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∞ performance for robotic systems, which is confined to the treatment of decaying disturbances, i.e. the disturbances those in the L2 space. To deal with the effect of persistent disturbances in robotic systems, we first provide a new treatment of ISS in the L∞ sense because bounded persistent disturbances should be intrinsically regarded as elements of the L∞ 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∞ 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.