Abstract. Proportional-Integral-Derivative (PID) controllers have been the heart of control systems engineering practice for decades because of its simplicity and ability to satisfactory control different types of systems in different fields of science and engineering in general. It has receive widespread attention both in the academe and industry that made these controllers very mature and applicable in many applications. Although PID controllers (or even its family counterparts such as proportional-integral [PI] and proportional-derivative [PD] controllers) are able to satisfy many engineering applications, there are still many challenges that face control engineers and academicians in the design of such controllers especially when guaranteeing control system robustness. In this paper, we present a method in improving a given PID control system focusing on system robustness by incorporating fractional-order dynamics through a returning heuristic. The method includes the use of the existing reference and output signals as well as the parameters of the original PID controller to come up with a new controller satisfying a given set of performance characteristics. New fractional-order controllers are obtained from this heuristic such as PI^λ and PI^λD^μ controllers, where λ,μ∈(0,2) are the order of the integrator and differentiator, respectively.

Received: October 27, 2012

AMS Subject Classification: 26A33, 37N35

Key Words and Phrases: fractional-order systems, PID controllers, unity-feedback system

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