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Adaptive Model Predictive Fault-Tolerant Control for Four-Wheel Independent Steering Vehicles with Sensitivity Estimation

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Abstract

This paper presents an adaptive model predictive fault-tolerant control (FTC) algorithm based on sensitivity estimation and exponential forgetting-based recursive least squares (RLS) for four-wheel independent steering vehicles. The model predictive control algorithm was designed according to physical constraints for four-wheel independent steering control with adaptive integral action. To improve the control performance in transient and steady-state regions, sensitivity-based adaptive rules for the weighting factor of the model predictive controller and integral gain were developed using the gradient descent method. The sensitivity was defined by a virtual relationship function and was estimated using RLS with a forgetting factor. Additionally, a FTC strategy with the equality constraint was proposed for enhancing the yaw-rate tracking control performance despite the existence of faults in the steering system. The proposed fault-tolerant steering control algorithm was developed in a MATLAB/Simulink environment, and its performance was evaluated via co-simulation in the MATLAB/Simulink and CarMaker software programs under various evaluation scenarios.

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Abbreviations

\(\dot{\psi}\) :

yaw rate, rad/s

\(\dot{\psi}_{\text{desired}}\) :

desired yaw rate, rad/s

m :

vehicle mass, kg

l f :

distance between mass center and front axle, m

l r :

distance between mass center and rear axle, m

l r :

distance between mass center and rear axle, m

l r :

distance between mass center and rear axle, m

I z :

rotational inertia of z-axis, kgm2

F x,i :

longitudinal force, N

C:

cornering stiffness, N/rad

F y,i :

lateral force, N

t w :

track tread, m

\(e_{\dot{\psi}}\) :

yaw-rate error, rad/s

δ :

wheel angle, rad

δ dri :

driver wheel input, rad

Δδ c :

controlled input, rad

Δδ opt :

MPC controlled input, rad

Δδ int :

integral controlled input, rad

δ total :

total wheel angle, rad

C int/C r :

estimated coefficient for integral/weighting factor

γ int / γ r :

adaptation gain for integral/weighting factor

ε int / ε r :

stability factor for integral/weighting factor

v x/v y/v z :

longitudinal/lateral/vertical velocity

A/A d/A e :

system matrix

B/B d/B e :

input matrix

F e :

disturbance matrix

w :

disturbance

x/x d/x e/x des :

state matrix

x, y, z :

longitudinal, lateral, and vertical

1, 2, 3, 4:

front-left, front-right, rear-left, and rear-right

ns :

neutral-state

des :

desired

d :

discretized

e,d :

discretized error

in :

inequality constraint

eq :

equality constraint

opt :

optimal control input

c :

controlled input

References

  • Acbi, B., El Najjar, M. E. B. and Cocquempot, V. (2019). Sensor and actuator fault diagnosis for a multi-robot system based on the Kullback-Leibler Divergence. 4th Conf. Control and Fault Tolerant System (SysTol), Casablanca, Morocco.

  • Adetola, V., DeHaan, D. and Guay, M. (2009). Adaptive model predictive control for constrained nonlinear systems. Systems and Control Letters 58, 5, 320–326.

    Article  MathSciNet  MATH  Google Scholar 

  • Akapan, V. A. and Hassapis, G. D. (2011). Nonlinear model identification and adaptive model predictive control using neural networks. ISA Trans. 50, 2, 177–194.

    Article  Google Scholar 

  • Chen, L., Li, X., Xiao, W., Li, P. and Zhou, Q. (2019a). Fault-tolerant control for uncertain vehicle active steering systems with time-delay and actuator fault. Int. J. Control, Automation and Systems 17, 9, 2234–2241.

    Article  Google Scholar 

  • Chen, T., Chen, L., Xu, X., Cai, Y. and Sun, X. (2019b). Simultaneous path following and lateral stability control of 4WD-4WS autonomous electric vehicles with actuator saturation. Advances in Engineering Software 128, 6, 46–54.

    Article  Google Scholar 

  • Gao, Z., Yang, L., Wang, H. and Li, X. (2017). Active fault tolerant control of elective power steering system with sensor fault. 36th Chinese Control Conf. (CCC), Da lian, China.

  • Hang, P., Chen, X., Fang, S. and Luo, F. (2017). Robust control for four-wheel-independent-steering electric vehicle with steer-by-wire system. Int. J. Automotive Technology 18, 5, 785–797.

    Article  Google Scholar 

  • He, L., Chen, G. Y. and Zheng, H. Y. (2015). Fault tolerant control method of dual steering actuator motors for steer-by-wire system. Int. J. Automotive Technology 16, 6, 977–987.

    Article  Google Scholar 

  • Heirung, T. A. N., Ydsite, B. E. and Foss, B. (2017). Dual adaptive model predictive control. Automatica 80, 6, 340–348.

    Article  MathSciNet  MATH  Google Scholar 

  • Hiraoka, T., Nishihara, O. and Kumamoto, H. (2004). Model-following sliding mode control for active four-wheel steering vehicle. Review of Automotive Engineering 25, 1, 305–313.

    Google Scholar 

  • Ishak, M. I., Ogino, H. and Yamamoto, Y. (2016). Improvement of mobility for in-wheel small electric vehicle with integrated four wheel drive and independent steering: A numerical simulation analysis. Int. J. Multidisciplinary and Current Research 4, 1, 308–316.

    Google Scholar 

  • ISO 3888-2 (2011). Passenger cars - Test track for a severe lane-change manoeuvre-Part 2: Obstacle avoidance.

  • Jeon, N. and Lee, H. (2016). Integrated fault diagnosis algorithm for motor sensor of in-wheel independent drive electric vehicles. Sensors 16, 12, 2106.

