Stability of an adaptive controller for a direct-drive servo-motor

A positioning system for a direct-drive servo-motor is considered. The controller consists of a PD (proportional plus derivative) or a PID (proportional plus integral plus derivative) feedback regulator to which feedforward compensation has been added. Stability can be ensured by different approaches. One of these approaches consists of positioning the poles inside the unit circle at predetermined positions chosen arbitrarily. Another approach is to determine the upper and lower boundaries of the controller´s gains and then to allow the poles to vary freely inside the stability zone without any further action, as long as they remain inside this zone. Possible implementations of a PD and of a PID have been studied. Stability conditions have been determined for each case by arbitrary pole placement as well as by the determination of the upper and lower boundaries on the controller´s gains