Nonlinear fuzzy MPC control for vehicles under extreme conditions
SUN Chuanbin1,2, DENG Shuchao1, YIN Guodong2
1.School of Mechanical Engineering, Anhui University of Technology, Ma’anshan 243032, China;
2.School of Mechanical Engineering, Southeast University, Nanjing 211189, China
摘要针对应急转向下车辆的横摆稳定性和侧倾稳定性，研究前轮主动转向（AFS）和直接横摆力矩（DYC）的非线性模型预测MPC集成控制。考虑轮胎侧偏刚度非线性变化，采用Takagi-Sugeon方法（T-S）建立4个车辆横摆-侧倾线性子系统，结合模糊观测器实时获取轮胎动态参数。为消除侧倾稳定性能约束，在T-S框架下建立改进横摆理想参考模型，引入侧倾稳定指标约束期望横摆角速度。根据横摆角速度、质心侧偏角、侧倾姿态的跟踪偏差和控制输入建立二次型评价函数，以驾驶员转向扰动为评价函数附加项，构建无限预测时域MPC最优性能指标，基于分布补偿方法设计非线性系统的模糊控制器MPC-TS，并根据轮胎侧偏特性设计自适应主动转向约束。通过LMIs方法将无限时域的非线性MPC控制转化凸优化过程，推导子系统转向扰动最小值问题的线性不等式。最后联合Trucksim-Simulink软件进行仿真测试，以Sine with Dwell和Fishhook曲线为驾驶员输入模拟应急转向过程，结果表明：在驾驶员应急转向的强非线性过程，MPC-TS方法能够显著增强横摆稳定性和侧倾稳定性，并适应低附和高附着路面。
Abstract：Aiming at yaw stability and roll stability of vehicle under emergency steering, nonlinear model predictive (MPC) integrated control of active front wheel steering (AFS) and direct yaw moment (DYC) was studied. Considering nonlinear variation of vehicle lateral stiffness, four linear yaw- roll subsystems of vehicle were established with Takagi-Sugeon theory (T-S), and dynamic parameters of tire were obtained with fuzzy observer in real time. In order to eliminate yaw stability constraint, an improved yaw ideal reference model was established under T-S framework, and a yaw stability index was introduced to constrain ideal yaw motion. Building optimal target in infinite prediction time domain with quadratic evaluation function of tracking deviation for yaw angular velocity, side-slip Angle, as roll motion and control input, model predictive fuzzy controller (MPC-TS) was designed based on distributed compensation scheme, with driver steering inputs as disturbance, and adaptive active steering constraints according to cornering characteristics. The nonlinear MPC control in infinite time domain was transformed into a convex optimization process with LMIS, and linear inequality of minimum value problem was derived under steering disturbance. Finally, simulation test was carried out with Trucksim-Simulink software, with Sine with Dwell curve and Fishhook curve as driver inputs to simulate emergency steering. Results show that despite in strongly nonlinear process under emergency steering disturbance, MPC-TS controller enhances yaw - roll stability of vehicle on both low adhesion and high adhesion road friction.
孙船斌1,2，邓书朝1，殷国栋2. 极限工况车辆非线性模糊MPC控制[J]. 振动与冲击, 2023, 42(13): 25-35.
SUN Chuanbin1,2, DENG Shuchao1, YIN Guodong2. Nonlinear fuzzy MPC control for vehicles under extreme conditions. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(13): 25-35.
[1]Ayers P, Khorsandi F. Reducing tractor rollover fatalities[J]. Resource Engineering & Technology for Sustainable World, 2017,24 (6): 6-7.
[2]Jing H, Wang R, Wang J, Chen N. Robust H∞ dynamic output-feedback control for four-wheel independently actuated electric ground vehicles through integrated AFS/DYC[J]. J Franklin Inst B, 2018,355 (18): 21-50.
[3]Zhongchao Liang, Jing Zhao, Zhen Dong, Yongfu Wang, Zhengtao Ding, Torque Vectoring and Rear-Wheel-Steering Control for Vehicle’s Uncertain Slips on Soft and Slope Terrain Using Sliding Mode Algorithm[J]. IEEE Trans. Veh. Technol, 2020, 69 (4): 3805-3815
[4]Zhang J, Li J. Integrated vehicle chassis control for active front steering and direct yaw moment control based on hierarchical structure[J]. Trans Inst Meas Control, 2019, 41 (9): 28-40.
[5]C. Zhou, X.H. Liu, Optimal sliding mode control for an active suspension system based on a genetic algorithm[J], Algorithms, 2018,11 (12):16-20.
[6]Termous H, Shraim H, Talj R, Francis C, Charara A. Coordinated control strategies for active steering, differential braking and active suspension for vehicle stability, handling and safety improvement[J]. Veh Syst Dyn, 2019, 57 (10): 1494-529.
[7]金辉,李世杰.基于极限车速的车辆稳定性控制研究[J].汽车工程,2018,40(1):48-56.
Jin Hui, Li Shijie. A Research on Vehicle Stability Control Based on Limited Speed[J]. Automotive Engineering, 2018, 40 (1): 48-56.
[8]李绍松,郭孔辉,仇韬, 等.极限工况下主动前轮转向汽车稳定性控制[J].汽车工程,2020,42(2):191-198.
Li Shaosong, Guo Konghui, Qiu Tao, et al. Stability Control of Vehicle with Active Front Steering Under Extreme Conditions[J]. Automotive Engineering, 2020, 42(2): 191-198.
[9]李道飞,喻凡. 基于最优轮胎力分配的车辆动力学集成控制[J]. 上海交通大学学报,2008,42(6):887-891.
