Monotonic convergence conditions in PD type iterative learning control

In this paper, we present a proportional - derivative (PD) type iterative learning control (ILC) for discrete-time systems, performing repetitive tasks. That is, the input of controlled system in current cycle is modified by using the PD strategy on the error achieved between the system output and the desired trajectory in the previous iteration. The convergence of the presented scheme is analyzed and an optimal design method is obtained to determine the PD learning coefficients. Furthermore a condition is achieved in terms of the system parameters so that the monotonic convergence of the presented method is guaranteed. An illustrative example is given to demonstrate the effectiveness of the proposed ILC.