考虑参数不确定性的主动悬架H_2/H_∞保性能控制
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摘要
针对车辆主动悬架系统参数不确定性所引起的控制稳定性问题,提出一种基于线性分式变换的混合H_2/H_∞保性能状态反馈控制策略.首先,为了提高车辆平顺性、确保汽车行驶安全性能,在考虑系统参数不确定的条件下建立1/4车辆主动悬架模型,并将车身垂向加速度的H_2范数作为控制输出性能指标并使其最小化,悬架动挠度约束和轮胎动载荷约束作为控制器的H_∞性能约束输出指标.然后,基于Lyapunov稳定性理论设计一种最优H_2/H_∞保性能状态反馈控制律,将保性能控制律问题转化为线性矩阵不等式的凸优化问题,并利用不确定矩阵结构信息进一步引入自由变量以降低控制器设计的保守性.最后,通过某1/4车辆主动悬架的仿真实验结果表明,所提出控制策略在外部路面扰动下能够使该主动悬架系统具有更好的扰动抑制能力,并能够明显改善车辆悬架综合性能.
Aiming at the control and stability problem of vehicle active suspension systems with parameter uncertainty,a mixed H_2/H_∞ guaranteed cost state feedback control strategy based on linear fractional transformation(LFT) is proposed. Firstly, to improve vehicle ride comfort and ensure the security of vehicle driving, the quarter dynamics model of vehicle active suspension is established when considering the uncertainties of the active suspension system. The H_2 norm of vehicle body acceleration is selected as the output performance index of the controller to be minimized, and the constraints of suspension dynamic deflection and tire dynamic load are determined as the H_∞ constraint performance output indicators of the designed controller. Then, based on the Lyapunov stability theory, an optimal mixed H_2/H_∞guaranteed cost state feedback control approach is presented to reduce the conservatism of controller design. Finally,a numerical example of quarter-vehicle active suspensions is provided, and the simulation results demonstrate that the proposed control strategy has better disturbance attenuation capability against the external road disturbance, and can obviously improve the overall performance of vehicle suspension.
Aiming at the control and stability problem of vehicle active suspension systems with parameter uncertainty,a mixed H_2/H_∞ guaranteed cost state feedback control strategy based on linear fractional transformation(LFT) is proposed. Firstly, to improve vehicle ride comfort and ensure the security of vehicle driving, the quarter dynamics model of vehicle active suspension is established when considering the uncertainties of the active suspension system. The H_2 norm of vehicle body acceleration is selected as the output performance index of the controller to be minimized, and the constraints of suspension dynamic deflection and tire dynamic load are determined as the H_∞ constraint performance output indicators of the designed controller. Then, based on the Lyapunov stability theory, an optimal mixed H_2/H_∞guaranteed cost state feedback control approach is presented to reduce the conservatism of controller design. Finally,a numerical example of quarter-vehicle active suspensions is provided, and the simulation results demonstrate that the proposed control strategy has better disturbance attenuation capability against the external road disturbance, and can obviously improve the overall performance of vehicle suspension.
引文
[1] Li H, Liu H, Hand S, et al. Multi-objective control for vehicle active suspension systems with random actuator delay[J]. Int J of Systems Science, 2011, 43(12):1-14.
[2] Pan H, Sun W, Gao H, et al. Finite-time stabilization for vehicle active suspension systems with hard constraints[J]. IEEE Trans on Intelligent Transportation Systems, 2015, 16(5):1-10.
[3]姜伟,王宏力,陆敬辉,等.连续时间多胞线性变参数系统变增益H∞/H2输出反馈控制[J].控制理论与应用, 2016, 33(9):1225-1235.(Jiang W, Wang H L, Lu J H, et al. Gain-scheduled H∞/H2 output feedback controller synthesis for continuous-time polytopic linear parameter varying systems[J]. Control Theory and Applications, 2016,33(9):1225-1235.)
