Control Optimization for a Low-cost Flywheel Module

Transcription

1 Control Optimization for a Low-cost Flywheel Module Koos van Berkel, Theo Hofman, Bas Vroemen, Maarten Steinbuch Abstract This paper describes a modeling and design approach in finding the optimal controller for a low-cost hybrid drive train on a pre-defined driving cycle. The hybrid drive train is characterized by a small energy capacity (flywheel) and discrete shifts between operation modes, due to the use of clutches. The main design criterion, is the minimization of the overall fuel consumption, whereas constraints are defined to describe the system s dynamics, kinematics and constraints. In addition, comfort criteria are defined as constraints, to avoid uncomfortable driving conditions. These criteria are used to find the optimal sequence of driving modes and generated engine torque over a defined driving cycle. Simulations show a fuel saving potential of 22 to 39%, dependent on the chosen driving cycle. Index Terms Optimal Control, Mechanical-Hybrid Vehicle, Flywheel, Continuously Variable Transmission (CVT) I. INTRODUCTION The market share of Continuously Variable Transmissions (CVTs) is still growing. Especially in the A-B-C vehicle segment in Asia this can be noticed. CVTs enable the Internal Combustion Engine (ICE) to operate in its energy-efficient region, thereby reducing the fuel consumption of the vehicle [1]. In the past decades, many transmission manufacturers have put effort in the development of the CVT towards a mature and low-cost technology [2]. Moreover, the potential for further improvement with respect to cost and efficiency is high with new upcoming technologies, such as slip control [3], extremum seeking control [4] and on-demand actuation systems [5]. Nevertheless, the increasing oil price and stricter becoming environmental regulations push the demand for higher fuel efficiency even further. Hybrid transmissions can give a significant improvement, as shown e.g., by Toyota and Honda. However, current battery-based systems are too expensive for this segment, due to the use of large battery packs and additional motor/generator(s). As a low-cost alternative, a mechanical-hybrid (also referred to as, mechybrid-) drive train design is proposed, which uses a steel-flywheel module and a push-belt CVT for energy storage and power transmission, respectively [6]. The modular design is schematically depicted in Fig. 1. This work is a part of the mechybrid project which is a common project of TU/e, DTI, Punch Powertrain, CCM, Bosch and SKF. The project is funded by the Dutch Ministry of Economic Affairs, Provincie Noord- Brabant and SRE. Koos van Berkel (Ph.D. candidate), Theo Hofman (assistant professor) and Maarten Steinbuch (full professor) are with the Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 56 MB Eindhoven, The Netherlands, Phone: , Fax: , k.v.berkel@tue.nl, t.hofman@tue.nl, m.steinbuch@tue.nl Bas Vroemen (vice-president) is with Drive Train Innovations, Croy 46, 5653 LD Eindhoven, The Netherlands, vroemen@dtinnovations.nl f T ice Engine Hybrid module C e C f C d Flywheel CVT Fig. 1. Hybrid drive train topology and signal flow, including the flywheel module, clutches and Continuously Variable Transmission (CVT). This concept uses the CVT to charge the flywheel (FW) with kinetic vehicle load during regenerative braking and to retrieve energy from the FW to propel the vehicle. The main fuel saving benefit can be attributed to the added hybrid functionalities: (1) recuperation of brake energy, (2) shuttingoff the ICE during standstill, and (3) elimination of the inefficient part load operation of the ICE, e.g., by driving on or charging of the FW. The hybrid module has a lowcost potential, as it is modular applicable to conventional CVTs, and it contains only low-cost mechanical components, such as a steel-flywheel, gears and compact clutches. Besides costs, mechanical-hybrid transmissions have physical advantages compared to electrical-hybrid transmissions in that the transmission efficiency and specific power are higher [7]. The controls however, may be more complex, due to mechanical constraints. For the given topology, these constraints are: 1) the energy storage capacity of the FW is relatively small, for reasons of packaging, cost and safety; 