考虑参数不确定性的主动悬架鲁棒H_2/H_∞混合控制
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摘要
基于线性矩阵不等式方法,提出了一种新的考虑参数不确定性的鲁棒H2/H∞控制器设计方法,并用于车辆主动悬架设计.假定系统不确定参数是范数有界的,通过引入同一个Lyapunov矩阵来同时满足闭环系统的H2和H∞性能条件,把鲁棒H2/H∞控制器设计转化为具有线性矩阵不等式约束的凸优化问题,进而应用内点法等凸优化技术进行求解.以四分之一车辆模型主动悬架设计为例,进行了数值仿真.结果表明,无论车辆簧上质量是否存在变异,鲁棒H2/H∞控制器均能给出很好的控制效果.
Based on the linear matrix inequality method,a new approach to the design of robust H2/H∞ controllers for linear systems with parameter uncertainties was proposed.The parameter uncertainties considered were assumed to be norm-bounded.By introducing a Lyapunov matrix to meet the H2 and H∞ performance constraints simultaneously for the resulting closed-loop system,the robust H2/H∞ controller design was transformed into a convex optimal problem with constraints of linear matrix inequalities,to which the existing convex optimization techniques such as the interior-point algorithm can be applied.To show the effect of the proposed robust H2/H∞ controller,the dynamic responses of a quarter car model with an active suspension subjected to road surface irregular excitations,either as a stationary random process or as a discrete time-history,were investigated.Numerical results show that whether the variation of the vehicle mass exists or not,the proposed robust H2/H∞ controller behaves very satisfactorily.
Based on the linear matrix inequality method,a new approach to the design of robust H2/H∞ controllers for linear systems with parameter uncertainties was proposed.The parameter uncertainties considered were assumed to be norm-bounded.By introducing a Lyapunov matrix to meet the H2 and H∞ performance constraints simultaneously for the resulting closed-loop system,the robust H2/H∞ controller design was transformed into a convex optimal problem with constraints of linear matrix inequalities,to which the existing convex optimization techniques such as the interior-point algorithm can be applied.To show the effect of the proposed robust H2/H∞ controller,the dynamic responses of a quarter car model with an active suspension subjected to road surface irregular excitations,either as a stationary random process or as a discrete time-history,were investigated.Numerical results show that whether the variation of the vehicle mass exists or not,the proposed robust H2/H∞ controller behaves very satisfactorily.
引文
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2 J.Marzbanrad,G.Ahmadi,H.Zohoor,Y.Hojjat.Stochasticoptimal preview control of a vehicle suspension.Journal ofSound and Vibration,2004,275(3-5):973~990
3 H.S.Roh,Y.Park.Stochastic optimal preview control of anactive vehicle suspension.Journal ofSound and Vibration,1999,220(2):313~330
4 A.Hac,I.Youn.Optimal design of active and semi-activesuspensions including time delays and preview.Journal ofVibration and Acoustics(ASME),1993,115:498~508
5史明光,方敏,陈无畏.基于LMI的四自由度车辆模型主动悬架H∞控制.合肥工业大学学报,2004,27(3):237~241(Shi Mingguang,Fang Min,Chen Wuwei.H∞controlfor the active suspension system in the 4 degree-of-freedomhalf-vehicle model based on the LMI method.Journal ofHefei University ofTechnology,2004,27(3):237~241(inChinese))
6 HChen,KHGuo.ConstrainedH∞control of active suspen-sions:an LMI approach.IEEE Transactions on Control Sys-tems Technology,2005,13(3):412~421
