Optimal fractional-order controller design using direct synthesis method

Yumuk E., Güzelkaya M., Eksin İ.

IET CONTROL THEORY AND APPLICATIONS, vol.14, no.18, pp.2960-2967, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 18
  • Publication Date: 2020
  • Doi Number: 10.1049/iet-cta.2020.0596
  • Journal Name: IET CONTROL THEORY AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2960-2967
  • Keywords: stability, transfer functions, control system synthesis, performance index, closed loop systems, three-term control, genetic algorithms, feedback, optimal control, optimal fractional-order controller design, direct synthesis method, second-order integer transfer function, optimal fractional-order closed-loop reference transfer function, optimal second-order integer closed-loop reference transfer function, integral square error criterion, genetic algorithm, PID CONTROLLERS, NUMERICAL ALGORITHM, STABILITY, SYSTEMS, PERFORMANCE
  • Istanbul Technical University Affiliated: Yes

Abstract

In this study, an optimal fractional-order controller is proposed for a type of fractional-order model utilising the direct synthesis method. In that respect, the fractional counterpart of the second-order integer transfer function is selected as a closed-loop reference transfer function. The stability region of the fractional-order closed-loop reference transfer function is given via a theorem and related lemmas. Considering that a unity feedback loop is used, the parameters of the fractional-order closed-loop reference transfer function are specified based on the integral square error performance index within the specified stability region using a genetic algorithm. The time-domain characteristics of the optimal fractional-order closed-loop reference transfer function are compared with those of the optimal second-order integer closed-loop reference transfer function. The fractional- and integer-order controllers that are designed based on optimal closed-loop reference transfer functions are implemented on a real-time system. The performance of the fractional-order controller outperforms that of the integer counterpart on the integral square error criterion. Moreover, the simulation and practical results are consistent with each other.