A New Analytic Method to Tune a Fractional Order PID Controller

Waleed Abdulwahhab, Omar; Hadi Abbas, Nizar

	A New Analytic Method to Tune a Fractional Order PID Controller
Journal of Engineering
Article 1, Volume 23, Issue 12, 2017, Pages 1-12
Authors
Omar Waleed Abdulwahhab; Nizar Hadi Abbas
Abstract
This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time invariant system is taken as a process to be controlled and the proposed method is applied to design the controller. The resultant control system exactly fulfills the control design specification, a feature that is laked in numerical design methods. Through matlab simulation, the step response of the closed loop system with the proposed controller and a conventional PID controller demonstrate the performance of the system in terms of time domain transient response specifications (rise time, overshoot, and settling time).
Keywords
Fractional order PID controller; gain crossover frequency; phase margin; peak magnitude at resonant frequency

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