An integral manifold approach to tracking control for a class of non-minimum phase linear systems using output feedback

Abstract

In this paper the tracking control problem for a class of SISO non-minimum phase linear systems containing n dominant slow modes and m parasitic fast modes using output feedback is considered. It is assumed that the reduced-order slow model obtained by neglecting the parasitic modes is minimum phase. It is shown that by using the integral manifolds approach it is possible to design a corrected control so that the full-order system restricted to the pth-order-corrected manifold is minimum phase. This, in principle, amounts to formally defining a new output for which the corrected system is minimum phase. By applying to the full-order system the corrected dynamical output feedback controller that is designed for the minimum phase corrected system, it is then possible for the actual output to track a class of desired trajectories with minimum accuracy of O( ε p ), where 0 < ε < 1 is the perturbation parameter and p is an arbitrarily large positive integer. Moreover, it is shown that the zero dynamics of the associated corrected slow subsystem is itself singularly perturbed. Therefore, the dynamical output feedback may contain both slow and fast dynamics. Numerical simulations are included to demonstrate the significant improvement that is possible to achieve by employing the proposed control strategy.