An improved fast error convergence topology for PD^α-type fractional-order ILC

The monotonic convergence of the PDα-type fractional-order iterative learning control algorithm is considered for a class of fractional-order linear systems. First, a theoretical analysis of the monotonic convergence of 1st and 2nd order PDα-type control algorithms is carried out in the typical terms of Lebesgue-p (Lp), and the sufficient conditions for their monotonic convergence are comprehended and extended to the case of N-order control algorithms; then the speed of convergence of the two is explained in detail. It is concluded that the conditions for convergence of the control algorithm are determined by the learning gain and the system’s properties are together determined. Simulation experiment verifies the accuracy of proposed scheme and the validity of the control algorithm.