Optimal LQR Controller Methods for Double Inverted Pendulum System on a Cart

Authors : Tayfun ABUT

Pages : 247-255

Doi:10.24012/dumf.1253331

View : 115 | Download : 235

Publication Date : 2023-06-20

Article Type : Research Paper

Abstract :Most of the systems in our lives are inherently nonlinear and unstable. In control problems in the field of engineering, the aim is to define the control laws that maximize the operating efficiency of these systems under diverse security coefficients, and constraints and minimize error rates. This study aimed to model and optimally control a Double-Inverted Pendulum System on a Cart insert ignore into journalissuearticles values(DIPSC);. A DIPSC was modeled using the Lagrange-Euler method, and classical and optimal Linear Quadratic Regulator insert ignore into journalissuearticles values(LQR); control methods were designed for the control of the system. The purpose of the designed controllers is to keep the arms of the double inverted pendulum on the moving cart vertically in balance and to bring the cart to the determined balance position. The critically important Q and R parameters of the LQR control technique that is one of the optimal control techniques were obtained using the Genetic Algorithm insert ignore into journalissuearticles values(GA);, Particle Swarm Optimization insert ignore into journalissuearticles values(PSO);, and Grey Wolf Optimization insert ignore into journalissuearticles values(GWO); algorithms. The DIPSC system was checked using classical LQR and optimal LQR methods. All obtained results are given graphically. The proposed methods are presented and analyzed in tabular form using Settling time and Mean-Square-Error insert ignore into journalissuearticles values(MSE); performance criteria.
Keywords : Double Inverted Pendulum System on a Cart DIPSC, , Optimal Control, Linear Quadratic Regulator LQR, , GA, PSO, GWO