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Optimal Tuning of a LQR Controller for an Inverted Pendulum Using the Bees Algorithm

Muhammed Arif Sen and Mete Kalyoncu
Department of Mechanical Engineering, Faculty of Engineering, University of Selçuk, Konya, Turkey

Abstract—The paper presents the design of a Linear Quadratic Regulator (LQR) controller for an Inverted Pendulum (IP) system using The Bees Algorithm (BA) to provide optimal parameters of LQR. Inverted Pendulum is a typical highly nonlinear and unstable system and widely used as a benchmark for testing different control techniques in control theory. LQR is an optimal control method that can achieve the closed loop control of multivariable dynamical systems with minimum control effort. In LQR controller design, state (Q) and control (R) weighting matrices are main design parameters which are defined by designer using trial and error method in general. Automatic tuning of the weighting matrices with an optimization algorithm ensure expected efficiency from LQR controller. Also the technique consider to design of time domain specifications like overshoot, rise time, settling time, and steady state error. In this paper, The Bees Algorithm optimizes the weighting matrices of LQR controller be able to move the cart in reference input with the minimum deflection of the pendulum’s angular position. The tuning aim is to minimize the objective function which consists of time domain responses of system in MATLAB/Simulink. The paper gives the simulation results obtained for the system demonstrating the efficiency and robustness of the proposed design method of LQR controller.

Index Terms—the bees algorithm, LQR controller tuning, optimal control, inverted pendulum

Cite: Muhammed Arif Sen and Mete Kalyoncu, "Optimal Tuning of a LQR Controller for an Inverted Pendulum Using the Bees Algorithm," Jounal of Automation and Control Engineering, Vol. 4, No. 5, pp. 384-387, October, 2016. doi: 10.18178/joace.4.5.384-387
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