Analytical one parameter method for PID motion controller settings

In this paper analytical expressions for PID-controllers settings for electromechanical motion systems are presented. It will be shown that by an adequate frequency domain oriented parametrization, the parameters of a PID-controller are analytically dependent on one variable only, the cross-over frequency of the open loop transfer function. Analytical expressions are derived that relate the cross-over frequency clearly to the performance criteria for the closed loop system. In this paper the latter is shown in detail for servo problems. The effectiveness of the outlined approach is demonstrated by experimental results that were obtained from a two DOF tilting mirror system