周期时变系统的鲁棒自适应重复控制

针对周期时变系统,提出一种鲁棒自适应重复控制方法.该方法利用周期学习律估计周期时变参数,并结合鲁棒自适应方法处理非周期不确定性.与现有重复控制不同的是,在控制器设计中引入了新变量—周期数,利用周期系统的重复特性,使界的逼近误差随周期数的增加而逐渐减少,保证了系统的全局渐近稳定性.同时将该方法应用于一类非线性参数化系统,使系统在非参数化扰动的情形下,输出误差仍能收敛于0,倒立摆模型的仿真验证了此结果.该设计方法适用于消除神经网络逼近误差对重复控制系统的影响,理论证明了基于神经网络的鲁棒自适应重复控制系统中所有变量的有界性和输出误差的渐近收敛性,关于机械臂模型的仿真结果验证了受控系统具有良好的跟踪性能.

Robust Adaptive Repetitive Control for Periodically Time-varying Systems

In this paper, a robust adaptive repetitive control algorithm is presented for periodically time-varying systems. The periodically time-varying parameters are estimated by periodic learning algorithms, and the non-periodic uncertainties are treated by robust adaptive approaches. Different from the existing repetitive control, a new variable periodic number is introduced to the control design. When this number increases, the convergence error will gradually decrease due to the repetition character of the periodic system, so that the global asymptotic stability is ensured. Further, this method is applied to a class of nonlinearly parameterized systems with non-parametric disturbances, and the tracking error converges asymptotically. This result is verified by a simulation of an invert pendulum model. Moreover, it is proven that the proposed design method is appropriate for the elimination of influence of approximation error of neural network. A theoretical analysis shows that the system output is convergent to the desired one and all signals in the network based robust adaptive repetitive control system are bounded. The simulation result of robotic manipulators shows a good tracking performance of the controlled system.