Feed-Forward Air-Fuel Ratio Control during Transient Operation of an Alternative Fueled Engine

Transcription

1 Feed-Forward Air-Fuel Ratio Control during Transient Operation of an Alternative Fueled Engine A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Andrew Michael Garcia, B.S. Graduate Program in Mechanical Engineering The Ohio State University 2013 Master s Examination Committee: Dr. Shawn Midlam-Mohler, Advisor Dr. Giorgio Rizzoni

2 c Copyright by Andrew Michael Garcia 2013

3 Abstract With the increasing government regulations for higher vehicle fuel economy and lower tailpipe emissions, today s automotive engineers are pushed to develop advanced vehicle architectures. Further, due to the high prices of oil, the consumer market is demanding for more fuel efficient vehicles. To adapt to the increasing demands, automotive manufacturers have been investing in the research of advanced vehicle technologies. The work described in this thesis details the development of a methodology to improve the feed-forward air-fuel ratio control during transient operation of an alternative fueled engine. Due to transport delays between the induction of the air-fuel mixture into the cylinder and the reading of the combustion exhaust gases from the oxygen sensor, conventional feedback control cannot be accurately used in transient operation. Since the engine used in this thesis is port-fuel injected, the fuel injection command is made a discrete amount of time before the intake valve opening. This gives the fuel time to vaporize in the intake runner before being inducted. Therefore, in order to achieve stoichiometric combustion, the amount of inducted air will have to be determined a discrete amount of time into the future. This work outlines the development of a control algorithm that improves the transient air-fuel ratio control by predicting the intake manifold air pressure forward in ii

4 time. Using model-based calibration techniques and engine dynamometer data, an intake manifold model was created. Coupling this model with a Forward Euler approximation, a predictive intake manifold pressure algorithm was developed. Adaptive models were implemented into the control algorithm to account for day-to-day variations in engine operation as well as calibration errors in the intake manifold model. The algorithm was verified in software validation with a mean value engine model and hardware validation in the engine dynamometer test cell. With the implementation of the predictive control algorithm, there was a vast improvement in air-fuel ratio control performance over the engine s previous control strategy. Oxygen sensor results showed a significant reduction in deviations from stoichiometric combustion, allowing the three-way catalyst to operate in its most efficient range. The research detailed in this thesis shows the effectiveness of using a model-based approach to air-fuel ratio control and the importance of adaptive algorithms for day-to-day changes in engine operation. iii

5 This thesis is dedicated to my parents for their endless love, patience, and support. iv

6 Acknowledgments I would like to thank the Center for Automotive Research for providing access to an unparalleled faculty and facilities to support my research. I would especially like to thank my advisor, Dr. Shawn Midlam-Mohler for his guidance and support throughout my graduate experience. His never-ending enthusiasm and dedication toward teaching has been paramount to success in my research. I would also like to thank Dr. Giorgio Rizzoni for his invaluable advice and support for the EcoCAR 2 program. I would like to thank my fellow graduate students, whom are always willing to share their knowledge and assistance. I would also like to thank the entire EcoCAR 2 team, their efforts in the design, build, and validation of our team s parallel-series plug-in hybrid electric vehicle (PHEV) has been nothing short of inspiring. I would especially like to thank my fellow team leaders Katherine Bovee, Jason Ward, Matthew Yard, Matthew Organiscak, Eric Gallo, Amanda Hyde, and David Walters for their knowledge, enthusiasm, and support. Finally, I would like to thank the U.S. DOE Graduate Automotive Technology Education (GATE) Center of Excellence for providing the funds and resources for the research in this thesis. v

7 Vita July 6, Born - Cleveland, Ohio December, B.S. Mechanical Engineering, The Ohio State University December, Graduate Research Associate, Department of Mechanical and Aerospace Engineering, The Ohio State University Publications Research Publications K. Bovee, A. Hyde, M. Yard, T. Trippel, M. Organiscak, A. Garcia, E. Gallo, M. Hornak, A. Palmer, J. Hendricks, S. Midlam-Mohler and G. Rizzoni Design of a Parallel-Series PHEV for the EcoCAR 2 Competition. SAE, Fields of Study Major Field: Mechanical Engineering vi

8 Table of Contents Page Abstract Dedication Acknowledgments Vita List of Tables ii iv v vi ix List of Figures xi Nomenclature xv 1. Introduction Motivation EcoCAR 2 Competition Ohio State University EcoCAR 2 Vehicle Architecture Thesis Overview Literature Review Introduction Air Dynamics Throttle Modeling Volumetric Efficiency Intake Manifold Modeling Air-Fuel Ratio Control Honda R18A3 Engine Tailpipe Emissions vii

9 3. Experimental Description Engine Instrumentation Data Acquisition System GM LE5 Mean Value Engine Model Control Algorithm Development Introduction Control Algorithm Description Summary Intake Manifold Modeling Introduction Throttle Model Volumetric Efficiency Model Intake Manifold Pressure Model Summary Control Algorithm Validation Introduction Software Validation Hardware Validation Recalibrating V e Map Implementation of Adaptive Control Strategies AFR Results Summary Conclusions and Future Work Conclusions Future Work Bibliography Appendices 122 A. Intake Manifold Model Subsystems viii

10 B. Adaptive Volumetric Efficiency Table Subsysems ix

11 List of Tables Table Page 2.1 Sensor specifications [1] Engine specifications [15] Relevant instrumented sensors on engine Constant engine parameters Model MAP Sensitivity Analysis MAP prediction performance Comparison among proposed 2-d lookup functions Comparison between original and recalibrated V e maps Error improvement using PI control Error improvement using V e adaptive control Closed-loop AFR results, area deviation Closed-loop AFR results, maximum % deviation Comparison of closed-loop AFR results for area deviation with steadystate algorithm recalibration Comparison of closed-loop AFR results for maximum % deviation with steady-state algorithm recalibration x

12 6.10 Open-loop AFR results, area deviation Open-loop AFR results, maximum % deviation Test operating points for open-loop AFR control performance comparison113 xi

13 List of Figures Figure Page 1.1 Ohio State University EcoCAR 2 vehicle architecture Three-way catalyst conversion efficiency [12] Variation in flow rate past a throttle [9] Isenthalpic flow model of a throttle [12] Affects of different flow phenomena on volumetric efficiency [8] Volumetric efficiency map of a 1.8L 4cyl E85 engine Model classification for an intake manifold [8] MAF and MAP reading from throttle transient at 1200 RPM Injection and transport delays [1] Honda R18A3 engine [15] Valve lift profiles of different cam settings [15] Intake manifold variable length runner [15] Emissions concentrations against air/fuel ratio [9] Intake side of engine Exhaust side of engine xii

14 3.3 Engine test setup [6] D Mean-value engine model for GM LE5 engine Control algorithm timing MAP prediction control algorithm MAP prediction SIMULINK model MAP prediction Stateflow diagram Throttle affective area map, raw data Throttle affective area map, function fit Model and experimental C d A value comparison Calculated and actual MAF value comparison MAF during throttle transient event Volumetric efficiency map, raw data Model and experimental VE value comparison Model and experimental MAF value comparison SIMULINK diagram of intake manifold model MAP during throttle transient event MAP prediction SIMULINK implementation in MVEM MVEM simulation results at varying engine operating points MVEM simulation results for throttle transient MVEM simulation results for throttle transient, with throttle rate limiter MVEM normalized error vs. iteration number xiii

15 6.6 MVEM simulation time vs. iteration number MAP prediction performance results, 1200 RPM C d A based V e 2-d lookup function MAF error between throttle and induction mass air flow Comparison between original and recalibrated V e maps at 1200 RPM SIMULINK implementation of adaptive PI model SIMULINK implementation of engine steady-state detection Steady-state detection for random transients MAP prediction SIMULINK diagram with adaptive PI model Improvement using adaptive PI model at 1200 RPM MAP prediction SIMULINK diagram with adaptive V e table V e table correction Layout of V e adaptation zones Improvement using adaptive V e table at 1200 RPM Day-to-day variability in V e multiplier AFR deviation from throttle tip-in, 1200 RPM, closed-loop AFR deviation from throttle tip-out, 1200 RPM, closed-loop Filter change comparison Steady-state detection comparison Open-loop AFR control performance comparison, 1200 RPM, kpa transient xiv

16 6.26 Method of calculating metrics for open-loop results Open-loop AFR control performance comparison, area deviation Open-loop AFR control performance comparison, max % deviation. 114 A.1 Subsystem: throttle model A.2 Subsystem: throttle model > flow restriction A.3 Subsystem: throttle model > flow restriction > unchoked flow A.4 Subsystem: throttle model > flow restriction > choked flow A.5 Subsystem: V e model A.6 Subsystem: V e model > V e to MAF B.1 VE Lookup Table B.2 VE Lookup Table > Zone Based Correction Control B.3 VE Lookup Table > Zone Based Correction Control > Zone Determination B.4 VE Lookup Table > Zone Based Correction Control > Zone Determination > X Zone Determination xv

17 Nomenclature t time step ṁ a,cyl mass air flow into cylinder ṁ a,th mass air flow through throttle η v volumetric efficiency γ specific heat ratio of air λ relative air to fuel ratio ρ a density of air C d coefficient of discharge C d A effective flow area HC hydrocarbons m a,im mass of air in intake manifold N engine speed p r pressure ratio of intake manifold air pressure to the ambient air pressure p a,im intake manifold pressure xvi

18 p amb ambient air pressure R universal gas constant T a,im intake manifold temperature T amb ambient air temperature V d total engine cylinder displacement volume V e volumetric efficiency V IM intake manifold volume A throttle plate open area AFR air to fuel ratio APC air per cylinder CAD crank angle degrees CNG compressed natural gas DOE Design of experiment ECU electronic control unit EGR exhaust gas recirculation HEV hybrid electric vehicle IAT intake air temperature IVO intake valve opening xvii

19 MAF manifold air flow MAP manifold absolute pressure MRB multiquadratic radial basis MVM mean value model PFI port fuel injection PHEV plug-in hybrid electric vehicle RMSE root-mean-square error RTD resistance temperature device VVT variable valve timing WOT wide open throttle xviii

20 Chapter 1: Introduction 1.1 Motivation With the increasing government regulations for higher vehicle fuel economy and lower tailpipe emissions, today s automotive engineers are pushed to develop advanced technology vehicles. Further, due to the high prices of oil, the consumer market is demanding for more fuel efficient vehicles. To adapt to the increasing demands, automotive manufacturers have been investing in the research of advanced technologies. These include engine technologies such as the use of variable valve timing or cylinder deactivation. Advances in vehicle aerodynamics have also been made with active grill shutters and improved body shapes to help reduce drag coefficients. Also, to help reduce oil dependence, the use of renewable sources such as ethanol and biodiesel has been utilized to fuel internal combustion engines. With the introduction of hybrid vehicles in the late 1990s, the automotive industry has since been able to dramatically increase the fuel economy and decrease tailpipe emissions. These vehicles include hybrid electric vehicles (HEV) and plug-in hybrid electric vehicles (PHEV). The vast improvement from hybrids comes from the combination of the high efficiencies of electric propulsion with the advanced technologies of internal combustions engines. Today, these technologies are being researched 1

21 by every major automotive manufacturer. As advanced technology vehicles become more ubiquitous in today s world, it is crucial to start educating future automotive engineers for the rigorous design process of these vehicles. 1.2 EcoCAR 2 Competition EcoCAR 2 is a three-year competition designed to offer an unparalleled realworld experience aimed to educate the next generation of automotive engineers. This competition, headline-sponsored by the United States Department of Energy and General Motors, is a continuation of a long series of Advanced Vehicle Technology Competitions. The goal of EcoCAR 2 is to reduce the environmental impact of a 2013 Chevrolet Malibu without compromising the performance, safety, and consumer acceptability of the vehicle. This requires the 15 competing universities from across North America to design, optimize, and build a new powertrain to create a fully functional prototype by the end of the third year. The first year of the competition is geared towards the initial design and simulation of the future vehicle. Through the use of vehicle energy consumption simulations, hardware-in-the-loop and software-in-the-loop applications, and computer-aided design, teams are able to begin the intense vehicle development process. The goal of year one is to develop vehicle technical specifications, select major powertrain components, complete the initial packaging strategies, and start designing the control strategies. In the second year of the competition, the process of building a mule vehicle begins. This involves a full teardown of the stock vehicle and integration of the powertrain components. By the end of year two, a fully functional mule vehicle is expected, which will be evaluated in a series of static and dynamic events. In year three, the teams 2

22 will refine the mechanical, electrical and control systems of their vehicle to produce a near-production quality vehicle. The prototype vehicles will then be evaluated on a multitude of metrics including: fuel economy, emissions, drivability, acceleration, braking, and consumer acceptability Ohio State University EcoCAR 2 Vehicle Architecture For the EcoCAR 2 competition, the Ohio State University team is designing a parallel-series plug-in hybrid electric vehicle that is capable of 50 miles of all-electric range. The vehicle is designed to drastically reduce fuel consumption with a projected utility factor weighted fuel economy of 75 miles per gallon gasoline equivalent, while meeting Tier II Bin 5 emissions standards. Several of the key features of the vehicle include: Multi-mode operation to allow operation in series, parallel, or all-electric operation. An on-board supervisory controller optimizes the switch among the different modes in real-time. A high-efficiency E85 internal combustion engine, that is able to operate with greater than 40% brake thermal efficiency. An automated manual transmission, developed completely by the team. Aggressive electric operation which includes high all-electric range and high all-electric performance. The overall architecture of the vehicle is shown in Figure 1.1. The front powertrain is consists of a Honda 1.8L E85 engine coupled to a Parker Hannifin electric machine. The power is sent to the wheels through a 6-speed automated manual transmission. 3

23 Figure 1.1: Ohio State University EcoCAR 2 vehicle architecture The rear powertrain includes a Parker Hannifin electric machine coupled to a Borg- Warner single speed gearbox. The battery pack is an A123 Systems 18.9 kw-hr, 340V battery pack. 1.3 Thesis Overview The research conducted in thesis will help improve the emissions and overall performance of the 1.8L alternative fueled engine used in the Ohio State EcoCAR 2 vehicle. This work outlines the development of a control algorithm that improves the transient air-fuel ratio control by predicting the intake manifold pressure forward in time. Using model-based calibration techniques and design of experiment engine dynamometer data, an intake manifold model was created and implemented into the 4

