From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis. (September 2019)

• Record Type: Journal Article
• Authors: Rahmani, Mohammad Reza; Jalali, Ali Akbar
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 41:Number 13(2019)
• Page Start: 3799
• Page End: 3807
• Publication Date: 2019-09
• Subjects: Complex-order differintegral -- fractional-order -- robust control system -- Nyquist stability; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331219836473
• Languages: English
• ISSNs: 0142-3312

Abstract

Complex-order differintegral (COD) is the extended version of fractional-order one in which the differintegral order can be a complex number rather than a real number. In comparison with fractional-order differintegral (FOD), the distinguishing feature of the COD is that the phase slope of its Bode diagram is a function of imaginary part of the complex order of the COD. In this paper, by the use of this property of the COD, a robust control system is proposed. The design procedure and the realization of the proposed COD-based closed-loop control system are discussed. Since the phase of COD's frequency response is a nonsymmetric function of frequency, stability analysis of the proposed control system is considered a problematic task. It is proven that for the stability of the control system, it is essential that the COD be applied in a limited frequency band that is derived by the use of the Nyquist stability criterion. Finally, some numerical examples are given to demonstrate the validity and superiority of the proposed complex-order control system.