Robust Fractional-order PID Tuning Method for a Plant with an Uncertain Parameter
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Robust Fractional-order PID Tuning Method for a Plant with an Uncertain Parameter Xu Li* and Lifu Gao Abstract: The robust design of fractional-order proportional-integral-differential (FOPID) controllers for controlled plants with uncertainty is a popular research topic. The well-studied “flat phase” condition is effective for the gain variation but not for variations in other parameters. This paper addresses the problem of tuning a robust FOPID controller for a plant with a known structure and an uncertain parameter (a coefficient or order in the plant transfer function). The method is based on preserving the phase margin of the open-loop system when the plant parameter varies around the nominal value. First, the partial derivatives of the gain crossover frequency with respect to the plant parameters are calculated. Then, the partial derivatives of the phase margin with respect to the plant parameters are obtained as the robust performance indexes. In addition, the equations needed to compute FOPID parameters that meet the specifications in the frequency domain are obtained and used as nonlinear constraints. Finally, the FOPID parameters can be obtained by optimizing the robust performance indexes under these constraints. Simulation experiments are carried out on examples with different types of uncertain parameters to verify the effectiveness of the tuning method. The results show that the requirements are fulfilled and that the system with the proposed FOPID controller is stable and robust to variations in the uncertain parameters. Comparisons clearly show that the controllers designed by the proposed method provide relatively robust performance. Keywords: FOPID controller, phase margin, plant parameter, robustness.
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INTRODUCTION
Research and applications in the fields of fractional calculus and nonintegral calculus have been increasingly favored and popularized by researchers over the past two decades, mainly because fractional calculus has been shown to play a prominent role in broad and abundant fields of science and engineering. To date, this tool has been successfully and widely applied in various fields, such as control systems [1–11] image processing [12], thermal systems [13], signal processing [14], and electrochemistry [15]. In the abovementioned applications, the performance of fractional-order controllers based on fractional calculus has been found to be outstanding, particularly when compared with the classic integer-order controller. In fact, fractional-order controllers can offer more possibilities for improving system performance than integer-order controllers [16].
can be attributed to its simple structure, strong robustness, reliable performance and easy implementation and manipulation in hardware. However, the general increase in the complexity of modern engineering platforms has led to a gradual increase in stringency in the selection of controllers, which has motivated the re-engineering of the PID framework. To preserve th
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