Pd-pd Type Learning Control for Uncertain Nonlinear Systems

In this paper, a new learning control, called PD-PD type learning control, is proposed for trajectory tracking of nonlinear systems with uncertainty and disturbance. In the developed control scheme, a PD feedback control with the current tracking errors and a PD type iterative learning control using the previous tracking errors are combined in the updating law. Explicit expressions have been developed for choosing the feedback control gains and the iterative learning gains, and an initial updating scheme is proposed to reduce and eliminate initial errors from iteration to iteration. It is proven that the final tracking error is guaranteed to converge toward the desired trajectory in the presence of varying uncertainty, disturbance, and initial errors. Comparing with the traditional iterative learning control, the new algorithm has potential benefits that include: fast convergence rate, more flexible choices of the learning gains, and monotonic convergence of the tracking error. The effectiveness of the proposed learning control method is demonstrated by simulation experiments. Due to the straightforward implementation and very good trajectory performance of the proposed control algorithm, it should be highly applicable to industrial systems.