Stationary Set Analysis for PD Controlled Mechanical Systems

This brief presents a comprehensive method to analyze the stationary set of the high-dimensional mechanical systems with proportional-derivative (PD) control. The system behavior is characterized by Filippov´s differential inclusion, in which the discontinuous disturbance mainly caused by static friction is modeled by a convex set-valued map with respect to the velocity. The stationary set of the closed-loop system is obtained by calculating the static solution in the sense of Filippov. The stationary set is also proved to be asymptotically stable, while the asymptotic stability cannot be obtained for proportional-integral-derivative (PID) controlled systems. Finally, the experiments on a three-axis rotation table are carried out to illustrate our analysis results.