Iterative Learning Control for Nonlinear Nonminimum Phase Plants¹

Learning control is a very effective approach for tracking control in processes occurring repetitively over a fixed interval of time. In this paper a robust learning algorithm is proposed for a generic family of nonlinear, nonminimum phase plants with disturbances and initialization error. The “stable-inversion” method of Devasia, Chen and Paden is applied to develop a learning controller for linear nonminimum phase plants. This is adapted to accommodate a more general class of nonlinear plants. The bounds on the asymptotic error for the learned input are exhibited via a concise proof. Simulation studies demonstrate that in the absence of input disturbances, perfect tracking of the desired trajectory is achieved for nonlinear nonminimum phase plants. Further, in the presence of random disturbances, the tracking error converges to a neighborhood of zero. A bound on the tracking error is derived which is a continuous function of the bound on the disturbance. It is also observed that perfect tracking of the desired trajectory is achieved if the input disturbance is the same at every iteration.