一类离散非线性系统基于幂次函数的显式高阶滑模预测控制算法
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摘要
针对一类不确定离散非线性系统,提出了一种显式高阶滑模预测控制算法:利用幂次函数趋近律和高阶滑模控制方法,结合预测控制策略,给出了一种高阶滑模预测模型,得到了显式的高阶滑模预测模型控制器,使其兼具滑模控制方法与预测控制方法的优点,有效削弱了滑模控制系统的抖振现象.最后用数值仿真算例证明了文章设计方法的有效性,与传统滑模预测控制相比,收敛速度更快,稳定性更好.
An explicit higher order sliding mode predictive control algorithm is presented for a class of nonlinear uncertain systems:By applying power exponential reaching law and higher order sliding mode method,employing predictive control strategy,construct a higher order sliding mode prediction model,and get the explicit higher order sliding mode predictive controller,the closed-loop system is proved having advantages of sliding mode control and predictive control,and effectively weakening the chattering phenomenon of sliding mode control system.Finally,the simulation results for a numerical example prove the effectiveness of the designed method,and compared with the traditional sliding mode predictive control,it has faster convergence speed and better stability.
An explicit higher order sliding mode predictive control algorithm is presented for a class of nonlinear uncertain systems:By applying power exponential reaching law and higher order sliding mode method,employing predictive control strategy,construct a higher order sliding mode prediction model,and get the explicit higher order sliding mode predictive controller,the closed-loop system is proved having advantages of sliding mode control and predictive control,and effectively weakening the chattering phenomenon of sliding mode control system.Finally,the simulation results for a numerical example prove the effectiveness of the designed method,and compared with the traditional sliding mode predictive control,it has faster convergence speed and better stability.
引文
[1]曾令武.一类仿射非线性系统滑模降阶控制器设计及其应用.硕士学位论文,南昌航空大学,2013.(Zeng L W.Sliding mode reduced order control design and application for a class of nonlinear affine system.Thesis for the Degree of Master,NanChang HangKong University,2013.)
[2]孟范伟.几类特殊非线性系统的H_∞无穷控制与设计.博士学位论文,哈尔滨工业大学,2013.(Meng F W.H_∞control and system design for some special classes of systems.Thesis for the Doctoral Degree,Harbin Institute of Technology,2013.)
[3]Veluvolu K C,Soh Y C,Cao W.Robust discrete-time nonlinear sliding mode state estimation of uncertain nonlinear systems.International Journal of Robust and Nonlinear Control,2007,17:803-828.
[4]郭益深,孙富春.一类具有参数不确定n阶多输入多输出非线性系统的Terminal滑模控制.控制理论与应用,2013,30(3):324-329.(Guo Y S,Sun F C.Terminal sliding-mode control for a class of nth-order multi-input multioutput nonlinear system with uncertain parameters.Control Theory and Application,2013,30(3):324-329.)
[5]Canale M,Fagiano L,Ferrara A,et al.Vehicle yaw control via second-order sliding-mode technique.IEEE Transactions on Industrial Electronics,2008,55(11):3908-3916.
[6]项基,苏宏业,褚健.一类不确定系统的滑模观测器设计.控制理论与应用,2006,23(6):996-1004.(Xiang J,Su H Y,Chu J.Sliding-mode observer design for a class of uncertain system.Control Theory and Application,2006,23(6):996-1004.)
[7]Levant A.Universal single-input-single-output(SISO)sliding mode controllers with finite-time convergence.IEEE Transactions on Automatic Control,2001,46(9):1447-1451.
[8]Levant A.Principles of 2-sliding mode design.Automatica,2007,43:576-586.
[9]蒲明,吴庆宪,姜长生,等.非匹配不确定高阶非线性系统的滑模控制新方法.控制理论与应用,2012,29(6):708-714.(Pu M,Wu Q X,Jiang C S,et al.New method of sliding-mode control for higher order nonlinear system with mismatched uncertainties.Control Theory and Application,2012,29(6):708-714.)
