, road gradient error Road parameter errors will be recognized as soon as the first vehicle of a platoon reaches the point which is afflicted by an error and measures the correct data of this point. Therefore, corrections in the calculated drive path for the platoon can be made as soon as the first vehicle delivers a measurement. Figure 6.17 shows a platoon facing a downhill slope. A road parameter error causes the platoon to assume the start of a downhill section earlier than it really starts. The first vehicle of the platoon starts to decelerate earlier than needed at time t = t. The error is recognized as soon as the first vehicle expects to be in the downhill section, but still faces level road. At time t = t 1, the first vehicle measures the start of the slope and the new velocity profile is calculated. The follower vehicles of the platoon have to follow the velocity profile of the first vehicle even though the correct velocity profile is now known better. If they would follow a new velocity profile so that their speed is increased compared to the lead vehicles, a crash would occur. A RPE is recognized as soon as the first vehicle measures the error. This is the case when the first vehicle hits a new road section which was assumed to have different parameters than measured. Figure 6.18 shows this situation where a platoon started accelerating too late in 64

73 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Figure Road Parameter Error front of an uphill segment. A possible cause is an error in the data about the position of the steep road section (shift). The engine torque is displayed for the weakest vehicle. During the steep slope, the optimal control solution for a single vehicle is given by the two possibilities of maximum engine torque during uphill slope and minimum engine torque during downhill slope (Section 3.1). For a platoon, adapting the maximum acceleration of the weakest vehicle for the whole platoon has shown to be highly energy-efficient. Therefore, the acceleration is given for all vehicles on the steep uphill section. After the steep road sections, the controller can perform actions in order to maintain the average velocity as soon as possible. Therefore, the parameter optimization is reduced to the selection of a final distance d f where the acceleration for the whole platoon is switched and the input torque for the weakest vehicle switches from minimum engine torque to maximum engine torque or vise versa. With this recalculation of the velocity profile, closed loop control is achieved. For the situation shown in Figure 6.18, the whole platoon has to follow the calculated velocity profile. A split-up between the 3 rd and the 4 th HDV in order to start accelerating earlier with the second sub-platoon can not be done due to the fact that this would cause a crash. However, situations where a split-up of the platoon would be an advantage in terms of energy consumption are conceivable. The issue of a split-up will be discussed in the following two sections. 65

74 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS T e max T e mi n d f Figure Parametric optimization after road parameter error occurrence RPE without velocity limit constrains In a first step, a road parameter error influence on the energy consumption was analyzed without any velocity limit constraints. Therefore, the HDVs cannot run into any velocities where they have to brake. The three above mentioned cases of RPE (shift, length error and gradient error) were analyzed on a 5m/±3% slope with a platoon of 5 HDVs. The simulation of an error in the assumed position of a slope is shown in Figure The platoon assumes the slope earlier (green line) or later (red line) than it is in reality. The solid line in the velocity profile shows the driven profile up to the point where the error is measured. At a distance of 5m, the first vehicle reaches the slope and realizes the error in the assumed position of the slope and a recalculation of the velocity profile is done. This is shown by the dashed line. The platoon will afterwards follow this new calculated velocity profile. The simulations for errors in the length and the inclination of a slope can be found in Appendix A.6. The resulting energy increase caused by road parameter errors in the three cases of a position error, a length error and a inclination error on a simple uphill and downhill profile lie between +.35% and +.91%. This increase is caused by the larger variation of the velocity profile. The distance between the vehicles of the platoon is not effected severely by this error and the brake is not used due to the fact that no speed limits are considered. As already shown in Section 4, the effect of an increaseed variation of the velocity on the energy consumption is minor. The measured dimension of increase in the energy consumption confirms that a split-up of the platoon is not an option. 66

