Static error estimation for a class of second-order PD controlled mechanical systems

This paper analyzes the static error of a class of second-order mechanical systems with PD control caused by dry friction. The results show that if the closed-loop system is over damped or critically damped, the static servo error may be the largest for the motion starting from the steady state. While the static servo error can be regulated according to the initial condition, if the closed-loop system is under damped. Finally, the simulations for a simple one-degree-of-freedom (1DOF) mass-spring system are carried out to illustrate our results.