基于T-S模糊模型的主动悬架滑模容错控制器设计
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摘要
针对主动悬架系统的质量参数不确定性以及作动器出现的随机故障对车辆行驶平顺性和控制稳定性带来的重要影响,该文提出一种基于T-S模糊模型的主动悬架滑模容错控制器设计方法。为了描述悬架参数不确定性,基于T-S模糊模型建立1/4车辆的非线性模型,利用故障调节因子表示作动器故障的大小,进而获得考虑悬架系统质量不确定性和作动器故障的车辆主动悬架控制模型。接着,将滑模控制与自适应理论结合,设计合适的滑模面函数和滑模容错控制律,以达到故障悬架系统的容错控制目的;并基于Lyapunov稳定性理论,对所提出控制器稳定性和悬架系统安全约束性能进行了分析。最后,给出一个仿真算例,验证了所设计控制器的有效性和适用性。
To resolve the problem of riding comfort and control stability caused by the variation of vehicle suspension sprung masses and the stochastic actuator faults, a novel sliding-mode fault tolerant controller design method is proposed for vehicle active suspension systems based on T-S fuzzy model. To describe the system parameter uncertainties of active suspensions, a quarter-vehicle nonlinear dynamic model based on T-S fuzzy approach is first established, in which a fault tuning factor is employed to denote the amplitude of actuator faults, thus the control plant of vehicle active suspension with considering the uncertainties of vehicle suspension sprung body masses and the actuator faults is obtained. Based on this control model, an appropriate sliding-mode surface function and fault tolerant control law are developed to realize the fault tolerant control of the fault suspension system through the combination of classical sliding control theory and adaptive control theory. Moreover, the stability analysis and suspension safety constraint performances are carried out by Lyapunov stability theory. Finally, a numerical example is provided to verify the effectiveness and applicability of the proposed fault tolerant controller under different road conditions.
To resolve the problem of riding comfort and control stability caused by the variation of vehicle suspension sprung masses and the stochastic actuator faults, a novel sliding-mode fault tolerant controller design method is proposed for vehicle active suspension systems based on T-S fuzzy model. To describe the system parameter uncertainties of active suspensions, a quarter-vehicle nonlinear dynamic model based on T-S fuzzy approach is first established, in which a fault tuning factor is employed to denote the amplitude of actuator faults, thus the control plant of vehicle active suspension with considering the uncertainties of vehicle suspension sprung body masses and the actuator faults is obtained. Based on this control model, an appropriate sliding-mode surface function and fault tolerant control law are developed to realize the fault tolerant control of the fault suspension system through the combination of classical sliding control theory and adaptive control theory. Moreover, the stability analysis and suspension safety constraint performances are carried out by Lyapunov stability theory. Finally, a numerical example is provided to verify the effectiveness and applicability of the proposed fault tolerant controller under different road conditions.
引文
[1]余志生.汽车理论[M].第5版.北京:机械工业出版社,2009.Yu Zhisheng.Automobile theory[M].5th ed.Beijing:China Machine Press,2009.(in Chinese)
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[3]Li H,Yu J,Hilton C,et al.Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach[J].IEEE Transactions on Industrial Electronics,2013,60(8):3328―3338.
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[6]Sun W,Zhao Z,Gao H.Saturated adaptive robust control for active suspension systems[J].IEEE Transactions on Industrial Electronics,2013,60(9):3889―3896.
[7]Rath J J,Defoort M,Karimi H R,et al.Output feedback active suspension control with higher order terminal sliding mode[J].IEEE Transactions on Industrial Electronics,2017,64(2):1392―1403.
[8]Huang Y,Na J,Wu X,et al.Adaptive control of nonlinear uncertain active suspension systems with prescribed performance[J].Isa Transactions,2015,54:145―155.
[9]Huang S J,Lin W C.Adaptive fuzzy controller with sliding surface for vehicle suspension control[J].IEEETransactions on Fuzzy Systems,2003,11(4):550―559.
[10]Wen S,Chen M Z Q,Zeng Z,et al.Fuzzy control for uncertain vehicle active suspension systems via dynamic sliding-mode approach[J].IEEE Transactions on Systems Man&Cybernetics Systems,2017,47(1):24―32.