24 control algorithm. The algorithm was verified using both software and hardware validation. A mean value engine model was used in the early stages of the development process, and an engine dynamometer test cell was used as the control algorithm matured. The effectiveness of the intake manifold prediction software was determined through simulation and engine dynamometer testing. The organization of this thesis is as follows: Chapter 2: Literature Review Chapter 2 provides background information on the modeling an engine s intake manifold dynamics, common solutions to air-fuel ratio control, and tailpipe emissions. The specifications for the engine used in this research are also included. Chapter 3: Experimental Description Chapter 3 discusses the engine instrumentation, data acquisition systems, and mean value engine model used in this thesis. Chapter 4: Control Algorithm Development Chapter 4 outlines the control algorithm for predicting the intake manifold pressure. Chapter 5: Intake Manifold Modeling Chapter 5 discusses the process of calibrating the intake manifold dynamics model. This includes modeling the throttle air flow and pumping efficiency of the engine. 5

25 Chapter 6: Control Algorithm Validation Chapter 6 details the process of validating the intake manifold pressure prediction control algorithm; this includes both software validation and hardware validation. Additionally, adaptive methods to improve the control algorithm performance are described. Chapter 7: Conclusions and Future Work Chapter 7 summarizes the work presented in this thesis and outlines work that can be completed in the future. 6

26 Chapter 2: Literature Review 2.1 Introduction The following sections provide background information regarding air flow modeling of an engine s intake system as well as control strategies used in this thesis. 2.2 Air Dynamics In order to minimize emissions in the tailpipe exhaust gasses, an engine typically must achieve a stoichiometric air to fuel ratio (AFR). This is because the three-way catalyst operates at its best efficiency within a narrow band around the stoichiometric AFR (λ = 1), as seen in Figure 2.1. If the engine runs under lean conditions (λ >1), then the reduction of nitrogen oxides is reduced. If the engine runs under rich conditions (λ <1), then the reduction of hydrocarbons and carbon monoxide begins to decrease. These conversion efficiencies hold true only if a three-way catalyst is used. There exists other types of catalysts such as the NO x trap catalyst, which is used on lean-burn gasoline engines. This type of catalyst is employed to provide the same efficiencies as the three-way catalyst but at a slightly leaner operating point than stoichiometric combustion [11]. The importance of maintaining the correct AFR results in the need for electronic control systems coupled with the appropriate sensors to obtain information needed to 7

27 Figure 2.1: Three-way catalyst conversion efficiency [12] make the correct control actions. Under steady-state conditions, the engine s control algorithm can achieve stoichiometric AFR with high accuracy through the use of the lambda sensor and feedback control. A lambda sensor is a sensor that can measure the net oxygen content of the exhaust gas which can be used to determine the current AFR. But, due to transport delays between the lambda sensor and the ECU as well as sensor response delays, feedback control cannot be accurately used in transient operation. Under transient conditions, a stoichiometric AFR is difficult to achieve as a fuel request typically must be made before the intake stroke begins; for the engine discussed in this paper, the fuel request must be made 700 crank angle degrees (CAD) before the intake stroke. This is to ensure that the fuel has maximum time to vaporize in the intake runner before it enters the combustion chamber. If the fuel is not vaporized, an emissions spike will occur. In order to achieve stoichiometric AFR during transient conditions, a feed forward control algorithm that is able to predict 8

28 Figure 2.2: Variation in flow rate past a throttle [9] the amount of air mass entering the combustion chamber a short amount of time in the future is required Throttle Modeling In an engine s air induction system, the throttle is responsible for metering the amount of air that enters into the intake manifold. By metering the air, the throttle is able to control the torque output of an engine in relation to the demand from the driver s accelerator pedal input. When the vehicle is under typical road-load conditions, the total pressure loss across the throttle plate can exceed 90 percent [9]. 9

29 Figure 2.2 shows the relationship among air flow rate, throttle angle, intake manifold pressure, and engine speed of a typical production engine. It can be seen that at a given engine speed, an increase in throttle position will result in a higher intake manifold pressure and air flow rate (assuming the cam shaft timing is fixed and EGR is held constant). This figure also shows the non-linear relationship among all the parameters. At lower throttle positions, a small increase in throttle position will result in a significant increase in air flow rate. At higher throttle positions, a small increase in throttle position will result in a relatively insignificant increase in air flow rate. When the engine is in transient operation, the mass air flow rate into the cylinders cannot be measured using a mass air flow (MAF) sensor because the sensor is typically located upstream of the throttle body. In this location, the intake manifold dynamics are completely neglected, resulting in errors for the mass flow rate into the cylinders. Instead, the mass air flow is calculated using information from the engine s throttle position sensor, manifold absolute pressure (MAP) sensor, and intake air temperature sensor. The air mass flow rate through the throttle valve can be calculated using standard orifice equations for compressible fluid flow [9]. These equations make two important assumptions. One assumption is that no losses occur in the accelerating portion of flow up to the narrowest point; all the potential energy stored in the flow is converted to kinetic energy, isentropically [12]. The second assumption is that after the narrowest point, the flow is fully turbulent and all the kinetic energy is dissipated into thermal energy [12]. Figure 2.3 shows the isenthalpic flow through the throttle valve. Based on the thermodynamic relationships of isentropic expansion, the following equations can be derived to calculate mass air flow through the throttle valve: 10

30 Figure 2.3: Isenthalpic flow model of a throttle [12] ṁ a,th = C ( ) 1 [ dap amb pa,im γ 2γ 1 RTamb p amb γ 1 ṁ a,th = C dap amb γ RTamb 2 γ + 1 ( pa,im γ+1 γ 1 p amb ) γ 1 ] γ (2.1) (2.2) p cr = 2 γ γ 1 = (for γ = 1.4) (2.3) γ + 1 where C d is the coefficient of discharge which indicates the losses due to turbulent friction and flow contraction, A is the throttle plate open area, p amb and T amb are the upstream pressure and temperature, p a,im is the downstream pressure in the intake manifold, R is the gas constant, and γ is the specific heat ratio. For convenience, the coefficient of discharge and throttle plate open area variables can be lumped into one variable parameter called the effective flow area (C d A). The effective flow area can be calculated using steady-state experimental data and Eq. 2.1 and

31 Equation 2.1 is used for pressure ratios across the throttle (p a,im /p amb ) greater than or equal to the critical pressure value which indicates unchoked flow. Equation 2.2 is used for pressure ratios across the throttle less than the critical pressure value which indicates choked flow. Equation 2.3 shows how to calculate the critical pressure value. When the flow is choked, the flow is no longer dependent on the intake manifold pressure or engine speed. Looking at Figure 2.2, it can be seen that below the critical pressure value (40.1 cmhg) the air flow rate is constant Volumetric Efficiency The volumetric efficiency (V e ) is a parameter that measures the overall effectiveness of a four-stroke engine s induction process. It is defined as the ratio of the actual mass of the inducted charge to the ideal mass of air that would fill the capacity of the cylinder based on either ambient or intake manifold conditions. The equation for volumetric efficiency is shown in Eq where: η v = m a,inducted m a,ideal (2.4) m a,ideal = ρ a V d (2.5) The ideal mass of air can be calculated by multiplying the density of air, ρ a, and the cylinder displacement volume, shown in Eq This mass can be defined in two different ways: with respect to ambient conditions or with respect to intake manifold conditions [9]. If the atmospheric air density is used, then the calculated volumetric efficiency represents the pumping performance across the entire inlet system. The 12

32 inlet system includes the air filter, airbox, throttle, manifold, runners, ports, and valves. If the air density of the intake manifold is used, then the calculated volumetric efficiency represents the pumping performance of the inlet ports, runners, and valves only. The typical maximum values of volumetric efficiency for naturally aspirated engines are between 80 and 90 percent [9]. An alternate equation can be used to calculate volumetric efficiency. It is defined as the ratio of the volume flow rate of air into the engine s intake system to the rate in which volume is displaced by the piston, shown in Eq This equation can be rewritten via the ideal gas law, shown in Eq Equation 2.7 is also known as the volumetric efficiency equation. η v = 2ṁ a ρ a V d N (2.6) η v = 2ṁ art p a,im V d N (2.7) Conditions that Affect Volumetric Efficiency Volumetric efficiency is dependent on the complex interactions of many factors inherent to the fuel, engine design, and engine operating conditions. Several of the factors are listed below [9]: Fuel type, fuel/air ratio, fraction of fuel vaporized in the intake system, and fuel heat of vaporization Mixture temperature as influenced by heat transfer Ratio of exhaust to inlet manifold pressures 13

33 Figure 2.4: Affects of different flow phenomena on volumetric efficiency [8] Compression ratio Engine speed Intake and exhaust manifold and port design Intake and exhaust valve geometry, size, lift, and timings These factors can be examined as quasi-steady affects. Therefore, they can be considered either independent of engine speed or can be described in terms of mean engine speed. Figure 2.4 shows how these factors affect volumetric efficiency as a function of engine speed. 14

34 Model Calibration As described previously, the volumetric efficiency of an engine is the result of many complex interactions within the system. Due to this complexity, the most practical way of determining the volumetric efficiency is through calibration data. This can be achieved by using the volumetric efficiency equation, Eq. 2.7, coupled with engine steady-state dynamometer data. To create a complete map that characterizes the volumetric efficiency of an engine, a wide range of operating points is tested. At each operating point, steady-state data is collected, including the MAF, intake air temperature (IAT), and engine speed data. Since the data is collected in steady-state, the MAF sensor provides a relatively accurate reading of the flowrate of inducted air. Using this data, the volumetric efficiency at each operating point can be calculated. Combining all the operating points will form a volumetric efficiency map that can be used to calculate the amount of air entering the engine s cylinders. Figure 2.5 shows the volumetric efficiency map of the engine utilized in this paper, the map was created using the procedure described above Intake Manifold Modeling The role of an intake manifold is to supply a fresh mixture of fuel and air to the engine cylinders. An intake manifold usually consists of a main plenum with individual runners that lead to each cylinder. The inlet of the plenum is bolted to the throttle body. The intake manifold geometry is designed to be able to ensure a proper charge delivery to all cylinders, maximize the amount of charge, and optimize the charge mixing and combustion. Due to the suction of the pistons during the intake 15

35 Volumetric Efficiency [%] MAP [kpa] Engine Speed [RPM] 5000 Figure 2.5: Volumetric efficiency map of a 1.8L 4cyl E85 engine stroke of an engine cycle and the presence of a throttle plate, the intake manifold is typically in partial vacuum. At wide open throttle (WOT) the plenum usually experiences a pressure of about 95 kpa, while at idling conditions the pressure is about 30 kpa [8]. In order to keep the engine operating at stoichiometric conditions, the air being inducted into the engine cylinders must be accurately represented. With a known amount of inducted air, the correct amount of fuel can be injected. To achieve this, a model of the intake manifold can be created to understand the dynamics of how air enters and exits the plenum and runners. 16

36 Figure 2.6: Model classification for an intake manifold [8] Levels of Modeling When modeling an engine component, such as the intake manifold, the fundamental choice has to be made for what kind of model accuracy and fidelity is needed. Thus, the desired balance of both accuracy and fidelity versus computation time governs the appropriate model structure [7]. The different levels of modeling an intake manifold can generally be classified into three types: three-dimensional, one-dimensional, and zero-dimensional. In general, as the model fidelity increases, the required computation time increases [2]. Further, these different levels of modeling require varying amounts of empirical data and model calibration effort to be able to build the model [3]. 17

37 Thee-dimensional models, often associated with computational fluid dynamics models, are studied not only in the three spatial dimensions but also in the time dimension. As a result of analyzing the system in four dimensions, a very high resolution study of the system dynamics can be studied. This fidelity allows the analysis of the 3D charge motion in the intake system including turbulent flow, dissipation, and flow across each runner. While this level of modeling results in the greatest accuracy and bandwidth, it is the most computationally intensive method. Thus, this method is not practical in real-time applications and is reserved for design optimization [8]. The one-dimensional model simplifies the previous method by removing two spatial dimensions. Therefore, it is assumed that the state variables of the system only vary in respect to one spatial dimension and time. The reduction in analyzed dimensions reduces the computational intensity, but keeps a relatively high bandwidth and small discretization length. This level of modeling allows the analysis of wave propagation which can facilitate in the tuning of an intake manifold. The zero-dimensional model further simplifies the previously described methods by not considering any spatial variation in the system s state variables. It is assumed that the thermodynamic properties are uniformly distributed. These models are also referred to as mean value models (MVM). This method can provide a lumped-parameter model that accurately describes the filling and emptying of a system [8]. The comparison of the different levels of modeling and their associated bandwidths and discretization lengths can be seen in Figure 2.6. For applications that require high fidelity such as flow junction design, multi-dimensional models are the most appropriate. But, for control system design and optimization, the one and zerodimensional models are more often used. This generalization can be attributed to the 18

38 lower order models exhibiting a more simplified model structure and lower required computational effort [7]. Filling and Emptying Model Using the filling and emptying model, a simple manifold model can be created that can portray the complex phenomena within an actual intake manifold with relatively high accuracy. Since the intake manifold dynamics are a large contribution to the overall engine dynamics, it will be considered as a mass and energy accumulator to capture the filling and emptying dynamics [8]. Several assumptions are made in this model: At any given time, the pressure and temperature inside the intake manifold is uniform The flow through the engine is constant All gaseous fluids follow the ideal gas law Using the continuity equation for the air flow in and out of the intake manifold the following dynamic equation can be derived: dm a,im dt = ṁ a,th Σṁ a,cyl (2.8) where m a,im is the mass of air in the intake manifold, ṁ a,th and ṁ a,cyl are the mass air flows through the throttle and into the cylinders. Using the ideal gas law and the mass of air in the intake manifold the following equation can be derived: m a,im = V IM R air T a,im p a,im (2.9) 19

39 By taking the derivative of Eq. 2.9 and combining it with Eq. 2.8 gives: dp a,im dt = R airt a,im V IM [ṁ a,th Σṁ a,cyl ] (2.10) This equation assumes that there is no rapid change in the intake manifold temperature (dt a,im /dt = 0). The total air flow into each of the engine s cylinders can be analyzed by a quasi-steady approximation using the speed density equation shown in Eq ṁ a = η v p a,im V d N 2RT (2.11) Substituting the speed density equation into Eq gives: dp a,im dt ( ηv V d N + 2V IM ) p a,im = ṁ a,th R air T a,im V IM (2.12) where the mass air flow through the throttle can be determined using either Eq. 2.1 or 2.2, depending on whether the air flow is choked or not. It can be seen that Eq is a first order equation for p a,im with a time constant that is reliant on the engine speed and volumetric efficiency. The equation for the time constant is shown in Eq It can be seen that as either the engine speed or volumetric efficiency increase, the intake manifold pressure state response time decreases. A more indepth derivation of this first-order equation can be found in [8]. Figure 2.7 shows the response from the MAF and MAP sensors to a throttle transient. The MAF sensor reading represents the change of air flow into the intake manifold due to the sudden change in throttle position. It can be seen that the sudden fluctuations in the mass air flow are damped out in the manifold air pressure reading. The data in Figure