    Article  Google Scholar 

  • Jiang, D., Danhua, L. and Wang, S. (2015). Additional yaw moment control of a 4WIS and 4WID Agricultural data acquisition vehicle. Int. J. Advanced Robotics Systems 12, 6, 78.

    Article  Google Scholar 

  • Jing, H., Wang, R., Chadli, M., Hu, C., Yan, F. and Li, C. (2015). Fault-tolerant control of four-wheel independently actuated electric vehicles with active steering systems. IFAC-PapersOnLine 48, 21, 1165–1172.

    Article  Google Scholar 

  • Kohler, J., Andina, E., Soloperto, R., Muller, M. A. and Allgower, F. (2019). Linear robust adaptive model predictive control: Computational complexity and conservatism. IEEE 58th Conf. Decision and Control (CDC), Nice, France.

  • Kommuri, S. K., Defoort, M., Karimi, H. R. and Veluvolu, K. C. (2016). A robust observer-based sensor fault-tolerant control for PMSM in electric vehicles. IEEE Trans. Industrial Electonic 63, 12, 7671–7681.

    Article  Google Scholar 

  • Li, B., Du, H. and Li, W. (2016). Fault-tolerant control of electric vehicles with in-wheel motors using actuator-grouping sliding mode controllers. Mechanical Systems and Signal Processing 72–73, 5, 462–485.

    Article  Google Scholar 

  • Lin, F., Chen, Y., Zhao, Y. and Wang, S. (2019). Path tracking of autonomous vehicle based on adaptive model predictive model predictive control. Int. J. Advanced Robotic Systems 16, 5, 1–12.

    Article  Google Scholar 

  • Lu, S. B., Lim, C. W. and He, Y. B. (2014). Steering-based fault-tolerant control for the braking failures of an independent driving electric vehicle. Proc. Institution of Mechanical Engineers 228, 9, 1017–1033.

    Article  Google Scholar 

  • Maeder, U. and Morari, M. (2010). Offset-free reference tracking with model predictive control. Automatica 46, 9, 1469–1476.

    Article  MathSciNet  MATH  Google Scholar 

  • Mayne, D., Rawlings, J., Rao, C. and Scokaert, P. (2000). Constrained model predictive control: Stability and optimality. Automatica 36, 2, 789–814.

    Article  MathSciNet  MATH  Google Scholar 

  • Meadows, E. and Badgwell, T. (1998). Feedback through steady-state target optimization for nonlinear model predictive control. J. Vibration and Control, 4, 61–74.

    Article  Google Scholar 

  • Muske, K. and Rawlings, J. (1993). Model predictive control with linear models. AIChE J. 39, 2, 262–287.

    Article  Google Scholar 

  • Pannocchia, G. and Kerrigan, E. (2003). Offset-free control of constrained linear discrete-time systems subject to persistent unmeasured disturbances. 42nd IEEE Conf. Decision and Control (CDC), Maui, Hawaii, USA.

  • Pannocchia, G. and Rawlings, J. (2003). Disturbance models for offset-free model predictive control. AIChE J. 49, 2, 426–437.

    Article  Google Scholar 

  • Ruscio, D. (2013). Model predictive control with integral action: A simple MPC algorithm. Modeling, Identification and Control 34, 3, 119–129.

    Article  Google Scholar 

  • Tan, L., Shuyou, Y., Guo, Y. and Chen, H. (2017). Sliding-mode control of four wheel steering systems. IEEE Int. Conf. Mechatronics and Automation (ICMA), Takamatsu, Japan.

  • Tan, Q., Dai, P., Zhang, Z. and Katupitiya, J. (2018). MPC and PSO based control methodology for path tracking of 4WS4WD vehicles. Applied Science 8, 6, 1–24.

    Article  Google Scholar 

  • Wang, L., Liu, X., Wang, X., Fu, B. and Xu, R. (2019). Research on differential performance of four-wheel independent steering of a hydraulic wheel-driving off-road vehicle. The J. Engineering 13, 1, 68–73.

    Article  Google Scholar 

  • Yang, H., Cocquempot, V. and Jiang, B. (2009). Optimal fault-tolerant path-tracking control for 4WS4WD electric vehicles. IEEE Trans. Intelligent Transportation Systems 11, 1, 237–243.

    Article  Google Scholar 

  • Zhang, Z., Zhang, X., Pan, H., Salman, W., Rasim, Y., Liu, X., Wnag, C., Yang, Y. and Li, X. (2017). A novel steering system for a space-saving 4WS4WD electric vehicle: Design, modeling, and road tests. IEEE Trans. Intelligent Transportation Systems 18, 1, 114–127.

    Article  Google Scholar 

  • Zong, C., Liu, C., Zheng, H. and Liu, J. (2013). Fault tolerant control against actuator failures of 4WID/4WIS electric vehicle. SAE Paper No. 2013-01-0405.

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Acknowledgement

This work was supported by a research grant from Hyundai Motor Group.

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Authors and Affiliations

  1. School of ICT, Robotics & Mechanical Engineering, Hankyong National University, Anseong, 17579, Korea

    Se Chan Oh, Tae Jun Song & Kwang Seok Oh

  2. Institute of Advanced Technology Development, Hyundai Motor Company, 150, Hyundaiyeonguso-ro, Namyang-eup, Hwaseong-si, Gyeonggi, 18280, Korea

    Min Jun Kim

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  1. Se Chan Oh
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Correspondence to Kwang Seok Oh.

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Oh, S.C., Song, T.J., Kim, M.J. et al. Adaptive Model Predictive Fault-Tolerant Control for Four-Wheel Independent Steering Vehicles with Sensitivity Estimation. Int.J Automot. Technol. 24, 829–850 (2023). https://doi.org/10.1007/s12239-023-0068-8

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  • DOI: https://doi.org/10.1007/s12239-023-0068-8

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