Non-linear PI regulators in control problems for holonomic mechanical systems

Abstract

In this paper we propose a solution to the regulation problem of holonomic mechanical systems without velocity measurements by constructing nonlinear PI controllers. An approach based on the Lyapunov functional method is used to analyse the stability of the closed-loop system which has the form of Volterra integro-differential equation. The paper presents the quasi-invariance principle for Volterra nonlinear integral differential equations. Furthermore, we present sufficient conditions that one can use to conclude the asymptotic stability of the closed-loop system via using a Lyapunov functional with semi-definite time derivative. The simulation results of the two-link robot manipulator demonstrate the effectiveness of the proposed PI controller.

Keywords

• Mechanical system
• regulation problem
• PI controller
• Volterra integro-differential equation
• Lyapunov functional