40 Amplitude MAF*10 [g/s] MAP [kpa] Time [s] (a) Tip in Amplitude MAF*10 [g/s] MAP [kpa] Time [s] (b) Tip out Figure 2.7: MAF and MAP reading from throttle transient at 1200 RPM was taken at an engine speed of 1200 RPM; with a relatively low engine speed, the time constant is longer. τ = 2V IM η v V d N (2.13) The filling and emptying model is very useful in analyzing the pressure variations due to changing load conditions. While this model can portray the complex interactions concerning the intake manifold with relatively high accuracy, there are several limitations. The model requires very accurate representations of empirical parameters such as volumetric efficiency (V e ) and the throttle effective flow area (C d A). Also, due to the relatively low bandwidth, the equation provides no insight into the pressure fluctuations due to individual cylinder induction events. Other events that are not 21

41 factored into the model include manifold temperature, backflow of exhaust gases into the intake manifold, and the presence of exhaust gas recirculation (EGR) [9], [8] Air-Fuel Ratio Control With the ever-tightening standards for vehicle exhaust emissions, the AFR control problem has been a topic of high interest. The invention of the three-way catalyst has been able to significantly reduce tailpipe emissions. But, in order for the catalyst to operate at its best efficiency the engine must operate within a very narrow band around the fuel s stoichiometric AFR as seen in Figure 2.1. The AFR can be described as the relative air-fuel ratio, λ: λ = (A/F ) actual (A/F ) stoich (2.14) where (A/F ) stoich is the ratio of air to fuel which achieves stoichiometric combustion. When (λ = 1), the mixture is at stoichiometric proportions. For (λ > 1), the mixture is fuel-lean, meaning that there is more air than needed in the mixture. For (λ < 1), the mixture is fuel-rich, or the mixture contains more fuel than needed for stoichiometric combustion [9]. Conventional AFR control consists of static look-up tables to determine fueling decisions, with feedback control from a lambda sensor. A lambda sensor measures the net oxygen content of the exhaust gas which can be used to determine the current relative AFR. With feedback control, conventional AFR control can achieve high accuracy under steady-state conditions. But, due to the time delays inherent to engine operation, the response time of conventional AFR control is too long for transient engine operation. These delays are due to the dynamic nature of the air and fuel flows, 22

42 Figure 2.8: Injection and transport delays [1] low-pass characteristics of sensors, and the transport delay for the charge mixture to cross the engine and be measured by the lambda sensors [1]. For engines that use a three-way catalyst, high bandwidth transient AFR control is necessary in order to achieve the highest conversion efficiency and to remain compliant with the industry s emissions standards [14]. Figure 2.8 shows a graphical representation of the injection delay and lambda sensor feedback transport delay. The injection delay is time from when the engine electronic control unit (ECU) receives sensor data and when the air-fuel mixture is inducted into the cylinder. This includes the computation duration for one step of the AFR control strategy, injection duration, and injection timing and in the case of port fuel injected (PFI) engines, fuel dynamics. For PFI engines, the fuel is injected 23

43 Table 2.1: Sensor specifications [1] Sensor type Accuracy Response time Manifold absolute pressure (MAP) ±1% 1 ms Mass air flow (MAF) ±2% 1-10 sec Throttle position ±3% in stationary flows 50 ms sec Exhaust gas oxygen 1-6% 50 ms Universal exhaust gas oxygen 1-6% > 50 ms into the take port a short amount of time before the intake valve is opened. This is done to give the fuel the maximum amount of time to vaporize before being inducted into the cylinder. After the fuel is injected into the intake port, a fraction of that fuel evaporates while the rest of the fuel forms a liquid film on the intake manifold wall. A certain amount of the fuel in the film will evaporate in time. This mass flux into and out of the film creates fueling dynamics that add delays in the injection commands. This delay is especially prevalent when in the engine block is cold. The transport delay is the time between the induction of the air-fuel mixture and the reading of the lambda sensor signal by the engine ECU. With conventional AFR control strategies, no control action can be taken until both the injection and transport delay have elapsed, significantly lowering the control system bandwidth [1]. There are several sensors that can be utilized the obtain information about the real-time air flow properties of the engine. Each sensor has its own characteristics for accuracy and response time. An AFR strategy should take into account these properties and structure the control algorithm with appropriate sensors. Table 2.1 shows common sensors used in AFR control strategies and their characteristics. Clearly, 24

44 the MAF sensor s response timing is significantly higher than any other sensor described. Despite the poor response time, this sensor still remains a popular method of determining the flow of air into the cylinders. In comparison, the MAP sensor and throttle position sensor are significantly faster. Using these two sensors, an accurate prediction of the mass air flow into the engine can be determined using the modeling methods described previously. While using the MAP and throttle position sensor to calculate mass air flow into the cylinders is significatly more accurate than using a MAF sensor in transient operation, the injection delay is still not accounted for. The engine used in the research discussed in this paper utilizes port fuel injection. This signifies that the fuel is injected into the intake port a small amount of time prior to the intake valve opening (IVO). For this engine, the fuel is injected 700 CAD before IVO. So, in order to achieve stoichiometric combustion, the fuel injected has to be in stochiometric proportion to the air entering the cylinder 700 degrees after it was injected. Forward Euler Scheme To solve this issue, the intake manifold pressure can be predicted a discrete amount of time into the future using Eq and a Forward Euler scheme [1]. Since the engine s ECU is a digital controller, a discrete form of the Forward Euler method is used. A general form is shown in Eq. 2.15, dy y (t + t) y(t) (t) dt t (2.15) 25

45 where t is the time step; no information can be derived on a time scale smaller than the time step. The time step must be chosen wisely as accuracy of the approximation worsens as the time step increases. Also, errors compound as each iteration is calculated. To reduce calculation error, the time step must be minimized without compromising the ECU s throughput. But, there will be a point of diminishing returns where the time step is so small that there is no increase in the scheme s accuracy due to computer round off errors [10]. Rearranging Eq to solve for the future value of the variable gives: y(n + 1) y(n) + t dy(n) dt (2.16) For this application, the intake manifold pressure is of interest. Adapting Eq for the intake manifold pressure gives: p a,im (n + 1) p a,im (n) + t dp a,im(n) dt (2.17) This equation can be solved by using Eq and the current pressure reading from the MAP sensor. It is assumed that the engine speed, manifold temperature, and throttle position remain constant. If the intake manifold pressure is known a discrete amount of time in the future, the mass air flow into the cylinder can be calculated using the speed density equation. With the future mass air flow known, the correct amount of fuel can be injected to achieve stoichiometric combustion. Linearizing Filling and Emptying Model Another method of determining the intake manifold pressure a small amount of time into the future is to linearize the intake manifold filling and emptying model, 26

46 shown in Eq With a linearized version of this equation, an analytical solution to the estimated future value of MAP can be determined [16]. As mentioned previously, the engine speed, intake manifold temperature, and throttle position remain constant throughout the prediction. The intake manifold filling and emptying model is linearized by expanding the air flow through the throttle as a function of the current intake manifold pressure. ṁ a,thr = (ṁ a,thr ) 0 + ( ṁa,thr p a,im ) (p a,im p a,im,0 ) (2.18) 0 The terms subscripted with 0 denote current measured sensor readings. Taking the partial derivative of the air flow through the throttle in respect to the current intake manifold pressure gives: ṁ a,thr = p a,im ṁ a,thr γ [ 1 p r γ 1 1 γ 2(pr p r) ] unchoked 0 choked (2.19) where p r is the ratio of the intake manifold air pressure to the ambient air pressure. Equation 2.18 is then subsituted back into the filling and emptying model along with the speed density equation: dp a,im dt = R airt a,im V IM [ ( ) ] ṁa,thr (ṁ a,thr ) 0 + (p a,im p a,im,0 ) p a, IM 0 ( ηv V d N 2V im ) p a,im (2.20) An analytical solution for the estimated value of intake manifold pressure in the future can be solved as: ( ) t ˆp a,im = (p a,im,0 p a,im,1 )exp + p a,im,1 (2.21) τ 27

47 where p a,im,1 is the steady-state solution for the projected intake manifold pressure. This can be solved by setting the left hand side of Eq to zero. t is the amount of time into the future the intake manifold pressure is being predicted. The time constant is given as: τ = { RTa,IM V IM [( ) ( )]} 1 ṁa,thr ηv NV d (2.22) p a, IM 0 30RT a,im A more detailed description of the derivation can be seen in [16]. Correcting Model Errors Due to the assumptions made in developing the intake manifold model and the heavy reliance on empirically derived parameters, the models above will inevitably exhibit errors in practice. Methods to reduce these errors will be described in this section. One of the main assumptions in the models mentioned previously is that the throttle position remains constant throughout the time that prediction is made. This assumption remains true in steady-state operation (with constant engine speed and spark timing). But, in transient events the throttle position a small amount forward in time will be slightly greater or less than the current position. This error in throttle position will cause the model to predict either a higher or lower manifold air flow through the throttle than the actual value, creating errors in the final MAP prediction. A solution to this assumption is to create a lead filter to predict the throttle position one discrete time step ahead in time [13]. The equation for the filter is shown below: 28

48 θ +1 (k) = (1 a)θ +1 (k 1) + a(2θ(k) θ(k 1)), 0 < a < 1 (2.23) where a is the filter constant, θ is the current throttle position, and θ +1 is the one step ahead throttle prediction. Another solution to correcting the throttle position is to delay the desired throttle position [1]. This is only viable in vehicles equipped with electronic throttle control. With electronic throttle control, the driver s throttle command can be stored in a memory buffer and a delayed command will be sent to the throttle actuator. Since the driver s command is stored in a memory buffer, the throttle position trace is known a small amount of time in the future allowing a more accurate MAP prediction [1]. Along with the assumptions made, the model also relies on accurate values of the the throttle effective area and volumetric efficiency. While using conventional techniques of obtaining these values through steady-state engine dynamometer tests can provide very accurate values of these parameters, they cannot account for dayto-day changes in ambient temperature, pressure, and humidity and engine aging. These changes can produce steady-state and dynamic errors in MAP prediction. To help correct the drift in these parameters, an on-line calibration method of adjusting the parameters can be created [16]. The example below shows a procedure to adapt volumetric efficiency in real-time. By rearranging Eq at steady-state the following equation can be derived: p a,im = 2RT a,imṁ a,th η v NV d (2.24) Taking the partial derivative of 2.24 with respect to volumetric efficiency and solving for the change in η v gives: 29

49 η2 vnv d η v = p a,im (2.25) 2RT a,im ṁ a,th where: p a,im is the error between the measured MAP and predicted MAP. With Eq. 2.25, an integral compensator can be made: η v = η v,0 + L p Σ η v K (2.26) where: η v,0 is the original mapped value, L p is the compensator gain, and Σ η v is a running cumulative sum of η v and K is a large number to average out the cumulative sum. A low value of L p would give good noise rejection while a higher value will give faster convergence. 2.3 Honda R18A3 Engine The engine used for the research contained in this paper is the R18A3 engine developed by Honda. The engine was originally designed to use compressed natural gas (CNG) as the fuel. To improve power and efficiency, the engine contains actuators to allow variable valve timing (VVT), and a variable length intake manifold. The basic engine specifications are listed in Table 2.2 and a model of the engine is shown in Figure 2.9. The engine has two cam profile settings: high output and delayed closure. The high output cam settings allows the valve timing to be synchronous with the engine cycle events [6]. The intake cam opens the intake valve at the beginning of the intake stroke and then closes the intake valve at the beginning of the compression stroke. This setting is used when maximum power output is demanded from the engine. The delayed valve closure setting allows the intake valve to remain open for 30

50 Table 2.2: Engine specifications [15] Property Value Unit Cylinder configuration In-line 4 - Bore stroke mm Displacement 1799 cm 3 Compression ratio 12.5:1 - Valve train SOHC VVT, inlet delayed close - Number of valves 4 per cylinder - Cylinder offset 12 mm Intake manifold Variable intake system - Figure 2.9: 2006 Honda R18A3 engine [15] 31

51 Figure 2.10: Valve lift profiles of different cam settings [15] a discrete amount of time during the compression stroke before eventually closing. This setting is used for when the required power output is low, such as maintaining a cruising speed. The delayed valve closure leads to better fuel economy by allowing a reduction in pumping losses due to the reduction in the effective compression ratio [15]. The valve lift profiles for each setting can be seen in Figure A variable-length intake manifold is also installed on this engine. Inside the intake manifold is a bypass valve that changes the effective intake manifold length when opened or closed, shown in Figure When the bypass valve is opened, the effective length is shorter. This setting is used primarily at high engine speeds. When the bypass valve is closed, the effective length is longer. This setting is used at lower engine speeds. By changing the effective intake manifold lengths at certain engine speeds, the wave dynamics inside the runners can be used to the engine s advantage, leading to a higher torque output. For this engine, the lengths are designed where the bypass valve should opened only at engine speeds above 5000 RPM [4]. For more 32

52 Figure 2.11: Intake manifold variable length runner [15] information about the engine and its performance and fuel economy improvement strategies, refer to [15]. 2.4 Tailpipe Emissions Pollutant formation and control has been a major concern in the past few decades, and spark-ignition and diesel engines are a major source of air pollution. The emissions species from spark-ignition engines include: oxides of nitrogen (nitric oxide, N O and NO 2 ), carbon monoxide (CO), and unburned or partially burned hydrocarbons (HC). Nitrogen oxides (NO x ) are formed in the high-temperature burned gases behind the combustion flame front. As the burned gas temperature increases, the rate of NO x formation increases. As the burned gas temperatures cool, the NO x reactions freeze and leave NO x concentrations in the tailpipe emissions. CO emissions can form when the fuel-air mixture is rich due to an insufficient amount of oxygen presence 33

53 Figure 2.12: Emissions concentrations against air/fuel ratio [9] 34

54 to completely burn all the carbon in the fuel. Also, CO emissions are produced in higher temperature burned gases, where dissociation occurs. HC emissions can be a result of several processes. The large in-cylinder pressures can force some of the gas mixture in the crevice volumes within the cylinder, which can be released later in the cycle. A quench layer of unburned hydrocarbons can form on the cylinder wall due to heat transfer and the flame burn zone not propagating throughout the entire cylinder. Another source of HC emissions may come from oil layers from piston lubrication that can absorb and desorb during combustion [9]. The air-fuel ratio plays a major role in determining the amount of engine emissions. Figure 2.12 shows the relationships among NO x, CO, and HC emissions and the air-fuel ratio. As the charge mixture goes rich, HC and CO emissions will increase while NO x decreases. As the charge mixture goes lean, the HC, CO, and NO x emissions decrease. But, HC emissions will start to increase at very lean mixtures due to cylinder misfires. At stoichiometric mixtures, NO x emissions are the highest. When the engine is operating in a narrow region around stoichiometric combustion, the three-way catalyst exhibits its highest conversion efficiency (see Fig. 2.1). Any deviation from stoichiometric combustion will significantly increase the vehicle s tailpipe emissions. 35

