Performance analysis for bounded persistent disturbances in PD/PID-controlled robotic systems with its experimental demonstrations

Abstract

This paper is concerned with performance analysis of proportional-derivative/proportional-integral-derivative (PD/PID) controller for bounded persistent disturbances in a robotic manipulator. Even though the notion of input-to-state stability (ISS) has been widely used to deal with the effect of disturbances in control of a robotic manipulator, the corresponding studies cannot be directly applied to the treatment of persistent disturbances occurred in robotic manipulators. This is because the conventional studies relevant to ISS consider the H-infinity performance for robotic systems, which is confined to the treatment of decaying disturbances, i.e. the disturbances those in the L-2 space. To deal with the effect of persistent disturbances in robotic systems, we first provide a new treatment of ISS in the L-infinity sense because bounded persistent disturbances should be intrinsically regarded as elements of the L-infinity space. We next derive state-space representations of trajectory tracking control in the robotic systems which allow us to define the problem formulations more clearly. We then propose a novel control law that has a PD/PID control form, by which the trajectory tracking system satisfies the reformulated ISS. Furthermore, we can obtain a theoretical argument about the L-infinity gain from the disturbance to the regulated output through the proposed control law. Finally, experimental studies for a typical 3-degrees of freedom robotic manipulator are given to demonstrate the effectiveness of the method introduced in this paper.