Model Predictive Engine Torque Control with Real-Time Driver-in-the-Loop Simulation Results

Transcription

1 21 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 3-July 2, 21 WeB19.3 Model Predictive Engine Torque Control with Real-Time Driver-in-the-Loop Simulation Results Chris Vermillion, Ken Butts, and Kevin Reidy Abstract This paper presents the design and simulation results for a novel off-idle engine torque control strategy that uses online model predictive control () to simultaneously manage drivability, emissions, and fuel economy, while delivering desired engine torque. In order to achieve a tractable optimization, a modular control approach is used, wherein is used to manipulate desired air/fuel ratio, engine air charge, spark advance, and variable valve timing, whereas lower level controllers are designed using conventional design techniques to deliver these desired values. The performance of the proposed control strategy is exhibited through simulation results on two test cases, including a driver-in-the-loop simulator. Results show that the model predictive torque control strategy yields a significant overall improvement in terms of a combined drivability, emissions, and fuel economy metric. I. INTRODUCTION A significant amount of recent powertrain control research has been geared towards model-based and optimizationbased control strategies for managing competing performance goals under off-idle driving scenarios, for a variety of engine types (it is worth noting that some very successful results, such as [1] and [2], have been attained for the complementary problem of idle speed control, with an excellent summary provided in [3]; however, our paper only considers off-idle operation). For example, the authors of [4] concentrate on a model-based control strategy that minimizes emissions. The authors of [] offer a hybrid approach to optimizing air fuel ratio and torque tracking, which ultimately allows for the indirect management of drivability and fuel economy concerns. The authors of [6] present experimental results that use model predictive control () to optimize fuel economy alone. The authors of [7] offer a control strategy to optimize emissions and fuel economy for a hybrid electric vehicle. The authors of [8] and [9] use a shortest path stochastic dynamic programming (SPSDP) approach to optimize fuel economy and drivability for a hybrid electric vehicle, where their work serves as a high level optimization that determines the optimal torque split between the motor and engine. Our work differs from each of the aforementioned works in at least one of the following two key respects: 1) We simultaneously consider fuel economy, drivability, and emissions (rather than a subset of the three); 2) We perform our optimization in an engine torque control framework, where our controller is ultimately C. Vermillion and Ken Butts are with the Toyota Technical Center, Ann Arbor, MI, 48, chris.vermillion@tema.toyota.com, ken.butts@tema.toyota.com K. Reidy is with California Polytechnic State University, San Luis Obispo, CA 9347, kreidy@calpoly.edu. responsible for delivering desired engine torque as interpreted by the driver s accelerator pedal position. In order to simultaneously consider fuel economy, drivability, and emissions while delivering desired torque, we fuse the concept of torque control with model predictive control () by performing an online optimization that considers competing performance interests. By performing our optimization in a torque control framework, we consider the engine as a single torque generation machine, rather than many separate subsystems. And in contrast to higherlevel control strategies such as [8] and [9] that determine the optimal torque request for the engine, our optimization represents a lower-level control strategy that calculates how to deliver this request. represents a very attractive control design method for calibrators, since the competing performance goals can be directly incorporated into the cost function to be optimized, and constraints can be explicitly enforced. To tackle the computational burden of online while maintaining the effectiveness of the optimization, we consider the full engine, including air, fuel, and combustion dynamics, but we replace low level air and fuel control loops with reference models that describe their ideal input/output behavior. This approach originates from our earlier work in [1] and represents a compromise between simplicity and accuracy in modular control design, wherein the low level dynamics are not neglected but are