Analytical Synthesis of a Class of Model-Reference Time-Varying Control Systems

A theoretical investigation is presented for synthesizing nonlinear controllers for a class of model-reference control systems, each consisting of a timevarying-parameter plant and a fixed-parameter model, with the model one order lower than the plant. The plant and the model may have different forms, provided that their static gains are equal to unity. The controller, upon sensing the difference between the plant response and the model response, adds a proper controlling signal into the plant to make its output approach the model output, even though the plant parameters are unpredictably time-varying over known ranges. Specifically, only the transient responses to step inputs are considered. A controller is synthesized to satisfy a sufficient condition for asymptotic stability of the, null model-plant error, as determined by the use of the direct method of Lyapunov. This is, essentially, a general extension of L. P. Grayson's work to a variety of model-reference control systems. Several sample systems have been simulated on an analog computer for experimental studies. All the test results have shown the controller thus synthesized to be remarkably effective.