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
