Design of PI and PID controllers with transient performance specification

Proportional-integral-derivative (PID) controllers are widely used in industrial control systems because of the reduced number of parameters to be tuned. The most popular design technique is the Ziegler–Nichols method, which relies solely on parameters obtained from the plant step response. However, besides being suitable only for systems with monotonic step response, the compensated systems whose controllers are tuned in accordance with the Ziegler–Nichols method have generally a step response with a high-percent overshoot. In this paper, tuning methods for proportional-integral (PI) and PID controllers are proposed that, like the Ziegler–Nichols method, need only parameters obtained from the plant step response. The methodology also encompasses the design of PID controllers for plants with underdamped step response and provides the means for a systematic adjustment of the controller gain in order to meet transient performance specifications. In addition, since all the development of the methodology relies solely on concepts introduced in a frequency-domain-based control course, the paper has also a didactic contribution.