Output Tracking of Non-Minimum Phase Dynamics

Abstract

This paper develops a general control algorithm for the exact output tracking of nonlinear systems with non-minimum phase dynamics. The control technique is causal and does not require preview or knowledge of the desired reference beforehand. Additionally, the control is independent of the operating condition and the desired reference. The main idea of the paper is to convert the output tracking problem into a slow state tracking problem for singularly perturbed systems. Previous work on singularly perturbed systems have shown asymptotic tracking of slow states only for a class of nonlinear systems that are linear in the fast states. However, this paper develops a control technique that does not have this restriction and is applicable to a general class of nonlinear singularly perturbed systems. The procedure is to compute the desired internal state trajectory and the control scheme that stabilizes the nonlinear system online, thereby guaranteeing asymptotic output tracking. Performance of this approach is demonstrated in simulation for two benchmark problems: the beam-ball example that is slightly non-minimum phase and fails to have a well-dened relative degree, and the Conventional Take-o and Landing (CTOL) non-minimum phase aircraft. Results presented in the paper show that the approach is able to accomplish perfect tracking while stabilizing the closed-loop system, while keeping all closed-loop signals bounded.