[11]高瑞贞,张京军,赵子月,等.基于改进遗传算法的半主动悬架系统模糊控制优化研究[J].工程力学,2012,29(1):240―248.Gao Ruizhen,Zhang Jingjun,Zhao Ziyue,et al.Research on the fuzzy control of semi-active suspension systems based on improved genetic algorithms[J].Engineering Mechanics,2012,29(1):240―248.(in Chinese)
[12]Gaspar P,Szaszi I,Bokor J.Design of robust controllers for active vehicle suspension using the mixedμsynthesis[J].Vehicle System Dynamics,2003,40(4):193―228.
[13]Na J,Huang Y,Wu X,et al.Active adaptive estimation and control for vehicle suspensions with prescribed performance[J].IEEE Transactions on Control Systems Technology,2017,26(6):2063―2077.
[14]Zhao F,Ge S S,Tu F,et al.Adaptive neural network control for active suspension system with actuator saturation[J].IET Control Theory and Applications,2016,10(14):1696―1705.
[15]高振刚,李晓雪,曹宇,等.基于作动器故障估计的汽车主动悬架容错控制研究[J].内蒙古大学学报(自然科学版),2016,47(5):533―541.Gao Zhengang,Li Xiaoxue,Cao Yu,et al.Fault tolerant control of active suspension based on actuator fault estimation[J].Journal of Inner Mongolia University(Natural Science),2016,47(5):533―541.(in Chinese)
[16]杨柳青,陈无畏,汪洪波.基于H2/H∞控制的汽车主动悬架最优鲁棒容错控制[J].中国机械工程,2012,23(24):3013―3019.Yang Liuqing,Chen Wuwei,Wang Hongbo.Optimal robust fault tolerant control for vehicle active suspension system based on H2/H∞approach[J].China Mechanical Engineering,2012,23(24):3013―3019.(in Chinese)
[17]杨柳青,陈无畏.基于传感器信号重构的汽车主动悬架主动容错控制[J].汽车工程,2013,35(12):1084―1091.Yang Liuqing,Chen Wuwei.Active fault tolerant control of vehicle active suspension based on sensor signal reconstruction[J].Automotive Engineering,2013,35(12):1084―1091.(in Chinese)
[18]陈双,钟孝伟.汽车主动悬架作动器故障诊断与控制补偿方法[J].汽车技术,2018(2):40―44.Chen Shuang,Zhong Xiaowei.Failure diagnosis and control compensation of vehicle active suspension actuator[J].Automobile Technology,2018(2):40―44.(in Chinese)
[19]Chen M C,Wang W Y,Su S F,et al.Robust T-Sfuzzy-neural control of uncertain active suspension systems[J].International Journal of Fuzzy Systems,2010,12(4):321―329.
[20]吴忠强,陈金钉,吴云双,等.基于T-S模型的汽车主动悬架H∞控制研究[J].振动与冲击,2007,26(11):64―69.Wu Zhongqiang,Chen Jinding,Wu Yunshuang,et al.H∞control of automotive active suspension based on T-Smodel[J].Journal of Vibration and Shock,2007,26(11):64―69.(in Chinese)
[21]朱芳来,蒋鹏,李晓航.基于T-S模糊模型的观测器和动态输出反馈容错控制器设计[J].西安交通大学学报,2016,50(9):91―96.Zhu Fanglai,Jiang Peng,Li Xiaohang.Design of observer and dynamic output feedback fault tolerant controller based on T-S fuzzy model[J].Journal of Xi’an Jiaotong University,2016,50(9):91―96.(in Chinese)
[22]徐光智,孙秀霞,董文瀚,等.非线性系统的自适应输出反馈优化跟踪控制[J].西安交通大学学报,2017,51(1):128―134.Xu Gaungzhi,Sun Xiuxia,Dong Wenhan,et al.Adaptive output feedback optimal tracking control for nonlinear systems[J].Journal of Xi’an Jiaotong University,2017,51(1):128―134.(in Chinese)
[23]Li H,Liu H,Gao H,et al.Reliable fuzzy control for active suspension systems with actuator delay and fault[J].IEEE Transactions on Fuzzy Systems,2012,20(2):342―357.