[10]凌睿,柴毅.MIM0非线性不确定系统二阶滑模控制.计算机工程与应用,2009,45(36):222-224.(Ling R,Chai Y.MIMO nonlinear uncertain system second order sliding mode control.Computer Engineering and Applications,2009,45(36):222-224.)
[11]袁赣南,左志丹,曲桂婷,等.二阶滑模变结构控制系统的滑模到达条件.华中科技大学学报(自然科学版),2013,41(6):70-75.(Yuan G N,Zuo Z D,Qu G T,et al.Reaching condition of sliding mode in second-order sliding mode variable structure control systems.J.Huazhong Univ.of Sci.and Tech.(Natural Science Edition),2013,41(6):70-75.)
[12]王坚浩,胡剑波.不确定非线性系统的自适应反推高阶终端滑模控制.控制与决策,2012,27"(3):413-418.(Wang J H,Hu J B.Adaptive backstepping high-order terminal sliding mode control for uncertain nonlinear systems.Control and Decision,2012,27(3):413-418.)
[13]陈杰,李志平,张国柱.不确定非线性系统的高阶滑模控制器设计.控制理论与应用,2010,27(5):563-569.(Chen J,Li Z P,Zhang G Z.Higher-order sliding-mode controller for a class of uncertain nonlinear systems.Control Theory and Application,2010,27(5):563-569.)
[14]赵占山,张静,孙连坤,等.有限时间收敛的滑模自适应控制器设计.山东大学学报(工学版),2012,42(4):74-78.(Zhao Z S,Zhang J,Sun L K,et al.Design of self-adaptive sliding mode controller with finite time convergence.Journal of Shandong University(Engineering Science),2012,42(4):74-78.)
[15]苏成利,王树青.一种基于Wiener模型的非线性预测控制算法.信息与控制,2007,36(1):86-92.(Su C L,Wang S Q.A nonlinear predictive control algorithm based on wiener model.Information and Control,2007,36(1):86-92.)
[16]Hokayem P,Cinquemani E,Chatterjee D,et al.Stochastic receding horizon control with output feedback and bounded controls.Automatica,2012,48:77-88.
[17]Khandekar A A,Patre B M.Discrete sliding mode control based on optimal sliding surface for time delay systems.India Conference of 2012 Annual IEEE,2012,81-85.
[18]李妍,毛志忠,王福利,等.基于分段Lyapunov函数的Hammerstein-Wiener非线性预测控制.控制与决策,2011,26(5):650-654.(Li Y,Mao Z Z,Wang F L,et al.Hammerstein-Wiener nonlinear predictive control based on piecewise Lyapunov function.Control and Decision,2011,26(5):650-654.)
[19]李庆良,雷虎民,杨志峰,等.一种基于及时学习的非线性系统滑模预测控制方法.控制与决策,2011,26(4):524-529.(Li Q L,Lei H M,Yang Z F,et al.Sliding mode predictive control for nonlinear systems based on lazy learning.Control and Decision,2011,26(4):524-529.)
[20]邢宗义,胡维礼,贾利民.基于T-S模型的模糊预测控制研究.控制与决策,2005,20(5):495-499.(Xing Z Y,Hu W L,Jia L M.Fuzzy predictive control based on T-S model.Control and Decision,2005,20(5):495-499.)
[21]何德峰,薛美盛,季海波.约束非线性系统构造性模型预测控制.控制与决策,2008,23(11):1301-1304.(He D F,Xue M S,Ji H B.Constructive model predictive control for constrained nonlinear systems.Control and Decision,2008,23(11):1301-1304.)
[22]宋立忠,陈少昌,姚琼荟.滑模预测离散变结构控制.控制理论与应用,2004,21(5):826-829.(Song L Z,Chen S C,Yao Q H.Discrete variable structure control algorithm based on sliding mode predictive.Control Theory and Application,2004,21(5):826-829.)
[23]周德文,高存臣,李自强.一种离散变结构控制趋近律.控制与决策,2008,23(3):306-309.(Zhou D W,Gao C C,Li Z Q.Reaching law of discrete-time variable structure control system.Control and Decision,2008,23(3):306-309.)
