Mathematical modelling and controllability analysis of fractional order coal mill pulverizer model

Gargi Trivedi; Ghanshyam  Malviya; Jaita  Sharma; Vishant  Shah

doi:10.59400/adecp2075

Gargi Trivedi Department of Applied Mathematics, Faculty of Technology and Engineering, The Maharja Sayajirao University of Baroda, Vadodara 390002, India
Ghanshyam Malviya Department of Applied Mathematics, Faculty of Technology and Engineering, The Maharja Sayajirao University of Baroda, Vadodara 390002, India; Institute of Sciences, Humanities and Liberal Studies, Indus University, Ahmedabad 382115, India
Jaita Sharma Department of Applied Mathematics, Faculty of Technology and Engineering, The Maharja Sayajirao University of Baroda, Vadodara 390002, India
Vishant Shah Applied Science and Humanities, School of Engineering, P P Savani University, Dhamdod 394125, India

Article ID: 2075

DOI: https://doi.org/10.59400/adecp2075

Keywords: fractional system; nonlinear systems; coal mill pulverizer model; pulverizer; coal mill; power plant; controllability analysis

Abstract

This paper investigates the controllability of nonlinear dynamical systems and their applications, with a focus on fractional-order systems and coal mill models. A novel theorem is proposed, providing sufficient conditions for controllability, including constraints on the steering operator and nonlinear perturbation bounds. The theorem establishes the existence of a contraction mapping for the nonlinear operator, enabling effective control strategies for fractional systems. The methodology is demonstrated through rigorous proof and supported by an iterative algorithm for controller design. Additionally, the controllability of a coal mill system represented as a nonlinear differential system, is analyzed. The findings present new insights into the interplay of fractional dynamics and nonlinear systems, offering practical solutions for real-world control problems.

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