基于改进扰动补偿趋近律的离散滑模控制
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摘要
考虑满足匹配条件的不确定离散系统,提出一种改进扰动补偿趋近律滑模控制算法,分析准滑动模态的动态特性.为了减小准滑模域带宽,重新将扰动变化率定义为二阶扰动差分;同时,引入饱和函数,通过设置适当的边界层厚度,使得系统准滑模域带宽达到O(T3)量级且无稳态抖振,从而提高系统的控制精度;最后通过仿真实验验证所提出算法的有效性.
Considering the uncertain discrete-time system satisfying matched conditions, an improved disturbance compensation reaching law based sliding mode control algorithm is presented, and the dynamic features of the quasisliding mode are analyzed. To decrease the bandwidth of the quasi-sliding mode domain, the changing rate of the disturbance is redefined as the second-order disturbance difference. In addition, the satuation function is introduced,and by setting proper thickness of the boundary layer, the bandwidth of the quasi-sliding mode domain can achieve the magnitude of the order O(T3) without steady-state chattering, which improves the control precision of the system.Simulation results verify the effectiveness of the presented algorithm.
Considering the uncertain discrete-time system satisfying matched conditions, an improved disturbance compensation reaching law based sliding mode control algorithm is presented, and the dynamic features of the quasisliding mode are analyzed. To decrease the bandwidth of the quasi-sliding mode domain, the changing rate of the disturbance is redefined as the second-order disturbance difference. In addition, the satuation function is introduced,and by setting proper thickness of the boundary layer, the bandwidth of the quasi-sliding mode domain can achieve the magnitude of the order O(T3) without steady-state chattering, which improves the control precision of the system.Simulation results verify the effectiveness of the presented algorithm.
引文
[1]Yu X,Wang B,Li X.Computer-controlled variable structure systems:The state-of-the-art[J].IEEE Trans on Industrial Informatics,2012,8(2):197-205.
[2]Young K D,Utkin V I,Ozguner U.A control engineer’s guide to sliding mode control[J].IEEE Trans on Control Systems Technology,1999,7(3):328-342.
[3]Milosavljevi??C.General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems[J].Automation and Remote Control,1985,46(30):307-314.
[4]Sarpturk S,Istefanopulos Y,Kaynak O.On the stability of discrete-time sliding mode control systems[J].IEEETrans on Automatic Control,2003,32(10):930-932.
[5]Furuta K.Sliding mode control of a discrete system[J]Systems and Control Letters,1990,14(2):145-152.
[6]Gao W,Wang Y,Homaifa A.Discrete-time variable structure control systems[J].IEEE Trans on Industrial Electronics,1995,42(2):117-122.
[7]朱齐丹,汪瞳.一种改进的离散时间系统变结构控制设计方法[J].自动化学报,2010,36(6):885-889.(Zhu Q D,Wang T.An improved design scheme of variable structure control for discrete-time systems[J]Acta Automatica Sinica,2010,36(6):885-889.)
[8]刘希,孙秀霞,董文瀚,等.一种新的约束变速趋近律离散滑模控制方法[J].自动化学报,2013,39(9):1552-1557.(Liu X,Sun X X,Dong W H,et al.A new discrete-time sliding mode control method based on restricted variable trending law[J].Acta Automatica Sinica,2013,39(9):1552-1557.)
[9]邬玲伟,孙明轩.无抖振离散重复控制器的设计与实现[J].控制理论与应用,2015,32(4):554-560.(Wu L W,Sun M X.Design and implementation of a chattering-free discrete-time repetitive controller[J]Control Theory&Applications,2015,32(4):554-560.)
[10]Eun Y,Kim J H,Kim K,et al.Discrete-time variable structure controller with a decoupled disturbance compensator and its application to a CNC servomechanism[J].IEEE Trans on Control Systems Technology,1999,7(4):414-423.
[11]Qu S,Xia X,Zhang J.Dynamics of discrete-time sliding-mode-control uncertain systems with a disturbance compensator[J].IEEE Trans on Industrial Electronics,2014,61(7):3502-3510.
[12]Bartoszewicz A.Discrete-time quasi-sliding-mode control strategies[J].IEEE Trans on Industrial Electronics,1998,45(4):633-637.
[13]孙明轩,王辉,范伟云.以幂次趋近的离散变结构重复控制[J].控制理论与应用,2012,29(11):1426-1432.(Sun M X,Wang H,Fan W Y.Discrete-time variable-structure repetitive control with power-rate reaching[J].Control Theory&Applications,201229(11):1426-1432.)
