A New Approach to the Tracking Control of Uncertain Nonlinear Multi-body Mechanical Systems

Abstract

This chapter presents a new approach for the tracking control of uncertain mechanical systems. Real-life multi-body systems are in general highly nonlinear and modeling them is intrinsically error prone due to uncertainties related to both their description and the description of the various forces that they may be subjected to. As such, in the modeling of such systems one only has in hand the so-called nominal system—a model based upon our best assessment of the system and our best assessment of the generalized forces acting on it. Uncertainties that are time-varying, unknown but bounded, are assumed in this chapter, and a new approach to the development of a closed-form controller is developed. The approach uses the concept of a generalized sliding surface. Its closed-form approach can guarantee, regardless of the uncertainty, that the uncertain system can track a desired reference trajectory that the nominal system is required to follow. An example of a simple multi-body system whose description is known only imprecisely is illustrated showing the simplicity of the approach and its efficacy in tracking the trajectory of the nominal system. The approach is easily implemented for a wide range of complex multi-body mechanical systems.