MOGWO-FOPID: Multi-Objective Gray Wolf Optimization Fractional Order PID Controllers in Quadruple Tank Process

The Quadruple Tank Process (QTP) is a laboratory model consisting of four interconnected water tanks, commonly used for control training and research purposes. The proficient regulation of the QTP is imperative, and a variety of controllers, including decentralized proportional-integral controllers, proportional controllers, integral controllers, derivative controllers, and integral-derivative-proportional controllers, are extensively utilized. A Fractional Order PID (FOPID) controller's effectiveness is largely determined by the precise organization of its parameters. This manuscript presents a Multi-Objective Gray Wolf Optimization Fractional Order PID (MOGWO-FOPID) framework, which employs the MOGWO algorithm to enhance the optimization of FOPID controller parameters for the QTP. The suggested methodology was executed and evaluated utilizing MATLAB, with its performance benchmarked against pre-existing, well-established tuning methodologies. Simulation findings indicated that the MOGWO-FOPID technique surpassed conventional methods. This superiority was corroborated through a variety of evaluation metrics, particularly emphasizing the Spacing Metric (SP) and Non-uniformity of Pareto Front (NPF) analysis. The outcomes reveal considerable advancements in both system stability and performance when employing the proposed methodology, thereby offering a more efficacious strategy for the optimization of FOPID parameters in the QTP.