METAHEURISTIC ALGORITHMS AND THEIR APPLICATIONS TO NONLINEAR SYSTEMS

Abstract

Researchers working on problems in engineering, computer science, biology, and the physical sciences are developing advanced mathematical methods for control. Technological advances have had a major impact on the use of new analytical methods for dealing with nonlinear problems. One of the most challenging parts of control theory is tuning the parameters of nonlinear systems for an optimum solution. In the past, metaheuristic methods were tried to address this problem. They have proved to be useful when dealing with complex systems. Metaheuristic optimization techniques, unlike deterministic algorithms, excel at addressing problems with uncertain search spaces. Optimization-based control is now favoured over conventional or intelligent control, and because of these aspects, a hybrid CSMSEOBL technique is suggested to accomplish this. Due to their ability to overcome single algorithm limitations without compromising their strength, hybrid techniques outperform stand-alone alternatives. It's a tweaked version of the SMS algorithm (state of matter search) in which Chaotic Maps and Elite opposition-based learning (EOBL) are combined with SMS to improve the system's efficiency and effectiveness. The SMS algorithm's fundamental concept is at the heart of the thermal energy motion system. The method is broken down into three states of matter: solid, liquid, and gas, each with its diversification-intensification ratio. The method begins with a gas state and progresses to a solid-state by changing the diversification-intensification ratio. The proposed approach is compared to other optimization algorithms on unimodal, multimodal, and fixed-dimension multimodal benchmark functions to demonstrate its efficacy. Proportional-integral-derivative (PID) controllers are the most commonly used controllers in process industries due to their accessibility, efficacy, and durability. The system becomes unstable when process parameters change and disturbances occur. Because of the increasing complexity of plant operations, adjusting the parameters of a PID controller to avoid failures and excellent transient performance has become more difficult in recent years. Optimal adjustment of PID parameters is now a difficult job for control engineers. PID Controller and its variants like FOPID and 2-DOF-PID controllers are used for controlling nonlinear control problems. To assess the performance of the developed hybrid metaheuristic algorithm simulation studies are carried on fifteen benchmark functions and three nonlinear control systems Continuously stirred tank reactor, Ball balancer, and D.C. motor. A comparative study in terms of setpoint response analysis, convergence analysis, statistical analysis, and trajectory analysis with other recent existing metaheuristic algorithms are also presented to prove the superiority of the proposed algorithm.