75 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Altitude [m] Road profile Assumed left shift of road profile Assumed right shift of road profile Altitude [m] Road profile Assumed left shift of road profile Assumed right shift of road profile Velocity [km/h] Velocity [km/h] Figure Road parameter error in the position of an uphill and downhill section. The energy consumption increases due to the occurrence of this error compared to the nominal profile with no error (blue). On the uphill section, the energy consumption increases by +.52% for left shift of 8m (green) and by +.75% for right shift of 8m (red). On the downhill section, the energy consumption increases by +.69% for left shift of 8m (green) and by +.73% for right shift of 8m (red). Platoon configuration: Back [2t - 3t - 4t (weak vehicle) - 3t - 4t] Front RPE with velocity constrains If a road parameter error occurs and velocity constraints are considered, the consumed energy does not depend in a trivial way on the driven velocity profile. It highly depends on the road profile, the vehicles and the velocity limits. The road parameter errors can be divided into the above mentioned cases of a shift error, a gradient error or a section length error. This allows to further investigate the causes and effects of an error and allows to draw conclusions. Shift error in the assumed position of the slope A shift error in the assumed position of a steep road segment is shown in Figure 6.2. The hill can be assumed too close to the platoon (blue dashed line) or too far away from the platoon (green dash-dotted line). The thin line shows the in front of the hill calculated velocity profile and the thick line shows the corrected velocity profile as soon as the error was measured. In the case of an overestimation of the distance between the platoon and the hill, the platoon can run into the upper speed limit which causes the vehicles to brake. If the hill is assumed to start closer to the platoon, the vehicles hold a lower velocity as long as they do not detect the hill. During the hill, they are able to follow the same velocity profile as with assumed correct distance (black solid line). Therefore, no increase in the brake usage is needed. The platoon has to hold an increased velocity for a short distance after the downhill in order to compensate for the missed average speed. It can be seen that assuming the hill too close (blue dashed line) causes an increase in the variation of the velocity profile which slightly increases the energy consumption, whereas assuming the distance to the hill too large can cause increased brake usage which highly increases the energy consumption. Similar to the downhill profile, the uphill profile can be considered. Underestimating the distance to the slope (blue dashed line) causes an increase in the variance while overestimat- 67

76 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS ing the distance causes the vehicles to run into a lower speed limit. Therefore, the vehicles have to shift gear which might result in a higher energy consumption. Figure 6.2. Velocity profiles for overestimated (blue dashed line) and underestimated (green dash-dotted line) distance to the hill. The small line shows the prior calculated profile, while the thick line shows the driven profile when the error was measured. An error in the assumption of the distance between the platoon and the slope is likely to occur due to errors in the position estimation of the vehicle (GPS data). However, by starting to decelerate (accelerate) in front of a downhill (uphill) earlier and holding the speed which was calculated to enter the slope can be seen as a method in order to significantly lower the effect of this error on the resulting energy consumption highly. This comes due to the fact that the increased variance only causes a slightly increased energy consumption. Gradi2or of the steep road section Figure 6.21 shows two situations where wrong map data about the inclination of the steep road section was considered. The green dash-dotted line shows the velocity profile driven with underestimation of the road gradient, while the blue dashed line shows the velocity profile driven for an overestimated gradient. The thin lines show the calculated velocity profile before the error was measured. It can be seen that it is likely to run into the velocity limit when the road gradient is underestimated (green dash-dotted line), which causes a high increase in the energy consumption. For a platoon of N=5 HDVs, the energy increase is measured around 2% if the start distance is 2m too short as it will be shown in Figure 6.23 Figure An underestimation of the slope gradient can cause the vehicles to run into velocity limits (green dash-dotted line) which might result in a highly increased energy consumption. An overestimation on contrast only results in an increase of the variance (blue dashed line) and therefore only a slight increase in the energy consumption. 68

77 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS Length error of the steep road section If the length of a steep road section is over- or underestimated, this error will be detected at the end of the slope when the first vehicle measures the truth length. Figure 6.22 illustrates this situation with an underestimation (green dash-dotted line) and an overestimation (blue dashed line) of the steep road section length. The thin line shows again the originally planned velocity profile without knowledge of the error. It can be seen that an underestimation of the steep road section length can cause the vehicles to hit velocity limits, while an overestimation increases the variance. The energy consumption is likely to highly increase when the steep road section length is underestimated due to brake usage or gear shifts. Figure Velocity profiles for the situations where the actual steep slope is longer than expected (underestimation, shown with blue-dashed line) and shorter than expected (overestimation, green dash-dotted line). General conclusions about road parameter errors when velocity limits are considered To summarize the above obtained results, it can be said that the chance of hitting velocity limits on downhills and uphills increases if the distance at which the platoon starts to decelerate in front of a hill is selected too short. The energy increase can directly be seen in the results from parametric optimization shown in Figure It can be said that the start distance d s in which the deceleration starts is crucial for the energy consumption if speed limits are considered. If it is selected larger than the optimal start distance, the energy consumption only slightly increases and gives space for errors during the hill. A position error of the hill can directly be seen as shift distance shift in the shown diagram. Generally, it can be stated that the effect of an error in the distance between the platoon and the hill on the energy consumption can be decreased by decelerating too early and holding the calculated velocity for the start of the hill until the hill starts. To prevent hitting velocity limits due to errors in the length or inclination of the slope, the velocity at the start of a downhill should rather be lower than calculated and on the start of an uphill rather be higher than calculated. A possible approach of an uphill and a downhill can be seen in Figure

