Lyapunov Stability Analysis of Switching Controllers in Presence of Sliding Modes and Parametric Uncertainties With Application to Pneumatic Systems

Abstract

This paper concerns the control and the stability analysis of pneumatic actuators, which are nowadays of widespread use in the industry. A problem related to the use of such actuators is the so-called stick-slip, due to the presence of dry friction in the system. In this paper, we provide an empirical switching control law that avoids this phenomenon as well as a general approach to the stability analysis of nonlinear systems that will let us prove the stability of the closed-loop system. The approach is based on casting the closed-loop system into a piecewise-affine form and finding a Lyapunov function for it. Such an approach will be able to cope with the special features of the controlled pneumatic system model, namely, the presence of sliding modes, a whole equilibrium set, and uncertainties on the values of a few parameters. At the end of this paper, we will show how such a method can be successfully applied to our experimental setup under several hypotheses.