Iterative Learning Control for Fractional Order Linear Systems with Time Delay Based on Frequency Analysis

To overcome the deficiencies of time delay in the repetitive control of fractional-order linear systems, PDα-type iterative learning control (ILC) law and P & convolution-type ILC law are designed for input and state time delay, respectively. Convergence conditions are derived in frequency domain via contraction mapping principle. Besides, the convergence frequency domain of proposed feedback controllers is obtained over a finite frequency range to design the controllers effectively. Then, the effectiveness of the proposed theoretical schemes is demonstrated using two numerical examples. The influence of time delay is eliminated, and output trajectory convergence to the desired one is guaranteed. Moreover, the Nyquist diagram of transfer function G(s) and time delay variation are analyzed in frequency domain to reveal the influence of convergence on the system.