78 CHAPTER 6. PARAMETER ERROR INFLUENCE AND CONTROL ACTIONS +2% Energy increase [%] +1.5% +1% +.5% % Start distance ds [m] Figure Parametric optimization result for the energy consumption for a platoon of N=5 HDV in front of a 5m -3% downhill section. Figure The dashed line shows the assumed velocity profile to drive. In order to avoid a high increase of the energy consumption if the assumption about the steep road section was afflicted by any errors, it is advantageous to approach the hill with the velocity profile shown with the solid black line. 7

79 Chapter 7 Conclusion and Outlook 7.1 Conclusion Both the concept of platooning of HDVs and the concept of look ahead control for a single vehicle have a big potential in future freight transportation in order to reduce fuel consumption and CO 2 emissions. Look ahead control has a high potential in terms of brake usage reduction, while platooning significantly decreases the air drag losses of HDVs and helps to increase the road capacity. In this thesis, the two concepts were analyzed and new control strategies were developed in order to unite the advantages of both concepts. Look ahead control for a single vehicle can be implemented by parametric optimization. The optimal control problem of minimizing the fuel consumption by maintaining a constant travel time for a single vehicle with road topography information can be reduced to a limited set of optimal inputs. This fact was used in order to implement a parametric optimization method to find the point of switching between the inputs. The solution showed to achieve high energy consumption reduction by reducing the brake usage and minor energy consumption reductions by reducing the variation of the velocity profile and therefore the mean air drag force. By considering more than one vehicle with short intermediate distance, the optimal control problem is not trivial to solve anymore. Therefore, an alternative approach of analyzing causes and effects of energy flows and losses was chosen. It revealed a major energy saving potential in reducing the brake usage by look ahead control and reducing the air drag losses by maintaining a short intermediate distance. In order to fulfill the requirement of a computationally simple and fuel efficient controller, the two energy saving possibilities were combined in order to draw control laws for a PLAC. It finds a common velocity profile which can be driven by all vehicles of a platoon and allows therefore to reduce the intermediate distance close to the minimum distance. In addition, the velocity profile is found such that only those HDVs have to brake which would have to brake in a single drive anyway. Therefore, it reduces the brake usage of the whole platoon. The implementation of this controller can be done in a similar way as the implementation of an LAC for a single vehicle. The dynamics of all vehicles can therefore be simplified by two differential equations, which results in a common velocity profile for all vehicles. By parametric optimization, the points where the acceleration is switched within the limited set of accelerations can be found. It could be shown that 71