55 Chapter 3: Experimental Description The Center for Automotive Research at The Ohio State University provided the facilities for the research described in this thesis. All the tests were completed in an engine dynamometer test cell containing a 200 horsepower, four-quadrant DC motor connected to a Honda 1.8L four cylinder engine. A dynamometer controller was utilized to maintain the engine speed to allow testing at different engine operating points. The engine was originally designed to run on compressed natural gas as a fuel, but has been converted to run on E85 fuel. To control the engine, a rapid prototyping, 128-pin Woodward engine control unit coupled with a variety of sensors mounted to the engine hardware were used. The engine control algorithms were designed in MATLAB and SIMULINK with the default SIMULINK block set as well as a proprietary Woodward Motohawk block set that allowed communication with the engine control hardware. Communication to the engine was conducted using a CAN Calibration Protocol (CCP) network and ETAS INCA software. 3.1 Engine Instrumentation The Honda engine used in this research is equipped with a variety of sensors to enable proper control of the engine. The sensors relevant to the research in this thesis are listed in Table 3.1. The locations of several of these sensors are shown in Figures 36

56 Table 3.1: Relevant instrumented sensors on engine Number Sensor name 1 Crankshaft position sensor 2 Engine coolant temperature 3 Engine knock indicator 4 Engine oil temperature 5 Fuel level 6 Fuel rail pressure 7 Intake air temperature 8 Manifold absolute pressure 9 Mass air flow 10 Pre-catalyst RTD 11 Pre-catalyst UEGO 12 Throttle position 3.1 and 3.2 where the numbered labels correspond to Table 3.1. The engine knock indicator listed in the table is a custom made copper tube that is rigidly attached to the original knock port on the engine block. The tube is routed into the dynamometer control room where it is attached to a funnel to allow knock events to be heard by the test operator. A cooling tower is attached to the engine s coolant ports to maintain the engine block temperature. The cooling tower uses an external water source and a thermostat to regulate the engine temperature to about 80 degrees celsius. 3.2 Data Acquisition System The engine test setup is instrumented with multiple devices to allow sensor signals and actuator commands to be transferred between the operator s computer and the engine. To communicate with the sensors and actuators that were attached to the 37

57 Figure 3.1: Intake side of engine Figure 3.2: Exhaust side of engine 38

58 original Honda engine wiring harness, a Woodward 128-pin ECU is used. The engine control code contained on the ECU is built using MATLAB and SIMULINK with the Motohawk development library. The Motohawk development library is a set of proprietary blocks which create an interface layer between the control code and the input/output pins of the ECU. The latest engine control codes are built using MAT- LAB s Real Time Workshop. Mototune, another software package from Woodward, allows the engine operator to flash new control builds onto the ECU as well as load the latest calibrations. For sensors that were not originally on the Honda engine s wiring harness, a series of ETAS modules are used to collect data signals. Four ETAS modules are used: the ES410, ES411, ES420, and LA4 Lambda Meter. The ES410 provides eight analog channels, while the ES411 provides eight analog channels with sensor supply voltages. The ES420 contains eight channels for thermocouples and the LA4 Lambda Meter allows data acquisition of the post-catalyst UEGO sensor. The four ETAS modules are daisy-chained together and connect to the operator s computer via a proprietary ETAS Ethernet cable [6]. INCA, data acquisition software provided by ETAS, is used for calibrating, monitoring, and recording engine data in real-time. The software allows the operator to send commands to the engine such as throttle position or spark timing. Simultaneously, sensor data such as engine coolant temperature or oil pressure can be monitored and recorded. Communication between the operator s computer and the Woodward ECU and ETAS daisy-chain is accomplished through the CCP. The computer is instrumented with a PCMCIA card that allows the interface between INCA and the 39

59 Figure 3.3: Engine test setup [6] data acquisition hardware. A block diagram of the test setup can be seen in Figure GM LE5 Mean Value Engine Model To assist in developing the throttle and intake manifold models and air prediction control, a mean-value engine model was utilized to simulate results. This model is a zero-dimensional model developed by Dr. Kenneth Follen. It simulates dynamics from a GM LE5 Eco-Tec, 2.4 liter, inline-4, gasoline engine. The model was created using mathematical models of several main subsystems in the engine coupled with experimental data obtained in a dynamometer cell. The subsystems modeled include: throttle, intake manifold, volumetric efficiency, fuel transport, and torque production dynamics. The model structure can be seen in Figure 3.4. The MVEM could easily 40

60 Figure 3.4: 0-D Mean-value engine model for GM LE5 engine be run at different operating conditions, allowing for a wide range of validation tests for the air prediction control model. While the engine specifications in this model are not the same as the Honda engine used in this research, the ability to simulate and validate the various parts of the air prediction algorithm was very useful in the control development. 41

61 Chapter 4: Control Algorithm Development 4.1 Introduction A control algorithm that more accurately injects the correct amount of fuel to achieve stoichiometric combustion during transient engine operation will be discussed in this chapter. Since the engine is port fuel injected, the fuel injection is made 700 degrees before the intake valve opening. This allows the fuel to vaporize in the intake manifold runner before being inducted into the cylinder. Therefore, in order to achieve stoichiometric combustion, the intake manifold air pressure will be determined up to 700 degrees into the future. To be able to predict the intake manifold air pressure, the dynamic model of the intake manifold pressure and the Forward Euler approximation will be used. This algorithm will be implemented using SIMULINK and Stateflow. 4.2 Control Algorithm Description In order to allow enough time for the fuel to vaporize inside the intake manifold, a fuel request must be made up to 700 degrees before the intake valve opening. This causes the controller to need to predict the cylinder air mass 700 degrees forward in time to maintain stoichiometric combustion. With the total amount of air inducted in the intake stroke estimated, the correct amount of fuel can be injected. The air per 42

62 Figure 4.1: Control algorithm timing cylinder can be calculated using Eq. 4.1; where ṁ a is the mass air flow rate in g/s and AP C is the air per cylinder in mg/stroke. This section will outline the control algorithm to approximate the mass air flow exiting the intake manifold a discrete amount of time in the future. A diagram outlining the air prediction timing is shown in Figure 4.1. AP C = ṁ a N (4.1) This control algorithm combines the models that will be developed in later chapters to create a dynamic intake manifold model and the Forward Euler approximation. Several assumptions are made when using this proposed control algorithm. The intake manifold temperature and engine speed are considered to change at a slower rate relative to the change intake manifold pressure. Thus, both values are assumed to be constant over the prediction horizon. Throughout this thesis the prediction horizon will be defined as the total time in the future the algorithm is approximating. Since the throttle trajectory in the future is unknown, the throttle percentage is also assumed to be constant. The pressure and temperature inside the intake manifold 43

63 are assumed to be constant as well as the air flow throughout the engine. And, all gaseous fluids are assumed to follow the ideal gas law. A flow diagram outlining the control algorithm is shown in Figure 4.2. The algorithm begins by collecting current readings from multiple sensors on the engine. These include: intake air temperature, manifold absolute air pressure, throttle position, and engine speed. These values are assumed to be constant throughout the entire algorithm. Next, the total time for the engine crankshaft to rotate 700 degrees, or the prediction horizon, is calculated. Equation 4.2 shows how to determine the prediction horizon using engine speed as an input. 1 min 1rev 700 deg N rev 360deg 60sec 1min = prediction horizon (sec) (4.2) With the prediction horizon determined, the total time will be divided into time increments determined by the number of iterations desired. These time increments will be referred to as the time step, t, in this algorithm. As mentioned in Section 2.2.4, to reduce calculation error, the time step must be minimized without compromising the ECU s throughput. The calculation of the time step is shown in Eq In the following sections, the number of iterations will be optimized to allow minimal error without overly taxing the ECU resources. The throttle effective area for the current engine operating point is also determined. prediction horizon number of iterations = t (4.3) With the time step and throttle effective area calculated, the algorithm will start an iteration loop which implements the intake manifold air pressure dynamic equation and the Forward Euler approximation. Using the aforementioned sensor data along 44

64 Figure 4.2: MAP prediction control algorithm 45

65 Table 4.1: Constant engine parameters Variable Description Value Units γ Specific heat ratio p crit Critical pressure ratio p baro Barometric pressure P a R Universal gas constant J/kg K V IM Intake manifold volume m 3 V d Engine total displacement volume m 3 with the engine parameters shown in Table 4.1, the rate of change of intake manifold pressure can be determined. Then, using the current MAP reading, the predicted intake manifold pressure t seconds in the future can be calculated using Eq This process is repeated until the number of desired iterations is completed. Note, each time the algorithm runs through an iteration, the value for the manifold air pressure is updated from the Forward Euler approximation. When all the iterations are completed, the final MAP value will be an approximated value for the intake manifold air pressure 700 degrees into the future. p a,im (n + 1) p a,im (n) + t dp a,im(n) dt (4.4) Once the control algorithm was determined, it was implemented in SIMULINK so the code could be transferred to run on the engine s ECU. Figure 4.3 shows the SIMULINK model. The model accepts inputs of IAT, MAP, throttle percentage, and engine speed. Equation 4.3 and 4.1 are implemented in a subsystem called Determine Time Step, while the throttle effective flow area is determined by a 2-d lookup table that will be derived in later sections. All these values are sent to a Stateflow diagram. 46

66 Figure 4.3: MAP prediction SIMULINK model Within this diagram, the intake manifold air pressure dynamic equation is solved and the Forward Euler approximation is implemented. The Stateflow repeats this calculation until the number of iterations reaches the desired iteration number. The Stateflow diagram then outputs the final value of the intake manifold air pressure, which represents the approximate MAP value 700 degrees in the future. Figure 4.4 shows the Stateflow diagram. Note that this whole algorithm is executed within one time step of the engine s ECU, which is 7 milliseconds for the ECU used in this research. 4.3 Summary A control algorithm was created that combines the intake manifold model discussed in an earlier chapter with a Forward Euler approximation to allow the intake manifold air pressure to be predicted forward in time. This algorithm allows the engine control system to more accurately predict the inducted air flow, thus leading 47

67 Figure 4.4: MAP prediction Stateflow diagram 48

68 to better emissions and performance. The control algorithm was adapted to run in SIMULINK so it can be easily implemented into the engine hardware. As mentioned previously, the control algorithm relies heavily on an accurate calibration of the C d A and V e parameters. The process of calibrating these parameters will be discussed in later chapters. Validation of the performance of this algorithm will also be conducted in later chapters both in simulation and on engine hardware. 49

69 Chapter 5: Intake Manifold Modeling 5.1 Introduction In order to be able to successfully predict the mass air flow into the engine s cylinders, an accurate model of the intake manifold pressure must be created. If a dynamic relationship of the intake manifold pressure is known, then the inducted air flow rate can be predicted a discrete amount of time into the future using Eq A zero-order model was chosen, described in Section 2.2.3, because the model will be implemented to run in real-time on the engine s ECU. The model requires an accurate representation of air flow through the throttle plate and the engine s efficiency as a pumping device. 5.2 Throttle Model To be able to accurately model the mass air flow into the intake manifold, a model of flow through the throttle plate is necessary. The methods described in will be used to create the model. To calculate the mass air flow through the throttle, several parameters need to be known including the throttle s effective flow area, current intake manifold pressure, and the ambient pressure and temperature. The effective flow area is a highly non-linear term and must be determined experimentally. 50

70 x CdA [m 2 ] Engine Speed [RPM] Throttle [%] Figure 5.1: Throttle affective area map, raw data The standard orifice equations for compressible flow shown in Eq. 2.1 and 2.2 are used to determine the effective flow area values at various engine operating points. At each operating point, steady-state engine data is recorded. Since the engine is in steady-state, the intake manifold dynamics are no longer present and the MAF sensor readings will be valid. Thus, the compressible flow equations can be solved for the effective flow area using the MAF sensor reading for the mass air flow along with the sensor readings from the MAP and IAT sensors. Using the C d A values at the different engine operating points, a 2-d lookup function was created to relate the throttle effective area to throttle position and engine speed. Previously, a DOE was conducted on the engine used in this thesis; the data from this DOE was used in the creation of throttle effective area and volumetric efficiency maps [6]. The number test points used to create the full map was determined using an iterative DOE process described in [6]. After the number of test points was 51

71 x CdA [m 2 ] Engine Speed [RPM] Throttle [%] Figure 5.2: Throttle affective area map, function fit determined a Halton sequence was used to determine which operating points to test [6]. For this DOE, a set of 151 operating points were recorded with throttle positions ranging from 0 to 100% and engine speeds ranging from 1000 to 4200 RPM. At each operating point, engine data was taken at steady-state for several important variables including MAP, MAF, IAT, brake torque, and exhaust temperature. The effective flow area was calculated for each of the 151 operating points and is shown in Figure 5.1. Using these test points, a 2-d function was created to relate the effective flow area to the throttle percentage and engine speed. From previous research, it was found that a multiquadratic radial basis (MRB) fit is the most accurate and provides the lowest root-mean-square error (RMSE). The MRB fit is a curve fit used offline to create a look-up table that is to be implemented on the engine s ECU. The resulting surface plot using the radial basis fit is shown in Figure

72 To validate the accuracy of the 2-d function, a set of 25 validation test points were taken at various engine operating points within the same ranges as the DOE. For each operating point, the throttle effective area was calculated in the same manner as the data points in the DOE. Since these points were not used in the initial creation of the lookup table, they will provide insight into how accurate the created 2-d function is in modeling the throttle s effective area. A comparison between the model C d A values and the calculated C d A values from the validation data are shown in Figure 5.3. For each validation operating point, the engine speed and throttle position were used in the model function to determine the model s C d A prediction. The calculated C d A values from the validation data set are on the x-axis while the predicted C d A values from the model are on the y-axis. If the model contained no prediction errors, then the slope of all the validation points would be one. Looking at 5.3, it can be seen that all the points are very close to the unity slope, indicating high accuracy in the C d A model. The next validation test is to determine how well the mass air flow can be predicted using the C d A model and the compressible flow equations. For each of the operating points in the validation data set, the steady-state data was sent to a SIMULINK model to determine the calculated MAF values. The engine speed and throttle position allows the throttle effective area to be calculated. The C d A value coupled with the ambient pressures and temperatures and intake manifold pressure allow the MAF to be calculated using either Eq. 2.1 or 2.2. The equation used is dependent on whether the flow is choked or not. The calculated MAF values are then compared to the actual MAF sensor values. Since the validation data was taken in steady-state the 53

