International Journal of applied mathematics and computer science

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Paper details

Number 4 - December 1998
Volume 8 - 1998

Distributed output feedback control of two-time-scale hyperbolic PDE systems

Panagiotis D. Christofides, Prodromos Daoutidis

This article focuses on systems of two-time-scale hyperbolic partial differential equations (PDEs), modeled in singularly perturbed form, for which the manipulated inputs, the controlled and the measured outputs are distributed in space. The objective is to synthesize distributed output feedback controllers that guarantee closed-loop stability and enforce output tracking, provided that the speed ratio of the fast versus the slow dynamical phenomena of the two-time-scale system is sufficiently large. Initially, singular perturbation methods are used to derive two separate PDE models which describe the fast and slow dynamics of the original system. These models are then used as a basis for the synthesis of well-conditioned distributed state feedback controllers that guarantee stability and enforce output tracking in the closed-loop system. Then, two distributed state observers are independently designed on the basis of the fast and slow subsystems, to provide estimates of the fast and slow states of the system. These state observers are coupled with the distributed state feedback controller to yield a distributed output feedback controller that enforces the desired objectives in the closed-loop system. The proposed methodology is applied to a convection-reaction process with time-scale multiplicity.