Multi-Algorithm-Based Optimization of LQR Controller Parameters for a Triple Inverted Pendulum System

Abstract

This study addresses the Linear Quadratic Regulator (LQR)-based control of a triple inverted pendulum system with nonlinear, unstable, and multivariable dynamics. Since LQR performance depends on the selection of the Q and R weighting matrices, a total of nine parameters are optimized using metaheuristic algorithms. Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), and Artificial Circulation System Algorithm (ACSA) are employed. The optimal LQR parameters obtained from each algorithm are compared under identical simulation conditions, and the performance is evaluated using ISE, ITAE, overshoot, settling time, and control effort. The results show that metaheuristic algorithms are effective in LQR parameter selection and improve the stabilization performance compared with the classical LQR controller. Among the investigated methods, ACSA-LQR achieves the best cart position performance, whereas GWO-LQR offers a favorable balance between control performance and convergence consistency.