73 4.5 x CdA Model [m 2 ] Validation points Unity slope CdA Calculated [m 2 ] x 10 4 Figure 5.3: Model and experimental C d A value comparison MAF sensor provides readings of high accuracy, allowing the use of its readings to validate the model. The results of this test are shown in Figure 5.4. It can be seen that almost all of the test points are within ± 5% of the values of the MAF sensor. The two outlying data points (tests 1 and 2) were taken at operating points at low RPM and low throttle. This operating region in the C d A model is highly non-linear and is difficult to measure and model. Despite the two outlying points, the validation results show that the C d A map created coupled with the compressible flow equations provides an accurate representation of mass air flow. Since this paper focuses on transient events in engine operation, a comparison between the MAF sensor reading and the calculated MAF using the created model 54

74 MAF error [%] Test Figure 5.4: Calculated and actual MAF value comparison during a throttle transient was conducted. Tests at 1200, 1400, 1600, and 2000 RPM were evaluated. At each engine speed, a throttle transient was conducted to change the engine load from approximately 30 kpa to 70 kpa. For each transient event, the MAF sensor reading was recorded along with throttle position, RPM, IAT, and MAP. Using SIMULINK, post-processing was conducted to calculate the MAF based off of the throttle model. The results of these tests are shown in Figure 5.5. It can be seen that the dynamic response of the throttle model is slightly quicker than that of the MAF sensor. As mentioned in Section 2.2.4, the MAF sensor has a response time on the order of 1 to 10 seconds. Since the throttle model uses the throttle position and MAP sensors (response times of about 1-50 milliseconds), the throttle model is able to capture the throttle change much quicker. The overshoot in 55

75 MAF [g/s] (a) 1200 RPM MAF [g/s] (b) 1400 RPM 4 MAF sensor Calculated MAF Time [s] (c) 1600 RPM 8 6 MAF sensor Calculated MAF Time [s] (d) 2000 RPM Figure 5.5: MAF during throttle transient event 56

76 air flow is due to the sudden increase in throttle position, which creates a high pressure differential across the throttle plate. This differential causes a sudden increase in air flow for a short period of time. With a faster response time, the throttle model can characterize higher frequency fluctuations in the mass air flow. It can be seen that there exists an appreciable amount of steady-state error between the calculated MAF and MAF sensor readings. These errors are due to inaccuracies of the C d A map in the throttle model. At 1200 RPM (Figure 5.5a), the steady-state errors are the most severe because of the high non-linearity in the lower RPM and throttle ranges for the C d A map. Also, the data taken from these transient tests were taken on different testing days in the engine dynamometer cell, which can have significant effects on the results. The changing ambient conditions and engine aging can cause the previously obtained calibration data to become invalid. 5.3 Volumetric Efficiency Model To be able to accurately model the mass air flow exiting the intake manifold into the engine s cylinders, an accurate model of the volumetric efficiency is required. The volumetric efficiency can then be used in the volumetric efficiency equation to calculate the mass air flow rate. Since volumetric efficiency is the result of many complex interactions within an engine s air system, the parameter was determined empirically. As outlined in Section 2.2.2, the volumetric efficiency was determined at multiple engine operating points during steady state operation. In the volumetric efficiency equation, if mass air flow rate, temperature, intake manifold pressure, and engine speed are known, then the volumetric efficiency can be solved for at that specific 57

77 Volumetric Efficiency [%] MAP [kpa] Engine Speed [RPM] 5000 Figure 5.6: Volumetric efficiency map, raw data operating point. Since the engine is in steady-state operation, the MAF sensor reading provides an accurate value for the mass air flow rate. The other parameters needed may be easily recorded during engine operation. Using the volumetric efficiency values at the different operating conditions, a 2-d lookup function was created to relate the volumetric efficiency to manifold absolute air pressure and engine speed. The same DOE data used to create the throttle effective area, mentioned in the previous section, will be used to create the V e plot. For each of the 151 test points, the volumetric efficiency was determined; Figure 5.6 shows all the points plotted in 3-d space. Using these test points, a 2-d function was created to determine the volumetric efficiency at certain operating points. From previous research, it was found that a cubic radial basis fit is the most accurate and provides the lowest RMSE [6]. The resulting surface plot using this function is shown in

78 To validate the accuracy of the 2-d function, the same set of 25 validation points used in the throttle modeling validation will be used. For each validation point, the volumetric efficiency was determined in the same manner as described earlier. Since the 2-d function was not derived from these points, the validation data can show the accuracy of the volumetric efficiency model. Figure 5.7 shows a comparison of V e values between the model and experimental results using the validation data. The x-axis shows the calculated V e value at each validation point using the speed density equation. The y-axis shows the V e value at each validation point evaluated from the 2-d function with the inputs of manifold absolute air pressure and engine speed. Theoretically, if the model was in perfect agreement with real-world testing, all of the validation points would be on the unity slope. Looking at Figure 5.7, it can be seen that all the test points are very close to the unity slope, which indicates the high accuracy of the model. The next test involves comparing the calculated mass air flow rate using the V e model and speed density equation to the mass air flow reading from the MAF sensor. For each validation operating point, the engine steady-state data was postprocessed in a SIMULINK model to determine the mass air flow. Using the mean values of MAP, IAT and RPM, the mass air flow could be calculated. These values are compared to the MAF sensor reading at each operating points and are shown in Figure 5.8. It can be seen that every test point is well within ± 5% error with respect to the MAF sensor. These validation results further indicate the high accuracy of the experimentally determined V e model and use of the volumetric efficiency equation. 59

79 VE Model [%] Validation points Unity slope VE Calculated [%] Figure 5.7: Model and experimental VE value comparison MAF error [%] Test Figure 5.8: Model and experimental MAF value comparison 60

80 5.4 Intake Manifold Pressure Model In order to predict the intake manifold air pressure a discrete amount of time into the future, a dynamic model of the intake manifold is necessary. As described in Section 2.2.3, a zero-order model of the intake manifold was derived, incorporating Eq The model considers the mass air flow into and out of the intake manifold using models of the throttle flow and volumetric efficiency, respectively. These models were developed and validated in previous sections of this chapter. The throttle model relies on compressible flow equations to determine the flow of air while the V e model relies on the empirically found parameter volumetric efficiency and the speed density equation. dp a,im dt = ṁ a,th R air T a,im V IM η vv d N 2V im p a,im (5.1) The entire model was implemented into SIMULINK, as shown in Figure 5.9. The intputs into the system are throttle position, engine speed, and intake air temperature. The integrator represents the intake manifold pressure. Both the throttle model and V e model are implemented into separate subsystems. The implementation of these models is shown in Appendix A. To validate the model, a series of tests were run on the engine dynamometer test setup. At 1200, 1600, 2000, 2800, and 3500 RPM, a throttle transient command was sent to the engine. The throttle transient caused an intake manifold pressure transient from about 30 kpa to 70 kpa at each engine speed. Among many parameters recorded, the IAT, RPM, and throttle percentage were included. For each test, these parameters were loaded into the SIMULINK model. The SIMULINK model was run 61

81 Figure 5.9: SIMULINK diagram of intake manifold model for the same duration as the dynamometer test and the simulated intake manifold air pressure was calculated for each time step of the simulation. The simulated MAP was compared to the measured MAP from the MAP sensor during the dynamometer test. It can be seen that during the steady-state parts of each test, the simulated MAP exhibits a steady-state error. This steady-state error is the result of errors in the C d A and V e 2-d lookup functions used in the models. If at a certain operating point, the throttle model and V e model do not agree (in terms of mass air flow), the resulting MAP will either be higher or lower than the actual value determined from the sensor. A numerical uncertainty analysis was conducted on the intake manifold model to determine the sensitivity of the model in respect to the calculated manifold air pressure values. At engine speeds of 1200, 1400, 1600, 2000 RPM and manifold pressures of around 20 kpa, perturbations were applied to the C d A and V e parameters. Each parameter was changed by ±5% and the resulting change in MAP was determined. 62

82 80 (a) 1200 RPM 80 (b) 1600 RPM MAP [kpa] MAP [kpa] Measured MAP Simulated MAP Time [s] (c) 2000 RPM 20 Measured MAP Simulated MAP Time [s] (d) 2800 RPM (e) 3500 RPM Figure 5.10: MAP during throttle transient event 63

83 Table 5.1: Model MAP Sensitivity Analysis Test Change in MAP [%] Engine speed [RPM] +5% C d A 5% C d A +5% V e 5% V e A table of the results is shown in Table 5.1. On average, a five percent deviation of either parameter would result in about a 3.4% change in MAP. These deviations from a small amount of error cause steady-state error in the simulated MAP. In the control algorithm, these errors will compound with each iteration of the control algorithm, creating significant steady-state errors in MAP. Methods of eliminating the steady-state error will be described in later sections of this paper. The dynamic nature of the intake manifold is captured accurately in the model. It can be seen that the measured MAP follows a first-order dynamic response that the model approximated. While there exists a steady-state error, the general shape of the changing intake manifold pressure is captured well in the model. 5.5 Summary A dynamic model of the intake manifold pressure was created using models of the throttle air flow and volumetric efficiency of the engine. Both the throttle and volumetric efficiency models required calibration data from the engine dynamometer to create 2-d lookup functions to model the C d A and V e parameters. These models were validated using validation data points from previously obtained DOE data. The 64

84 throttle and volumetric efficiency models were combined into the full intake manifold pressure model. Simulations utilizing engine dynamometer data allowed comparisons to be made between simulated and measured MAP. While the simulated MAP results showed steady-state errors, the dynamics were captured accurately. Solutions to the steady-state error will be addressed in later sections. 65

85 Chapter 6: Control Algorithm Validation 6.1 Introduction To validate the control algorithm, the MVEM described in Section 3.3 will be used. This model will provide a software-in-the-loop test bed for the control algorithm to allow errors to be corrected before the code is implemented on the engine s ECU. Although the engine in the MVEM is not the same one used for the research in this thesis, the model will provide excellent insight on validating if the code can predict the intake manifold air pressure successfully. Next, engine data from the dynamometer cell will be collected and post-processed in MATLAB. This will further the control development by using actual engine data to produce results from the algorithm. 6.2 Software Validation The control algorithm described in Chapter 4 was validated in simulation. A simulator was used to verify the functionality of the control algorithm before it is implemented on the engine hardware. Further, using a simulator speeds up the development and refinement of the control algorithm; algorithm changes can be implemented in a vastly shorter period of time compared to using actual hardware. Since the simulator can run faster than real-time, different engine operating points can be tested very quickly. The simulator also allows the measurement of variables that 66

86 Figure 6.1: MAP prediction SIMULINK implementation in MVEM are difficult to measure in real-world testing. To validate the control algorithm, the MVEM model described in Section 3.3 will be used as the plant model. Although this model is not calibrated to the engine used in this research, it will provide results necessary in validating the accuracy of the control algorithm. The control algorithm was combined with the MVEM in a SIMULINK diagram, shown in Figure 6.1. The inputs into the MVEM were throttle position and engine speed. The ambient air pressure and temperature were assumed to be kpa and degrees C, respectively. The outputs of the plant model were intake air temperature and intake manifold air pressure. The outputs of the MVEM along with the throttle position and engine speed were fed into the MAP prediction control algorithm, whose output was the predicted MAP 700 CAD in the future. The control algorithm used the same 2-d functions for throttle effective area and volumetric efficiency as the MVEM used. Also, the engine constant parameters such as piston displacement and intake manifold volume were changed to match those of the modeled engine. 67

87 Figure 6.2 shows simulation results at different engine operating points. For each simulation, a transient throttle command was created and the resulting MAP and predicted MAP values were recorded. There are three different signals shown in each plot in Figure 6.2, the current MAP, predicted MAP, and correct MAP. The current MAP corresponds to the manifold air pressure output from the plant model. The predicted MAP is the output of the MAP prediction control algorithm. And, the correct MAP is the signal that represents the correctly predicted intake manifold air pressure for a 700 CAD prediction horizon. The correct MAP was found by shifting the current MAP signal earlier in time by an amount equal to the prediction horizon. The time duration of the prediction horizon can be calculated using Eq In Figure 6.2, results are shown for engine operating points at 1200 and 1600 RPM. For each engine speed, throttle transients from 15 to 25 degrees and 25 to 15 degrees were commanded. It can be seen that up until the current MAP increases, the current and prediction MAPs are the same value. But, once the current MAP increases, the predicted MAP very closely matched that of the correct MAP signal trace. The transient dynamics are predicted well with the intake manifold model and the Euler approximation is able to accurately predict the intake manifold air pressure forward in time. A more in-depth look at one of the simulations is shown in Figure 6.3. This figure shows results for a simulation run at an engine speed of 1200 RPM and throttle transient from 15 to 25 degrees. The top plot shows the same information as Figure 6.2. The middle plot shows the throttle position, while the bottom plot shows the MAP error for both the current and predicted MAP traces. The MAP error is defined as the difference between a MAP value and the correct MAP value at a discrete point 68

88 Current Predicted Correct MAP [kpa] MAP [kpa] Current Predicted Correct Time [s] (a) 1200 RPM, tip in Time [s] (b) 1200 RPM, tip out Current Predicted Correct MAP [kpa] MAP [kpa] Current Predicted Correct Time [s] (c) 1600 RPM, tip in Time [s] (d) 1600 RPM, tip out Figure 6.2: MVEM simulation results at varying engine operating points 69

89 80 MAP [kpa] Current Predicted Correct Time [s] Throttle [%] MAP error [kpa] Time [s] Current Predicted Time [s] Figure 6.3: MVEM simulation results for throttle transient 70

