Quantitative design of a class of nonlinear systems with parameter uncertainty

Abstract

Abstract This paper considers the case in which a linear time‐invariant (LTI) but uncertain plant suffers from nonlinearities y=n(x) which can be expressed as y=K n +η(x), |η(x)|≤ M , with K , a possibly uncertain scalar. This covers a large and very important class of nonlinearities encountered in practice such as friction, backlash, dead zone and quantization. Quantitative design techniques are presented for this class for the satisfaction of specifications. Special attention is paid to the avoidance of limit cycles using describing function theory, although the design method is also amenable of application using other stability criteria such as the circle criteria. Numerical examples are developed illustrating the design procedure.