Study On Initial Value Problem Of The Pd-type Iterative Learning Control With Time-delay

Iterative learning control is a new control technology, which is a branch of intelligent control theory and particularly suitable for a controlled object with a repetitive motion. Iterative learning control is to use the previous or the previous iteration of the input information and the output generated by error correction to modify iteration by iteration control signal, in order to achieve in a limited time interval in the expected output trajectory tracking. Iterative learning control of the initial conditions (initial state) requirement is gradually relaxed, a solution to any arbitrary initial state tracking problem can be applied to iterative learning control for more general control system. All practical control systems are nonlinear, so the absolute linear systems don't exist.As the Phenomenon existed universally in the real controlled objects, time-delay is generated by some actions from transmission, measure and so on. And often results in the in stability and poor performance. So it is meaningful and valuable to study the control problem for time-delay systems.Based on the studying of ILC, under normal circumstances, it is usually assumed that each iterations of the controlled object are running in the initial state exactly at the expected outputs. If the initial value is not the expected output, but in its certain neighborhood, then we put such questions as the initial value of iterative learning control. Initial value problem will affect the tracking accuracy of iterative learning control.This article mainly study the initial value problem of time-delayed PD-type ILC. Specifically, this algorithm considers the following three conditions: the iterative initial condition as same as the desired initial condition, the iterative initial condition is fixed and the iterative initial condition is random. The convergence of this PD iterative learning algorithm was discussed by this three condition, The sufficient conditions which guarantee the convergence of the closed-loop system are theoretically given。By means of Bellman Gronwall inequality andλ-norm theory, the convergence of the algorithms is also proved. The simulation indicate that this PD-type iterative learning algorithm is not only suitable for system with initial iterative error but also has the rapid convergence speed, so it is verified that this algorithm is effective.