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- Title
From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis.
- Authors
Rahmani, Mohammad Reza; Jalali, Ali Akbar
- 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.
- Subjects
ROBUST control; CLOSED loop systems; INTEGRATORS; REAL numbers; COMPLEX numbers; STABILITY criterion
- Publication
Transactions of the Institute of Measurement & Control, 2019, Vol 41, Issue 13, p3799
- ISSN
0142-3312
- Publication type
Article
- DOI
10.1177/0142331219836473