A Nonlinear Stability Analysis for the Robust Position Control Problem of Robot Manipulators via Disturbance Observer

In this paper, a new nonlinear stability analysis is proposed for the robust position control problem of robot manipulators via Disturbance Observer (DOb). Although a DOb has long been used in the robust motion control systems, it suffers from the insufficient and impractical analysis and design methods. Nonlinearities of motion control systems are generally ignored to simplify analyses; however, they may significantly influence the stability and performance of motion control systems. The paper shows that a DOb based two degrees of freedom robust position controller equals to a passivity based controller. The error of a DOb based two degrees of freedom robust position control system is uniformly ultimately bounded when it is applied to a trajectory tracking control problem of robot manipulators. The error bound is directly determined by the bandwidth of DOb and nominal inertia matrix. As they are increased, the error bound shrinks. However, the bandwidth of DOb and nominal inertia matrix are limited by the practical constraints such as noise and sampling period; therefore, the error cannot be freely decreased. Asymptotic stability is achieved if the robust position control system is applied into a regulator, i.e., point to point, position control problem of robot manipulators. It is shown that not only the robustness but also the stability of the robust position control system is improved by increasing the bandwidth of DOb. Besides, decreasing nominal inertia may degrade the stability of the robust position control system, drastically. New practical design methods are given by using the proposed analysis method. Simulation results are given to show the validity of the proposals.