Sampled-Data Iterative Learning Control

Iterative Learning Control(ILC) was first put forward by Arimoto etc.al. in 1984. It is mainly applied in systems which characters repeated operation. ILC could adjust the control input with tracking error in order to make the real output converge to the idea trajectory precisely during a limited period. Since then, more and more attention has been paid to the ILC. Researchers have put forward many ILC algorithms toward different kinds of systems and proved the convergence of these algorithms based on reasonable assumptions and advanced mathematical methods. The ILC has got great development.However, the majority of algorithms applied in industry should go via computers. This leads to the consideration of sampled time for iterative learning control. We call it Sampled-Data Iterative Learning Control (SDILC).SDILC, with the conception of sampled time to ILC, is a branch of ILC.This paper presents one-order PD type SDILC algorithm and high-order PID type algorithm for a class of nonlinear time-delayed system with disturbances. By using Taylor's series which is different with traditional analysis tool, a rigorous proof is given for the convergence of one-order and high-order algorithm respectively. As there is no terms of integral, the calculation will be much easier comparing with the traditional one. Meanwhile, this paper delves into the problem of combining Model Reference Adaptive Control and SDILC which is called Model Reference Adaptive Sampled-Data Iterative Learning Control(MRASDILC). For a class of MIMO system with time-varying parameters, the convergence condition of MRASDILC is given in term of Riccati Equation. First, this paper focuses on designing MRASDILC algorithm by Lyapunov function in order to ensure its stability in time domain. Secondly, this paper proves its convergence in iteration domain. Besides, different prove methods are discussed. Finally, in section 5, numerical examples are given to support the theoretical analysis in this paper.