Globally stable PID-like control of mechanical systems

Decoupled PID control with actuator constraints and velocity measurement or estimation achieves global asymptotic stability of the desired configuration, if there is some friction in the controlled mechanical system and the signals to be integrated are limited accordingly. Stability analysis using the direct Lyapunov method and Gershgorin's “circle theorem” gives these limits and physically meaningful lower bounds on position control gains. A simple procedure is proposed for selecting the design parameters and determining the gains of the controllers.