Adaptive control using variable structure systems
Adaptive control is employed in control systems required to operate satisfactorily regardless of parameter variations, external disturbances and changes in the environment. A conceptually simple approach to adaptive control is the model reference approach which yields a nonlinear feedback system. In a model reference control system the system output is made to follow the output of a specified model. There are numerous approaches to the design of model reference adaptive control systems (MRAC). In this thesis the theory of variable structure systems (VSS) is studied and applied in the design of MRAC systems. VSS are inherently nonlinear feedback systems which exhibit certain adaptive properties including insensitivity to a range of parameter variations and certain external disturbances when operating in the sliding mode. The application of VSS theory to the problem of adaptive model-following has demonstrated the simplicity of the design. It also ensures the asymptotic stability of the controlled system and provides direct control over the error transient. The notion of system zeros arises naturally when tackling the problem of output model-following control systems. Certain interrelations between VSS, system zeros and the output model following problem have suggested a new method for computing the zeros of linear multivariable square systems. A fundamental operator in VSS is shown to be a projector. The employment of projector theory in the study of VSS provides further insight into their operation. Furthermore new methods for constructing the switching hyperplanes matrix are formulated by utilizing projector theory. The linear control law ensuring output model-following and the necessary order reduction is shown to be identical to the equivalent control encountered in VSS. The control law also decouples the system, assigns arbitrary poles and possesses certain adaptive properties. The extension of VSS theory to output model following systems using output information is also discussed.