线性时不变系统的切换控制器设计及H2性能实现
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摘要
在复杂的控制系统中,使用单一的线性时不变(linear time invariant, LTI)控制器不能有效地处理对象的动态变化或者满足系统更多的性能要求,基于此本文主要针对于一个LTI对象设计一个切换控制器,该切换控制器包含多个预先且独立设计的LTI控制器,所有的这些LTI控制器都能够使闭环系统稳定且满足相应H2控制性能准则.基于本文提出的H2性能状态空间实现方法,设计的切换控制器不仅可以保证在任意切换的情况下整个闭环系统满足某一H2性能,而且可以保证局部子系统的切换点满足相应的H2性能,仿真结果验证了方法的有效性.
The use of single linear time invariant(LTI) controller can't address dynamic changes of the plant or satisfy more performance requirements of the system efficiently in complex control systems. Therefore, a switching controller is designed for the LTI plant in the paper, which includes several LTI controllers designed beforehand and independently that can make the closed-loop system stable and satisfy corresponding H_2 control performance criteria. The switching controller, which is designed according to H_2 performance state space realization method proposed in this paper, not only can guarantee certain H_2 performance of the overall closed-loop system under arbitrary switching, but also guarantee corresponding H_2 performance of local subsystems at each switching points. Finally, the effectiveness of proposed method is testified by the simulation results.
The use of single linear time invariant(LTI) controller can't address dynamic changes of the plant or satisfy more performance requirements of the system efficiently in complex control systems. Therefore, a switching controller is designed for the LTI plant in the paper, which includes several LTI controllers designed beforehand and independently that can make the closed-loop system stable and satisfy corresponding H_2 control performance criteria. The switching controller, which is designed according to H_2 performance state space realization method proposed in this paper, not only can guarantee certain H_2 performance of the overall closed-loop system under arbitrary switching, but also guarantee corresponding H_2 performance of local subsystems at each switching points. Finally, the effectiveness of proposed method is testified by the simulation results.
引文
[1]LIBERZON D.Switching in Systems and Control.New York:Springer Science&Business Media,2012.
[2] FALCHETTO V B, SOUZA M, FIORAVANTI A R, et al. H2 and H∞analysis for discrete-time constrained switched linear systems.IFAC-PapersOnLine, 2017, 50(1):2076–2081.
[3] ZHAI G, HU B, YASUDA K, et al. Stability analysis of switched systems with stable and unstable subsystems:an average dwell time approach. International Journal of Systems Science, 2001, 32(8):1055–1061
[4] RIEDINGER P. A switched LQ regulator design in continuous time.IEEE Transactions on Automatic Control, 2014, 59(5):1322–1328.
[5] WANG Jiapeng, HU Yueming, LUO Jiaxiang. Adaptive neural dynamic surface tracking control for a class of switched nonlinear systems. Control Theory&Applications, 2017, 34(10):1396–1402.(王加朋,胡跃明,罗家祥.一类非线性切换系统的自适应神经动态面控制.控制理论与应用, 2017, 34(10):1396–1402.)
[6] SU Q, WANG P, LI J, et al. Stabilization of discrete time switched systems with state constraints based on mode dependent average dwell time. Asian Journal of Control, 2017, 19(1):67–73.
[7] LI X, YANG H, HUANG H, et al. A switching controller for high speed cell transportation by using a robot-aided optical tweezers system. Automatica, 2018, 89:308–315.
[8] HE Yong, ZHANG Weiguo, WANG Minwen, et al. Switching linearparameter-varying controller for morphing aircraft based on multiobjective. Control Theory&Applications, 2015, 32(11):1518–1525.(何墉,章卫国,王敏文,等.基于多目标控制的变体飞行器切换线性变参数控制器.控制理论与应用, 2015, 32(11):1518–1525.)
[9] PEQUITO S, PAPPAS G J. Structural minimum controllability problem for switched linear continuous-time systems. Automatica, 2017,78:216–222.
[10] LIN H, ANTSAKLIS P J. Stability and stabilizability of switched linear systems:a survey of recent results. IEEE Transactions on Automatic control, 2009, 54(2):308–322.
[11] HESPANHA J O P, MORSE A S. Switching between stabilizing controllers. Automatica, 2002, 38(11):1905–1917.
[12] KUCERA V. Analysis and Design of Discrete Linear Control Systems. NJ, USA:Prentice-Hall, Inc, 1991.
[13] YOULA D, JABR H, BONGIORNO J. Modern wiener-hopf design of optimal controllers–part II:the multivariable case. IEEE Transactions on Automatic Control, 1976, 21(3):319–338.
