Determination of all robustly stabilizing fractional-order PID controllers

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Lee, Yung K.
Watkins, John Michael

Lee, Yung K.; Watkins, John Michael. 2013. Determination of all robustly stabilizing fractional-order PID controllers. ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference, v.1:Paper No. DSCC2012-MOVIC2012-8768:pp. 433-440


In this paper, a method is provided for determining all fractional-order (FO) proportional–integral-derivative (PID) controllers that robustly stabilize a single-input and single-output (SISO) transfer function of arbitrary order with a time delay. The parameters of the FO PID controllers are determined in the frequency domain and are given in terms of the proportional gain Kp, integral gain Ki, and derivative gain Kd. In this paper, they will be plotted on the (Kp, Ki), (Kp, Kd), and (Ki, Kd) planes. For a robust stability condition, a multiplicative weight is selected to bound all multiplicative errors of the closed-loop system. In particular, this technique can be used even when the transfer function of a system is not available, as long as the system frequency response can be obtained. An example is given to illustrate the applicability and effectiveness of the method presented.

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