Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

• Published in: International journal of applied mathematics and computer science Vol. 29; no. 2; pp. 311 - 326
• Main Authors: Bingi, Kishore, Ibrahim, Rosdiazli, Karsiti, Mohd Noh, Hassam, Sabo Miya, Harindran, Vivekananda Rajah
• Format: Journal Article
• Language: English
• Published: Zielona Góra De Gruyter Poland 01.06.2019; Sciendo
• Subjects: Approximation; Controllers; Curve fitting; fractional-order pid controller; Frequency domain analysis; Frequency ranges; Frequency response; integer-order approximation; Integers; Mathematical analysis; matsuda approximation; oustaloup approximation; Proportional integral derivative; Robust control; Stability analysis; Time domain analysis
• ISSN: 2083-8492; 1641-876X; 2083-8492
• DOI: 10.2478/amcs-2019-0023

Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results.