Robust control strategies for a class of nonlinear systems with an ill-defined relative degree

Abstract

Differential geometry theory has become one of the most promising design tools for nonlinear processes in the past decade. Several differential geometry techniques, such as input–output linearization and input-state linearization, have received considerable attention in the literature. However, one of the main assumptions often needed in the design of nonlinear controller by means of differential geometry is a nonlinear system with a well-defined relative degree. Nonlinear systems with an ill-defined relative degree will have an input–output linearizing law with singularities. This problem restricts the application of the feedback linearization technique in many engineering systems. One approach to this problem is to use approximate linearization techniques but this tends to yield very sluggish responses. In this paper, we investigate the applicability of a composite control scheme consisting of heuristic-based approximate linearization and backstepping design for a nonlinear system with an ill-defined relative degree. Two procedures are used to deal with this problem. In the first step, a function approximates the Lie derivative of the process output along with the input function to avoid the occurrence of singularity. Then, a nonlinear controller with an integral action-based back-stepping design is proposed to ensure that both a stable process and improved performance are obtained. Numerical simulations that illustrate the effectiveness of this approach are given.