Artificial Bee Colony Algorithm Based Linear Quadratic Optimal Controller Design for a Nonlinear Inverted Pendulum

Abstract

This paper presents a linear quadratic optimal controller design for a nonlinear inverted pendulum. Linear Quadratic Regulator (LQR), an optimal control method, is usually used for control of the dynamical systems. Main design parameters in LQR are the weighting matrices; however there is 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. Also it is time consuming and highly depends on designer’s experience. In this paper LQR is used to control an inverted pendulum as a nonlinear dynamical system and the Artificial Bee Colony (ABC) algorithm is used for selecting weighting matrices to overcome LQR design difficulties. The ABC algorithm is a swarm intelligence based optimization algorithm and it can be used for multivariable function optimization efficiently. The simulation results justify that the ABC algorithm is a very efficient way to determine LQR weighting matrices in comparison with trial and error method.