Research Papers

Handling Delays in Yaw Rate Control of Electric Vehicles Using Model Predictive Control With Experimental Verification

[+] Author and Article Information
Milad Jalali

Mechanical Engineering Department,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: mjalaliy@uwaterloo.ca

Amir Khajepour

Mechanical Engineering Department,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada

Shih-ken Chen, Bakhtiar Litkouhi

Global Research and Development Center,
General Motors Company,
Warren, MI 48090-9055

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 4, 2015; final manuscript received June 20, 2017; published online August 9, 2017. Assoc. Editor: Azim Eskandarian.

J. Dyn. Sys., Meas., Control 139(12), 121001 (Aug 09, 2017) (8 pages) Paper No: DS-15-1420; doi: 10.1115/1.4037166 History: Received September 04, 2015; Revised June 20, 2017

In this paper, a new approach is proposed to deal with the delay in vehicle stability control using model predictive control (MPC). The vehicle considered here is a rear-wheel drive electric (RWD) vehicle. The yaw rate response of the vehicle is modified by means of torque vectoring so that it tracks the desired yaw rate. Presence of delays in a control loop can severely degrade controller performance and even cause instability. The common approaches for handling delays are often complex in design and tuning or require an increase in the dimensions of the controller. The proposed method is easy to implement and does not entail complex design or tuning process. Moreover, it does not increase the complexity of the controller; therefore, the amount of online computation is not appreciably affected. The effectiveness of the proposed method is verified by means of carsim/simulink simulations as well as experiments with a rear-wheel drive electric sport utility vehicle (SUV). The simulation results indicate that the proposed method can significantly reduce the adverse effect of the delays in the control loop. Experimental tests with the same vehicle also point to the effectiveness of this technique. Although this method is applied to a vehicle stability control, it is not specific to a certain class of problems and can be easily applied to a wide range of model predictive control problems with known delays.

