Study Of Control Approach For Systems With Repetitive Characteristics

Iterative learning control(ILC) makes use of previous control information, and uses the easy algorithm to track accurately the desired trajectory in a limited time. Furthermore ILC doesn’t depend on precise mathematic models. Thereby ILC is applied in the complicated system with nonlinearity and tight coupling, and has a strong application background. On the other hand, repetitive processes are a distinct class of 2D systems, whose information propagation along the pass is in a limited time. Repetitive processes are applied in not only the research of ILC but also the control of actual systems. But the most of research has considered the analysis and synthesis of linear repetitive processes, while the actual systems are always time-varying. LPV systems are a peculiar kind of linear systems that depend on the real-time measurable parameters, and are applied to represent time-varying dynamical systems. Meanwhile, he delay phenomenon is ubiquitous in practical due to the transmission of information or energy. In conclusion, the research of LPV repetitive processes is of important theoretical and engineering significance.Design method of a new feedback-assisted high-order iterative learning controller is given for a class of nonlinear systems with uncertainty and disturbance. The given controller introduces PD-type control as the feedback part under the traditional high-order iterative learning control, which uses the feedback part to suppress the influence of disturbance on system, and the convergence discussion of the algorithm is given using l-norm. In addition, for a class of nonlinear systems with initial state disturbance, a PD-type iterative learning controller with variable learning gain of an arbitrary initial state was proposed. The proposed controller uses iterative learning of initial state to reduce tracking error caused by initial state disturbance, and employs iterative learning control law with variable learning gain to improve the control accuracy and the convergent speed.A robust delay-dependent 2L L￥- state feedback controller and a 2L L￥- dynamic output feedback controller are designed for continuous and discrete linear parameter-varying(LPV) repetitive processes with parameter-varying delays. Firstly, by making use of a parameter-dependent Lyapunov-Krasovskii functional(LKF), the sufficient conditions for 2L L￥-(2l l￥- if system is discrete) performance analysis are proposed. Subsequently, by introducing a slack matrix, the product terms existed between the parameter-dependent LKF matrices and the system matrices are decoupled. Finally, approximate basis functions and gridding technique are applied to transform PLMIs into a convex optimization problem of finite dimensional linear matrix inequalities(LMIs).Design method of a robust iterative learning controller based on two-demensional(2D) is given. Firstly, consider control activity and learning activity independently, a continuous-discrete 2D model is built that can describe the process of ILC systems accurately. Subsequently, a sufficient condition of system convergence and the method to calculate the parameters of the controller, thus avoiding the blindness of choosing the parameters of the general controller.