Li Daofei; Yu Fan. Integrated Vehicle Dynamics Controller Design Based on Optimum Tire Force Distribution [J]. Journal of shanghai jiaotong university, 2008, 42 (6):887-891.
[10]赵强,孙柱. 基于卡尔曼滤波的车辆液压主动横向稳定杆最优控制研究[J]. 重庆交通大学学报（自然科学版）, 2020,39(11):128-135.
Zhao Qiang, Sun Zhu. Optimal Control of Hydraulic Active Lateral Stabilizer of Vehicle Based on Kalman Filter[J]. Journal of Chongqing Jiaotong University(Natural Sciences) ,2020, 39 (11) : 128-135.
[11]殷国栋,陈南. 4WS车辆μ综合鲁棒主动侧倾操纵性能控制[J]. 东南大学学报（自然科学版）, 2006,36(3): 384-388.
Yin Guodong, Chen Nan. Active roll μ synthesis robust control for 4WS vehicle steering performance[J]. Journal of Southeast University, 2006, 36(3): 384-388.
[12]李玉善,迟元欣,季学武,等. 基于Pareto最优均衡理论的商用车路径跟踪与抗侧倾协同控制研究[J]. 汽车工程, 2019, 41(6): 654-661, 687.
Li Yushan, Chi, Yuanxin, Ji, XuewuLiu et al. A Research on Cooperative Path Tracking and Anti-roll Control of Commercial Vehicle Based on Pareto Optimal Equilibrium Theory[J]. Automotive Engineering, 2019, 41 (6): 654-661, 687.
[13]周兵,颜丙超,吕绪宁. 基于主动横向稳定杆和 AFS 的车辆稳定性协调控制[J]. 振动与冲击,2015(18):111-117.
Zhou Bing, Yan Bing-chao, Lv Xuning. Coordinated control of vehicle yaw and roll stability based on ARS and AFS[J]. Journal of Vibration and Shock, 2015(18): 111-117.
[14]Xinbo Ma, Pak Kin Wong, Jing Zhao, Zhengchao Xie. Cornering stability control for vehicles with active front steering system using T-S fuzzy based sliding mode control strategy[J]. Mechanical Systems and Signal Processing, 2019,125: 347-364.
[15]W. Zhao, Y. Lin, J. Wei, G. Shi, Control strategy of a novel electric power steering system integrated with active front steering function[J]. Sci. China Technol. Sci, 2011, 54: 1515-1520.
[16]Z.A. Kadir, S.A. Mazlan, H. Zamzuri, K. Hudha, N.H. Amer. Adaptive fuzzy-PI control for active front steering system of armoured vehicles: outer loop control design for firing on the move system[J]. Strojniski Vestnik-J. Mech. Eng, 2015, 61: 187-195.
[17]Ataei M, Khajepour A, Jeon S. Model predictive control for integrated lateral stability, traction/braking control, and rollover prevention of electric vehicles[J]. Veh Syst Dyn, 2020;58(1): 49-73.
[18]周红标,张钰,柏小颖,等. 基于自适应模糊神经网络的非线性系统模型预测控制[J]. 化工学报,2020,71(7):3201-3212.
Zhou Hongbiao, Zhang Yu, Bao Xiaoying, et al. Model predictive control of nonlinear system based on adaptive fuzzy neural network[J]. CIESC Jorunal,2020,71(7):3201-3212.
[19]辛喆,陈海亮,林子钰,等. 智能汽车的路面附着极限横向轨迹跟踪控制[J]. 机械工程学报, 2020, 56(14): 138-145.
Xin Zhe, Chen Hailiang, Lin Ziyu, et al. Lateral Trajectory Following for Automated Vehicles at Handling Limits[J]. Journal of Mechanical Engineering, 2020, 56(14): 138-145.
[20]Li Shengbo, Jia Zhenzhong, Li Keqiang, et al. Fast online computation of a model predictive controller and its application to fuel economy：Oriented adaptive cruise control[J]. IEEE Transactions on Intelligent Transportation System, 2015, 16(3): 1199-1209.
[21]郭孔辉,丁海涛.轮胎附着极限下差动制动对汽车横摆力矩的影响[J].汽车工程, 2002, 24(2): 101-104.
Guo Konghui, Ding Haitao. The Effect of Yaw Moment through Differential Braking under Tire Adhesion Limit[J]. Automotive Engineering, 2002, 24(2): 101-104.
[22]孙船斌，方琳，童宝宏 等.基于T-S模型的载货车辆动态参数滑模控制[J]. 振动与冲击, 2021, 40 (12): 254-264.
Sun Chuanbin, Fanglin, Tong Baohong, et al. Dynamic parameter sliding mode control of truck based on a T-S model[J]. Journal of vibration and shock, 2021, 40(12): 254-264.
[23]Wang L X, Mendel J M. Fuzzy Basis Functions, Universal Approximation, and Orthogonal Least Squares Learning[J]. IEEE Translations on Neural Networks, 1992, 3(5): 807-814.
[24]Fredrik Bruzelius. A theoretical justification of the sine with dwell manoeuvre[J]. Vehicle System Dynamics, 2015, 53(4), 493-505.
[25]魏振亚,王其东,王慧然,等. 基于主动转向与差动制动协调的双级预警车道偏离防止预测控制[J]. 汽车工程,2019, 41(8): 934-943,952.
Wei Zhenya, Wang Qidong, Wang Huiran, et al. Predictive Control for Lane Departure Prevention with Two-stage Warning Based on Coordination of Active Steering and Differential Braking[J]. Automotive Engineering, 2019, 41(8): 934-943, 952.
