Input Constrained Positioning Control for a Class of Euler-Lagrange Systems with Discontinuities

Abstract

In this paper, a nonlinear positioning control scheme is proposed for a class of Euler-Lagrange systems acted by static friction. A compromise method of the constrained control input and the high accuracy position servo requirement is introduced to construct a PD -like controller. Based on the Filippov-framework, it's proved that the equilibrium point set of the closed-loop system is equal to the static solution set, which gives the maximum range of the state-steady servo error. By using the generalized Lyapunov method and Laselle's invariant principle, we prove that any trajectory of the closed-loop system will converge to the stationary set. Moveover, unlike the high gain feedback, the PD -like controller can regulate its feedback gain with respect to the servo error such that it is also available for the input constrained case. Finally, to demonstrate the proposed controller, some simulation results are presented.