Design of control systems with multiple memoryless nonlinearities for inputs restricted in magnitude and slope

Abstract

This paper develops a methodology for designing a control system composed of a linear time-invariant system interconnecting with multiple decoupled time-invariant memoryless nonlinearities. The design problem is to determine parameters of the system such that its outputs and the nonlinearity inputs always remain within prescribed bounds for all exogenous inputs whose magnitude and slope satisfy certain bounding conditions. By using Schauder fixed point theorem, we show that a design associated with a linear system is also a solution of the problem. Based on this, we further develop surrogate design criteria in the form of the inequalities that can readily be solved in practice. Sufficient conditions for the solvability of such inequalities are given for deadzone and saturation. To show the usefulness and the effectiveness of the methodology, a design example of a load frequency control system with time delay is carried out where deadzone and saturation are taken into account.