Robust Control of a Flexible-Link Manipulator

Abstract

The aim of the present case study is to design a control system for a single-link flexible manipulator. A two-mode dynamic model of the manipulator is first obtained by using the Lagrangian-assumed modes method. This is followed by the modeling of uncertainties involved in the manipulator. The uncertainties include the real parametric uncertainties in the payload mass as well as in the hub and structural damping factors. These parameters are the basic uncertainty source in the dynamic behaviors of the flexible-link manipulators. The μ-synthesis method is then applied to design a robust, noncollocated controller on the feedback signals of joint angle and tip acceleration. In the design, in order to obtain a feasible solution, a simplified uncertainty description is considered in the D–K iterations. Appropriate weighting functions are chosen in the design to ensure robust stability and robust performance. It is shown in this chapter that good robust performance has been achieved in the design. The closed-loop system exhibits excellent tip-motion performance for a wide range of payload mass and the system efficiently suppresses the elastic vibrations during the fast motion of the manipulator tip. Finally, the advantages of the μ-controller over a conventional, collocated PD controller are demonstrated.