[24]Li H,Liu H,Gao H.Actuator delayed active vehicle suspension control:A T-S fuzzy approach[C].IEEEInternational Conference on Fuzzy Systems,2011:2358―2363.
[25]Sam Y M,Osman J H S,Ghani M R A.A class of proportional-integral sliding mode control with application to active suspension system[J].Systems and Control Letters,2004,51(3):217―223.
[26]Chen P C,Huang A C.Adaptive sliding control of non-autonomous active suspension systems with time-varying loadings[J].Journal of Sound and Vibration,2005,282(3):1119―1135.
[27]Lin J,Lian R J,Huang C N,et al.Enhanced fuzzy sliding mode controller for active suspension systems[J].Mechatronics,2009,19(7):1178―1190.
[28]Deshpande V S,Mohan B,Shendge P D,et al.Disturbance observer based sliding mode control of active suspension systems[J].Journal of Sound and Vibration,2014,333(11):2281―2296.
[29]王威,宋玉玲,王体春,等.非确定因素下汽车半主动悬架的智能控制[J].工程力学,2012,29(9):337―342.Wang Wei,Song Yuling,Wang Tichun,et al.Intelligent control of automotive semi-active suspension with uncertain factors[J].Engineering Mechanics,2012,29(9):337―342.(in Chinese)
[30]张丽萍,弓栋梁.基于H2/H∞控制的汽车主动悬架被动容错控制[J].汽车技术,2017(11):44―49.Zhang Liping,Gong Dongliang.Passive fault-tolerant control for vehicle active suspension system based on H2/H∞control[J].Automobile Technology,2017(11):44―49.(in Chinese)
[31]Feng G.A survey on analysis and design of model-based fuzzy control systems[J].IEEE Transactions on Fuzzy Systems,2006,14(5):676―697.
[32]Choi H D,Ahn C K,Shi P,et al.Dynamic output-feedback dissipative control for T-S fuzzy systems with time-varying input delay and output constraints[J].IEEE Transactions on Fuzzy Systems,2017,25(3):511―526.
[33]Sun W,Pan H,Gao H.Filter-based adaptive vibration control for active vehicle suspensions with electrohydraulic actuators[J].IEEE Transactions on Vehicular Technology,2016,65(6):4619―4626.
[34]Du H,Zhang N.Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint[J].IEEE Transactions on Fuzzy Systems,2009,17(2):343―356.
[35]王威,薛彦冰,宋玉玲,等.基于GA优化控制规则的汽车主动悬架模糊PID控制[J].振动与冲击,2012,31(22):157―162.Wang Wei,Xue Yanbing,Song Yuling,et al.Fuzzy-PIDcontrol strategy for an active suspension based on optimal control laws with genetic algorithm[J].Journal of Vibration and Shock,2012,31(22):157―162.(in Chinese)
[36]Liu S,Zhou H,Luo X,et al.Adaptive sliding fault tolerant control for nonlinear uncertain active suspension systems[J].Journal of the Franklin Institute,2016,353(1):180―199.
[2]周兵,赵保华.汽车主动悬架自适应模糊PID控制仿真研究[J].湖南大学学报(自然科学版),2009,36(12):27―30.Zhou Bing,Zhao Baohua.Simulation study of self-adaptive fuzzy-PID control of active suspension[J].Journal of Hunan University(Natural Sciences),2009,36(12):27―30.(in Chinese)
[3]Li H,Yu J,Hilton C,et al.Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach[J].IEEE Transactions on Industrial Electronics,2013,60(8):3328―3338.
[4]贾启芬,于雯,刘习军,等.汽车悬架系统的分段线性非线性振动机理的研究[J].工程力学,2005,22(1):88―92.Jia Qifen,Yu Wen,Liu Xijun,et al.Dynamic characteristics of bilinear suspension system of vehicles[J].Engineering Mechanics,2005,22(1):88―92.(in Chinese)
[5]喻凡,张勇超.馈能型车辆主动悬架技术[J].农业机械学报,2010,41(1):1―6.Yu Fan,Zhang Yongchao.Technology of regenerative vehicle active suspensions[J].Transactions of the Chinese Society of Agricultural,2010,41(1):1―6.(in Chinese)
[6]Sun W,Zhao Z,Gao H.Saturated adaptive robust control for active suspension systems[J].IEEE Transactions on Industrial Electronics,2013,60(9):3889―3896.