approximated. In Section II, we quantify each performance metric (drivability, fuel economy, and emissions), provide a description of the dynamic model used for control design, and present the overall control structure. In Section III, we describe the details for the reference model selection, low level control design, and, most notably, design for engine torque control. Finally, in Section IV, we present simulation results for two cases, namely: 1) A tip-in/tip-out case that focuses on the drivability/fuel economy tradeoff exhibited during fuel cut and recovery; 2) A section of a federal test procedure (FTP) cycle using a driver-in-the-loop simulator. II. PROBLEM FORMULATION AND MODEL OVERVIEW A. Essential Model Components Our work is concerned with a longitudinal dynamics model for a full-sized Toyota vehicle with a 2.4 liter, 4 cylinder spark-ignition gasoline engine and a 4-speed automatic transmission. The overall model description is given /1/$ AACC 149

2 TABLE I MODEL VARIABLES Submodel Variable Description Units Engine θ throttle angle rad Inputs IPW fuel pulse width µ s V V T cmd valve timing cmd. deg. adv. δ spark advance deg. T pump pump torque N-m Engine W fuel fuel flow rate g/s Outputs CO CO emissions g/s HC HC emissions g/s NO NO emissions g/s Teng net net eng. torque N-m ω eng engine rot. speed rad/s Engine V V T actual VVT deg. adv. Internals W air air flow to cyl. g/s φ 14.6 W fuel W air - T ex exhaust temp. deg. C T comb combustion torque N-m CO exh exhaust CO emis. g/s HC exh exhaust HC emis. g/s NO exh exhaust NO emis. g/s φ tp tailpipe equiv. rat. - Driveline ω eng eng. speed rad/s Inputs GR gear ratio - ω tire tire rot. speed rad/s Driveline F tire tire/road force N Outputs T pump pump torque N-m Driveline T turb turbine torque N-m Internals ω turb turbine rot. spd. rad/s θ turb turbine rot. pos. rad Veh. In F tire tire/road force N Veh. Out v veh veh. speed m/s ω tire tire rot. spd. rad/s θ tire tire rot. pos. rad Veh. Intl. m a HF high freq. accel. s m 2 a veh vehicle accel. s 2 in Fig. 1, with inputs, outputs, and internal variables for each submodel are given in Table I. 1) Engine Submodel: The engine submodel contains an intake manifold, fuel injection dynamics, exhaust emissions, catalyst, and rotational dynamics model. The control inputs to the engine include throttle angle (θ), fuel injection pulse width (IPW), spark advance (δ), and intake variable valve timing (V V T ). The intake manifold and exhaust emissions models are proprietary Toyota models, whereas standard fuel injection and rotational dynamics models from [11] are used, and the form of the catalyst model is based on [12]. 2) Driveline Submodel: The driveline submodel includes a standard K-factor model for the hydraulic torque converter, cascaded with an automatic transmission, cascaded with spring-damper driveline dynamics, which are a function of ω turb, ω tire, θ turb, and θ tire. Fig. 1. Main diagram of the model components and interconnections between the engine, driveline, and vehicle models. 3) Vehicle Submodel: The vehicle submodel represents a standard model for longitudinal vehicle dynamics, simply consisting of a rolling resistance and aerodynamics term. B. Performance Criteria - Quantified The performance of the engine/driveline/vehicle system consists of three components, namely drivability, fuel economy, and emissions. Drivability, J d, is characterized by the high-frequency component of vehicle acceleration, which is calculated as follows: J d = a HF (s) = a 2 HF(t)dt, (1) t s.1s + 1 a veh(s). Fuel economy is straightforwardly calculated in terms of the total fuel consumed, normalized by distance traveled, and is given by: t J f = W fuel (t)dt t v veh (t)dt. (2) Finally, emissions is measured as a combination of carbon monoxide, hydrocarbons, and nitric oxide at the tailpipe, and is given by: J e = t (α CO CO(t)+α HC HC(t)+α NO NO(t))dt, (3) where α CO, α HC, and α NO are used to weight the importance of the various emissions components. For this work, we take α CO =.1, α HC = α NO = 1. The three components to performance can be combined into the composite cost function, J total, through the relationship: J total = a f J f + a e J e + a d J d, a f = 1, (4) a e = 1, a d = 1, These three performance components, J d, J f, and J e, will serve as the basis for our optimization, though the components themselves will be modified slightly in order to fit in the framework. C. Overall Control Structure The overall closed loop system is shown in Fig. 2, whereas the specifics of the powertrain controller are shown in Fig. 3. Static maps are used for the electronic pedal control and transmission controller, which choose Teng des and GR, 146