90 in time. It can be seen that the predicted MAP is unable to successfully match the correct MAP trace until the throttle position starts its transient. This is because the intake manifold model relies on throttle position to be able to predict the mass air flow into the intake manifold. If there is no change in throttle, then the model will assume the engine is still in steady-state and the rate of change of the intake manifold air pressure will remain zero. But, once the throttle position changes, the control algorithm is able to successfully predict the MAP forward in time. Looking at the bottom plot, the MAP error goes to zero after the throttle increase, while the current MAP error remains until the engine returns to steady-state again. It is apparent that the lack of knowledge of the throttle position ahead of time can cause significant errors. Before the throttle change, the predicted MAP trace accumulated as much error as the current MAP trace. In this case, the error reached about 30 kpa in a single point in time, which can cause a significant deviation in the resulting air-fuel ratio. Since the engine was running at 1200 RPM, this is one of the worst case scenarios because the lower the engine speed, the greater the prediction horizon. While the simulation run in Figure 6.3 shows a good representation of what would result in real-world testing, the throttle response is largely inaccurate. It assumes that the throttle can follow a step command instantaneously. This is inaccurate as the throttle plate has an inertia as well as a counteracting force from the throttle plate return spring. To more accurately model the throttle movement, a rate limiter was applied to the throttle command. A rate limiter applies a maximum and minimum slew rate to an incoming signal. Previous research was completed to determine what the correct slew rate for the throttle is. Using throttle position data from a vehicle 71

91 80 MAP [kpa] Current Predicted Correct Time [s] Throttle [%] MAP error [kpa] Time [s] Current Predicted Time [s] Figure 6.4: MVEM simulation results for throttle transient, with throttle rate limiter 72

92 drive cycle, the speed of the throttle at different points in time was determined. The resulting slew rate was 233 deg/s [5]. Using a rate limiter on the throttle, another simulation was run at an engine speed of 1200 RPM and a throttle transient of 15 to 25 degrees, and is shown in Figure 6.4. It can be seen that the throttle trace no longer represents a step input; the trace ramps up to the final value. This is due to the rate limit of 233 deg/s set on the throttle command. The results are for the most part similar to those of Figure 6.3, except the predicted MAP does not match the correct MAP immediately after the throttle transient started. After the throttle starts to move, the predicted MAP moves towards the correct MAP, but it is not instantaneous. This is due to the throttle change not being instantaneous. Since the control algorithm assumes the throttle effective flow area is constant throughout the prediction horizon, the control algorithm will contain errors while the throttle is ramping into its final position. This is because the throttle position it is using to predict MAP forward in time is not the actual throttle position 700 CAD later. It can be seen that once the throttle reaches its desired set point, the predicted MAP error goes to zero because the throttle position remains constant from that point on. With the control algorithm successfully predicting intake manifold air pressure, the number of iterations must be optimized. As the number of iterations increases, the time step in the Euler approximation will decrease. As mentioned previously, the accuracy of the approximation increases as the time step is reduced. But, an increasing amount of iterations will require more throughput from the engine s ECU, which may cause operational problems if the ECU becomes overloaded. Figure 6.5 shows a graph of the MAP error versus the number of control algorithm iterations. 73

93 Normalized Error Normalized Error No Prediction Number of Iterations Figure 6.5: MVEM normalized error vs. iteration number Simulation Time [s] Number of Iterations Figure 6.6: MVEM simulation time vs. iteration number 74

94 The MAP error is the cumulative error from a degree transient at 2000 RPM. The number of iterations ranged from 10 to 30. The plot shows the cumulative error normalized against the cumulative error from using the current MAP reading without prediction. It can be seen that at lower iteration numbers, the control algorithm produces a larger amount of error than not using prediction at all. After thirteen iterations, the MAP prediction algorithm performs better than the current MAP. But, after sixteen iterations there is no increase in performance from the MAP prediction algorithm. At this point, the increases in accuracy from increasing the iteration number are smaller than the round off errors from the computer. The computational time was also considered when optimizing the iteration number. For each test, the simulation time was determined. This was done by inserting timers in the MATLAB code that recorded the computers clock time before and after the simulation. Figure 6.6 shows the simulation time versus the number of iterations. As the number of iterations increased, the simulation time also increased. This is because the computer has to re-calculate another set of equations for each increase in iteration number. Thus, in terms of computational time, the number of iterations must be minimized. Considering the results from Figure 6.5, sixteen or more iterations would provide the most accurate results. This would lead to choosing sixteen iterations as the most optimal number. But, since the accuracy diminishes with iterations immediately under sixteen iterations, eighteen iterations will be chosen. This will give a small safety buffer as the control algorithm may perform differently for different test cases. 75

95 6.3 Hardware Validation With the control algorithm validated in simulation using the MVEM, the next step is to use actual engine data from the dynamometer to further validate the performance. For the following tests, engine data at different operating points were recorded and post-processed in MATLAB and SIMULINK. In the SIMULINK diagram, the engine data were fed into the model as time varying traces that were used with the MAP prediction algorithm. The implementation into SIMULINK is shown in Figure 4.2. To validate the algorithm, tests were conducted at engine speeds of 1200, 1400, 1600, and 2000 RPM. For each engine speed, a throttle transient was commanded to produce a MAP transient of about kpa. Figure 6.7 shows the results for the tests run at 1200 RPM. The plots show the current, predicted, and correct MAP traces as well as the MAP error for the current and predicted MAP traces. It can be seen that there is exists about a 2 to 3 kpa error throughout the entire test for the predicted algorithm. This is due to the steady-state error present at the lower and higher intake manifold pressures. This error is to be expected from the results in Section 5.4 where it was determined that a small deviation from the true value of either the throttle effective area or volumetric efficiency parameters can produce appreciable errors in the resulting manifold air pressure. These errors are further worsened by the fact that the algorithm runs eighteen iterations in open-loop, meaning that the error will compound with each iteration. The results of each test are listed in Table 6.1. For each test, the absolute value of the MAP error was integrated with respect to time for the current and predicted MAP traces. The errors for each predicted MAP trace were then normalized against 76

96 MAP [kpa] Current Predicted Correct Time [s] MAP [kpa] Current Predicted Correct Time [s] MAP Error [kpa] Current Predicted MAP Error [kpa] Current Predicted Time [s] (a) Tip in Time [s] (b) Tip out Figure 6.7: MAP prediction performance results, 1200 RPM Table 6.1: MAP prediction performance Test Engine speed [RPM] MAP transient [kpa] Normalized MAP error

97 the current MAP trace s errors. It can be seen that for every test the MAP prediction performance was worse than using the current MAP values. Again, these large amounts error in each test are due to a mismatch in calculated mass air flow between the throttle and volumetric efficiency models Recalibrating V e Map The steady-state errors that are persistant in the initial hardware tests are due to a disagreement between the throttle and volumetric efficiency model. At steady-state, the intake manifold dynamics are zero and both the throttle and volumetric efficiency models should be calculating the same value for mass air flow. If the calculated values are different, then an offset of MAP will occur since the model is incorrectly showing that there is a greater influx of outflux of air mass in the intake manifold causing a change in the manifold air pressure. A proposed solution to this problem is to recalibrate the volumetric efficiency model so that it calculates the same mass air flow as the throttle model at every engine operating point. If the calculated mass air flow is matched for both models, dp a,im /dt will be zero, thus creating no change in the current MAP in steady-state. To recalibrate the volumetric efficiency model, the 2-d lookup function for the V e parameter will need to be recalculated. This parameter was originally calculated using the volumetric efficiency equation (Eq. 2.7), with steady-state engine dynamometer data. For the mass air flow, the MAF sensor reading was used. To allow both the throttle and volumetric efficiency models to be in agreement, the volumetric efficiency parameter will need to be determined using the mass air flow calculated from the throttle model. This involves using throttle position and engine speed to determine 78

98 the throttle effective area, which is used in the flow restriction model. Since the mass air flow calculated from the throttle model is used to determine the volumetric efficiency 2-d lookup function at a certain engine operating point, the calculated mass air flows from the throttle and volumetric efficiency model will be equivalent. To recalibrate the volumetric efficiency 2-d lookup function, the same 151 test points used to calibrate the model in Section 5 were used. For each test point, the volumetric efficiency parameter based on the throttle model s mass air flow was calculated. With the 151 C d A based volumetric efficiency points determined, another 2-d lookup function was created. The inputs to the function would remain the same as the original function, intake manifold pressure and engine speed. The MATLAB package sftool was used to create the 2-d lookup function. This package allows test points to be loaded into the graphical user interface and the user can apply different fitting functions to determine the best fit. Three different types of fits were considered for creating the 2-d lookup function: biharmonic interpolant with and without outliers and lowess. The biharmonic model is a radial basis function interpolant. The lowess model uses locally weighted linear regression to smooth data. For the biharmonic model, functions were created with and without points that were considered outliers from the calibration data. To validate the function fits, the same 25 test points used to validate the model in Chapter 5 were used. Using the resulting 2-d functions from each fit, the mass air flow from the volumetric efficiency model was calculated at a certain engine point and compared to the mass air flow calculated from the throttle model. The RMSE was calculated for all 25 validation test points for each 2-d function. The results are shown in Table 6.2. With the lowest RMSE, the biharmonic interpolant with outliers 79

99 Table 6.2: Comparison among proposed 2-d lookup functions Interpolation Method RMSE [g/s] Biharmonic interpolant (w/o outliers) Biharmonic interpolant (w/ outliers) Lowess Original was chosen to be the new recalibrated V e function. The percent MAF error for each of the validation points is shown in Figure 6.9. It can be seen that all but two test points are within 5 percent error, providing confidence of a good fit. The resulting surface plot of the function is shown in Figure 6.8. The general shape of the surface is similar to typical volumetric efficiency maps, except at lower engine speeds and manifold air pressures. In this area of the map, the throttle effective area parameter is highly non-linear. With the new volumetric efficiency 2-d lookup function implemented in the SIMULINK diagram, the same tests in Table 6.1 were completed. Figure 6.10 plots a comparison between the original and recalibrated V e maps for the test run at 1200 RPM for a throttle tip in. It can be seen that while steady-state error still exists, the magnitude of steady state-error has been decreased. The rest of the results are shown in Table 6.3. This table compares the normalized MAP error between both the original and recalibrated V e maps. For every test except at an engine speed of 2000 RPM, the recalibrated map improved on the cumulative MAP error, but the results are still not an improvement over using the current reading from the MAP sensor. This is because the steady-state error in MAP still exists in all the tests. This steady-state error is a result of the sensitivity of the intake manifold model. As found in previous sections, 80

100 Volumetric Efficiency [%] MAP [kpa] Engine Speed [RPM] 5000 Figure 6.8: C d A based V e 2-d lookup function MAF Error [%] Test Figure 6.9: MAF error between throttle and induction mass air flow 81

101 MAP [kpa] MAP [kpa] Current Predicted Correct Time [s] 40 Current Predicted Correct Time [s] MAP Error [kpa] Current Predicted MAP Error [kpa] Current Predicted Time [s] (a) Old V e map Time [s] (b) New V e map Figure 6.10: Comparison between original and recalibrated V e maps at 1200 RPM 82

102 Table 6.3: Comparison between original and recalibrated V e maps Test Normalized MAP error Engine speed MAP transient Without V e [RPM] [kpa] re-cal With V e re-cal % change a five percent deviation in either the throttle effective area or volumetric efficiency parameters can cause about a 3.4% error in MAP. This error is further exacerbated by the fact that the control algorithm iterates the model 18 times, during which the error is compounded with each iteration. Even though the volumetric efficiency map was recalibrated using the throttle model mass air flow, the 2-d lookup function cannot perfectly match the throttle model mass air flow at every operating point. This is seen in Figure 6.9, where the majority of the validation tests showed lower than five percent error in MAF calculation. And, with a small disagreement in air flow calculation, the steady-state MAP error can be significant Implementation of Adaptive Control Strategies A major source of the error that is making the intake manifold pressure prediction model worse than using the current MAP sensor reading is the existence of steadystate error. When the engine is in steady-state, the current and predicted MAP values should be the same. One cause of the steady-state error are the imperfections 83

103 in the model calibration. Even though both the throttle and volumetric efficiency models were calibrated with relatively good accuracy, small errors still exist. One source of error is that the 2-d look-up function for the C d A parameter has a high rate of change with small deviations of either the throttle position or intake manifold pressure. Thus, small errors in the calibration will cause steady-state errors in the resulting calculated MAP. Another source of error comes from obtaining the correct intake manifold temperature reading which can affect the V e model. Currently, the temperature is taken from the IAT sensor, which is integrated into the MAF sensor. Since the IAT sensor is placed upstream of the intake manifold in the air system, the assumption that the IAT sensor temperature reading is equivalent to the temperature of the intake manifold is not correct. With the presence of an engine block that is at a much higher temperature than the ambient temperature, the intake manifold temperature will often be higher than the temperature at the IAT sensor. Also, with the intake valve closing after the compression stroke begins, there will be a finite amount of reverse flow into the intake manifold from the engine cylinders, causing higher intake manifold temperatures. Another cause of steady-state error are the day-to-day changes in engine operation. These include engine aging and changes in ambient conditions for temperature, pressure, and humidity. These changes cannot be accounted for in a model without adaptive control. As determined previously, any small error in the model can produce significant deviations in the predicted intake manifold pressure values. A solution to these problems of steady-state error would be to implement a control algorithm that uses feedback from sensors to correct the model. For this model, feedback from the 84

104 Figure 6.11: SIMULINK implementation of adaptive PI model MAP sensor will be used to correct the error between the current and predicted MAP in steady-state. Adaptive PI Model To allow the use of feedback control to correct error in the model, an adaptive PI model was implemented into the control algorithm. The inputs are the current and predicted intake manifold pressure values, and the output is the adjusted predicted intake manifold pressure. An adaptive PI model was chosen instead of an adaptive PID model because the derivative term is very sensitive to measurement noise. The methodology of the model is shown in The setpoint of the system is the current MAP. The error between the predicted and current MAP values is calculated. This error is applied to the proportional and integral terms of the controller. The proportional term corrects using the present error, while the integral term corrects using a cumulative sum of past errors. The integral term allows the system to eliminate steady-state error. A weighted sum of both terms is calculated and the resulting 85

105 multiplying factor is applied to the predicted MAP value. A heuristic approach to tuning the controller gains was taken, which is similar to the Ziegler-Nichols method of gain tuning. The proportional gain was tuned first, with the integral following. The desired settling time was under five seconds with less than five percent overshoot. The gains were manually tuned until the desired response was achieved. The proportional and integral gains are and kp a 1, respectively. The adaptive PI model should only be correcting MAP when the engine is operating in steady-state. This is because during a transient, the adaptive PI model will try to correct the predicted MAP towards the current MAP. But, during transients the current MAP is incorrect. In steady-state the predicted and current MAP values should be equivalent. To allow the control algorithm to only be active during steadystate, the adaptive PI model was placed in an enabled subsystem in SIMULINK which is activated only in steady-state operation. To control the enabling and disabling of the adaptive PI model, an algorithm to determine if the engine is operating in steady-state will need to be created. In this thesis, engine steady-state operation will be defined as a state in operation in which transients of the engine speed and intake manifold air pressure values have ceased over a small period of time. A steady-state detection algorithm was created and implemented in SIMULINK. The algorithm structure is shown in The inputs into the subsystem are the current engine speed and intake manifold pressure and the output is a binary value indicating if the engine is operating in steady-state. For the engine to be in steady-state, both the engine speed and intake manifold air pressure cannot exhibit transients. To determine if a variable is exhibiting a transient, the present value of the variable is compared to a past value. If the difference between 86

