Systematically derived weights based order diminution of continuous systems using GWO algorithm

Abstract

In this research article, approximation of higher order systems (HOSs) is proposed by minimizing the errors between time moments (TMs) and Markov parameters (MPs) of HOS and desired reduced order model (ROM) using grey wolf meta-heuristic optimization algorithm by utilizing systematic procedure of finding weights. The TMs and MPs of HOS and ROM are utilized to frame the objective function. The weights associated with the objective function are determined by systematic procedure namely analytic hierarchy process (AHP). The multi-objective problem is converted into single-objective problem by utilizing these weights. In objective function, normalized errors are minimized using grey wolf optimization (GWO) algorithm to derive the desired ROM. To ensure the steady state matching between HOS and its ROM, first TMs of HOS and desired ROM are matched. The Hurwitz stability criterion is utilized to retain the stability of HOS. The determination of efficacy of proposed method is attained by considering two test systems. The comparative analysis is also done by considering time domain specifications (TDSs) and error indices (EIs) for these test systems. The TDSs considered for comparative analysis are rise time, peak time, settling time and peak. The errors such as integral-absolute-error (IAE), integral-square-error (ISE), integral-time-absolute-error (ITAE), integral-time-square-error (ITSE), integral-time-square-absolute-error (IT2AE) and integral-time-squared-square-error (IT2SE) between HOS and those of the ROMs are tabulated as EIs. The comparative analysis demonstrates the productiveness and efficacy of the proposed method. The utility of proposed method is ensured by providing the step response, impulse response, Bode plot and Nyquist plot.