[4] Sun W, Zhao Y, Li J, et al. Active suspension control with frequency band constraints and actuator input delay[J].IEEE Trans on Industrial Electronics, 2012, 59(1):530-537.
[5] Sun W, Zhao Z, Gao H. Saturated adaptive robust control for active suspension systems[J]. IEEE Trans on Industrial Electronics, 2013, 60(9):3889-3896.
[6] Guo L X, Zhang L P. Robust H∞control of active vehicle suspension under non-stationary running[J]. J of Sound and Vibration, 2012, 331(26):5824-5837.
[7] Lauwerys C, Swevers J, Sas P. Design and experimental validation of a linear robust controller for an active suspension of a quarter car[C]. American Control Conf.Boston:IEEE, 2004:1481-1486.
[8] Takahashi M, Hiraoka S, Suzuki T. Gain-scheduling H∞control to improve ride comfort and driving stability for vehicle active suspension[J]. Vehicle Engineering, 2014,2:21-30.
[9] Choi H D, Ahn C K, Lim M T. Dynamic output-feedback H∞control for active half-vehicle suspension systems with time-varying input delay[J]. Int J of Control Automation and Systems, 2016, 14(1):59-68.
[10] Fallah M S, Bhat R, Xie W F. H∞robust control of active suspensions:A practical point of view[C]. American Control Conf. St. Louis:IEEE, 2009:1385-1390.
[11] Li H, Liu H. Multi-objective H∞control for vehicle active suspension systems with random actuator delay[J]. Int J of Systems Science, 2012, 43(12):2214-2227.
[12] 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 Trans on Systems Man and Cybernetics Systems, 2017, 47(1):24-32.
[13] Sun W, Gao H, Kaynak O. Adaptive backstepping control for active suspension systems with hard constraints[J].IEEE/ASME Trans on Mechatronics, 2013, 18(18):1072-1079.
[14] 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 Trans on Industrial Electronics,2013, 60(8):3328-3338.
[15] Ghazaly N M, Ahmed A S, Ati A S, et al. H∞control of active suspension system for a quarter car model[J]. Int J of Vehicle Structures and Systems, 2016, 8(1):35-40.
[16] Choi S B, Han S S. H∞control of electrorheological suspension system subjected to parameter uncertainties[J]. Mechatronics, 2003, 13(7):639-657.
[17] Turkay S, Akcay H. Influence of tire damping on the H2 optimally designed half-car active suspensions[C].Int Conf on Control Applications. San Antonio:IEEE,2008:444-449.
[18] Chen H, Ma M. Constrained H2 control of active suspensions using LMI optimization[C]. Chinese Control Conf. Harbin:IEEE, 2006:702-707.
[19] Abdellari E, Mehdi D, M’Saad M. On the design of active suspension system by H∞and mixed H2/H∞:An LMI approach[C]. American Control Conf. Chicago:IEEE,2000:4041-4045.
[20] Badran S M. Robust LMI-based controller design using H∞and mixed H2/H∞for semi-active suspension system[J]. Editorial Committees, 2012, 2(8):172-180.
[21] Orukpe P E, Zheng X, Jaimoukha I M, et al.Model predictive control based on mixed H2/H∞control approach for active vibration control of railway vehicles[J]. Vehicle System Dynamics, 2008, 46(S1):151-160.
[22] Akcay H, Turkay S. Influence of tire damping on mixed H2/H∞synthesis of half-car active suspensions[J]. J of Sound and Vibration, 2009, 322(1):15-28.
[23] Sun W, Gao H, Kaynak O. Finite frequency H∞control for vehicle active suspension systems[J]. IEEE Trans on Control Systems Technology, 2011, 19(2):416-422.
[24]张勇超.车辆电磁主动悬架鲁棒控制研究[D].上海:上海交通大学机械与动力工程学院, 2012.(Zhang Y C. Study on robust control for vehicle active electromagnetic suspension[D]. Shanghai:School of Mechanical and Power Engineering, Shanghai Jiao Tong University, 2012.)