106 Figure 6.12: SIMULINK implementation of engine steady-state detection the two values is lower than a specified tolerance, then the variable is considered to be in steady-state. Since the sensor data is susceptible to noise, a first-order filter is applied to the input signals, shown in Eq F (s) = s + 1 (6.1) To test the performance of the steady-state detection algorithm, a series of engine transients were input into the detection algorithm. Figure 6.13 shows the MAP trace and steady-state status. The shaded sections of the graph indicate portions of the trace the algorithm determined to be steady-state operation. Looking at the graph, it can be seen that the algorithm can successfully determine which portions of the trace the engine was in steady-state. The adaptive PI model and steady-state detection subsystems were implemented into the base algorithm, shown in Figure Eight validation tests were performed on the base algorithm with the adaptive PI model. At 1200, 1400, 1600, and 2000 RPM, throttle transients producing MAP 87

107 Figure 6.13: Steady-state detection for random transients transients of about and kpa were conducted. Similar to the analyses done previously in this chapter, the cumulative MAP error was recorded over a small period in time during the transient step and was compared to the performance without adaptive parameters. In Figure 6.15, a comparison between the base control algorithm and the updated algorithm with adaptive parameters is shown. For the updated algorithm it can be seen that before the transient begins, the steady-state error is eliminated. This is because the adaptive PI model has driven the error to zero since the engine is in steady-state. After the transient is over, there is steady-state error. This is a result of the adaptive PI model resetting during the transient; the multiplier is set back to the default value of one. The error after the transient is ramping down as the engine returns to steady-state operation and the adaptive PI model is the changing 88

108 Figure 6.14: MAP prediction SIMULINK diagram with adaptive PI model 89

109 MAP [kpa] Current 30 Predicted Correct Time [s] MAP [kpa] Current 30 Predicted Correct Time [s] 10 8 Current Predicted 10 8 Current Predicted MAP Error [kpa] 6 4 MAP Error [kpa] Time [s] Time [s] (a) Without adaptive PI model (b) With adaptive PI model Figure 6.15: Improvement using adaptive PI model at 1200 RPM 90

110 Table 6.4: Error improvement using PI control Test Normalized MAP error Engine speed MAP transient Without PI [RPM] [kpa] model With PI model % change the multiplier accordingly. The same analysis was completed for each test and the normalized error against the base algorithm was calculated. The normalized MAP error between the algorithm with and without adaptive PI model is shown in Table 6.4. It can be seen for every test, there was a significant reduction in error. And, for the first time, the control algorithm performed better than using the current MAP in terms of MAP error. The tests run at engine speed of 1400 and 2000 RPM produced 0.96 and 0.91 normalized error. The significant reduction in error is due to the adaptive PI model being able to successfully drive the steady-state error to zero. Adaptive V e Model With the addition of the adaptive PI model, the steady-state error was able to be significantly reduced. But, the adaptive PI model is only active in steady-state, which causes the controller gain to be reset every time a transient occurs. This gives motivation to develop an algorithm that can adapt to changing engine operating conditions and learn in on-line operation of the engine s ECU. If the algorithm can 91

111 remember the corrections, then the steady-state error can be eliminated after the transient engine events. To correct for the steady-state error, an algorithm was created that adjusts a multiplier that is applied to the current volumetric efficiency. The steady-state error is the result of a mismatch in the mass flow rates of air into and out of the intake manifold. At steady-state, the mass air flow rates should be equivalent since there is no change in intake manifold pressure. By adjusting the volumetric efficiency, the mass air flow rate out of the intake manifold can be adjusted to match that of the mass of air flowing into the intake manifold. The adapting volumetric efficiency table algorithm implemented into the base algorithm is shown in Figure 6.16, and the algorithm subsystems are shown in Appendix B. The inputs into the algorithm are the current engine speed, intake manifold pressure, error between the current and predicted MAP values, and steady-state status. The output of the system is the adjusted volumetric efficiency parameter. As mentioned previously, the steady-state error in MAP will be corrected by adjusting a multiplier that is applied to the current volumetric efficiency. This multiplier is adjusted according to the error between the predicted and current MAP values. The desired time for convergence of the predicted MAP to the current MAP for the algorithm was set to be about 60 seconds. This duration was chosen because this is a correction stored in memory and to ensure the validity of the correction, a longer duration was used. This prevents any short disturbances to be rejected in the on-line correction. For short disturbances, the adaptive PI model (with a settling time of 5 seconds) will be able to correct the errors in the short-term. In this algorithm, 0.01% of the MAP error is either added or subtracted to the multiplier, depending on 92

112 Figure 6.16: MAP prediction SIMULINK diagram with adaptive V e table 93

113 whether the predicted MAP is higher or lower than the current MAP. To determine the percentage of error added to the multiplier, the average steady-state MAP error was found. The average steady-state among tests run at engine speeds of 1200, 1400, 1600, and 2000 RPM was about 2 kpa. In simulation, it was determined that with a 2 kpa MAP error, taking 0.01% of the MAP error and adding it to the multiplier will yield about a 60 second convergence rate. The results of this simulation are shown in Figure It can be seen that within the first five seconds, the steady-state error is driven to zero; this is because the adaptive PI model is active along with the adaptive volumetric efficiency table algorithm. After the adaptive PI model has converged, the MAP error is showing to be zero. But, since the adaptive volumetric efficiency table algorithm scopes the MAP error prior to the adaptive PI model, the magnitude of actual MAP error can still be used to correct the volumetric efficiency parameter. During this time, the adaptive volumetric efficiency table algorithm is adjusting the volumetric efficiency multiplier from its default value of 1. About 60 seconds later, the multiplier converges to a value of about 0.7. On the way to the convergence of the volumetric efficiency multiplier, the adaptive PI model s multiplier settles back down to 1. This is because the adaptive volumetric efficiency table algorithm is slowly correcting the volumetric efficiency parameter, and the adaptive PI model does not need to adjust the final predicted MAP as much. When the volumetric efficiency parameter settles to its final value of 0.7, the PI multiplier settles back to a value of 1. Since the volumetric efficiency multiplier may not be assumed to be constant throughout the entire engine operating range, the 2-d volumetric efficiency look-up table was split into sixteen different zones. The different zones are shown in Figure 94

114 45 MAP [kpa] 40 Actual Future Correct Future Predicted MAP Error [kpa] 2 1 Experimental Predicted VE Multiplier PI Multiplier Time [s] Figure 6.17: V e table correction 95

115 Figure 6.18: Layout of V e adaptation zones While the most accurate method of adaptation would be to have a zone multiplier for each operating point, it would not be practical. One reason is that the algorithm would be constantly adapting as the operating points changed, also the amount of memory required to store a multiplier for each point would be unreasonable. Sixteen zones were chosen in that it provides fine enough discretization of the volumetric efficiency table without overly taxing the ECU or having the algorithm constantly learning on-line. Further calibration of the appropriate amount of zones will be completed in-vehicle, where the algorithm will experience real-world drive traces. Hysteresis bands were also implemented into the zone-based control. This prevents the adaptation learning from chattering between zones when the operating point is close to the edge of a zone. 96

116 The methodology of the zone-based adaptation is shown in Appendix B. The inputs into the system are the current volumetric efficiency, current MAP error, steadystate status, and engine speed and intake manifold pressure data. The output of the system is the corrected volumetric efficiency value. Within the zone-based adaptation subsystem, the characteristics of the zone-based control are set. These include the number of zones, minimum range value, incremental range value, and hysteresis threshold. The minimum range value is the smallest value the respective variable can be, while the incremental range value is the size of the zone with respect to the variable. The hysteresis threshold is the size of the hysteresis bands applied to all zones with respect to the variable. For the engine used in this research, the engine speed and intake manifold pressure variables were both split into four zones. The engine speed range is 1000 to 4200 RPM, while the MAP range is 0 to 112 kpa. To test the performance of the adaptive volumetric efficiency table algorithm, the same eight validation tests as used previously in this thesis were performed. At 1200, 1400, 1600, and 2000 RPM, throttle transients producing MAP transient of about and kpa were conducted. The cumulative MAP error was recorded over a small period of time during the transient step and was compared to the performance without the additional adaptive parameters. For these tests, the adaptive volumetric efficiency table was given time to adapt and learn before the data was recorded. In Figure 6.19, a comparison between the base algorithm with adaptive PI model versus the base algorithm with adaptive PI model and adaptive volumetric efficiency table is shown. The results are both from the tests run at an engine speed of 1200 RPM with a throttle tip-in. It can be seen that both algorithms are able to successfully drive steady-state error to zero before the throttle transient. As discussed 97

117 MAP [kpa] Current 30 Predicted Correct Time [s] MAP [kpa] Current Predicted Correct Time [s] 10 8 Current Predicted 10 8 Current Predicted MAP Error [kpa] 6 4 MAP Error [kpa] Time [s] (a) With adaptive PI model Time [s] (b) With V e adaptation Figure 6.19: Improvement using adaptive V e table at 1200 RPM 98

118 previously, since the engine is in steady-state before the transient, the adaptive PI model is active and drives the predicted MAP towards the current MAP. Similarly, the adaptive volumetric efficiency table algorithm is able to adjust the V e multiplier to create zero steady-state error. After the transient, the base algorithm with only adaptive PI model exhibits steady-state error. This is because the adaptive PI model resets during a transient, and the algorithm will have to re-adjust the PI multiplier to bring the steady-state error to zero. The MAP error is slowly decreasing, but a significant amount of MAP error is accumulating during the PI convergence. With the addition of the adaptive volumetric efficiency table algorithm, the steady-state error after the throttle tip-in was decreased greatly. This is because the algorithm was able to adapt and store the appropriate correction to the V e parameter in memory. And, since the steady-state values before and after the throttle transient are correct, the MAP value accuracy during the transient itself was increased. The results shown in Figure 6.19b, are very similar to the simulation results shown in Figure 6.4. Looking at the simulation results, the only source of error in MAP values comes from the lack of knowledge forward in time of the throttle position. This results in an inability to correctly predict MAP forward in time until the throttle position actual changes. Similar results are shown in the transient with the addition of the adaptive volumetric efficiency table algorithm. The results from the rest of the eight validation tests are shown in Table 6.5. For every test, there was a significant reduction in the normalized MAP error with the addition of the adaptive volumetric efficiency table algorithm. On average, there was about a 70 percent reduction in normalized MAP error. This large reduction in error 99

119 Table 6.5: Error improvement using V e adaptive control Test Normalized MAP error Engine speed MAP transient Without V e [RPM] [kpa] adapt With V e adapt % change is due to the algorithm successfully eliminating steady-state error before and after the throttle transients. One of the driving factors of creating an on-line adaptive volumetric efficiency table is the effect of day-to-day changes in the engine operating conditions. These changes can invalidate the empirically calibrated C d A and V e tables, causing significant errors in MAP prediction. To see how much the day-to-day changes effect the model, the V e multiplier was tracked from different testing sessions throughout the course of a couple months. Figure 6.20 shows the results of the V e multiplier from Zone 5 of the zone-based adaptive algorithm throughout time. It can be seen that there is a great deal of variability on the multiplier, ranging from about 0.6 to 1. During the November tests, it can be seen that there are drastic changes even between just a couple days of testing. On November 9, the multiplier was 1.01 and then on November 10 it was Two days later on November 12, the multiplier was back 100

120 V e Multiplier /12 12/12 01/13 02/13 Date Figure 6.20: Day-to-day variability in V e multiplier up to This great amount of variability in the V e parameter reinforces the need for adaptive algorithms in the control AFR Results To further validate the control algorithm, oxygen sensor data was recorded in the engine dynamometer cell to analyze the AFR results from throttle transient. Looking at the AFR data will provide an excellent indication to the performance of the control algorithm. As discussed previously, any deviation from stoichiometric combustion will lead to increased emissions when a three-way catalyst is used. Thus, during transient engine events, it is desired that the AFR trace show minimal deviations from stoichiometric combustion (λ = 1). 101

121 No prediction Prediction Equivalence Ratio Time [s] Figure 6.21: AFR deviation from throttle tip-in, 1200 RPM, closed-loop No prediction Prediction Equivalence Ratio Time [s] Figure 6.22: AFR deviation from throttle tip-out, 1200 RPM, closed-loop 102

122 Figures 6.21 and 6.22 show AFR results from the tests run at an engine speed of 1200 RPM with a throttle tip-in and tip-out, respectively. For these tests, the closed-loop AFR control algorithm was enabled, which means feedback control from the oxygen sensor was used to assist in adjusting the fueling to allow stoichiometric combustion. Figure 6.21 shows the results of a throttle tip-in event. Baseline results using the previous engine air mass estimation algorithm (simply the speed density equation) are compared to results using the control algorithm created in this thesis. Looking at the results without prediction software, it can be seen that the beginning of the throttle transient causes a large deviation of almost 20% toward lean combustion. Deviations of this magnitude can be dangerous in that engine knock events can occur along with increased tailpipe emissions. With the prediction software implemented, the initial deviation was reduced by about 50%. Also, the subsequent deviations were minimized compared to those in the results without prediction. Figure 6.22 shows the results of a throttle tip-out event. Similar results as the previous test occurred; not using the prediction software caused a large initial AFR deviation during the initial throttle change. The initial deviation spiked about 15% towards rich combustion. Using the prediction software, the initial deviation was reduced by about 55%. The same eight tests used previously in this thesis were conducted to analyze the AFR results using the air-prediction control algorithm. At 1200, 1400, 1600, and 2000 RPM, throttle transient producing MAP transients of about and kpa were conducted. Two metrics of performance were measured, the area deviation from the setpoint equivalence ratio and the maximum deviation from the setpoint equivalence ratio. The area deviation was found by integrating the absolute value of the deviation from the control s equivalence ratio setpoint value over time. Area 103

123 Table 6.6: Closed-loop AFR results, area deviation Test Area deviation Engine speed MAP transient [RPM] [kpa] No prediction Prediction % change Table 6.7: Closed-loop AFR results, maximum % deviation Test Maximum % deviation Engine speed MAP transient [RPM] [kpa] No prediction Prediction % change

