Fractional-Order PID Controller Design for a Transfer-Function-Based Third-Order System Using Particle Swarm Optimization

Abstract

In recent times, the application of fractional derivatives has become quite apparent in modeling mechanical and electrical properties of real materials. Fractional integrals and derivatives have found wide application in the control of dynamical systems, when the controlled system or/and the controller is described by a set of fractional order differential equations. This paper presents an effective tuning strategy for conventional and fractional-order PID controllers applied to the load frequency control problem of a multi-area power system. The proposed approach combines classical tuning methods with modern optimization techniques to enhance closed-loop dynamic performance. Initial controller parameters are obtained using the Ziegler–Nichols and Astrom–Hagglund methods and further refined using Particle Swarm Optimization to minimize the Integral Squared Error performance index. A state-space model of a four-area interconnected power system is developed, and system responses are evaluated through MATLAB/Simulink simulations. Comparative analysis is carried out among conventional PID, PSO-tuned PID, and PSO-tuned fractional-order PID controllers. Simulation results demonstrate that the PSO-tuned fractional-order PID controller provides superior transient performance, including reduced overshoot, faster settling time, and improved stability margins. The study confirms that combining fractional-order control with intelligent optimization techniques significantly enhances load frequency control performance in multi-area power systems.