Robustness of PID-controlled Manipulators vis-à-vis Actuator Dynamics and External Disturbances

Abstract

We present a robustness analysis for PID-controlled robot manipulators. For robot manipulators under the influence of external disturbances and a wide class of neglected dynamics, we provide establish uniform semiglobal practical asymptotic stability and propose a tuning procedure of the PID gains in order to achieve any given precision from any given bounded set of initial conditions. In contrasts to other works on robust stability of PIDs, we do not use La Salle's principle but provide a strict Lyapunov function. The perturbations that we consider include discontinuous functions of the state, such as coulomb friction. As corollaries of our main results, one may conclude the same stability property for the case of motion control using linear PID.