In this paper a new optimum tuning method of PI controllers in first-ordertime-delay systems, based on the deadbeat response to a step setpointvariation, is presented. The deadbeat performance, already studied for theplants without delay, consists of a fast achievement of the steady state withan overshoot included in a narrow band and with minimum rise and settlingtimes. In the proposed method the rise and settling times are both replacedwith the integral of the squared error and the constraint, which requires acontroller output less than a preset value, is added. The transient behaviouris strictly evaluated by means of the analytical solutions of the relativedifferential difference equations, obtained by the method of steps for thefirst time. Moreover the proposed tuning method is compared with other threemethods, selected among the most used, which are the Ziegler-Nicholstime-domain and frequency-domain and the Zhuang and Atherton ISTE ones. Finallytuning charts, having as coordinates the two PI controller parameters andprovided with the borderlines of the stability region, are introduced.
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