Optimal PID Parameter Design Using MATLAB's fminsearch Simplex Method

This project presents an optimal PID parameter design using MATLAB programming language and the fminsearch simplex method for parameter optimization. The PID controller represents a fundamental control mechanism widely employed to regulate system outputs and maintain alignment with desired reference values. Through systematic optimization of PID parameters (proportional, integral, and derivative gains), we can significantly improve system stability, response speed, and overall control performance. The implementation leverages MATLAB's fminsearch function, which utilizes the Nelder-Mead simplex algorithm - a direct search method that doesn't require numerical gradients. This approach operates by constructing a simplex (a geometric figure with n+1 vertices in n-dimensional space) and iteratively transforming it through reflection, expansion, and contraction operations to locate the parameter combination that minimizes the objective function. Key implementation aspects include defining an appropriate cost function (typically ITAE, IAE, or ISE criteria) that quantifies system performance, establishing parameter constraints, and configuring optimization tolerances. The algorithm systematically evaluates different PID parameter combinations while monitoring convergence criteria to ensure optimal solution discovery. Through this optimization framework, we obtain superior PID parameters that yield enhanced control system performance, including reduced overshoot, faster settling times, and improved disturbance rejection capabilities. The MATLAB implementation provides a practical approach for automating PID tuning processes across various control system applications.