80 CHAPTER 7. CONCLUSION AND OUTLOOK the resulting PLAC achieves an energy consumption for a platoon with five HDVs which lie 1.3%-1.9% above a lower minimum energy consumption. Compared to a single drive of all vehicles with an LAC or a CC, the PLAC achieves energy savings of around 2% or higher if velocity limits are considered. Simulation results confirmed that the strategy of maintaining a platoon even in extreme configuration is highly beneficial to any split-up scenarios. The method presented in order to find a common velocity profile selects the acceleration of the whole platoon according to the acceleration range of the weakest vehicle (most limited acceleration range) in the platoon. This method is sensitive to errors in the assumption of the acceleration range and errors in the data about the road topography or the localization of the platoon. This can lead to a split-up of the platoon or can increase the fuel consumption by an increase in brake usage. By intentionally underestimating the maximum acceleration and overestimating the minimum acceleration and approaching the desired speed at the beginning of a slope to early, this effects can be prevented. Finally it can be stated that simple rules for controlling a platoon were found which highly decrease the fuel consumption. Closed loop control can be achieved by repeatedly solving the parametric optimization and finding the points to switch between the accelerations. This could be implemented in a later state by using MPC. 7.2 Outlook and Future Work A PLAC which reduces the fuel consumption by maintaining a constant travel time has been designed in this thesis through a simplified vehicle and environment model. The high fuel saving possibilities found with this model for control with a PLAC are auspicious and demand for real implementation. The high fuel saving potential largely depends on the reduction of the aerodynamic drag through platooning. The data about the reduction of the air drag force was obtained in empirical experiments in a wind channel and shown in Section For all situations where a platoon is maintained with short and only slightly changing distances, the model should well apply and deliver reliable results. As soon as large distance differences among the platoon occur, the model can not be taken for granted to deliver reliable results. Therefore, conclusions about a split-up of a platoon should be handled with particular caution. In this thesis, the brake of a vehicle was used in order to extend the acceleration range of below the lower limit reached by minimum engine torque. The same could be done for the upper limit of the acceleration by a gear shift. This would allow a vehicle to have a wider acceleration range and would therefore enlarge the possibilities of a controller. Gear shifts require a largely more complex engine model. HDVs need a considerable time to shift gear during which no engine torque is applied in order to power the HDV. A more complex engine model should therefore be considered for further analysis of platoon look ahead control. The larger acceleration range through gear shifts could be tested with the framework for a PLAC presented in this thesis. 72

81 References [1] 82.11p. Status of project IEEE 82.11, Task Group p, Wireless Access in Vehicular Environments (WAVE). May 21. [2] A. Alam. Fuel-efficient distributed control for heavy duty vehicle platooning, 211. Licentiate Thesis, KTH, School of Electrical Engineering (EES). [3] A. Alam, A. Gattami, and K. H. Johansson. An experimental study on the fuel reduction potential of heavy duty vehicle platooning. In 13th International IEEE Conference on Intelligent Transportation Systems, Madeira, Portugal, September 21. [4] A. Alam, A. Gattami, K. H. Johansson, and C. J. Tomlin. Establishing safety for heavy duty vehicle platooning : a game theoretical approach. In IFAC World Congress, 211. [5] A. Alam, A. Gattami, and K. H. Johansson. Suboptimal decentralized controller design for chain structures: Applications to vehicle formations. In CDC-ECE, pages IEEE, 211. [6] A. Alam, J. Måtensson, and K. H. Johansson. Look-ahead cruise control for heavy duty vehicle platooning. In 16th International IEEE Conference on Intelligent Transportation Systems, Hague, The Netherlands, October 213. [7] B. De Schutter, T. Bellemans, S. Logghe, J. Stada, B. De Moor, and B. Immers. Advanced traffic control on highways. Journal A, 4(4):42 51, December [8] R. A. Dunlap. The Golden Ratio and Fibonacci Numbers. World Scientific, [9] European Commission. Directorate General Transport and Statistical Office of the European Communities. EU Transport in Figures: Statistical Pocketbook. Publications Office of the European Union, 212. [1] European Commission. Directorate General Energy and Transport. Road Freight Transport Vademecum. Office for Official Publications of the European Communities, 29. [11] Anders Fröberg. Efficient Simulation and Optimal Control for Vehicle Propulsion. PhD thesis, Linköpings universitet, May 28. [12] A. Fröberg, E. Hellström, and L. Nielsen. Explicit fuel optimal speed profiles for heavy trucks on a set of topograhic road profiles. In SAE World Congress, Electronic Engine Controls, 26. II

82 REFERENCES [13] A. Fröberg and L. Nielsen. Optimal control utilizing analytical solutions for heavy truck cruise control. In Linköping University, Departmental Reports, 28. [14] E. Hellström. Look-ahead Control of Heavy Vehicles. PhD thesis, Linköping University, 21. [15] E. Hellström, M. Ivarsson, Jan Åslund, and Lars Nielsen. Look-ahead control for heavy trucks to minimize trip time and fuel consumption. In 5th IFAC Symposium on Advances in Automotive Control, Monterey, CA, USA, 27. [16] E. Holma. Data requirements for a look-ahead system. Master s thesis, Linköping University, Department of Electrical Engineering, 27. [17] Scania CV AB. Annual report. Scania CV AB, 21. III