124 deviation is important to analyze as it is an indication of not only how far the AFR deviates from stoichiometric combustion, but for how long the deviation lasts. The results of the area deviation and maximum percent deviation are shown in Tables 6.6 and 6.7, respectively. It can be seen that for all tests shown, there were significant performance increases when the prediction software was implemented. The average percentage reduction in the area deviation and maximum percent deviation were both 45%. Recalibration of Steady-State Algorithm To further improve the performance of the MAP prediction control algorithm, the steady-state detection was recalibrated. One source of error in the results is the time delay between when an engine transient occurs and when the algorithm is able to detect the transient. Every moment the engine is in a transient state and the prediction algorithm is not active, air charge estimation error will occur and large AFR deviations will result. Thus, the quicker the algorithm can detect a transient event, the less AFR deviations will occur and consequently less tailpipe emissions. Currently the previous steady-state algorithm takes about 40 ms to respond to a transient event. To improve the steady-state detection performance, the first-order filter constant was changed as well as the threshold tolerance. The methodology of the original steady-state algorithm is outlined in Section The first-order filter was implemented into the algorithm to smooth out the sensor data from the MAP sensor. But, the addition of a first-order filter adds a delay to the system. To quicken the response, the filter constant was adjusted to accommodate a wider bandwidth. The new filter equation is shown in Eq

125 MAP [kpa] MAP MAP filtered old MAP filtered new Time [s] Figure 6.23: Filter change comparison A simulation to compare the responses of both filters to a MAP transient was run, and the results are shown in Figure The traces for the MAP sensor data, and the filtered MAP using both the old and recalibrated filters are shown. For the recalibrated filter, it can be seen that the response is much faster than that of the old filter. With a quicker filter response, the time delay for transient event detection will be shorter. F (s) = s + 1 (6.2) Another change to the algorithm was adjusting the threshold value in which the algorithm considers the engine to be in steady-state. As mentioned in a previous chapter, the algorithm subtracts past MAP values from the current MAP values, and 106

126 if the result is less than the threshold value the engine is considered to be in steadystate. With a conservative threshold value, the algorithm will take longer to consider itself in transient operation, but will be more robust in rejecting sensor noise. A balance between a quick-responding threshold value and one that rejects noise data from being flagged as transient operation is needed. For the re-calibration of the algorithm, the MAP tolerance was changed from 0.60 kpa difference to a 0.30 kpa difference. A simulation was run to compare the steady-state detection performance between the old and recalibrated steady-state detection algorithms and the results are shown in Figure The recalibrated algorithm takes about 20 ms to respond to a transient event, which is a 20 ms improvement over the previous algorithm. Also, the new steady-state algorithm is able to detect a return to steady-state operation after the transient is over much quicker than that of the old algorithm. There was about a 300 ms improvement in detection time. To further test the performance of the new steady-state detection algorithm, the same eight validation tests performed previously were run again with the new algorithm implemented. The results for the area deviation and maximum percent deviation are shown in Tables 6.8 and 6.9. Each table outlines the percent improvement of the addition of the MAP prediction software before and after the recalibration of the steady-state algorithm. The percent improvement of the recalibrated steady-state algorithm over the old algorithm was also calculated. Looking at Table 6.8, generally there was a significant improvement in area deviation; on average there was a 14% improvement over the old calibration. Two tests showed a worse performance. The tests run at engine speeds of 1200 and 2000 RPM for a throttle tip in showed a -13 and -2 % change. Similar results were shown for 107

127 MAP [kpa] MAP S.S. old *100 S.S. new * Time [s] Figure 6.24: Steady-state detection comparison Table 6.8: Comparison of closed-loop AFR results for area deviation with steady-state algorithm recalibration Engine speed [RPM] Test MAP transient [kpa] New cal. [% improve.] Old cal. [% improve.] % change

128 Table 6.9: Comparison of closed-loop AFR results for maximum % deviation with steady-state algorithm recalibration Engine speed [RPM] Test MAP transient [kpa] New cal. [% improve.] Old cal. [% improve.] % change the maximum percent deviation shown in Table 6.9, on average there was a 19% improvement over the old calibration. The only test to show worsened performance was a throttle tip-in at an engine speed of 2000 RPM with a -8% change. There were also two tests that showed no improvement. Open Loop Performance To further validate the air prediction control algorithm, tests were conducted with open-loop control only. This means that both feedback loops from the oxygen sensors were turned off. Open-loop AFR control performance was evaluated because the influence of the closed-loop feedback loops was removed. This provides a better insight on how the predictive feed-forward algorithm alone performs against the original algorithm. 109

129 No prediction Prediction Equivalence Ratio Time [s] Figure 6.25: Open-loop AFR control performance comparison, 1200 RPM, kpa transient The same eight validation tests as performed previously were conducted for the open-loop tests. Figure 6.25 shows the AFR results for both the original and predictive algorithms for the test conducted at 1200 RPM with a throttle tip-in. Both algorithms showed a lean spike in engine operation, this is due to the throttle tipin. The sudden increase in air flow is unable to be detected by the control software immediately so an inadequate amount of fuel is provided to have stoichiometric combustion. Similar to closed-loop results, there is a large decrease in both the maximum percent deviation and area deviation of the AFR trace with the addition of the new algorithm. 110

130 Equivalence Ratio Maximum % deviation Area deviation Time [s] Figure 6.26: Method of calculating metrics for open-loop results When looking at Figure 6.25, it can be seen that the AFR traces do not settle down to the setpoint value in engine steady-state operation. This is because the control algorithm for air calculation is running in open-loop, which means that there is no feedback to correct for errors. Thus, the steady-state deviations from the setpoint are caused from errors in the calibration of engine maps such as volumetric efficiency or injector characterization. Since the steady-state AFR values are not necessarily at the same value, a method of calculating the same metrics used previously will have to be established. The reference value in which the maximum percent and area deviation will be calculated from will be the steady-state value after the engine transient is over. The calculation method of the metrics is shown in Figure

131 Table 6.10: Open-loop AFR results, area deviation Test Area deviation Engine speed MAP transient [RPM] [kpa] No prediction Prediction % change Table 6.11: Open-loop AFR results, maximum % deviation Test Maximum % deviation Engine speed MAP transient [RPM] [kpa] No prediction Prediction % change

132 Table 6.12: Test operating points for open-loop AFR control performance comparison Test Engine Speed [RPM] MAP transient [kpa] The rest of the validation tests are summarized in Tables 6.10 and Table 6.10 shows the results for the amount of deviation area from the steady-state setpoint. For every test case, there was an improvement with the addition of the prediction algorithm. algorithm. On average, there was about a 55% improvement over the old control Table 6.11 shows the results of the maximum percent deviation from the steady-state setpoint. Similar to the previous results, there was a significant improvement for every test case. On average, there was about a 60% improvement in maximum percent deviation with the addition of the prediction algorithm. The prediction control algorithm was also benchmarked against a production competitor sedans control algorithm. The competitor sedan data from a FTP drive cycle was taken. With these results, portions of the cycle were analyzed, specifically looking at the current intake manifold pressure, engine speed, and resulting AFR traces. From the FTP cycle, four engine transient test points were determined and the same tests were evaluated on the engine dynamometer for the prediction control algorithm. These tests are summarized in Table The results are shown in Figures 6.27 and 6.28 for the area deviation and maximum percent deviation, respectively. For each test, the results for the algorithm with and without prediction and the competitor algorithm are shown. Similar to 113

133 No prediction Prediction Competitor algo Area deviation Test Figure 6.27: Open-loop AFR control performance comparison, area deviation No prediction Prediction Competitor algo Max % deviation Test Figure 6.28: Open-loop AFR control performance comparison, max % deviation 114

134 the previous results, the addition of the prediction algorithm significantly improved the performance over the original control algorithm. Compared to the competitors algorithm, the prediction algorithm was able to achieve a smaller area deviation for every test. For the maximum percent deviation, the prediction algorithm was able to significantly improve upon the original control algorithm for every test. For Tests 1, 2 and 3, the prediction software was an improvement over the competitor algorithm. For Test 4, the competitor algorithm performed slightly better than the prediction algorithm. 6.4 Summary The proposed control algorithm was validated in both software and hardware validation. In the software validation, the prediction control algorithm was implemented with a mean value engine model to verify performance before the algorithm was implemented on engine hardware. The algorithm proved to successfully predict the MAP forward in time, and the simulations showed what the ideal results would like (Figure 6.1). Further, the simulations allowed the optimization of the number of iterations to run for the control algorithm. Next, the control algorithm was validated using data collected from the engine dynamometer cell. Initial results showed a significant amount of steady-state error, which gave motivation for the V e map recalibration and implementation of adaptive control strategies. With these additions to the code, the hardware results matched closely with the software simulation results. The control algorithm was then evaluated using the AFR trace data in both open and closed-loop operation. The control algorithm was not only able to make significant improvements 115

135 over the original control algorithm, but over a competitive production sedan s control algorithm. 116

136 Chapter 7: Conclusions and Future Work 7.1 Conclusions In this thesis, a model-based design approach to air-fuel ratio control was successfully created and validated. The resulting control algorithm combines an intake manifold model with a Forward Euler approximation. To create the intake manifold model, steady-state engine dynamometer data from a 151 point DOE test was used to calibrate the throttle air flow and volumetric efficiency models. The intake manifold model was validated in simulation against engine dynamometer data. The results showed significant steady-state error, but an accurate representation of the dynamics of the intake manifold pressure variable was produced. The validated intake manifold model was the combined with the Forward Euler approximation to create a predictive intake manifold air pressure algorithm. The control algorithm was validated in both software and hardware validation. In software validation, the control algorithm was combined with a mean value engine model. From this, rapid control development of the control algorithm was completed. The software validation provided an insight on what the ideal results a successful algorithm would yield as well as an optimization of the number of iterations for the control algorithm to run. In hardware validation the control algorithm was validated in both offline post-processing of engine dynamometer data and in real-time implementation 117

137 on the engine ECU. The initial results showed a significant amount of steady-state error, which gave motivation to implement adaptive control strategies. An adaptive PI model was created which allowed the elimination of steady-state error until an engine transient occurred. A zone-based adaptive volumetric efficiency table was also implemented which was able to significantly reduce steady-state error by storing the corrections in memory. The oxygen sensor data also was analyzed to validate the performance of the control algorithm. AFR traces from both closed and open-loop operation were collected. For both cases, the control algorithm was proven to have a significant performance increase over the original control algorithm. And, in open-loop control, the predictive control algorithm was able to be competitive with a production sedan s control algorithm. 7.2 Future Work While the validation of the air prediction control algorithm showed positive results, there are several improvements that can be implemented to further its performance. One improvement is the implementation of throttle command buffering. This involves storing the throttle command from the driver in the ECU s memory. By delaying the driver s throttle command, the control algorithm achieves a priori knowledge of the future throttle commands, which allows the MAP to be successfully predicted throughout the entire engine transient. In order to successfully implement throttle command buffering, a dynamic model of the throttle plate dynamics will need to be created. 118

138 Another possible addition to the control algorithm is intake manifold volume tuning. Since the filling and emptying process of the intake manifold may not utilize the entire volume of the manifold, the system response may have a different time constant than that of the model. Using parameter identification techniques, the actual used intake manifold volume can be found, which will correct the model s time constant. Additionally, the algorithm should undergo in-vehicle calibration. This is essential to complete before the control algorithm is permanently implemented into the ECU in the vehicle. During this validation process, further tuning and optimization of parameters such as number of control algorithm iterations and number of adaptation zones can be completed. Performing in-vehicle validation will allow further calibration of the control algorithm by creating drive cycles that cannot be easily replicated in the engine dynamometer cell. 119

139 Bibliography [1] E. Hendricks A. Chevalier, C. Vigild. Predicting the port air mass flow of si engines in air/fuel ratio control applications. SAE International, [2] K. M. Bovee. Design of the architecture and supervisory control strategy for a parallel-series plug-in hybrid electric vehicle. Master s thesis, The Ohio State University, [3] R. B. Cooley. Engine selection, modeling, and control development for an extended range electric vehicle. Master s thesis, The Ohio State University, [4] J. M. Davis. Development of an e85 engine for the ecocar challenge hybrid vehicle competition. Master s thesis, The Ohio State University, [5] R. V. Everett. Transient air dynamics modeling for an advanced alternative fueled engine. Master s thesis, The Ohio State University, [6] R. V. Everett. An improved model-based methodology for calibration of an alternative fueled engine. Master s thesis, The Ohio State University, [7] K. M. Follen. A System Dynamics Modeling Methodology for Compressible Fluid Flow Systems with Applications to Internal Combustion Engines. PhD thesis, The Ohio State University, [8] K. Srinivasan G. Rizzoni. Module set. ME 7326: Powertrain Dyanamics, The Ohio State University, [9] J. B. Heywood. Internal Combustion Engine Fundamentals. McGraw-Hill, [10] D. A. Jones. Differential equations. MAT 275, Arizona State University, [11] T. Watanabe K. Iwachido, T. Onodera. Nox trap catalyst technologies to attain 99.5efficiency for lean burn gasoline engine application. SAE International, [12] C. H. Onder L. Guzzella. Introduction to Modeling and Control of Internal Combustion Engine Systems. Springer,

140 [13] S. Magner M. Jankovic. Air-charge estimation and prediction in spark ignition internal combustion engines. Proceedings of the American Control Conference, [14] I. Gruden J.D. Powell N. P. Fekete, U. Nester. Model-based air-fuel ratio control of a lean multi-cylinder engine. SAE International, [15] H. Goto O. Watanabe, S. Nakajima and T. Matsunaga. Development of cng engine with variable valve timing electronic control. SAE International, [16] W. Cheng T. Tseng. An adaptive air/fuel ratio controller for si engine throttle transients. SAE International,

141 Appendix A: Intake Manifold Model Subsystems This appendix shows the subsystems of the intake manifold SIMULINK model shown in Figure

142 Figure A.1: Subsystem: throttle model Figure A.2: Subsystem: throttle model > flow restriction 123

143 Figure A.3: Subsystem: throttle model > flow restriction > unchoked flow Figure A.4: Subsystem: throttle model > flow restriction > choked flow 124

144 Figure A.5: Subsystem: V e model Figure A.6: Subsystem: V e model > V e to MAF 125

145 Appendix B: Adaptive Volumetric Efficiency Table Subsysems This appendix shows the subsystems of the adaptive volumetric efficiency table SIMULINK model. 126

146 Figure B.1: VE Lookup Table 127

147 Figure B.2: VE Lookup Table > Zone Based Correction Control 128

148 Figure B.3: VE Lookup Table > Zone Based Correction Control > Zone Determination 129

149 Figure B.4: VE Lookup Table > Zone Based Correction Control > Zone Determination > X Zone Determination 130