A New Optimum Tuning Method of Pi Controllers in First-order Time-delay Systems

In this paper a new optimum tuning method of PI controllers in first-order time-delay systems, based on the deadbeat response to a step setpoint variation, is presented. The deadbeat performance, already studied for the plants without delay, consists of a fast achievement of the steady state with an overshoot included in a narrow band and with minimum rise and settling times. In the proposed method the rise and settling times are both replaced with the integral of the squared error and the constraint, which requires a controller output less than a preset value, is added. The transient behaviour is strictly evaluated by means of the analytical solutions of the relative differential difference equations, obtained by the method of steps for the first time. Moreover the proposed tuning method is compared with other three methods, selected among the most used, which are the Ziegler-Nichols time-domain and frequency-domain and the Zhuang and Atherton ISTE ones. Finally tuning charts, having as coordinates the two PI controller parameters and provided with the borderlines of the stability region, are introduced.