Optimal Design of Linear Quadratic Regulator Controller for Asymmetric Structure Using Metaheuristic Algorithm

ABSTRACT This study presents the optimal design of a linear quadratic regulator (LQR) controller for an active control system applied to an asymmetric structure, using various metaheuristic algorithms. The performance of the LQR controller strongly depends on the proper selection of the weighting matrices. In the present study, metaheuristic algorithms utilized for finding weighting matrices for the LQR controller include particle swarm optimization (PSO), genetic algorithm (GA), gray wolf optimizer (GWO), whale optimization algorithm (WOA), ant lion optimizer (ALO), and an improved gray wolf optimizer (IGWO). The optimization process considers torsionally stiff, flexible, and coupled structures to analyze the wide range of structures. The minimization of structural displacement and acceleration is considered as objective functions, along with the response effectiveness factor considered as a constraint for optimization. The responses are determined by numerically solving the governing equation of motion using the state‐space approach. Furthermore, the performance of each algorithm is evaluated based on the minimization of the objective function, time required, and effort ratio. The results demonstrate the effectiveness of each algorithm in identifying the optimal LQR weighting matrices, with comparative analyses highlighting their relative efficiency, convergence rates, and robustness in dealing with the asymmetry of the structure. GWO and WOA showcase superior performance in achieving optimal solutions as compared with other algorithms and exhaustive search methods.