Quadratic optimal control of an inverted pendulum using artificial bee colony algorithm

This study presents a quadratic optimal controller for an inverted pendulum which is designed with Linear Quadratic Regulator (LQR) using the Artificial Bee Colony (ABC) algorithm. LQR, an optimal control method, is used for control of the dynamical systems in usual. Main design parameters in LQR are the weighting matrices; however there are no relevant systematic techniques presented to choose these matrices. Generally, selecting weighting matrices is performed by trial and error method since there is no direct relation between weighting matrices and time domain specifications like overshoot percentage, settling time, and steady state error. In this study LQR is used to control an inverted pendulum system with DC motor as a nonlinear dynamical system and the ABC algorithm which is a swarm intelligence based optimization algorithm is used to select weighting matrices to overcome LQR design difficulties. The simulation results justify that the ABC algorithm is a very efficient way to determine LQR weighting matrices in comparison with a method in literature.