3 respectively. The model predictive engine torque controller uses available engine measurements in order to optimize φ des, Wair des, V V T cmd, and δ. Inner loop controllers are designed to realize φ des and W des air. Fig. 2. Overall closed-loop system diagram, illustrating the interactions between the driver, powertrain controller, and plant. where MAF represents the intake mass air flow sensor measurement, and controller gains are determined semiheuristically in order to approximately match the closed loop air/fuel ratio control behavior to the reference model, F φ (s). C. Air Flow Control Air flow control uses gain scheduled model reference control in order to design a controller of the form: θ(s) = C 1 W des air (s) + C 2 Ŵ air (s), (7) where Ŵair(s) is the estimated cylinder air flow, using a nonlinear model of the intake manifold with the MAF sensor measurement. C 1 (s) and C 2 (s) are determined using single-input/single-output (SISO) model reference control [13], based on a linearized intake manifold model given by: W air (s) = a 1 ms + a m b 2 ms 2 + b 1 θ(s), (8) ms + 1 where V V T is taken as constant for the linearization. D. Formulation The torque controller consists of three main components, namely a state observer, torque converter model (for approximating pump torque), and the optimization itself. Fig. 3. Overall powertrain control structure. III. CONTROL DESIGN This section details the control design of both the optimization and the inner loop controllers for throttle control and air/fuel ratio control. A. Reference Model Selection Reference models, F φ (s) and F air (s), which represent target closed loop behavior from φ des to φ and Wair des to W air, respectively, are agreed upon at the outset of the design process. The optimization assumes that these target behaviors are met, replacing the complex air and fuel dynamics with their respective reference models. Considering that the fuel and air dynamics are on the order of.1.2 seconds, and in an attempt to synchronize the dynamics associated with air-fuel ratio control and throttle control, we choose the following reference model: 1 F φ (s) = F air (s) =.1s + 1, () for both air/fuel ratio control and throttle control. B. Air/Fuel Ratio Control Air/fuel ratio control is performed by means of a feedforward scheme and a feed-back (PI) control for steady state error correction. The overall controller is given as: IPW(s) = G ff (s)maf(s)+ Kφ p s + K φ i s (φ des (s) φ(s)), (6) Fig. 4. Model predictive control structure. An estimate of the engine states, ˆx eng (k), which is required for the optimization, is provided by a nonlinear observer with a linear correction term, specifically: ˆx eng (k+1) = f(ˆx eng (k), u eng (k))+l(y eng (k) ŷ eng (k)), (9) where f(x eng (k), u eng (k)) represents the nonlinear dynamic model of the engine, u(k) represents the outputs of the optimization, and y eng (k) represent the measurable engine outputs. Specifically, u, y eng, and x eng are given by: u(k) = [ φ des (k) W des air (k) V V T cmd (k) δ(k) ] T, y eng (k) = [ ω eng (k) MAF(k) φ(k) φ tp (k) ] T, x eng = [ ω eng MAF φ V V T T f ] T, where: T f (s) = 1.1s + 1 T net eng(s), (1) 1461

4 which will be used by the optimization to predict the effect of engine torque on high frequency vehicle acceleration (since the optimization does not see the driveline dynamics). The optimization itself is a minimization of a cost function over a horizon length, N, where the output of the minimization is an optimal control trajectory, u o (k): u o (k) = arg min J(x eng (k), u(k)), k+n 1 g(x eng (i k), u(i k)) = ā t (T eng (i k) T des eng(k)) 2 where g f,e,d represent the contributions of fuel economy, emissions, and drivability to the cost. The notation (i k) represents the value of a variable at step i as predicted (or, in the case of u, optimized) at step k. The set U characterizes the limits on φ des, Wair des, V V T cmd, and δ. Upon completion of one instance of the optimization, the first control input of u o (k) is implemented, namely: u(k) = u o (k k), (11) and the optimization is repeated at the next step (k + 1). The expressions for g f,e are given by: where: g f (x eng (k + N k)) = m fuel(i k) θ eng (i k), (12) g e (x eng (i k), u(i k)) = W air (i k)(φ(i k) 1) 2,(13) m fuel (k + N k) = θ eng (k + N k) = k+n 1 i=k k+n 1 i=k W fuel (i k) T, (14) ω eng (i k) T. () The fuel economy penalty (12) represents an approximation of (2) using engine variables. The form of the