2) shifts between driving modes are more or less discrete, as clutches are used to (dis)engage the ICE and FW. 3) the use of the FW is limited by the kinematic constraints of the drive train. To make full use of the hybrid functionalities, a controller is required which steers the sub-systems of the hybrid drive train in an optimal sense, while respecting these constraints. The design of such controller will be explained next. A. Integral control optimization problem The hybrid drive train controller manages the power flows at system level, by creating set-points for the low-level subsystem controllers, which control the dynamics in the hybrid drive train [8]. One of the main questions regarding this controller is [9], [1]: how can the secondary mover, i.e., flywheel system, be utilized to minimize the fuel consumption, without compromising driveability issues such as comfort and noise? This integral control optimization problem may E f v v a v 73

2 be divided into two sub-control problems acting on different time scales, related to the fuel consumption and driveability issues, respectively. 1) Energy Management Strategy (EMS): the objective is to minimize the fuel consumption, while respecting the systems s dynamics, kinematics and constraints. This controller manages the power flows in the hybrid drive train, considered on a large time scale (> 1s). Dynamic effects that act on a short time scale (< 1s) are neglected. More specifically, the EMS selects the optimal driving modes and the torque generated by the ICE. The control design considers power losses which result from clutch engagements, and avoids driving mode shifts which result in engine noise issues. 2) Drive Train Control (DTC): the objective is to obtain a similar comfort level as that of a conventional drive train. This controller controls the drive train dynamics that act on a short time scale (< 1s), such as undesired oscillations introduced by the clutch (dis-) engagements, by optimal actuation of the clutches, the CVT, or both. The design avoids control actions which result in excessive power dissipation, such as letting a clutch continuously slip during propulsion. In this paper, we will address the design of an optimal EMS; the design of an optimal DTC will not be discussed. B. Main contribution and outline of this paper EMS design approaches for hybrid electric vehicles are well covered in literature, among others, in [11], [12], and [13]. Mechanical-hybrid vehicles, however, may have different characteristics, due to mechanical constraints. For mechanical hybrid vehicles, few optimal EMS design approaches are found. Strategies that consider discrete driving mode shifts and a small energy capacity, are found in [14] and [15], but are sub-optimal. Optimal strategies are found in [16] and [17], but do not consider discrete driving mode shifts. This paper presents the modeling and design of an optimal EMS for the proposed mechanical-hybrid drive train. The main design criterion for the optimal EMS, is the minimization of the overall fuel consumption, while respecting the system s kinematics, dynamics and constraints. In addition, comfort criteria are defined as constraints, to avoid uncomfortable situations. Dynamic Programming (DP) is applied to find the global optimal sequence of driving modes and the torque generated by the ICE, for a given driving cycle. Although the resulting optimal EMS is not onlineimplementable, as the future driving profile is assumed to be exactly known, a benchmark is set for the fuel saving potential of the proposed hybrid drive train, and a basis is made for the design of an online-implementable EMS. The outline is as follows: Section II describes modeling of the hybrid drive train components. Section III describes the hybrid drive train model for different driving modes, and for the shifts in between. Section IV defines the optimization problem and describes the applied optimization method. Section V presents the simulation results. Finally, Section VI summarizes the conclusions and future work. II. COMPONENT MODELS The main components of the hybrid drive train are the Internal Combustion Engine (ICE), flywheel system (FW), clutches, CVT, and vehicle. Table I summarizes some characteristics. This section describes the modeling of these components. Some (efficiency) models are, because of their non-linear behavior, described by look-up tables, based on static experiments. For such models, intermediate points are calculated by linear interpolation. Dynamic effects, such as drive train oscillations, are not considered. Fig. 2 shows the resulting dynamic model of the hybrid drive train. TABLE I BASE COMPONENT CHARACTERISTICS Engine 1 4-cylinder 1.5-l gasoline internal combustion engine, peak power 76 kw (at 6 rpm), peak torque 14 Nm (at 4 rpm), peak efficiency 23 g/kwh. Flywheel 1 Vacuum-placed 15-kJ steel-flywheel, peak power 35 kw, max. speed 3. rpm, inertia.3 kgm 2, gear ratio 1 : 12, system mass 27 kg. Transmission 1 Push-belt driven Continuously Variable Transmission, max. input torque 14 Nm, ratio range 6., final drive ratio 1 : 5.41, integrated pump, peak efficiency 91%. Vehicle 2 + Smart ForFour (25), mass kg, inertia of 2 passengers all wheels 1.2 kgm 2, aerodynamic drag coefficient.31, frontal area 1.86 m 2, rolling resistance 143 N. 1 Data based on experimental results. 2 Data based on estimated parameters. Flywheel T f,drag Engine T ice T e,drag Fig. 2. J f J e r g T e e T f f Clutches C f C e C d T p p CVT r cvt T s s cvt r d T w w Vehicle J w + T w,drag Dynamic model of the hybrid drive train (compliances are omitted). A. Internal Combustion Engine The ICE model is based on its engine and flywheel inertia J e, on which three torques are acting: the generated torque T ice, drag torque T e,drag and external torque T e, which depends on the selected driving mode, see Section III-A. The dynamics and constraints in discrete time format, using a simple forward Euler scheme, are given by ω e,k+1 = ω e,k + 1 J e (T ice,k T e,k T e,drag (ω e,k )), (1) T e,drag,k (ω e,k ) T ice,k T e,wot,k (ω e,k ), (2) ω e,min ω e,k ω e,max. (3) with a fixed time step T = 1 s. The discrete time sample is indicated by subscript k. Here, ω e is the 74

3 rotational speed of the ICE and T e,wot the generated Wide-Open-Throttle torque, described by a look-up table. T e,drag (ω e ) is modeled as a second order polynomial for positive speeds, using nonnegative coefficients based on experimental results, and equals zero at zero speed. The injected fuel mass rate m f (g/s) is described by a look-up table: m f,k = Λ(ω e,k,t ice,k ). B. Flywheel The FW model is based on its inertia J f, on which two torques are acting: the drag torque T f,drag and external torque T f, which depends on the selected driving mode (see, Section III-A). The dynamics and constraints are given by ( ω f,k+1 = ω f,k + r2 g T f,k 1 ) T f,drag (ω f,k ), (4) J f r g ω f,min ω f,k ω f,max. (5) Here, ω f is the rotational speed of the flywheel clutch. Constraints on T f are described by the constraints on the CVT s input shaft, by (1). T f,drag (ω f ) is modeled as a second order polynomial for positive speeds, using nonnegative coefficients based on experimental results, and equals zero at zero speed. This drag torque describes the total system s losses, including bearing-, gear-, seal-, and air drag losses. The gear gives a constant gear ratio r g between ω f and the flywheel. The FW s State-of-Energy (SoE) E f (J) equals C. Clutches E f,k = J f 2rg 2 ωf,k 2. (6) The hybrid drive train contains three actively controlled clutches: the engine clutch (subscript e ), flywheel clutch (subscript f ) and drive clutch (subscript d ). The drive clutch has conventional dimensions, suitable to launch the vehicle with. The engine and flywheel clutch are smaller, only suitable to synchronize with the intermediate shaft, and to crank the ICE. The clutch state model is discrete: C z = when disengaged and C z = 1 when engaged, for z {d,e,f}. When shifting between states, the clutch slips, and torque transmission T c is assumed to be accurately controlled. Power loss due to speed difference ω c equals D. CVT P clutch = T c ω c, (7) The CVT provides a continuous variable speed ratio r cvt between the primary (subscript p ) and secondary pulley shaft (subscript s ) defined by r cvt,k := ω s,k /ω p,k. The final drive gives a constant speed ratio between the secondary pulley shaft and the wheel shaft (subscript w ) defined by r d := ω w /ω s. Constraints apply to r cvt, its change r cvt,k := r cvt,k+1 r cvt,k and primary torque T p : r cvt,min r cvt,k r cvt,max, (8) c r cvt,k r