Controller synthesis for performance stabilization of unstable, uncertain plants

The purpose of this undergraduate thesis is to lay the foundation for a simple approach to control system design, namely by the characteristic relation, and to develop several tools using that design approach that satisfy necessary and sufficient conditions for performance stabilization. Under consideration are generalized plants, which may be unstable as well as uncertain, in a unitary feedback SISO system. We seek a controller that would sufficiently stabilize the family of plants perturbed from the nominal plant, including unstable plants. Although some authors have reported the essential approach developed in this thesis, eg. [7], while others have implied it, eg. [I]and [S] it nevertheless appears to have been overlooked in its simplicity as a design methodology that reaches into the heart of the design problem. Thus techniques are conventionally preferred which are more complex in their application and which in some cases are less powerful. We wish to demonstrate the design methodology of the characteristic relation, and show how it touches upon and elucidates control theory in general. it is believed that further research may be conducted along the lines of this undergraduate honors thesis