Title: Reduced-order modelling-based FOPID controller design for interval-model Zeta converter using Bode envelope

Authors: V.P. Meena; Preeti Meena; V.P. Singh; Ahmad Taher Azar; Saim Ahmed

Addresses: Department of Electrical and Electronics Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, Karnataka, 560035, India ' Department of Electrical Engineering, Indian Institute of Technology Jodhpur, Rajasthan, 342030, India ' Electrical Engineering Department, Malaviya National Institute of Technology, Jaipur, Rajasthan, 302017, India ' College of Computer and Information Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia; Automated Systems and Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh, Saudi Arabia; Faculty of Computers and Artificial Intelligence, Benha University, Benha, 13518, Egypt ' College of Computer and Information Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia; Automated Systems and Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh, Saudi Arabia

Abstract: This paper proposes the design of a fractional-order proportional-integral-derivative (FOPID) controller for an interval-modelled Zeta converter, employing the Bode envelope method. The approach employs reduced-order modelling, employing dirct truncation and Routh-Padé approximation for numerator and denominator polynomials, respectively. The Zeta converter's mathematical model, derived via state-space averaging (SSA), is initially a fourth-order interval model, subsequently reduced to a first-order interval model. The primary objective is to design an FOPID controller that meets specific performance criteria, such as the desired gain crossover frequency and phase margin. To achieve this, the teacher-learning-based optimisation (TLBO) algorithm minimises the objective function, determining optimal controller parameters. Step-and-bode responses are provided to demonstrate the controller's effectiveness and applicability.

Keywords: reduced-order modelling; FOPID controller; interval model; Zeta converter; Bode envelope; TLBO; teacher-learning-based optimisation; SSA; state-space averaging.

DOI: 10.1504/IJAAC.2025.145907

International Journal of Automation and Control, 2025 Vol.19 No.3, pp.287 - 305

Received: 13 Mar 2024
Accepted: 09 May 2024
Published online: 30 Apr 2025 *

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