[7]Rath J J,Defoort M,Karimi H R,et al.Output feedback active suspension control with higher order terminal sliding mode[J].IEEE Transactions on Industrial Electronics,2017,64(2):1392―1403.
[8]Huang Y,Na J,Wu X,et al.Adaptive control of nonlinear uncertain active suspension systems with prescribed performance[J].Isa Transactions,2015,54:145―155.
[9]Huang S J,Lin W C.Adaptive fuzzy controller with sliding surface for vehicle suspension control[J].IEEETransactions on Fuzzy Systems,2003,11(4):550―559.
[10]Wen S,Chen M Z Q,Zeng Z,et al.Fuzzy control for uncertain vehicle active suspension systems via dynamic sliding-mode approach[J].IEEE Transactions on Systems Man&Cybernetics Systems,2017,47(1):24―32.
[11]高瑞贞,张京军,赵子月,等.基于改进遗传算法的半主动悬架系统模糊控制优化研究[J].工程力学,2012,29(1):240―248.Gao Ruizhen,Zhang Jingjun,Zhao Ziyue,et al.Research on the fuzzy control of semi-active suspension systems based on improved genetic algorithms[J].Engineering Mechanics,2012,29(1):240―248.(in Chinese)
[12]Gaspar P,Szaszi I,Bokor J.Design of robust controllers for active vehicle suspension using the mixedμsynthesis[J].Vehicle System Dynamics,2003,40(4):193―228.
[13]Na J,Huang Y,Wu X,et al.Active adaptive estimation and control for vehicle suspensions with prescribed performance[J].IEEE Transactions on Control Systems Technology,2017,26(6):2063―2077.
[14]Zhao F,Ge S S,Tu F,et al.Adaptive neural network control for active suspension system with actuator saturation[J].IET Control Theory and Applications,2016,10(14):1696―1705.
[15]高振刚,李晓雪,曹宇,等.基于作动器故障估计的汽车主动悬架容错控制研究[J].内蒙古大学学报(自然科学版),2016,47(5):533―541.Gao Zhengang,Li Xiaoxue,Cao Yu,et al.Fault tolerant control of active suspension based on actuator fault estimation[J].Journal of Inner Mongolia University(Natural Science),2016,47(5):533―541.(in Chinese)
[16]杨柳青,陈无畏,汪洪波.基于H2/H∞控制的汽车主动悬架最优鲁棒容错控制[J].中国机械工程,2012,23(24):3013―3019.Yang Liuqing,Chen Wuwei,Wang Hongbo.Optimal robust fault tolerant control for vehicle active suspension system based on H2/H∞approach[J].China Mechanical Engineering,2012,23(24):3013―3019.(in Chinese)
[17]杨柳青,陈无畏.基于传感器信号重构的汽车主动悬架主动容错控制[J].汽车工程,2013,35(12):1084―1091.Yang Liuqing,Chen Wuwei.Active fault tolerant control of vehicle active suspension based on sensor signal reconstruction[J].Automotive Engineering,2013,35(12):1084―1091.(in Chinese)
[18]陈双,钟孝伟.汽车主动悬架作动器故障诊断与控制补偿方法[J].汽车技术,2018(2):40―44.Chen Shuang,Zhong Xiaowei.Failure diagnosis and control compensation of vehicle active suspension actuator[J].Automobile Technology,2018(2):40―44.(in Chinese)
[19]Chen M C,Wang W Y,Su S F,et al.Robust T-Sfuzzy-neural control of uncertain active suspension systems[J].International Journal of Fuzzy Systems,2010,12(4):321―329.
