任意初态下的扰动系统学习控制
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摘要
针对任意初态下带有扰动的线性定常系统,提出了相应的控制算法。该算法将受控过程分成无穷个子过程,系统利用上一子过程的输入输出信息来调节当前过程的输入,以期获得更好的控制效果。在控制过程中,基于迭代学习控制思想,借助初始修正手段,可使系统的跟踪误差达到任意小,且当系统无扰动时,在指定区间内可实现完全跟踪。最后,通过仿真算例,验证了算法的有效性。
A control algorithm for the linear time-invariant system is presented in this paper. It divides the controlled process into infinite subprocesses. For each subprocess, the system uses the input and output information of the last subprocess to adjust the current input in order to achieve a better control effect. In the control process, based on the iterative learning control theory, this algorithm solves the control problem using the initial rectifying methods. It can make the tracking error of the system converge to an arbitrarily small range, and achieve complete tracking if there is no disturbance in the specified time period. Finally, the effectiveness of the stated algorithm is demonstrated by the simulation result.
A control algorithm for the linear time-invariant system is presented in this paper. It divides the controlled process into infinite subprocesses. For each subprocess, the system uses the input and output information of the last subprocess to adjust the current input in order to achieve a better control effect. In the control process, based on the iterative learning control theory, this algorithm solves the control problem using the initial rectifying methods. It can make the tracking error of the system converge to an arbitrarily small range, and achieve complete tracking if there is no disturbance in the specified time period. Finally, the effectiveness of the stated algorithm is demonstrated by the simulation result.
引文
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[17]TAYEBI A,CHIEN C.A unified adaptive iterative learning control framework for uncertain nonlinear systems[J].IEEE Transactions on Automatic Control,2007,52(10):1907-1913.
[18]CHIEN C,HSU C,YAO C.Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors[J].IEEE Transactions on Fuzzy Systems,2004,12(5):724-732.
[19]孙明轩.有限时间迭代学习控制[J].系统科学与数学,2010,30(6):733-741.SUN M X.Finite-time iterative learning control[J].Journal of Systems Science and Mathematical Sciences,2010,30(6):733-741.
[20]谢华英,孙明轩.有限时间死区修正迭代学习控制器的设计[J].控制理论与应用,2009,26(11):1225-1231.XIE H Y,SUN M X.Design of iterative learning controllers with finite-time dead-zone modification[J].Control Theory&Applications,2009,26(11):1225-1231.
[21]齐丽强,孙明轩,管海娃.非参数不确定系统的有限时间迭代学习控制[J].自动化学报,2014,40(7):1320-1327.QI L Q,SUN M X,GUAN H W.Finite-time iterative learning control for systems with nonparametric uncertainties[J].Acta Automatica Sinica,2014,40(7):1320-1327.
[22]YIN C K,XU J X,HOU Z S.A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters[J].IEEE Transactions on Automatic Control,2010,56(11):2665-2670.
[2]ARIMOTO S,KAWAMURA S,MIYAZAKI F.Bettering operation of robots by learning[J].Journal of Intelligent&Robotic Systems,1984,1(2):123-140.
[3]BRISTOW D,THARAYIL M,ALLEYNE A G.Asurvey of iterative learning control[J].IEEE Control Systems Magazine,2006,26(3):96-114.
[4]ISHIHARA T,ABE K,TAKEDA H.A discretetime design of robust iterative learning controllers[J].IEEE Transactions on Systems Man and Cybernetics Part B,1992,22(1):74-84.
[5]SAAB S S,VOGT W G,MICKLE M H.Learning control algorithms for tracking‘slowly’varying trajectories[J].IEEE Transactions on Systems Man and Cybernetics Part B,1997,27(4):657-670.
[6]HEINZINGER G,FENWICK D,PADEN B,et al.Stability of learning control with disturbances and uncertain initial conditions[J].IEEE Transactions on Automatic Control,1992,37(1):110-114.
[7]WANG D W.Convergence and robustness of discrete time nonlinear systems with iterative learning control[J].Automatica,1998,34(11):1445-1448.
[8]ARIMOTO S.Learning control theory for robotic motion[J].International Journal of Adaptive Control and Signal Processing,1990,4(6):543-564.
[9]LEE H S,BIEN Z.Study on robustness of iterative learning control with nonzero initial error[J].International Journal of Control,1996,64(3):345-359.
[10]PARK P,BIEN Z,HWANG D.A study on the robustness of a PID-type iterative learning controller against initial state error[J].International Journal of Systems Science,1999,30(1):49-59.
[11]SUN M X,WANG D W.Initial condition issues on iterative learning control for nonlinear systems with time delay[J].International Journal of Systems Science,2001,32(11):1365-1375.
[12]李国军,陈东杰,韩一士.带有初态误差的高阶多智能体系统一致性跟踪[J].应用数学学报,2018,41(2):156-171.LI G J,CHEN D J,HAN Y S.Consensus tracking of high-order multi-agent systems with initial state errors[J].Acta Mathematicae Applocatae Sinica,2018,41(2):156-171.
[13]LI X D,CHOW T W S,HO J K L,et al.Iterative learning control with initial rectifying action for nonlinear continuous systems[J].IET Control Theory&Applications,2009,3(1):49-55.
[14]LI X D,WEI Y S.Iterative learning control for linear discrete-time systems with high relative degree under initial state vibration[J].IET Control Theory&Applications,2016,10(10):1115-1126.
[15]MENG D Y,MOORE K L.Robust iterative learning control for nonrepetitive uncertain systems[J].IEEETransactions on Automatic Control,2017,62(2):907-913.
[16]XU J X,TAN Y.A composite energy function-based learning control approach for nonlinear systems with timevarying parametric uncertainties[J].IEEE Transactions on Automatic Control,2002,47(11):1940-1945.
[17]TAYEBI A,CHIEN C.A unified adaptive iterative learning control framework for uncertain nonlinear systems[J].IEEE Transactions on Automatic Control,2007,52(10):1907-1913.
[18]CHIEN C,HSU C,YAO C.Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors[J].IEEE Transactions on Fuzzy Systems,2004,12(5):724-732.
[19]孙明轩.有限时间迭代学习控制[J].系统科学与数学,2010,30(6):733-741.SUN M X.Finite-time iterative learning control[J].Journal of Systems Science and Mathematical Sciences,2010,30(6):733-741.
[20]谢华英,孙明轩.有限时间死区修正迭代学习控制器的设计[J].控制理论与应用,2009,26(11):1225-1231.XIE H Y,SUN M X.Design of iterative learning controllers with finite-time dead-zone modification[J].Control Theory&Applications,2009,26(11):1225-1231.
[21]齐丽强,孙明轩,管海娃.非参数不确定系统的有限时间迭代学习控制[J].自动化学报,2014,40(7):1320-1327.QI L Q,SUN M X,GUAN H W.Finite-time iterative learning control for systems with nonparametric uncertainties[J].Acta Automatica Sinica,2014,40(7):1320-1327.
[22]YIN C K,XU J X,HOU Z S.A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters[J].IEEE Transactions on Automatic Control,2010,56(11):2665-2670.