Optimization of active controlled system for structures using metaheuristic algorithms

This study presents a method for optimization of weighting matrices of the linear quadratic regulator (LQR) control algorithm in order to design an optimal active control system using metaheuristic algorithms. The LQR is a widely used control technique in engineering for designing optimal controllers for linear systems by minimizing a quadratic cost function. However, the performance of the LQR strongly depends on the appropriate selection of weighting matrices, which are usually determined by some thumb rule or exhaustive search method. In the present study, for the optimization of weighting matrices, four metaheuristic algorithms including, Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Grey Wolf Optimizer (GWO) and, Whale Optimization Algorithm (WOA) are considered. To generate optimal weighting matrices, the objective function used consists of displacement and absolute acceleration. During the optimization process, a response effectiveness factor is also checked for displacement and acceleration as a constraint for the proper selection of weighting matrices. To study the effectiveness of optimized active control system to those for the exhaustive search method, the various controlled responses of the system are compared with the corresponding uncontrolled system. The optimized weighting matrices effectively reduce the displacement, velocity, and acceleration responses of the structure. Based on the simulation study, it can be observed that GWO performs well compared to the PSO, GA, and WO algorithms. By employing metaheuristic algorithms, this study showcases a more efficient and effective approach to finding optimal weighting matrices, thereby enhancing the performance of active control systems.