[20]吴忠强,陈金钉,吴云双,等.基于T-S模型的汽车主动悬架H∞控制研究[J].振动与冲击,2007,26(11):64―69.Wu Zhongqiang,Chen Jinding,Wu Yunshuang,et al.H∞control of automotive active suspension based on T-Smodel[J].Journal of Vibration and Shock,2007,26(11):64―69.(in Chinese)
[21]朱芳来,蒋鹏,李晓航.基于T-S模糊模型的观测器和动态输出反馈容错控制器设计[J].西安交通大学学报,2016,50(9):91―96.Zhu Fanglai,Jiang Peng,Li Xiaohang.Design of observer and dynamic output feedback fault tolerant controller based on T-S fuzzy model[J].Journal of Xi’an Jiaotong University,2016,50(9):91―96.(in Chinese)
[22]徐光智,孙秀霞,董文瀚,等.非线性系统的自适应输出反馈优化跟踪控制[J].西安交通大学学报,2017,51(1):128―134.Xu Gaungzhi,Sun Xiuxia,Dong Wenhan,et al.Adaptive output feedback optimal tracking control for nonlinear systems[J].Journal of Xi’an Jiaotong University,2017,51(1):128―134.(in Chinese)
[23]Li H,Liu H,Gao H,et al.Reliable fuzzy control for active suspension systems with actuator delay and fault[J].IEEE Transactions on Fuzzy Systems,2012,20(2):342―357.
[24]Li H,Liu H,Gao H.Actuator delayed active vehicle suspension control:A T-S fuzzy approach[C].IEEEInternational Conference on Fuzzy Systems,2011:2358―2363.
[25]Sam Y M,Osman J H S,Ghani M R A.A class of proportional-integral sliding mode control with application to active suspension system[J].Systems and Control Letters,2004,51(3):217―223.
[26]Chen P C,Huang A C.Adaptive sliding control of non-autonomous active suspension systems with time-varying loadings[J].Journal of Sound and Vibration,2005,282(3):1119―1135.
[27]Lin J,Lian R J,Huang C N,et al.Enhanced fuzzy sliding mode controller for active suspension systems[J].Mechatronics,2009,19(7):1178―1190.
[28]Deshpande V S,Mohan B,Shendge P D,et al.Disturbance observer based sliding mode control of active suspension systems[J].Journal of Sound and Vibration,2014,333(11):2281―2296.
[29]王威,宋玉玲,王体春,等.非确定因素下汽车半主动悬架的智能控制[J].工程力学,2012,29(9):337―342.Wang Wei,Song Yuling,Wang Tichun,et al.Intelligent control of automotive semi-active suspension with uncertain factors[J].Engineering Mechanics,2012,29(9):337―342.(in Chinese)
[30]张丽萍,弓栋梁.基于H2/H∞控制的汽车主动悬架被动容错控制[J].汽车技术,2017(11):44―49.Zhang Liping,Gong Dongliang.Passive fault-tolerant control for vehicle active suspension system based on H2/H∞control[J].Automobile Technology,2017(11):44―49.(in Chinese)
[31]Feng G.A survey on analysis and design of model-based fuzzy control systems[J].IEEE Transactions on Fuzzy Systems,2006,14(5):676―697.
[32]Choi H D,Ahn C K,Shi P,et al.Dynamic output-feedback dissipative control for T-S fuzzy systems with time-varying input delay and output constraints[J].IEEE Transactions on Fuzzy Systems,2017,25(3):511―526.
[33]Sun W,Pan H,Gao H.Filter-based adaptive vibration control for active vehicle suspensions with electrohydraulic actuators[J].IEEE Transactions on Vehicular Technology,2016,65(6):4619―4626.
[34]Du H,Zhang N.Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint[J].IEEE Transactions on Fuzzy Systems,2009,17(2):343―356.
[35]王威,薛彦冰,宋玉玲,等.基于GA优化控制规则的汽车主动悬架模糊PID控制[J].振动与冲击,2012,31(22):157―162.Wang Wei,Xue Yanbing,Song Yuling,et al.Fuzzy-PIDcontrol strategy for an active suspension based on optimal control laws with genetic algorithm[J].Journal of Vibration and Shock,2012,31(22):157―162.(in Chinese)
[36]Liu S,Zhou H,Luo X,et al.Adaptive sliding fault tolerant control for nonlinear uncertain active suspension systems[J].Journal of the Franklin Institute,2016,353(1):180―199.