GWO based Robust Stabilization of DC Motor Fractional Order Speed Control System with Interval Coefficients

Robust stability analysis (RSA) is of significant concern for the robust behaviour of real-world control system applications. A stabilization strategy that assures stability and exhibits robust performance for a specified limit of system perturbations is necessary. This article presents an optimal robust stabilization method for a closed loop fractional order proportional integral derivative (FOPI^λD^µ) system involving DC motor with interval parametric uncertainty. To determine the optimum value of parameters for a FOPI^λD^µ controller to control the speed of a DC motor, Grey Wolf Optimizer (GWO), Genetic Algorithm (GA), Nelder-Mead (NM), Jaya and Whale Optimizer Algorithm (WOA) are applied with the same objective function involving ITAE criterion. FOPI^λD^µ offers two additional tuning parameters unlike a nominal PID controller and hence the former gives more flexibility in controller design than the latter in terms of transient response. The FOPID controller provides a faster closed-loop output augmented with improved robust properties of the system. Despite inherent non-linearities and time variation in system parameters, FOPI^λD^µ controllers depict enhanced performance. Using the concept of conformal mapping, robust stability analysis of fractional order polynomials is done with uncertain interval structure using Vertex and Edge theorem. Based on the value set, this paper demonstrates numerical and graphical optimal robust stability analysis of a system with variations observed in five parameters, considering the minimum argument root of the polynomial of the aforementioned closed-loop system.