非匹配不确定系统的滑模控制及在电机控制中的应用
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摘要
针对具有匹配与非匹配不确定的非线性系统,设计基于干扰观测器和多幂次趋近律的滑模控制策略.首先,通过干扰观测器估计系统的不确定,实现估计误差在有限时间内收敛;其次,基于积分型滑模面,并结合多幂次趋近律,设计了连续滑模控制律,避免了传统滑模的抖振问题.与基于单幂次和双幂次趋近律的滑模控制策略相比,所设计的基于多幂次趋近律的控制策略,提高了系统的收敛速度.最后,通过数值仿真和永磁同步电机控制仿真验证了所设计的控制策略的有效性.
A sliding mode control(SMC) strategy based on disturbance observer and multi power reaching law is proposed for a nonlinear system with matched and mismatched uncertainties. Firstly, the disturbance is estimated via the disturbance observer, and the estimation error converges in finite time. Secondly, with multi power reaching law, the continuous controller based on integral sliding mode surface is designed, where the chattering problem in the traditional sliding mode control is avoided. Compared with single power reaching law and double power reaching law based-SMC strategy, the multi power reaching law based SMC increases the convergence speed. Finally, the numerical simulation and permanent magnet synchronous motor(PMSM) control simulation are done to demonstrate the performance of the developed control strategy.
A sliding mode control(SMC) strategy based on disturbance observer and multi power reaching law is proposed for a nonlinear system with matched and mismatched uncertainties. Firstly, the disturbance is estimated via the disturbance observer, and the estimation error converges in finite time. Secondly, with multi power reaching law, the continuous controller based on integral sliding mode surface is designed, where the chattering problem in the traditional sliding mode control is avoided. Compared with single power reaching law and double power reaching law based-SMC strategy, the multi power reaching law based SMC increases the convergence speed. Finally, the numerical simulation and permanent magnet synchronous motor(PMSM) control simulation are done to demonstrate the performance of the developed control strategy.
引文
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[21]ZHANG Hexin,FAN Jinsuo,MENG Fei,et al.A new double power reaching law for sliding mode control.Control and Design,2013,28(2):289-293.(张合新,范金锁,孟飞,等.一种新型滑模控制双幂次趋近律.控制与决策,2013,28(2):289-293.)
[22]DEFOORT M,FLOQUET T,KOKOSY A,et al.A novel higher order sliding mode control scheme.Systems&Control Letters,2009,58(2):102-108.
[23]ZHANG Yao,MA Guangfu,GUO Yanning,et al.A multi power reaching law of sliding mode control design and analysis.Acta Automatica Sinica,2016,42(3):466-472.(张瑶,马广富,郭延宁,等.一种多幂次滑模趋近律设计与分析.自动化学报,2016,42(3):466-472.)
[24]GUO Y,ZHANG Y,MA G,et al.Multi-power sliding mode guidance for mars powered descent phase.The 11th UKACC(United Kingdom Automatic Control Council)International Conference on Control.New York:IEEE,2016:129-134.
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[26]GAO Weibing.Theory and Design Method for Variable Sliding Mode Control.Beijing:Science Press,1996.(高为炳.变结构控制的理论及设计方法.北京:科学出版社,1996.)
[27]YU S H,YU X H,SHIRINZADEH B,et al.Continuous finite time control for robotic manipulators with terminal sliding mode.Automatica,2005,41(11):1957-1964.
[28]BHAT S P,BERNSTEIN D S.Geometric homogeneity with application to finite-time stability.Mathematics of Control,Signals and Systems,2005,17(2):101-127.
[29]SUN H B,LI S H,YANG J,et al.Global output regulation for strictfeedback nonlinear systems with mismatched nonvanishing disturbance.International Journal of Robust and Nonlinear Control,2015,25(15):2631-2645.
[30]LI S,SUN H,YANG J,et al.Continuous finite-time output regulation for disturbed systems under mismatching condition.IEEE Transaction on Automatic Control,2015,60(1):277-282.
[31]FANG Yiming,NIU Ben,ZHANG Yongchao,et al.Fast dynamic sliding mode control for speed of permanent synchronous motor.Electric Machines and Control Application,2012,39(4):43-47.(方一鸣,牛犇,张永潮,等.永磁同步电机转速快速动态滑模控制.电机与控制应用,2012,39(4):43-47.)
[2]CHANG Xuejian,PENG Bo,LIU Ling,et al.A novel nonsingular terminal sliding mode observer for sensorless.control of permanent magnet synchronous motor.Journal of Xi’an Jiaotong University,2016,50(1):1-8.(常雪剑,彭博,刘凌,等.新型非奇异终端滑模观测器的永磁同步电机无传感控制.西安交通大学学报,2016,50(1):1-8.)
[3]XIONG Shaofeng,WANG Weihong,WANG Sen.Nonsingular fast terminal sliding-mode guidance with intercept angle constraint.Control Theory&Applications,2014,31(3):269-278.(熊少锋,王卫红,王森.带攻击角度约束的非奇异快速终端滑模制导律.控制理论与应用,2014,31(3):269-278.)
[4]WANG F,ZONG Q,DONG Q,et al.Disturbance observer-based sliding mode backstepping control for a re-entry vehicle with input constraint and external disturbance.Transactions of the Institute of Measurement and Control,2015,38(2):1-17.
[5]VAN M,GE S S,REN H L.Finite time fault tolerant control for robot manipulators using time delay estimation and continuous nonsingular fast terminal sliding mode control.IEEE Transactions on Cybernetics,2017,47(7):1681-1693.
