Design PID controllers for desired time-domain or frequency-domain response

Practical requirements on the design of control systems, especially process control systems, are usually specified in terms of time-domain response, such as overshoot and rise time, or frequency-domain response, such as resonance peak and stability margin. Although numerous methods have been developed for the design of the proportional-integral-derivative (PID) controller, little work has been done in relation to the quantitative time-domain and frequency-domain responses. In this paper, we study the following problem: Given a nominal stable process with time delay, we design a suboptimal PID controller to achieve the required time-domain response or frequency-domain response for the nominal system or the uncertain system. An H∞ PID controller is developed based on optimal control theory and the parameters are derived analytically. Its properties are investigated and compared with that of two developed suboptimal controllers: an H2 PID controller and a Maclaurin PID controller. It is shown that all three controllers can provide the quantitative time-domain and frequency-domain responses.