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Borrelli, F. , Falcone, P. , Keviczky, T. , and Asgari, J. , 2005, “ MPC-Based Approach to Active Steering for Autonomous Vehicle Systems,” Int. J. Veh. Auton. Syst., 3(2), pp. 265–291. [CrossRef]
Palmieri, G. , Barbarisi, O. , Scala, S. , and Glielmo, L. , 2009, “ A Preliminary Study to Integrate LTV-MPC Lateral Vehicle Dynamics Control With a Slip Control,” 48th IEEE Conference on Decision and Control (CDC), Shanghai, China, Dec. 15–18, pp. 4625–4630.
Jalaliyazdi, M. , Khajepour, A. , Kasaeizadeh, A. , Litkouhi, B. , and Chen, S.-K. , 2014, “ Control of Electric Vehicles Using a Model Predictive Controller With Closed Form Solution,” ASME Paper No. IMECE2014-38316.
Falcone, P. , Borrelli, F. , Tseng, H. E. , Asgari, J. , and Hrovat, D. , 2008, “ Linear Time-Varying Model Predictive Control and Its Application to Active Steering Systems: Stability Analysis and Experimental Validation,” Int. J. Robust Nonlinear Control, 18(8), pp. 862–875. [CrossRef]
Jalali, M. , Khajepour, A. , Chen, S.-K. , and Litkouhi, B. , 2016, “ Integrated Stability and Traction Control for Electric Vehicles Using Model Predictive Control,” Control Eng. Pract., 54, pp. 256–266. [CrossRef]
Morari, M. , Baotic, M. , and Borrelli, F. , 2003, “ Hybrid Systems Modeling and Control,” Eur. J. Control, 9(2), pp. 177–189. [CrossRef]
Borrelli, F. , Bemporad, A. , and Morari, M. , 2015, “ Predictive Control for Linear and Hybrid Systems,” University of California, Berkeley, CA, accessed Sept. 30, 2016, http://www.mpc.berkeley.edu/mpc-course-material/mpc_book.pdf
Borrelli, F. , Bemporad, A. , Fodor, M. , and Hrovat, D. , 2006, “ An MPC/Hybrid System Approach to Traction Control,” IEEE Trans. Control Syst. Technol., 14(3), pp. 541–552. [CrossRef]
Cortes, P. , Rodriguez, J. , Silva, C. , and Flores, A. , 2012, “ Delay Compensation in Model Predictive Current Control of a Three-Phase Inverter,” IEEE Trans. Ind. Electron., 59(2), pp. 1323–1325. [CrossRef]
Li, Y. , Yin, G. , Jin, X. , Bian, C. , and Li, J. , 2015, “ Impact of Delays for Electric Vehicles With Direct Yaw Moment Control,” ASME J. Dyn. Syst. Meas. Control, 137(12), p. 121005. [CrossRef]
Khosravani, S. , Kasaiezadeh, A. , Khajepour, A. , Fidan, B. , Chen, S. , and Litkouhi, B. , 2014, “ Torque-Vectoring-Based Vehicle Control Robust to Driver Uncertainties,” IEEE Trans. Veh. Technol., 64(8), pp. 3359–3367. [CrossRef]
Yazici, H. , Guclu, R. , Kucukdemiral, I. B. , and Parlakci, M. A. , 2012, “ Robust Delay-Dependent H Control for Uncertain Structural Systems With Actuator Delay,” ASME J. Dyn. Syst. Meas. Control, 134(3), p. 031013. [CrossRef]
Chen, L.-K. , and Ulsoy, A. G. , 2002, “ Design of a Vehicle Steering Assist Controller Using Driver Model Uncertainty,” Int. J. Veh. Auton. Syst., 1(1), pp. 111–132. [CrossRef]
Shuai, Z. , Zhang, H. , Wang, J. , Li, J. , and Ouyang, M. , 2014, “ Combined AFS and DYC Control of Four-Wheel-Independent-Drive Electric Vehicles Over CAN Network With Time-Varying Delays,” IEEE Trans. Veh. Technol., 63(2), pp. 591–602. [CrossRef]
Jalaliyazdi, M. , Khajepour, A. , Chen, S.-K. , and Litkouhi, B. , 2015, “ Handling Delays in Stability Control of Electric Vehicles Using MPC,” SAE Paper No. 2015-01-1598.
Zhu, T. , Khajepour, A. , Goodarzi, A. , Chen, S.-K. , and Litkouhi, B. , 2015, “ Development of an Optimal Driver Command Interpreter for Vehicle Dynamics Control,” Int. J. Veh. Auton. Syst., 13(1), pp. 43–64. [CrossRef]
Rezaeian, A. , Zarringhalam, R. , Fallah, S. , Melek, W. , Khajepour, A. , Chen, S. K. , Moshchuk, N. , and Litkouhi, B. , 2015, “ Novel Tire Force Estimation Strategy for Real-Time Implementation on Vehicle Applications,” IEEE Trans. Veh. Technol., 64(6), pp. 2231–2241. [CrossRef]
Matuttis, H.-G. , and Chen, J. , 2014, Understanding the Discrete Element Method: Simulation of Non-Spherical Particles for Granular and Multi-Body Systems, Wiley, New York. [CrossRef]
Jalaliyazdi, M. , 2016, “ Integrated Vehicle Stability Control and Power Distribution Using Model Predictive Control,” Ph.D. thesis, University of Waterloo, Waterloo, ON, Canada. http://hdl.handle.net/10012/10579
Brach, R. , and Brach, M. , 2011, “ The Tire-Force Ellipse (Friction Ellipse) and Tire Characteristics,” SAE Paper No. 2011-01-0094.
Ferreau, H. , Kirches, C. , Potschka, A. , Bock, H. , and Diehl, M. , 2014, “ qpOASES: A Parametric Active-Set Algorithm for Quadratic Programming,” Math. Program. Comput., 6(4), pp. 327–363. [CrossRef]
Klehmet, U. , Herpel, T. , Hielscher, K.-S. , and German, R. , 2008, “ Delay Bounds for CAN Communication in Automotive Applications,” 14th GI/ITG Conference in Measuring, Modelling and Evaluation of Computer and Communication Systems (MMB), Dortmund, Germany, Mar. 31–Apr. 2, pp. 1–15. http://ieeexplore.ieee.org/document/5755051/
Tang, P. L. , and de Silva, C. W. , 2006, “ Compensation for Transmission Delays in an Ethernet-Based Control Network Using Variable-Horizon Predictive Control,” IEEE Trans. Control Syst. Technol., 14(4), pp. 707–718. [CrossRef]
MATLAB, 2011, “ MATLAB Version (R2011b),” Mathworks, Natick, MA.
Mechanical Simulation Corporation, 2002, “ CarSim User Manual,” Mechanical Simulation Corporation, Ann Arbor, MI, Vol. 48013.


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Fig. 1

Double-track vehicle model used as prediction model

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Fig. 2

Proposed strategy for dealing with pure delays

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Fig. 3

Procedure for finding system state at the end of pure delay period

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Fig. 4

Overall delay is approximated by a pure delay and a first-order delay in series

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Fig. 5

Adding first-order delay in the prediction model. The filter block (currently in position 2) can take one of the positions 1 through 4.

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Fig. 6

Block diagram of the simulated control loop. The delay block shifts the control actions 200 ms in time and applies a first-order delay with time constant of 100 ms.

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Fig. 7

Steering wheel angle in flick maneuver

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Fig. 15

Torque adjustments made by controllers A and B (experiment)

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Fig. 14

Vehicle sideslip angle with controllers A and B (experiment)

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Fig. 13

Yaw rate tracking performance of controllers A and B (experiment)

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Fig. 12

Steering wheel angle and the lateral acceleration of the vehicle in maneuvers with controllers A and B (experiment)

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Fig. 11

Experimental setup for measurement and control of vehicle yaw rate

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Fig. 10

The RWD electric Equinox vehicle used in experimental tests

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Fig. 9

Comparison of the torque adjustments of controller A and B

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Fig. 8

Comparison of yaw rate tracking performance and vehicle sideslip angle with controllers A and B




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