cvt,k c r cvt,k, (9) T p,min T p,k T p,max. (1) Here, the shift-speed constraint is modeled as in [1], with shift-speed constant c. The transmission efficiency of the CVT system η cvt, for both positive and negative torques, is described by a look-up table: η cvt,k = Ω(ω w,k,t w,k,r cvt,k ). The transmission efficiency includes losses by the pump and final drive, using a conventional control strategy [18]. E. Vehicle The vehicle is modeled by the inertia of the wheels including the total vehicle mass J w, on which two torques are acting: drag torque T w,drag and the drive train s propulsion torque T w. For given vehicle velocity v v and acceleration a v, and neglecting any wheel slip, the required T w equals T w,k = T w,drag,k (v v,k )+ J w r w a v,k. (11) Here,T w,drag,k (v v ) is modeled as a second order polynomial for positive velocity, using nonnegative coefficients based on estimated parameters of the vehicle, and equals zero at standstill. The effective wheel radius gives a constant speed ratio, defined by r w := v v /ω w. III. HYBRID DRIVE TRAIN MODEL The hybrid drive train is controlled with two control inputs u := [u 1,u 2 ] T, i.e., the operation mode of the hybrid drive train (or, driving mode), and the generated engine torque, such that u k = [φ k+1,t ice,k ] T. Here, driving mode φ is defined by the states of the engine C e and flywheel clutch C f. The state of the drive clutch C d is defined (in a mathematical way) accordingly. φ(c e,c f ) := [C e,c f ] T, (12) C d = C e +C f C e C f. (13) Furthermore, three states are definedx k := [x 1,x 2,x 3 ] T, i.e., the engine and flywheel speed, to describe their dynamics and current driving mode to detect driving mode shifts, such that x k = [ω e,k,ω f,k,φ k ] T. The pre-defined driving cycle is introduced as a disturbance w k = (v v,k,a v,k ) T. This section describes the hybrid drive train dynamics for each driving mode, as well as for the shifts in between. A. Driving modes Four quasi-static driving modes are identified, in which none of the clutches is slipping (i.e., they can be disengaged or engaged). The driving mode prescribes which mover is used to propel the vehicle, i.e., either the ICE or the FW. 1) Standstill (φ = [,] T ): the ICE is shut-off and disengaged, the FW might be rotating while disengaged. The CVT speed ratio is set to its lowest gear. 2) FW Driving (φ = [,1] T ): the FW either propels, or brakes the vehicle. The ICE is shut-off and disengaged. 75

4 3) FW Charging (φ = [1,1] T ): the ICE propels the vehicle, while simultaneously, the FW is charged (T f < ), or discharged (T f > ) to assist the ICE. The charging torque T f is controlled by T ice. For comfort reasons, torque assist by the FW is not desired with this drive train design; during high power demand, the decreasing engine noise frequency contradicts with the driver s expectation. This comfort constraint is described by u 1,k {φ φ k [1,1] T, T f,k (x k,u k,w k ) > } (14) 4) ICE Driving (φ = [1,] T ): The ICE propels the vehicle, whereas the disc brakes brake the vehicle. The ICE s operation point is controlled by T ice. For a given driving cycle, the wheel torque T w,k may be calculated with (11), such that CVT input torque T p,k equals T p,k = η 1 cvt,k (ω w,k,t w,k,r cvt,k )r cvt,k r d T w,k. (15) The required T p is supplied by the external torque(s) of the engaged mover(s). For each driving mode, the required external torque of the mover(s) is summarized, as well as speed ratio r cvt, in Table II. Note that, with Standstill and FW Driving, u 2 is not specified as the ICE is shut-off. TABLE II DRIVE TRAIN OPERATION DURING VARIOUS DRIVING MODES φ description u 2 T e T f r cvt [,] T Standstill n/a r cvt,min [,1] T FW Driving n/a T p ω s/ω f [1,1] T FW Charging T ice T p T f T p T e ω s/ω f [1,] T ICE Driving T ice T p ω s/ω e Constraints apply, see, (2), (3), (5), (8), (9), (1), (14) B. Shifting between driving modes There are 4!/2 = 12 different shifts possible between the 4 driving modes. These shifts may require additional actions by the drive train, such as torque transmission through slipping clutches and cranking of the ICE. Six different shift actions are distinguished, of which one or more take place during each shift, as summarized in Table III. Note that, while shifting from one mode to another, torque is transmitted through the drive train to propel the vehicle. 