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PID tuning revisited: guaranteed stability and non-fragility

In this paper we present a study of some PID tuning techniques that are based on first-order models with time delays. Using a characterization of all stabilizing PID controllers, each tuning rule is analyzed to first determine if the proportional gain value dictated by that rule, lies inside the range of admissible proportional gains. Then, the integral and derivative gain values are examined to determine conditions under which the tuning rule exhibits resilience with respect to controller parameter perturbations. Furthermore, a new tuning rule is presented for resilient controller design.