A Computer-aided Design of Robust Regulators

Abstract The objective of this paper ĩs to present a design methodology for linear and nonlinear regulators by applying mathematical programming techniques. Starting with the linear vector equations x ˙ ( t ) = P x ( t ) + q u ( t ) , u ( t ) = − r T x an algorithmic procedure is outlined for selecting the regulator parameter vector r within the framework of classical time and frequency domain specifications, as well as the quadratic optimality criterion. For nonlinear regulators described by nonlinear vector equations x ˙ ( t ) = Px ( t ) + q φ [ u ( t ) ] , u ( t ) = − r T x ( t ) attention is focused on the design of absolutely stable regulators subject to prescribed exponential stability and sector maximization requirements. Reformulating the performance specifications in terms of a set of inequalities, a feasible region is delineated in the regulator parameter space. Then, maximization of the volume of an imbedded hypercube (or hypersphere) inside the region via mathematical programming methods, results in an easily visualized solution set, this feature being particularly attractive in building robust regulators to meet real-world implementation tolerances and system parameter uncertainities.