Composite feedback control of linear singularly perturbed systems: a bond graph approach

Abstract

A procedure to obtain a composite control of linear systems with singular perturbations modelled by bond graphs is presented. The state feedback gains of the composite control based on the slow and fast bond graph models are separately designed. The composite control system is formed by: (1) The original Bond Graph in an Integral causality assignment (BGI) with a state feedback of the fast and slow dynamics. (2) An additional bond graph denoted by Singular Perturbed Bond Graph (SPBG) with a state feedback whose storage elements have integral and derivative causality for the slow and fast dynamics, respectively. The advantages of this approach are: (1) From the BGI, the reduced fast models for open and closed loop systems in a direct way are obtained. (2) From the SPBG, the reduced slow models are determined where the change of the causality of the storage elements for the fast dynamics produces inverse matrices required in the traditional approach. (3) The mathematical models are not required. A junction structure of the bond graph with a composite control to determine the mathematical model of the closed loop system is proposed. Finally, the modelling and control of two illustrative examples applying the proposed methodology are described.