[6]LIU Yu,WEI Zhongchao,GAO Xinmai,et al.A scalar control method to the brushless doubly-fed generator.Journal of Hubei U-niversity of Technology,2014,29(1):29-32.(刘愉,韦忠朝,高信迈,等.无刷双馈发电机的一种标量控制方法.湖北工业大学学报,2014,29(1):29-32.)
[7]FENG Y,YU X H,MAN Z H.Non-singular terminal sliding mode control of rigid manipulators.Automatica,2002,38(12):2159-2167.
[8]PU Ming,JIANG Tao,LIU Peng.Nonsingular terminal sliding mode control for a class of 3-order nonlinear systems.Control Theory&Applications,2017,34(5):683-691.(蒲明,蒋涛,刘鹏.一类3阶非线性系统的非奇异终端滑模控制.控制理论与应用,2017,34(5):683-691.)
[9]YU X H,MAN Z H.Fast terminal sliding-mode control design for nonlinear dynamical systems.IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications,2002,49(2):261-264.
[10]YANG L,YANG J.Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems.International Journal of Robust and Nonlinear Control,2011,21(16):1865-1879.
[11]EATRADA A,FRIDMAN L.Quasi-continuous HOSM control for systems with unmatched Perturbations.Automatica,2010,46(11):1916-1919.
[12]WON M,HEDRICK J K.Multiple-surface sliding control of a class of uncertain nonlinear systems.International Journal of Control,1996,64(4):693-706.
[13]CAO X J,XU J X.Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems.IEEE Transactions on Automatic Control,2004,49(8):1355-1360.
[14]YANG J,LI S H,YU X H.Sliding-mode control for systems with mismatched uncertainties via a disturbance observer.IEEE Transactions on Industrial Electronics,2013,60(1):160-169.
[15]YANG J,LI S H,SU J Y,et al.Continuous nonsingular terminal sliding mode control for systems with matched and mismatched disturbances.Automatica,2013,49(7):2287-2291.
[16]HWANG C L.Sliding mode control using time-varying switching gain and boundary layer for electrohydraulic position and differential pressure control.IEE Proceedings-Control Theory and Applications,1996,143(4):325-332.
[17]XU J X,PAN Y J,LEE T H.A gain scheduled sliding mode control scheme using filtering techniques with applications to multi-link robotic manipulators.Journal of Dynamic Systems,Measurement and Control,2000,122(4):641-649.
[18]LIAN R J.Adaptive self-organizing fuzzy sliding-mode radial basisfunction neural-network controller for robotic systems.IEEE Transactions on Industrial Electronics,2014,61(3):1493-1503.
[19]GAO W B,HUNG J C.Variable structure control of nonlinear systems:a new approach.IEEE Transactions on Industrial Electronics,1993,40(1):45-55.
[20]LI Peng,MA Jianjun,ZHENG Zhiqiang.Sliding mode control approach based on nonlinear integrator.Control Theory&Applications,2011,28(5):619-624.(李鹏,马建军,郑志强.采用幂次趋近律的滑模控制稳态误差界.控制理论与应用,2011,28(5):619-624.)
[21]ZHANG Hexin,FAN Jinsuo,MENG Fei,et al.A new double power reaching law for sliding mode control.Control and Design,2013,28(2):289-293.(张合新,范金锁,孟飞,等.一种新型滑模控制双幂次趋近律.控制与决策,2013,28(2):289-293.)
[22]DEFOORT M,FLOQUET T,KOKOSY A,et al.A novel higher order sliding mode control scheme.Systems&Control Letters,2009,58(2):102-108.
[23]ZHANG Yao,MA Guangfu,GUO Yanning,et al.A multi power reaching law of sliding mode control design and analysis.Acta Automatica Sinica,2016,42(3):466-472.(张瑶,马广富,郭延宁,等.一种多幂次滑模趋近律设计与分析.自动化学报,2016,42(3):466-472.)
[24]GUO Y,ZHANG Y,MA G,et al.Multi-power sliding mode guidance for mars powered descent phase.The 11th UKACC(United Kingdom Automatic Control Council)International Conference on Control.New York:IEEE,2016:129-134.
[25]SHTESSEL Y B,SHKOLNIKOV I A,LEVANT A.Smooth secondorder sliding modes:missile guidance application.Automatica,2007,43(8):1470-1476.
[26]GAO Weibing.Theory and Design Method for Variable Sliding Mode Control.Beijing:Science Press,1996.(高为炳.变结构控制的理论及设计方法.北京:科学出版社,1996.)
[27]YU S H,YU X H,SHIRINZADEH B,et al.Continuous finite time control for robotic manipulators with terminal sliding mode.Automatica,2005,41(11):1957-1964.
[28]BHAT S P,BERNSTEIN D S.Geometric homogeneity with application to finite-time stability.Mathematics of Control,Signals and Systems,2005,17(2):101-127.
[29]SUN H B,LI S H,YANG J,et al.Global output regulation for strictfeedback nonlinear systems with mismatched nonvanishing disturbance.International Journal of Robust and Nonlinear Control,2015,25(15):2631-2645.
[30]LI S,SUN H,YANG J,et al.Continuous finite-time output regulation for disturbed systems under mismatching condition.IEEE Transaction on Automatic Control,2015,60(1):277-282.
[31]FANG Yiming,NIU Ben,ZHANG Yongchao,et al.Fast dynamic sliding mode control for speed of permanent synchronous motor.Electric Machines and Control Application,2012,39(4):43-47.(方一鸣,牛犇,张永潮,等.永磁同步电机转速快速动态滑模控制.电机与控制应用,2012,39(4):43-47.)