Performance analysis of the speed servomechanism with the adaptive PI controller

An adaptive proportional and integral controller for digital speed control in electrical drives is derived and analysed. Adaptation of the controller parameter is gradient descent procedure. The adaptive controller is derived from the discrete-time model of a digitally controlled speed servomechanism. Discrete-time model is obtained from the Z-transforms of the system signals and elements. Applied controller has distributed structure, i.e. integral action is placed in the direct path, while proportional action is positioned in the feedback path of the system. Thus, it provides improved system accuracy, while it maintains sufficient level of system relative stability. Due to presence of feedback in the system and controller structures, gradient of criterion function is computed through a recurrent procedure. Performance analysis of the speed servo-mechanism with the adaptive proportional and integral controller is performed in complex domain, using root locus techniques. The analysis indicates controller parameter influence on the system stability and reference tracking capability. Further, it shows that the adaptive controller yields zero steady state error and step disturbance rejection, as well as good system performance in the presence of modelling errors. Experiments, performed as reference tracking tasks, support the analysis.