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(infinity) 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.