State feedback H∞ control of manipulators with flexible joints and links

A two-stage control strategy, composed of rigid-body-motion-based partial feedback linearization and state feedback H_∞ control for robotic manipulators with flexible joints and links is presented. The partial feedback linearization control synthesized by the differential geometric structure algorithm is an input-output decoupling and linearization feedback law capable of precise rigid-body-motion-based trajectory tracking, but the zero dynamics of the unobservable nonlinear elastic subsystem remains unstable. In order to actively suppress the elastic vibrations, it is necessary to sacrifice the perfect rigid-body-motion-based tracking capability somewhat by introducing a robust stabilization control in the vicinity of the desired trajectory. The use of state feedback H_∞ control with integral action for the synthesis of the robust stabilization control is able to achieve active damping of elastic vibration and robust tracking of motor dynamics. A two-link arm is used in the numerical study