The authors use the classical theory of singularly perturbed systems to design a dynamical feedback controller which allows solution of control problems, involving sliding manifolds, within a prescribed approximation error. The dynamical feedback controller is the solution of a differential equation containing a small parameter in >0. The equation is derived from the data of the considered problem. The controller turns out to be an absolutely continuous function and so the chattering phenomenon is practically eliminated. The relationship between the controller and the equivalent control is investigated. The behavior of the controlled response of the system to disturbances is also studied.
Variable structure control problems and the theory of singular perturbations / R. Johnson; P. Nistri. - STAMPA. - (1992), pp. 2370-2375. (Intervento presentato al convegno Decision and Control 1992/International Institute of Electrical and Electronics Engineers tenutosi a Tucson AZ USA nel dicembre 1992) [10.1109/CDC.1992.371367].
Variable structure control problems and the theory of singular perturbations
JOHNSON, RUSSELL ALLAN;
1992
Abstract
The authors use the classical theory of singularly perturbed systems to design a dynamical feedback controller which allows solution of control problems, involving sliding manifolds, within a prescribed approximation error. The dynamical feedback controller is the solution of a differential equation containing a small parameter in >0. The equation is derived from the data of the considered problem. The controller turns out to be an absolutely continuous function and so the chattering phenomenon is practically eliminated. The relationship between the controller and the equivalent control is investigated. The behavior of the controlled response of the system to disturbances is also studied.
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