emissions penalty (penalizing deviation from stoichiometry instead of penalizing CO, HC, and NO directly) simplifies the optimization significantly, recognizing that φ = 1 represents the optimal air/fuel setting for emissions due to high conversion efficiency of all species at this operating condition. Because the expression for drivability in (1) is based on high frequency acceleration, a HF, which is not available at the engine level, this drivability metric is approximated using the high frequency component of engine torque (T eng ) as follows: g d (x eng (i k), u(i k)) = (T eng (i k) T f (i k)) 2 γ 1 + γ 2 + (ln(( ωeng(i k) ω turb (i k) )n )), 2 n = 4, γ 1,2 = 1. (16) J(x eng (k), u(k)) = g(x eng (i k), u(i k)) i=k The second term captures the fact that when engine and +ā f g f (x eng (i + N k)), turbine speeds are equal, this results in a flow reversal within the torque converter and leads to significant drivabilityrelated problems. subject to: u(i k) U, i For this application, the update rate is taken as 2 where: Hz (a step time of. seconds). The horizon length for the u(k) = [ u(k k)... u(k + N 1 k) ] T optimization is chosen to be 1 second (2 steps), which is reflective of several times the time constants of the engine subsystem. The online optimization used in this paper +ā e g e (x eng (i k), u(i k)) relies on the computation of the sensitivity function, as in +ā d g d (x eng (i k), u(i k)) [14], which captures the sensitivity of the cost function to the control inputs and iteratively follows two steps: ā t = 1 ā f = 1 1) Calculation of J(xeng(k),u(k)) u(k) u sc(k) u ; sc(k) 2) A one-dimensional search along this direction; ā e = 1 Here, u sc represents a scaling of u by the ranges of each ā d =. control input IV. SIMULATION RESULTS In this section, we evaluate the performance of the model predictive torque controller in two different test scenarios, namely: 1) A tip-in/tip-out test case where the pedal position incurs step inputs between degrees and a fixed value; 2) A driver-in-the-loop test case where a real driver attempts to track part of a federal test procedure (FTP) setpoint trace. In order to provide some benchmarking of our controller s performance, we consider the following baseline controller: θ = θ pedal, { } 1, θ 4 φ des = θ 4, o.w., (17) δ = δ = δ MBT, V V T cmd = V V T (ω eng, θ). Here, the driver s pedal input is directly mapped to the throttle angle and φ des = 1 except in instances when θ pedal is close to zero, where fuel is cut off in a heuristic manner. Spark advance (δ) is taken as maximum brake torque spark advance (δ MBT ). V V T is determined from a base engine map for this particular engine and vehicle. A. Tip-in/Tip-out Tests Our first set of tests involves the driver letting off and then reapplying the accelerator pedal, which are referred to as tipout and tip-in, respectively. Figs. -7 show the vehicle speed

5 trace, quantitative performance (related to torque tracking, drivability, fuel economy, and emissions), and control inputs, respectively. These figures demonstrate that model predictive torque control does indeed do a better job than the baseline of simultaneously managing fuel economy, emissions, and drivability. Also noteworthy is the fact that fuel cut occurs as a consequence of the optimization, without requiring any additional heuristic rules which are typically incorporated in order to achieve fuel cutoff during tip-out events. Table II gives the raw values of J f, J e, and J d over the course of the simulation, as well as the total, J total, demonstrating quantitatively that the model predictive torque controller outperforms the baseline. Throttle Angle (degrees) Spark Advance (degrees) Inj. Pulse Width ( µ s) Variable Valve Timing (degress) Fig. 7. Control signals for the tip-in/tip-out tests. TABLE II 3 TIP-IN/TIP-OUT PERFORMANCE Vehicle Speed (m/s) Metric J f J e J d J total Torque Tracking Error (N m) Fig Cumulative Fuel Consumption (g) Fig. 6. Vehicle speed trace for tip-in/tip-out tests. Cumulative Emissions (g) Cumulative Drivability Performance (m/s) 1 CO/1 1 HC NO.12 CO/1 HC.1 NO Performance variables for the tip-in/tip-out tests. A target PC, which contains a 2.8GHz Xeon processor and executes compiled C-code from Real Time Workshop TM ; A Quanser Q4 rapid prototyping card, which interprets the driver s pedal input. The target PC, where the optimization takes place, provides the computational capability for our optimization to be executed in no more than.3 seconds (which is below the update time of.s). The FTP tests with the driver in the loop were done