A Unified Approach for Sensitivity Design of PID Controllers in the Frequency Domain

Abstract: In this paper a graphical technique is introduced for finding all continuous-time and discrete-time proportional integral derivative (PID) controllers that satisfy an H∞ sensitivity constraint of an arbitrary order transfer function with time delay. These problems can be solved by finding all achievable PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is that it only depends on the frequency response of the system. The delta operator is used to describe the controllers, because it not only possesses numerical properties superior to the discrete-time shift operator, but also converges to the continuous-time controller as the sampling period approaches zero. A unified approach allows us to use the same procedure for discrete-time and continuoustime H∞ sensitivity design of PID controllers.