[24]孙彪,孙秀霞.基于幂次函数的预测滑模控制算法.信息与控制,2011,40(1):39-60.(Sun B,Sun X X.An algorithm of predictive sliding mode control based on power-function.Information and Control,2011,40(1):39-60.)
[25]杨雪.离散非线性系统的滑模预测控制算法研究.硕士学位论文,曲阜师范大学,2014.(Yang X.Research on sliding mode predictive control algorithm for discrete nonlinear systems.Thesis for the Degree of Master,Qufu Normal University,2014.)
[26]高存臣,刘云龙,李云艳.不确定离散变结构控制系统的趋近律方法.控制理论与应用,2009,26(7):781-785.(Gao C,Liu Y L,Li Y Y.A reaching-law method for uncertain discrete variable-structure control systems.Control Theory and Application,2009,26(7):781-785.)
[27]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.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.Acta Automatica Sinica,2013,39(9):1552-1557.)
[28]Mihoub M,Nouri A S,Abdennour R B.A second order discrete sliding mode observer for the variable structure control of a semi-batch reactor.Control Engineering Practice,2011,19:1216—1222.
[2]孟范伟.几类特殊非线性系统的H_∞无穷控制与设计.博士学位论文,哈尔滨工业大学,2013.(Meng F W.H_∞control and system design for some special classes of systems.Thesis for the Doctoral Degree,Harbin Institute of Technology,2013.)
[3]Veluvolu K C,Soh Y C,Cao W.Robust discrete-time nonlinear sliding mode state estimation of uncertain nonlinear systems.International Journal of Robust and Nonlinear Control,2007,17:803-828.
[4]郭益深,孙富春.一类具有参数不确定n阶多输入多输出非线性系统的Terminal滑模控制.控制理论与应用,2013,30(3):324-329.(Guo Y S,Sun F C.Terminal sliding-mode control for a class of nth-order multi-input multioutput nonlinear system with uncertain parameters.Control Theory and Application,2013,30(3):324-329.)
[5]Canale M,Fagiano L,Ferrara A,et al.Vehicle yaw control via second-order sliding-mode technique.IEEE Transactions on Industrial Electronics,2008,55(11):3908-3916.
[6]项基,苏宏业,褚健.一类不确定系统的滑模观测器设计.控制理论与应用,2006,23(6):996-1004.(Xiang J,Su H Y,Chu J.Sliding-mode observer design for a class of uncertain system.Control Theory and Application,2006,23(6):996-1004.)
[7]Levant A.Universal single-input-single-output(SISO)sliding mode controllers with finite-time convergence.IEEE Transactions on Automatic Control,2001,46(9):1447-1451.
[8]Levant A.Principles of 2-sliding mode design.Automatica,2007,43:576-586.
[9]蒲明,吴庆宪,姜长生,等.非匹配不确定高阶非线性系统的滑模控制新方法.控制理论与应用,2012,29(6):708-714.(Pu M,Wu Q X,Jiang C S,et al.New method of sliding-mode control for higher order nonlinear system with mismatched uncertainties.Control Theory and Application,2012,29(6):708-714.)
[10]凌睿,柴毅.MIM0非线性不确定系统二阶滑模控制.计算机工程与应用,2009,45(36):222-224.(Ling R,Chai Y.MIMO nonlinear uncertain system second order sliding mode control.Computer Engineering and Applications,2009,45(36):222-224.)
[11]袁赣南,左志丹,曲桂婷,等.二阶滑模变结构控制系统的滑模到达条件.华中科技大学学报(自然科学版),2013,41(6):70-75.(Yuan G N,Zuo Z D,Qu G T,et al.Reaching condition of sliding mode in second-order sliding mode variable structure control systems.J.Huazhong Univ.of Sci.and Tech.(Natural Science Edition),2013,41(6):70-75.)
[12]王坚浩,胡剑波.不确定非线性系统的自适应反推高阶终端滑模控制.控制与决策,2012,27"(3):413-418.(Wang J H,Hu J B.Adaptive backstepping high-order terminal sliding mode control for uncertain nonlinear systems.Control and Decision,2012,27(3):413-418.)