using a 1 second speed setpoint trace composed by different sections of an FTP cycle, which examines the entire speed range of the vehicle and requires the vehicle to shift through all four gears. Results are shown in Figs. 8-1, and in Table III. The results show that the model predictive torque control outperforms the baseline controller with regard to all three performance metrics. V. CONCLUSIONS AND FUTURE WORK In this paper, we presented a novel model predictive torque controller that simultaneously considers fuel economy, B. Federal Test Procedure - Driver in the Loop A federal test procedure (FTP) cycle was attempted with a driver in the loop, where the controller and model were running in real time, using MATLAB s xpc Target TM software. The experimental setup included: A driver seat and pedal assembly; A host PC, wherein the main Simulink model lies; TABLE III FTP PERFORMANCE - DRIVER IN THE LOOP Metric J f J e J d 7 76 J total

6 Vehicle Speed (m/s) Setpoint Throttle Angle (degrees) Spark Advance (degrees) Inj. Pulse Width ( µ s) Variable Valve Timing (degress) Fig. 8. Speed traces for an FTP cycle with a driver in the loop. Fig. 1. Control signals for an FTP cycle with a driver in the loop. Torque Tracking Error (N m) Cumulative Fuel Consumption (g) Fig Cumulative Drivability Performance (m/s) Cumulative Emissions (g) CO/1 HC NO CO/1 HC NO Performance variables for an FTP cycle with a driver in the loop. drivability, and emissions in its optimization. We demonstrated through two different types of simulations that this controller outperforms the baseline control strategy. Because the real-time simulations were run on a relatively fast PC, rather than an engine ECU or rapid prototyping system, future work will include computational benchmarking that will quantify the gaps between our current capabilities and the requirements for experimentally validating the proposed torque control strategy. Additional future work will include the incorporation of temperature constraints into the optimization, in addition to refining our approximation of the drivability metric within the cost function. [3] D. Hrovat, J. Sun, Models and Control Methodologies for IC Engine Idle Speed Control Design, Control Engineering Practice, pp , [4] A. Stefanopoulou, I. Kolmanovsky, J. Freudenberg, Control of Variable Geometry Turbocharged Diesel Engines for Reduced Emissions, IEEE Transactions on Control Systems Technology, pp , 2. [] N. Giorgetti, G. Ripaccioli, A. Bemporad, I. Kolmanovsky, D. Hrovat, Hybrid Model Predictive Control of Direct Injection Stratified Charge Engines, IEEE/ASME Transactions on Mechatronics, Vol. 11, 26. [6] B. Saerens, M. Diehl, J. Swevers, E. Van den Bulck, Model Predictive Control of Automotive Powertrains - First Experimental Results, Proceedings of the IEEE Conference on Decision and Control, Cancun, MX, 28. [7] C. Lin, H. Peng, J. Grizzle, A Stochastic Control Strategy for Hybrid Electric Vehicles, Proceedings of the American Control Conference, Boston, MA, 24. [8] D. Opila, D. Aswani, R. McGee, J. Cook, J. Grizzle, Incorporating Drivability Metrics into Optimal Energy Management Strategies for Hybrid Vehicles, Proceedings of the IEEE Conference on Decision and Control, Cancun, MX, 28. [9] D. Opila, X. Wang, R. McGee, J. Cook, J. Grizzle, Performance Comparison of Hybrid Vehicle Energy Management Controllers on Real-World Drive Cycle Data, Proceedings of the American Control Conference, St. Louis, MO, 29. [1] C. Vermillion, J. Sun, K. Butts, Model Predictive Control Allocation - Design and Experimental Results on a Thermal Management System, Proceedings of the American Control Conference, St. Louis, MO, 29. [11] L. Guzzella, C. Onder, Introduction to Modeling and Control of Internal Combustion Engine Systems, Springer, 24. [12] E. Brandt, Dynamic Modeling of Three-way Catalyst for Advanced Emissions Control Systems, Ph.D. Dissertation, University of Michigan, [13] P. Ioannou, J. Sun, Robust Adaptive Control, Prentice Hall, [14] G. Seenumani, J. Sun, H. Peng, A Numerically Efficient Iterative Procedure for Hybrid Power System Optimization Using Sensitivity Functions, Proceedings of the American Control Conference, 27. REFERENCES [1] K. Butts, N. Sivashankar, J. Sun, Application of l 1 Optimal Control to the Engine Idle Speed Control Problem, IEEE Transactions on Control Systems Technology, pp , [2] S. Di Cairano, D. Yanakiev, A. Bemporad, I. Kolmanovsky, D. Hrovat, An Design Flow for Automotive Control Applications to Idle Speed Regulation, Proceedings of the IEEE Conference on Decision and Control, Cancun, MX,