1) ICE start: The ICE is cranked by the FW. The additional torque T e,start to crank the ICE to its desired speed ω e,k+1 {ω e,min, ω f,k }, is provided by the FW through the slipping engine clutch, and is modeled as: ω e,k+1 ω e,k T e,start,k = J e +T e,drag (ω e,k+1 ). (16) T 2) Vehicle Launch: The vehicle is propelled at low vehicle velocity; the drive clutch is slipping. The requiredt p remains unchanged, but power is dissipated in the drive clutch. TABLE III SHIFTS BETWEEN DRIVING MODES φ k φ k+1 actions / constraints [, ] [, 1] Vehicle Launch [, ] [1, 1] Vehicle Launch, ICE Start [, ] [1, ] Vehicle Launch, ICE Start [, 1] [, ] Vehicle Braking [1, 1] [, ] Vehicle Braking [1, ] [, ] Vehicle Braking [, 1] [1, 1] ICE Start, Duty-Cycle Shifting [, 1] [1, ] Power-shift, CVT Shift, ICE Start [1, ] [, 1] Power-shift, CVT Shift [1, 1] [, 1] Disengage Mover [1, 1] [1, ] Disengage Mover [1, ] [1, 1] CVT Shift, ICE Noise 3) Vehicle Braking: All clutches are disengaged and the disc brakes decelerate the vehicle. 4) Power-Shift: The speed of the desired mover (M2) is higher than that of currently used mover (M1). Then, while ω p is gradually increased by the CVT to synchronize with M2, M1 is disengaged and torque T p is provided by M2 through the slipping drive clutch; power is dissipated. 5) CVT Shift: The speed of the desired mover (M2) is lower than that of currently used mover (M1). Then, ω p is gradually decreased by the CVT, to synchronize with both M1 and M2, such that the movers can switch smoothly; virtually, no power is dissipated. Note that when shifting from the ICE to FW, the ICE is shut-off afterwards. 6) Disengage Mover: A mover is disengaged; no power is dissipated. Note that, when the FW is disengaged, the engine s speed might change, such that additional torque is required to accelerate or decelerate the engine inertia. The corresponding change in engine noise is expected to be acceptable, as in practice, this shift only takes place when the vehicle s acceleration changes. Next, two comfort constraints are defined. 7) ICE Noise: When shifting from ICE Driving to FW Charging, while ω f > ω e, the engine s noise suddenly increases, which is not expected by the driver. In order to avoid this situation, the next comfort constraint is defined: u 1 {φ φ k+1 [1,1] T, φ k = [1,] T,ω f,k > ω e,k } (17) 8) Duty-Cycle Shifting: Duty-cycle shifting between FW Driving and FW charging might be a fuel-efficient way to propel the vehicle at constant velocity, but not comfortable to the driver, due to the alternating ICE noise. This comfort constraint is described using a nonnegative coefficient a c (m/s 2 ), which defines constant velocity: u 1 {φ φ k+1 [1,1] T, φ k = [,1] T, a v,k < a c } (18) 76

5 IV. OPTIMIZATION The control objective is to minimize the overall fuel consumption, over a pre-defined driving cycle of length N: min u k J = N m f (x k,u k,w k ) T, (19) k=1 while respecting constraints (1-11) to describe the system s dynamic and kinematic relations, constraints (14), (17), and (18) to avoid uncomfortable driving conditions, and an endvalue constraint for the FW s SoE to assure a zero net-energy balance of the FW, over the total driving cycle: E f (N) = E f (1), (2) The signal flow of this optimization problem is schematically depicted in Fig. 1. Five driving cycles are considered: the Japan 1-15 mode (JP115), Japan Cycle 8 (JC8), New European Driving Cycle (NEDC), Federal Test Procedure 75 (FTP75) and our own driving cycle (Hurk), see Fig. 3. The four standard cycles are widely used for certified fuel consumption measurements. The Hurk driving cycle is added to represent a more aggressive, real-life type of driving. such that control input u 2 may be omitted for φ = [1,] T. Using this optimization, it is observed that the engine s acceleration is relatively small. With the assumption that the resulting inertial torque is negligible, state x 1 may also be omitted. Note that during driving mode shifts, however, the inertial torque may not be neglected, as engine speed accelerations might be significant. In this situation, the acceleration can be estimated without x 1, as current and desired engine speed are known from the driving mode shifts. V. RESULTS Fig 4 shows the simulation results for the NEDC. From top to bottom, the five graphs depict, respectively, the vehicle s velocity, the optimal driving modes, the optimal generated engine torque, the FW s SoE and the power loss in slipping clutches. The hybrid functionalities are used as follows: the FW is used to launch the vehicle; the FW is charged by the ICE during vehicle acceleration at low velocity; the FW propels the vehicle at low constant velocities; the FW is charged by regenerative braking; the ICE propels the vehicle at higher vehicle velocities. 