Reliable computation of PID gain space for general second-order time-delay systems

ABSTRACT This paper addresses the problem of determining the stability gain space of a PID controller for general second-order time-delay systems. First, a review of existing results and the associated drawbacks is presented. Subsequently, a new algorithm to compute the entire PID stability gain space is developed. The new algorithm is based upon existing results on the relationship between the stability of a quasi-polynomial and its derivatives, an extended version of the Hermit–Biehler theorem, and also the Nyquist criterion. The algorithm entails extraction of an admissible range for the PID parameter Kp, and then based on this range, a stability region in the (Ki − Kd) plane is computed. Well-known examples are studied to demonstrate the reliability and accuracy of the results.

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