7姜立标,王薇,谢东,等.汽车半主动空气悬架自适应模糊神经网络控制.哈尔滨工业大学学报,2005,37(12):1747~1750(Jiang Libiao,Wang Wei,Xie Dong,et al.Self-adaptive fuzzy neural network control for automo-tive semi-active air suspension.Journal ofHarbin InstituteofTechnology,2005,37(12):1747~1750(in Chinese))
8郑玲,邓兆祥,李以农.汽车半主动悬架的滑模控制及鲁棒性.汽车工程,2004,26(6):678~682(Zheng Ling,Deng Zhaoxiang,Li Yinong.Sliding mode control for semi-active suspension systems and its robustness.AutomotiveEngineering,2004,26(6):678~682(in Chinese))
9孙建民,柳贡民.基于LMS自适应滤波的汽车主动悬架研究.振动与冲击,2004,23(4):139~143(Sun Jian-min,Liu Gongmin.Study on automobile active suspensionbased on LMS adaptive filter.Journal of Vibration andShock,2004,23(4):139~143(in Chinese))
10 JC Doyle.Guaranteed margins for LQG regulators.IEEETransactions on Automatic Control,1978,AC-23(4):756~757
11陈虹,赵桂军,孙鹏远,郭孔辉.H2和H∞主动悬架统一的理论框架与比较.汽车工程,2003,25(1):1~6(ChenHong,Zhao Guijun,Sun Pengyuan,Guo Konghui.H2andH∞active suspensions:a unified theoretic framework andcomparison.Automotive Engineering,2003,25(1):1~6(in Chinese))
12 LH Xie,MY Fu,CE de Souza.H∞control and quadraticstabilization of systems with parameter uncertainty via out-put feedback.IEEE Transactions on Automatic Control,1992,37(8):1253~1256
13张远勤,林桐,穆静,严世榕.基于LMI的建筑结构地震动H2/H∞混合控制.福州大学学报(自然科学版),2004,32(1):60~64(Zhang Yuanqin,Lin Tong,Mu Jing,Yan Shirong.H2/H∞control for seismic-excited buildingsbased on linear matrix inequalities(LMI).Journal ofFuzhou University(Natural Science),2004,32(1):60~64(in Chinese))
14 HN Wu,YC Fei.MixedH2/H∞robust output feedbackcontrol for uncertain linear systems.Control Theory and Ap-plications,2000,17(3):367~373
15吴志刚.线性鲁棒控制的理论与计算.大连:大连理工大学出版社,2003(Wu Zhigang.Theory and computation oflinear robust control.Dalian:Dalian University of Technolo-gy Press,2003(in Chinese))
16钟万勰,吴志刚,谭述君.状态空间控制理论与计算.北京:科学出版社,2007(Zhong Wanxie,Wu Zhigang,TanShujun.Theory and computation of control based on statespace.Beijing:Science Press,2007(in Chinese))
17林家浩,张亚辉.随机振动的虚拟激励法.北京:科学出版社,2004(Lin Jiahao,Zhang Yahui.Pseudo-excitationmethod for random vibration analysis.Beijing:SciencePress,2004(in Chinese))
18俞立.鲁棒控制—线性矩阵不等式处理方法.北京:清华大学出版社,2002(Yu Li.Robust control:linear matrixinequality approach.Beijing:Tsinghua University Press,2002(in Chinese))
19 CT Lai,CH Fang,SW Kau,CH Lee.RobustH2control ofnorm-bounded uncertain continuous-time system-an LMIapproach.2004 IEEE International Symposium on ComputerAided Control Systems Design,Taipei,Taiwan,2004:243~248
20 CTQin,GR Duan.Optimal robust guaranteed cost controlof uncertain linear continuous time systems via dynamicaloutput feedback.Proceedings of the 6th World Congress onIntelligent Control and Automation,Dalian,China,2006:2441~2445
21余志生.汽车理论.北京:机械工业出版社,2000(YuZhisheng.Automotive Engineering.Beijing:China MachinePress,2000(in Chinese))
2 J.Marzbanrad,G.Ahmadi,H.Zohoor,Y.Hojjat.Stochasticoptimal preview control of a vehicle suspension.Journal ofSound and Vibration,2004,275(3-5):973~990
3 H.S.Roh,Y.Park.Stochastic optimal preview control of anactive vehicle suspension.Journal ofSound and Vibration,1999,220(2):313~330
4 A.Hac,I.Youn.Optimal design of active and semi-activesuspensions including time delays and preview.Journal ofVibration and Acoustics(ASME),1993,115:498~508