[14]苏磊,姚宏,张志浩,等.非匹配离散系统无抖振鲁棒准滑模控制[J].控制与决策,2015,30(3):551-555.(Su L,Yao H,Zhang Z H,et al.Chattering-free robust quasi-sliding mode control for unmatched discrete-time systems[J].Control and Decision,2015,30(3):551-555.)
[15]刘涛,刘贺平,屈微.基于离散时变趋近律的准滑模控制[J].控制与决策,2010,25(5):797-800.(Liu T,Liu H P,Qu W.Quasi-sliding-mode control based on discrete time-variant reaching law[J].Control and Decision,2010,25(5):797-800.)
[16]Abidi K,Xu J X,Yu X.On the discrete-time integral sliding-mode control[J].IEEE Trans on Automatic Control,2007,52(4):709-715.
[17]Haibo Du,Xinghuo Yu,Michael Z Q Chen,et al Chattering-free discrete-time sliding mode control[J]Automatica,2016,68(C):87-91.
[2]Young K D,Utkin V I,Ozguner U.A control engineer’s guide to sliding mode control[J].IEEE Trans on Control Systems Technology,1999,7(3):328-342.
[3]Milosavljevi??C.General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems[J].Automation and Remote Control,1985,46(30):307-314.
[4]Sarpturk S,Istefanopulos Y,Kaynak O.On the stability of discrete-time sliding mode control systems[J].IEEETrans on Automatic Control,2003,32(10):930-932.
[5]Furuta K.Sliding mode control of a discrete system[J]Systems and Control Letters,1990,14(2):145-152.
[6]Gao W,Wang Y,Homaifa A.Discrete-time variable structure control systems[J].IEEE Trans on Industrial Electronics,1995,42(2):117-122.
[7]朱齐丹,汪瞳.一种改进的离散时间系统变结构控制设计方法[J].自动化学报,2010,36(6):885-889.(Zhu Q D,Wang T.An improved design scheme of variable structure control for discrete-time systems[J]Acta Automatica Sinica,2010,36(6):885-889.)
[8]刘希,孙秀霞,董文瀚,等.一种新的约束变速趋近律离散滑模控制方法[J].自动化学报,2013,39(9):1552-1557.(Liu X,Sun X X,Dong W H,et al.A new discrete-time sliding mode control method based on restricted variable trending law[J].Acta Automatica Sinica,2013,39(9):1552-1557.)
[9]邬玲伟,孙明轩.无抖振离散重复控制器的设计与实现[J].控制理论与应用,2015,32(4):554-560.(Wu L W,Sun M X.Design and implementation of a chattering-free discrete-time repetitive controller[J]Control Theory&Applications,2015,32(4):554-560.)
[10]Eun Y,Kim J H,Kim K,et al.Discrete-time variable structure controller with a decoupled disturbance compensator and its application to a CNC servomechanism[J].IEEE Trans on Control Systems Technology,1999,7(4):414-423.
[11]Qu S,Xia X,Zhang J.Dynamics of discrete-time sliding-mode-control uncertain systems with a disturbance compensator[J].IEEE Trans on Industrial Electronics,2014,61(7):3502-3510.
[12]Bartoszewicz A.Discrete-time quasi-sliding-mode control strategies[J].IEEE Trans on Industrial Electronics,1998,45(4):633-637.
[13]孙明轩,王辉,范伟云.以幂次趋近的离散变结构重复控制[J].控制理论与应用,2012,29(11):1426-1432.(Sun M X,Wang H,Fan W Y.Discrete-time variable-structure repetitive control with power-rate reaching[J].Control Theory&Applications,201229(11):1426-1432.)
[14]苏磊,姚宏,张志浩,等.非匹配离散系统无抖振鲁棒准滑模控制[J].控制与决策,2015,30(3):551-555.(Su L,Yao H,Zhang Z H,et al.Chattering-free robust quasi-sliding mode control for unmatched discrete-time systems[J].Control and Decision,2015,30(3):551-555.)
[15]刘涛,刘贺平,屈微.基于离散时变趋近律的准滑模控制[J].控制与决策,2010,25(5):797-800.(Liu T,Liu H P,Qu W.Quasi-sliding-mode control based on discrete time-variant reaching law[J].Control and Decision,2010,25(5):797-800.)
[16]Abidi K,Xu J X,Yu X.On the discrete-time integral sliding-mode control[J].IEEE Trans on Automatic Control,2007,52(4):709-715.
[17]Haibo Du,Xinghuo Yu,Michael Z Q Chen,et al Chattering-free discrete-time sliding mode control[J]Automatica,2016,68(C):87-91.