Fractional-Order PID Parameter Tuning Using Particle Swarm Optimization Algorithm

This project implements fractional-order PID controller parameter tuning using particle swarm optimization (PSO) algorithm within MATLAB R2007 environment. The PSO algorithm is an evolutionary optimization technique inspired by social behavior patterns, particularly effective for parameter adjustment and optimization problems in control systems. The implementation utilizes MATLAB's optimization toolbox and custom functions to establish the PSO framework for parameter search. The fractional-order PID controller represents an advanced version of conventional PID controllers, incorporating fractional calculus operators to enhance system response characteristics. This implementation involves defining the fractional-order transfer function and integrating it with the PSO optimization loop. Key MATLAB functions employed include particle swarm optimization routines, fractional-order operator implementations using Grünwald-Letnikov or Caputo definitions, and performance index calculations based on integral absolute error (IAE) or integral time absolute error (ITAE) criteria. The code structure typically consists of three main components: initialization of PSO parameters (swarm size, iteration count, inertia weight), objective function definition incorporating the fractional-order PID control system, and iterative optimization process with velocity and position updates. The algorithm evaluates candidate solutions by simulating the control system response and minimizing the defined performance index. Through the integration of particle swarm optimization and fractional-order PID control, this approach significantly improves control system performance metrics including response speed, overshoot reduction, and stability margins. The MATLAB R2007 platform provides the necessary computational environment for mathematical modeling and engineering simulations, ensuring reliable implementation of both the optimization algorithm and control system analysis.