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.
- Dynamic Systems and Control Division
Determination of All Robustly Stabilizing Fractional-Order PID Controllers
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Lee, YK, & Watkins, JM. "Determination of All Robustly Stabilizing Fractional-Order PID Controllers." Proceedings of the ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference. Volume 1: Adaptive Control; Advanced Vehicle Propulsion Systems; Aerospace Systems; Autonomous Systems; Battery Modeling; Biochemical Systems; Control Over Networks; Control Systems Design; Cooperative and Decentralized Control; Dynamic System Modeling; Dynamical Modeling and Diagnostics in Biomedical Systems; Dynamics and Control in Medicine and Biology; Estimation and Fault Detection; Estimation and Fault Detection for Vehicle Applications; Fluid Power Systems; Human Assistive Systems and Wearable Robots; Human-in-the-Loop Systems; Intelligent Transportation Systems; Learning Control. Fort Lauderdale, Florida, USA. October 17–19, 2012. pp. 433-440. ASME. https://doi.org/10.1115/DSCC2012-MOVIC2012-8768
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