[25]张志勇,刘鑫,黄彩霞,等.具有参数不确定性的车辆座椅悬架H∞输出反馈半主动控制[J].振动与冲击,2013, 32(14):93-97.(Zhang Z Y, Liu X, Huang C X, et al. H∞output feedback semi-active control for a vehicle seat suspension with parametric uncertainty[J]. Vibration and Shock, 2013,32(14):93-97.)
[26] Khargonekar P P, Petersen I R, Zhou K. Robust stabilization of uncertain linear systems:Quadratic stability and H∞control theory[J]. IEEE Trans on Automatic Control, 1990, 35(3):356-361.
[27] Petersen I R, Anderson BDO, Jonckheere E A. A first principles solution to the non-singular H∞control problem[J]. Int J of Robust and Nonlinear Control, 1991,1(3):171-185.
[28] Jbilou K, Messaoudi A, Taba?K. Some schur complement identities and applications to matrix extrapolation methods[J]. Linear Algebra&Its Applications, 2004, 392(1):195-210.
[29]江洪,李仲兴,周文涛,等.基于遗传算法的ECAS系统中三级阻尼匹配优化设计[J].机械工程学报, 2009,45(10):278-283.(Jiang H, Li Z X, Zhou W T, et al. Optimum match design of tri-grade adjustable damper in ECAS system based on genetic algorithm[J]. J of Mechanical Engineering, 2009,45(10):278-283.)
[30] Chen H, Guo K H. Constrained H∞control of active suspensions:An LMI approach[J]. IEEE Trans on Control Systems Technology, 2005, 13(3):412-421.
[2] Pan H, Sun W, Gao H, et al. Finite-time stabilization for vehicle active suspension systems with hard constraints[J]. IEEE Trans on Intelligent Transportation Systems, 2015, 16(5):1-10.
[3]姜伟,王宏力,陆敬辉,等.连续时间多胞线性变参数系统变增益H∞/H2输出反馈控制[J].控制理论与应用, 2016, 33(9):1225-1235.(Jiang W, Wang H L, Lu J H, et al. Gain-scheduled H∞/H2 output feedback controller synthesis for continuous-time polytopic linear parameter varying systems[J]. Control Theory and Applications, 2016,33(9):1225-1235.)
[4] Sun W, Zhao Y, Li J, et al. Active suspension control with frequency band constraints and actuator input delay[J].IEEE Trans on Industrial Electronics, 2012, 59(1):530-537.
[5] Sun W, Zhao Z, Gao H. Saturated adaptive robust control for active suspension systems[J]. IEEE Trans on Industrial Electronics, 2013, 60(9):3889-3896.
[6] Guo L X, Zhang L P. Robust H∞control of active vehicle suspension under non-stationary running[J]. J of Sound and Vibration, 2012, 331(26):5824-5837.
[7] Lauwerys C, Swevers J, Sas P. Design and experimental validation of a linear robust controller for an active suspension of a quarter car[C]. American Control Conf.Boston:IEEE, 2004:1481-1486.
[8] Takahashi M, Hiraoka S, Suzuki T. Gain-scheduling H∞control to improve ride comfort and driving stability for vehicle active suspension[J]. Vehicle Engineering, 2014,2:21-30.
[9] Choi H D, Ahn C K, Lim M T. Dynamic output-feedback H∞control for active half-vehicle suspension systems with time-varying input delay[J]. Int J of Control Automation and Systems, 2016, 14(1):59-68.
[10] Fallah M S, Bhat R, Xie W F. H∞robust control of active suspensions:A practical point of view[C]. American Control Conf. St. Louis:IEEE, 2009:1385-1390.
[11] Li H, Liu H. Multi-objective H∞control for vehicle active suspension systems with random actuator delay[J]. Int J of Systems Science, 2012, 43(12):2214-2227.
[12] 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 Trans on Systems Man and Cybernetics Systems, 2017, 47(1):24-32.
