AN INTEGRAL MANIFOLD APPROACH TO TRACKING CONTROL FOR A CLASS OF NONMINIMUM-PHASE LINEAR-SYSTEMS USING OUTPUT-FEEDBACK

In this paper the tracking control problem for a class of SISO non-min imum phase linear systems containing n dominant slow modes and m paras itic fast modes using output feedback is considered. It is assumed tha t the reduced-order slow model obtained by neglecting the parasitic mo des is minimum phase. It is shown that by using the integral manifolds approach it is possible to design a corrected control so that the ful l-order system restricted to the pth-order-corrected manifold is minim um phase. This, in principle, amounts to formally defining a new outpu t for which the corrected system is minimum phase. By applying to the full-order system the corrected dynamical output feedback controller t hat is designed for the minimum phase corrected system, it is then pos sible for the actual output to track a class of desired trajectories w ith minimum accuracy of O(epsilon(p)), where 0 < epsilon < 1 is the pe rturbation parameter and p is an arbitrarily large positive integer. M oreover, it is shown that the zero dynamics of the associated correcte d slow subsystem is itself singularly perturbed. Therefore, the dynami cal output feedback may contain both slow and fast dynamics. Numerical simulations are included to demonstrate the significant improvement t hat is possible to achieve by employing the proposed control strategy. Copyright (C) 1996 Elsevier Science Ltd.