Nonlinear robust observer-based position controller for the 3-DOF parallel kinematic machine

Abstract

This paper proposes a solution to the problem of the state observation and position control by output feedback for a nonlinear three degrees-of-freedom (3-DOF) parallel kinematic machine (PKM) system, based on the limited signal availability (moving platform displacement measurements only). The unknown velocity signals are estimated via a nonlinear robust observer which is designed for the nonlinear system with observable linear dynamics part and bounded nonlinearities and disturbances, and which guarantees global exponential stability of the observation error. A proportionalderivative (PD) controller is designed to solve the position control problem, utilizing the estimated velocity, as well as the gravitation compensation, dynamic friction and external disturbance compensation for the PKM. The closed-loop system is proven to have global asymptotic stability according to the Lyapunov's analysis method and LaSalle's invariance principle. Performance of the resulting observer and controller is illustrated in a simulation study of a 3-DOF PKM.