$\text{H}_{\infty}$ Control Design of PID-Like Controller for Speed Drive Systems

The proportional-integral-derivative (PID) controller has been widely used in industrial servo drives for its simplicity and reliability. This paper employs H
_∞
control to design the PID-like controller for both velocity and current feedback loops. A dedicated design formulation is proposed such that three control parameters can be obtained directly by H
_∞
control. The weighting functions involved in H
_∞
control design are specified in terms of motor specifications to provide an initial design, and then the relative weights are chosen iteratively to further achieve the required performance. To reduce the effects of sensor noises and phase delay, an H
_∞
observer design is formulated dually to construct a PID-like speed observer. The present approach aims to adopt modern control tools that ensure the stability of the closed-loop system to characterize the PID-like controllers such that the desired control performance can be achieved systematically. An illustrated design example is given to demonstrate the proposed design approach for both the speed controller and the observer in practice. Experimental results show that the H
_∞
PID-like controller is superior to a classical cascade design in terms of disturbance rejection ability.