1 JP NEDC Hurk Time [s] 1 JC FTP Time [s] Fig. 3. Five typical driving cycles: Japan 1-15 (JP115), Japan Cycle 8 (JC8), New European Driving Cycle (NEDC), Federal Test Procedure 75 (FTP75) and our own real-life driving cycle (Hurk). A. Dynamic Programming The optimization problem defined by (19) is solved using DP. The conventional drive train (without hybrid module) is simulated using the same model, with restricted control input φ = [1,]. The DP algorithm scans at each time instant, every possible combination of control inputs and states to find the global optimal solution [19]. Therefore, to avoid excessive computation time, the optimization problem is reduced as follows. It is assumed that with ICE Driving, the optimal control input u 2 is independent of the optimal control input u 1, as T ice does not influence the FW s SoE. Then, the optimal T ice may be calculated for each {x,w} a priori: T ice,k = arg min m f (x k,u k,w k ) φk =[1,] T, (21) T ice,k φ [-] Tice [Nm] Ef [kj] Pclutch [kw] [1,] [1,1] [,1] [,] Time [s] Fig. 4. Optimal EMS results for the NEDC: the velocity profile (v v), optimal driving modes (φ), optimal generated engine torque (T ice ), FW s SoE (E f ), and the power loss due to slipping clutches (P clutch ). The fuel saving potential for the considered driving cycles are summarized in Table IV. Dependent on the driving cycle, It is seen that the hybrid module provides a potential fuel saving of 22 39%. The variations in the fuel saving can be explained with the driving cycle characteristics, e.g., the NEDC and FTP75 score a lower fuel saving, as they contain high-way parts where the hybrid module is not used. For two driving cycles, the results are analyzed in more detail: (1) the relatively static NEDC, which contains relatively 77

6 TABLE IV FUEL CONSUMPTION FOR FIVE DIFFERENT DRIVING CYCLES JP115 JC8 NEDC FTP75 Hurk Conventional (l/1km) Hybrid (l/1km) Fuel saving (%) many constant-velocity parts and low accelerations; and (2) the relatively dynamic Hurk cycle, which contains relatively many, but also high accelerations and decelerations, see Fig. 3. These results are shown in Table V. As expected, the hybrid module improves the combustion efficiency for both driving cycles, as inefficient part-load operation of the ICE is reduced, and the ICE is shut-off while standing still. The FW is charged differently: with the NEDC, the FW is mainly charged by the ICE during the low-acceleration parts, whereas with the Hurk cycle, the FW is mainly charged by the kinetic vehicle load during the high-deceleration parts. Also, the relatively dynamic velocity profile of the Hurk cycle requires a higher frequency in driving mode shifts and cranking of the ICE, than the relatively static NEDC. TABLE V OPTIMAL EMS RESULTS FOR THE NEDC AND HURK CYCLE NEDC Hurk conv. hybrid conv. hybrid Fuel efficiency Combustion efficiency (g/kwh) Vehicle efficiency (l/1km) Energy source to charge FW Brake energy (%) n/a 35.1 n/a 77.7 ICE energy (%) n/a 64.9 n/a 22.3 Transmission losses Flywheel (%) Clutches (%) CVT (%) Energy management strategy Driving mode shifts (1/min) Cranking of the ICE (1/min) The combustion efficiency and transmission efficiencies are calculated with respect to the ICE s net-power, i.e., including the ICE s drag losses. VI. CONCLUSIONS AND FUTURE WORK A dynamic simulation model is presented of a hybrid drive train with typical mechanical characteristics, i.e., a relatively small energy storage capacity, discrete shifts between driving modes and relatively many kinematic constraints. An optimization problem is defined, which minimizes the fuel consumption, while respecting the system s dynamics, kinematics and (comfort) constraints, which is solved using DP. 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