A Comparison of Feedback Linearization and Sliding Mode Control for a Nonlinear System

Nonlinear systems are ubiquitous in nature and their effective control usually involves careful design of the controller and its parameters. This choice can involve a trial and error process that depends on the specific system. However, several hints on the behavior of general controllers can help the design process. This paper aims at providing hints for this design by presenting a comparison of two approaches, with two variants, for the control of a nonlinear system. These approaches are an input-output linearization with static-state feedback and dynamic-state feedback, and a sliding mode control with both fixed and adaptive gain. The obtained results for each method allow a discussion of their behavior in the presence and absence of disturbances.

I. Introduction

The proper control of a nonlinear system is a challenging task that involves the careful design of the controller and, in several cases, a deep understanding of the dynamic behavior. Due to the wide nature of nonlinear systems, methods that are applicable to some of them might not be directly applicable to others and the study of the control methods is usually done on a case basis. In this paper, the nonlinear system that will be taken into account is the so-called PVTOL (Planar Vertical Take-Off and Landing) aircraft [1]. This is a simplified aircraft model that has a minimum number of states and inputs, only considering the motion within a plane, but retains the main features that must be considered when designing control laws for a real aircraft. The stabilization control of the PVTOL is an interesting nonlinear problem since it is a non-minimum phase system, which implies that its zero dynamics is unstable and the exact feedback linearization is not directly applicable [2]. It is also an underactuated system that has three degrees of freedom but only two control inputs.