[13] Sun W, Gao H, Kaynak O. Adaptive backstepping control for active suspension systems with hard constraints[J].IEEE/ASME Trans on Mechatronics, 2013, 18(18):1072-1079.
[14] 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 Trans on Industrial Electronics,2013, 60(8):3328-3338.
[15] Ghazaly N M, Ahmed A S, Ati A S, et al. H∞control of active suspension system for a quarter car model[J]. Int J of Vehicle Structures and Systems, 2016, 8(1):35-40.
[16] Choi S B, Han S S. H∞control of electrorheological suspension system subjected to parameter uncertainties[J]. Mechatronics, 2003, 13(7):639-657.
[17] Turkay S, Akcay H. Influence of tire damping on the H2 optimally designed half-car active suspensions[C].Int Conf on Control Applications. San Antonio:IEEE,2008:444-449.
[18] Chen H, Ma M. Constrained H2 control of active suspensions using LMI optimization[C]. Chinese Control Conf. Harbin:IEEE, 2006:702-707.
[19] Abdellari E, Mehdi D, M’Saad M. On the design of active suspension system by H∞and mixed H2/H∞:An LMI approach[C]. American Control Conf. Chicago:IEEE,2000:4041-4045.
[20] Badran S M. Robust LMI-based controller design using H∞and mixed H2/H∞for semi-active suspension system[J]. Editorial Committees, 2012, 2(8):172-180.
[21] Orukpe P E, Zheng X, Jaimoukha I M, et al.Model predictive control based on mixed H2/H∞control approach for active vibration control of railway vehicles[J]. Vehicle System Dynamics, 2008, 46(S1):151-160.
[22] Akcay H, Turkay S. Influence of tire damping on mixed H2/H∞synthesis of half-car active suspensions[J]. J of Sound and Vibration, 2009, 322(1):15-28.
[23] Sun W, Gao H, Kaynak O. Finite frequency H∞control for vehicle active suspension systems[J]. IEEE Trans on Control Systems Technology, 2011, 19(2):416-422.
[24]张勇超.车辆电磁主动悬架鲁棒控制研究[D].上海:上海交通大学机械与动力工程学院, 2012.(Zhang Y C. Study on robust control for vehicle active electromagnetic suspension[D]. Shanghai:School of Mechanical and Power Engineering, Shanghai Jiao Tong University, 2012.)
[25]张志勇,刘鑫,黄彩霞,等.具有参数不确定性的车辆座椅悬架H∞输出反馈半主动控制[J].振动与冲击,2013, 32(14):93-97.(Zhang Z Y, Liu X, Huang C X, et al. H∞output feedback semi-active control for a vehicle seat suspension with parametric uncertainty[J]. Vibration and Shock, 2013,32(14):93-97.)
[26] Khargonekar P P, Petersen I R, Zhou K. Robust stabilization of uncertain linear systems:Quadratic stability and H∞control theory[J]. IEEE Trans on Automatic Control, 1990, 35(3):356-361.
[27] Petersen I R, Anderson BDO, Jonckheere E A. A first principles solution to the non-singular H∞control problem[J]. Int J of Robust and Nonlinear Control, 1991,1(3):171-185.
[28] Jbilou K, Messaoudi A, Taba?K. Some schur complement identities and applications to matrix extrapolation methods[J]. Linear Algebra&Its Applications, 2004, 392(1):195-210.
[29]江洪,李仲兴,周文涛,等.基于遗传算法的ECAS系统中三级阻尼匹配优化设计[J].机械工程学报, 2009,45(10):278-283.(Jiang H, Li Z X, Zhou W T, et al. Optimum match design of tri-grade adjustable damper in ECAS system based on genetic algorithm[J]. J of Mechanical Engineering, 2009,45(10):278-283.)
[30] Chen H, Guo K H. Constrained H∞control of active suspensions:An LMI approach[J]. IEEE Trans on Control Systems Technology, 2005, 13(3):412-421.