QLC-based design of reference tracking controllers for systems with asymmetric saturating actuators

Abstract

Quasilinear Control (QLC) is a set of methods for designing reference tracking and disturbance rejection controllers for systems with nonlinear actuators and sensors. While most QLC methods are applicable to systems with symmetric nonlinearities, the current paper provides a technique for asymmetric ones, specifically, asymmetric saturating actuators. As in the symmetric case, the approach is based on the method of stochastic linearization, which reduces nonlinear systems to quasilinear ones. In the symmetric case, each nonlinear element is replaced by a gain. In the asymmetric case, however, each nonlinear element is replaced not only by a gain, but also by a bias. The latter leads to steady state errors incompatible with the usual error coefficients. Therefore, the performance of these quasilinear systems must be characterized not only by a root locus, but by another locus as well - the tracking error locus. In this paper these performance loci are characterized, methods for their calculation and sketching are presented, and the results are utilized for tracking controllers design.