An Optimized Fractional-Order PID (FOPID) Controller for a Non-Linear Conical Tank Level Process

This work discusses the design of a non-integer-order PID controller for a non-linear conical tank liquid level process using Nelder-Mead (NM) algorithm and compares its performance with Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) based controllers. The paper presents the energy utilization of the actuator and compare its performance using both integer-order PID (IOPID) and fractional-order PID (FOPID) controllers. The conical tank consists of four operating regions with a height of 7 cm for each region. A first-order plus dead time (FOPDT) model of the conical tank process for a region between (14-21) cm is considered in this work, which is identified using the two-point method. The servo and regulatory responses of the conical tank system with IOPID and FOPID controllers are presented and performance indices are evaluated and compared. Both simulation and experimental results show that Nelder-Mead (NM) optimized FOPID controller has a better set-point tracking and controller response compared to the classical IOPID controller, PSO tuned FOPID, and GA tuned FOPID.