Linear fractional order controllers

Linear fractional order controllers: A survey in the frequency domain

Ahmadi Dastjerdi, A. (TU Delft Mechatronic Systems Design)
Vinagre, Blas M. (University of Extremadura)
Chen, Yang Quan (University of California)
Hassan HosseinNia, S. (TU Delft Mechatronic Systems Design)

2019

Today, there is a great tendency toward using fractional calculus to solve engineering problems. The control is one of the fields in which fractional calculus has attracted a lot of attention. On the one hand, fractional order dynamic models simulate characteristics of real dynamic systems better than integer order models. On the other hand, Fractional Order (FO) controllers outperform Integer Order (IO) controllers in many cases. FO-controllers have been studied in both time an frequency domain. The latter one is the fundamental tool for industry to design FO-controllers. The scope of this paper is to review research which has been carried out on FO-controllers in the frequency domain. In this review paper, the concept of fractional calculus and their applications in the control problems are introduced. In addition, basic definitions of the fractional order differentiation and integration are presented. Then, four common types of FO-controllers are briefly presented and after that their representative tuning methods are introduced. Furthermore, some useful continuous and discrete approximation methods of FO-controllers and their digital and analogue implementation methods are elaborated. Then, some Matlab toolboxes which facilitate utilizing FO calculus in the control field are presented. Finally, advantages and disadvantages of using FO calculus in the control area are discussed. To wrap up, this paper helps beginners to get started rapidly and learn how to select, tune, approximate, discretize, and implement FO-controllers in the frequency domain.

CRONE generations
Fractional calculus
Fractional order lead/lag compensators
Fractional order PID
Frequency domain analysis
Toolboxes for fractional order controllers
Tuning methods for fractional order controllers

http://resolver.tudelft.nl/uuid:aec95eb0-cac9-4c63-8f8e-f1f90d16c226

https://doi.org/10.1016/j.arcontrol.2019.03.008

2021-06-21

1367-5788

Annual Reviews in Control, 47, 51-70

Accepted Author Manuscript

Institutional Repository

review

© 2019 A. Ahmadi Dastjerdi, Blas M. Vinagre, Yang Quan Chen, S. Hassan HosseinNia