Variable structure control systems

Master Thesis


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University of Cape Town


The primary aims of this thesis, is to provide a body of knowledge on variable structure system theory and to apply the developed design concepts to control practical systems. It introduces the concept of a structure. The main aim in designing variable structure controllers, is to synthesize a variable structure system from two or more single structure systems, in such a way that the ensuing system out-performs its component structures. When a sliding mode is defined, the ensuing closed loop behaviour of the system is invariant to plant parameter changes and external disturbances. A variable structure controller was designed for a servo motor and successfully applied to the system. In practice, the phase plane representative point does not slide at infinite frequency with infinitesimal amplitude along the switching surface(s). Thus, the concept of a quasi-sliding regime was introduced. For high performance system specifications, the phase plane representative point could cycle about the origin. In some instances, sliding could be lost. For high speed applications, a novel design modification ensured that the system did not lose sliding. In addition, the controller could track a rapidly changing set point. Successful results support the developed theory.