FOMCON Toolbox-Based Direct Approximation of Fractional Order Systems Using Gaze Cues Learning-Based Grey Wolf Optimizer

Abstract

This study discusses a new method for the fractional-order system reduction. It offers an adaptable framework for approximating various fractional-order systems (FOSs), including commensurate and non-commensurate. The fractional-order modeling and control (FOMCON) toolbox in MATLAB and the gaze cues learning-based grey wolf optimizer (GGWO) technique form the basis of the recommended method. The fundamental advantage of the offered method is that it does not need intermediate steps, a mathematical substitution, or an operator-based approximation for the order reduction of a commensurate and non-commensurate FOS. The cost function is set up so that the sum of the integral squared differences in step responses and the root mean squared differences in Bode magnitude plots between the original FOS and the reduced models is as tiny as possible. Two case studies support the suggested method. The simulation results show that the reduced approximations constructed using the methodology under consideration have step and Bode responses more in line with the actual FOS. The effectiveness of the advocated strategy is further shown by contrasting several performance metrics with some of the contemporary approaches disseminated in academic journals.

Keywords

• reduced order model
• fractional-order systems
• swarm intelligence algorithm
• gaze cues learning-based grey wolf optimizer
• FOMCON toolbox
• metaheuristic