Approximate tracking of periodic references in a class of bilinear systems via stable inversion

Josep M. Olm; Xavier Ros-Oton

doi:10.3934/dcdsb.2011.15.197

Article Contents

2011, Volume 15, Issue 1: 197-215. Doi: 10.3934/dcdsb.2011.15.197

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Approximate tracking of periodic references in a class of bilinear systems via stable inversion

Josep M. Olm^1, and
Xavier Ros-Oton^2,

1.
Department of Applied Mathematics IV, Universitat Politècnica de Catalunya, Av. Víctor Balaguer, s/n, 08800 Vilanova i la Geltrú
2.
Department of Applied Mathematics I, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028 Barcelona

Received: December 2009

Revised: August 2010

Published: July 2011

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Abstract

This article deals with the tracking control of periodic references in single-input single-output bilinear systems using a stable inversion-based approach. Assuming solvability of the exact tracking problem and asymptotic stability of the nominal error system, the study focuses on the output behavior when the control scheme uses a periodic approximation of the nominal feedforward input signal $u_d$. The investigation shows that this results in a periodic, asymptotically stable output; moreover, a sequence of periodic control inputs $u_n$ uniformly convergent to $u_d$ produce a sequence of output responses that, in turn, converge uniformly to the output reference. It is also shown that, for a special class of bilinear systems, the internal dynamics equation can be approximately solved by an iterative procedure that provides of closed-form analytic expressions uniformly convergent to its exact solution. Then, robustness in the face of bounded parametric disturbances/uncertainties is achievable through dynamic compensation. The theoretical analysis is applied to nonminimum phase switched power converters.

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Mathematics Subject Classification: Primary: 93C10, 93C15; Secondary: 34H05.

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