[13]陈杰,李志平,张国柱.不确定非线性系统的高阶滑模控制器设计.控制理论与应用,2010,27(5):563-569.(Chen J,Li Z P,Zhang G Z.Higher-order sliding-mode controller for a class of uncertain nonlinear systems.Control Theory and Application,2010,27(5):563-569.)
[14]赵占山,张静,孙连坤,等.有限时间收敛的滑模自适应控制器设计.山东大学学报(工学版),2012,42(4):74-78.(Zhao Z S,Zhang J,Sun L K,et al.Design of self-adaptive sliding mode controller with finite time convergence.Journal of Shandong University(Engineering Science),2012,42(4):74-78.)
[15]苏成利,王树青.一种基于Wiener模型的非线性预测控制算法.信息与控制,2007,36(1):86-92.(Su C L,Wang S Q.A nonlinear predictive control algorithm based on wiener model.Information and Control,2007,36(1):86-92.)
[16]Hokayem P,Cinquemani E,Chatterjee D,et al.Stochastic receding horizon control with output feedback and bounded controls.Automatica,2012,48:77-88.
[17]Khandekar A A,Patre B M.Discrete sliding mode control based on optimal sliding surface for time delay systems.India Conference of 2012 Annual IEEE,2012,81-85.
[18]李妍,毛志忠,王福利,等.基于分段Lyapunov函数的Hammerstein-Wiener非线性预测控制.控制与决策,2011,26(5):650-654.(Li Y,Mao Z Z,Wang F L,et al.Hammerstein-Wiener nonlinear predictive control based on piecewise Lyapunov function.Control and Decision,2011,26(5):650-654.)
[19]李庆良,雷虎民,杨志峰,等.一种基于及时学习的非线性系统滑模预测控制方法.控制与决策,2011,26(4):524-529.(Li Q L,Lei H M,Yang Z F,et al.Sliding mode predictive control for nonlinear systems based on lazy learning.Control and Decision,2011,26(4):524-529.)
[20]邢宗义,胡维礼,贾利民.基于T-S模型的模糊预测控制研究.控制与决策,2005,20(5):495-499.(Xing Z Y,Hu W L,Jia L M.Fuzzy predictive control based on T-S model.Control and Decision,2005,20(5):495-499.)
[21]何德峰,薛美盛,季海波.约束非线性系统构造性模型预测控制.控制与决策,2008,23(11):1301-1304.(He D F,Xue M S,Ji H B.Constructive model predictive control for constrained nonlinear systems.Control and Decision,2008,23(11):1301-1304.)
[22]宋立忠,陈少昌,姚琼荟.滑模预测离散变结构控制.控制理论与应用,2004,21(5):826-829.(Song L Z,Chen S C,Yao Q H.Discrete variable structure control algorithm based on sliding mode predictive.Control Theory and Application,2004,21(5):826-829.)
[23]周德文,高存臣,李自强.一种离散变结构控制趋近律.控制与决策,2008,23(3):306-309.(Zhou D W,Gao C C,Li Z Q.Reaching law of discrete-time variable structure control system.Control and Decision,2008,23(3):306-309.)
[24]孙彪,孙秀霞.基于幂次函数的预测滑模控制算法.信息与控制,2011,40(1):39-60.(Sun B,Sun X X.An algorithm of predictive sliding mode control based on power-function.Information and Control,2011,40(1):39-60.)
[25]杨雪.离散非线性系统的滑模预测控制算法研究.硕士学位论文,曲阜师范大学,2014.(Yang X.Research on sliding mode predictive control algorithm for discrete nonlinear systems.Thesis for the Degree of Master,Qufu Normal University,2014.)
[26]高存臣,刘云龙,李云艳.不确定离散变结构控制系统的趋近律方法.控制理论与应用,2009,26(7):781-785.(Gao C,Liu Y L,Li Y Y.A reaching-law method for uncertain discrete variable-structure control systems.Control Theory and Application,2009,26(7):781-785.)
[27]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.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.Acta Automatica Sinica,2013,39(9):1552-1557.)
[28]Mihoub M,Nouri A S,Abdennour R B.A second order discrete sliding mode observer for the variable structure control of a semi-batch reactor.Control Engineering Practice,2011,19:1216—1222.