83 Appendix A IV

84 APPENDIX A. A.1 Master Thesis Definition Master Thesis Fuel e cient platooning of heavy duty vehicles through road topography preview information Program / Specialisation: Control Engineering Student: Lukas Bühler KTH Personnummer: 8652-T816 ETH student number: Examiner: Co-Examiner at ETH: Supervisors: Prof. Karl Henrik Johansson Prof. Manfred Morari Assad Alam Jonas Mårtensson Background Road freight transport is a growing business and builds a centerpiece of modern economics. As fuel prices are rising and the environmental impact of CO 2 emissions on the climate become more severe, the freight transport sector demands for fuel saving transport methods. A strong focus in Scania s product development is to reduce the fuel consumption of their heavy duty vehicles (HDV). Studies showed that platooning (vehicle convoy) contributes as one possible solution to save fuel and reduce CO 2 emissions due to the decreased aerodynamical energy losses. By reducing the inter-vehicle time gap, the fuel consumption of HDVs can be reduced by up to 7.7% [1]. Controllers using radar and vehicle to vehicle (V2V) communication systems were developed in order to replace the driver as a controller of a HDV in a platoon and shorten the inter-vehicle time. However, it is not clear how a platoon should act or be arranged when taking the road topography into account to achieve even further fuel saving. Problem Formulation The aim of this thesis is to find control strategies for platooning HDVs by considering road topography preview information. With an optimal control strategy, the fuel consumption of a HDV platoon should be minimized while maintaining the over all travel time. In terms of fuel saving, maintaining a constant velocity is the preferred control strategy for a given travel time. This is obvious when examining the aerodynamic force on the vehicle which increases with the velocity according F drag v 2. An HDV is typically not able to maintain its velocity when traveling uphill and experiences a speed increase with negative slopes. Figure 1 shows the speed and throttle input profile for a single HDV on an uphill and downhill slope controlled with road topography preview information. On the flat road, the normal cruise controller (CC) sets the throttle input u = u cruise. As soon as the ahead road topography preview information reveals that the HDV can not maintain its velocity, the controller finds the distances d 1 and d 4 where the throttle input is maximized u = u max on an uphill slope or minimized u = on a downhill slope. A cost function J(,T t ) depending on the fuel consumption and the travel time T t will be minimized by the controller. 1 V

85 APPENDIX A. Figure 1: Uphill and downhill slopes with velocity profile and throttle input The problem of controlling a single HDV has already been examined [2]. In this Thesis, control stratagies for a platoon with N 2 HDV will be found. Compared to [2], the controller output should not take any value, but the values u =[,u cruise,u max ]whereu cruise is set by the cruise controller (CC). Methods / Expected Results The thesis will be divided into the following work packages: 1. Problem analysis for a single N = 1 HDV: Specification of road profiles (uphill, downhill, up-downhill, down-uphill) Analytical optimization of control shape for each profile. Sensitivity analysis for all parameters p (slope, vehicle mass m v, d 2, d 3,etc.) Design of feedback control strategies based on p 2. Controller design for N = 2 HDV 3. Controller design for N 2 HDV Simulations will be done using Matlab/Simulink and visualizations/animations will be programmed for better understanding. Time Plan February March April May June July August September Holidays Thesis Start Work Package 1 Work Package 2 Work Package 3 Extra time to write thesis Thesis Hand-In Oral Defense References [1] Assad Alam, Fuel-E cient Distributed Control for Heavy Duty Vehicle Platooning. Licentiate Thesis, KTH Royal Institute of Technology, 211. [2] Erik Holma, Data Requirements for a Look-Ahead-System. Master Thesis, Linköpings Universitet, 27. August 2, 213 Lukas Bühler 2 VI

86 APPENDIX A. A.2 Declaration of Originality Declaration of Originality This sheet must be signed and enclosed with every piece of written work submitted at ETH. I hereby declare that the written work I have submitted entitled Fuel-Efficient Platooning of Heavy Duty Vehicles through Road Topography Preview Information is original work which I alone have authored and which is written in my own words.* Author(s) Last name Bühler First name Lukas Supervising lecturer Last name Morari First name Manfred With the signature I declare that I have been informed regarding normal academic citation rules and that I have read and understood the information on 'Citation etiquette' ( students/exams/plagiarism_s_en.pdf). The citation conventions usual to the discipline in question here have been respected. The above written work may be tested electronically for plagiarism. Stockholm, Place and date Signature *Co-authored work: The signatures of all authors are required. Each signature attests to the originality of the entire piece of written work in its final form. Print form VII