[14] LIU Zhikang, YAO Yu. Linear Robust Control. Beijing:Science Press, 2012.(刘志康,姚郁.线性鲁棒控制.北京:科学出版社, 2012.)
[15] XIE W. H∞performance realisation and switching controller design for linear time-invariant plant. IET Control Theory&Applications,2016, 10(4):424–430.
[16] ZHOU K, DOYLE J C, GLOVER K. Robust and Optimal Control.New Jersey:Prentice hall, 1996.
[17] BLANCHINI F, MIANI S, MESQUINE F. A separation principle for linear switching systems and parametrization of all stabilizing controllers. IEEE Transactions on Automatic Control, 2009, 54(2):279–292.
[18] SATO T, LIU K Z. LMI solution to general H2 suboptimal control problems. Systems&Control Letters, 1999, 36(4):295–305.
[19] DOYLE J C, GLOVER K, KHARGONEKAR P P, et al. State-space solutions to standard H2 and H∞control problems. IEEE Transactions on Automatic Control, 1989, 34(8):831–847.
[2] FALCHETTO V B, SOUZA M, FIORAVANTI A R, et al. H2 and H∞analysis for discrete-time constrained switched linear systems.IFAC-PapersOnLine, 2017, 50(1):2076–2081.
[3] ZHAI G, HU B, YASUDA K, et al. Stability analysis of switched systems with stable and unstable subsystems:an average dwell time approach. International Journal of Systems Science, 2001, 32(8):1055–1061
[4] RIEDINGER P. A switched LQ regulator design in continuous time.IEEE Transactions on Automatic Control, 2014, 59(5):1322–1328.
[5] WANG Jiapeng, HU Yueming, LUO Jiaxiang. Adaptive neural dynamic surface tracking control for a class of switched nonlinear systems. Control Theory&Applications, 2017, 34(10):1396–1402.(王加朋,胡跃明,罗家祥.一类非线性切换系统的自适应神经动态面控制.控制理论与应用, 2017, 34(10):1396–1402.)
[6] SU Q, WANG P, LI J, et al. Stabilization of discrete time switched systems with state constraints based on mode dependent average dwell time. Asian Journal of Control, 2017, 19(1):67–73.
[7] LI X, YANG H, HUANG H, et al. A switching controller for high speed cell transportation by using a robot-aided optical tweezers system. Automatica, 2018, 89:308–315.
[8] HE Yong, ZHANG Weiguo, WANG Minwen, et al. Switching linearparameter-varying controller for morphing aircraft based on multiobjective. Control Theory&Applications, 2015, 32(11):1518–1525.(何墉,章卫国,王敏文,等.基于多目标控制的变体飞行器切换线性变参数控制器.控制理论与应用, 2015, 32(11):1518–1525.)
[9] PEQUITO S, PAPPAS G J. Structural minimum controllability problem for switched linear continuous-time systems. Automatica, 2017,78:216–222.
[10] LIN H, ANTSAKLIS P J. Stability and stabilizability of switched linear systems:a survey of recent results. IEEE Transactions on Automatic control, 2009, 54(2):308–322.
[11] HESPANHA J O P, MORSE A S. Switching between stabilizing controllers. Automatica, 2002, 38(11):1905–1917.
[12] KUCERA V. Analysis and Design of Discrete Linear Control Systems. NJ, USA:Prentice-Hall, Inc, 1991.
[13] YOULA D, JABR H, BONGIORNO J. Modern wiener-hopf design of optimal controllers–part II:the multivariable case. IEEE Transactions on Automatic Control, 1976, 21(3):319–338.
[14] LIU Zhikang, YAO Yu. Linear Robust Control. Beijing:Science Press, 2012.(刘志康,姚郁.线性鲁棒控制.北京:科学出版社, 2012.)
[15] XIE W. H∞performance realisation and switching controller design for linear time-invariant plant. IET Control Theory&Applications,2016, 10(4):424–430.
[16] ZHOU K, DOYLE J C, GLOVER K. Robust and Optimal Control.New Jersey:Prentice hall, 1996.
[17] BLANCHINI F, MIANI S, MESQUINE F. A separation principle for linear switching systems and parametrization of all stabilizing controllers. IEEE Transactions on Automatic Control, 2009, 54(2):279–292.
[18] SATO T, LIU K Z. LMI solution to general H2 suboptimal control problems. Systems&Control Letters, 1999, 36(4):295–305.
[19] DOYLE J C, GLOVER K, KHARGONEKAR P P, et al. State-space solutions to standard H2 and H∞control problems. IEEE Transactions on Automatic Control, 1989, 34(8):831–847.