Control signal constraints and filter order selection for PI and PID controllers

Large control signal derivatives or inter-sample differences may harm actuators. An optimization constraint limiting such variations, related to measurement noise, is derived. Using the constraint, optimal PI, PID and measurement filters with different orders are designed for several processes and compared to the optimal linear controller of high order found via Youla parametrization. Simulations of load disturbance rejections and measurement noise sensitivities are shown and conclusions on filter order selection for PI and PID controllers are drawn.