5史明光,方敏,陈无畏.基于LMI的四自由度车辆模型主动悬架H∞控制.合肥工业大学学报,2004,27(3):237~241(Shi Mingguang,Fang Min,Chen Wuwei.H∞controlfor the active suspension system in the 4 degree-of-freedomhalf-vehicle model based on the LMI method.Journal ofHefei University ofTechnology,2004,27(3):237~241(inChinese))
6 HChen,KHGuo.ConstrainedH∞control of active suspen-sions:an LMI approach.IEEE Transactions on Control Sys-tems Technology,2005,13(3):412~421
7姜立标,王薇,谢东,等.汽车半主动空气悬架自适应模糊神经网络控制.哈尔滨工业大学学报,2005,37(12):1747~1750(Jiang Libiao,Wang Wei,Xie Dong,et al.Self-adaptive fuzzy neural network control for automo-tive semi-active air suspension.Journal ofHarbin InstituteofTechnology,2005,37(12):1747~1750(in Chinese))
8郑玲,邓兆祥,李以农.汽车半主动悬架的滑模控制及鲁棒性.汽车工程,2004,26(6):678~682(Zheng Ling,Deng Zhaoxiang,Li Yinong.Sliding mode control for semi-active suspension systems and its robustness.AutomotiveEngineering,2004,26(6):678~682(in Chinese))
9孙建民,柳贡民.基于LMS自适应滤波的汽车主动悬架研究.振动与冲击,2004,23(4):139~143(Sun Jian-min,Liu Gongmin.Study on automobile active suspensionbased on LMS adaptive filter.Journal of Vibration andShock,2004,23(4):139~143(in Chinese))
10 JC Doyle.Guaranteed margins for LQG regulators.IEEETransactions on Automatic Control,1978,AC-23(4):756~757
11陈虹,赵桂军,孙鹏远,郭孔辉.H2和H∞主动悬架统一的理论框架与比较.汽车工程,2003,25(1):1~6(ChenHong,Zhao Guijun,Sun Pengyuan,Guo Konghui.H2andH∞active suspensions:a unified theoretic framework andcomparison.Automotive Engineering,2003,25(1):1~6(in Chinese))
12 LH Xie,MY Fu,CE de Souza.H∞control and quadraticstabilization of systems with parameter uncertainty via out-put feedback.IEEE Transactions on Automatic Control,1992,37(8):1253~1256
13张远勤,林桐,穆静,严世榕.基于LMI的建筑结构地震动H2/H∞混合控制.福州大学学报(自然科学版),2004,32(1):60~64(Zhang Yuanqin,Lin Tong,Mu Jing,Yan Shirong.H2/H∞control for seismic-excited buildingsbased on linear matrix inequalities(LMI).Journal ofFuzhou University(Natural Science),2004,32(1):60~64(in Chinese))
14 HN Wu,YC Fei.MixedH2/H∞robust output feedbackcontrol for uncertain linear systems.Control Theory and Ap-plications,2000,17(3):367~373
15吴志刚.线性鲁棒控制的理论与计算.大连:大连理工大学出版社,2003(Wu Zhigang.Theory and computation oflinear robust control.Dalian:Dalian University of Technolo-gy Press,2003(in Chinese))
16钟万勰,吴志刚,谭述君.状态空间控制理论与计算.北京:科学出版社,2007(Zhong Wanxie,Wu Zhigang,TanShujun.Theory and computation of control based on statespace.Beijing:Science Press,2007(in Chinese))
17林家浩,张亚辉.随机振动的虚拟激励法.北京:科学出版社,2004(Lin Jiahao,Zhang Yahui.Pseudo-excitationmethod for random vibration analysis.Beijing:SciencePress,2004(in Chinese))
18俞立.鲁棒控制—线性矩阵不等式处理方法.北京:清华大学出版社,2002(Yu Li.Robust control:linear matrixinequality approach.Beijing:Tsinghua University Press,2002(in Chinese))
19 CT Lai,CH Fang,SW Kau,CH Lee.RobustH2control ofnorm-bounded uncertain continuous-time system-an LMIapproach.2004 IEEE International Symposium on ComputerAided Control Systems Design,Taipei,Taiwan,2004:243~248
20 CTQin,GR Duan.Optimal robust guaranteed cost controlof uncertain linear continuous time systems via dynamicaloutput feedback.Proceedings of the 6th World Congress onIntelligent Control and Automation,Dalian,China,2006:2441~2445
21余志生.汽车理论.北京:机械工业出版社,2000(YuZhisheng.Automotive Engineering.Beijing:China MachinePress,2000(in Chinese))
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