Design of linear quadratic regulator (LQR) based on genetic algorithm for inverted pendulum

Abstract

One of the crucial problems in the dynamics and automatic control theory is balancing of an inverted pendulum robot by moving a cart along a horizontal path. This task is often used as a benchmark for difierent method comparison. In the practical use of the LQR method, the key problem is how to choose weight matrices Q and R correctly. To obtain satisfying results the experiments should be repeated many times with difierent parameters of weight matrices. These LQR parameters can be tuned by a Genetic Algorithm (GA) technique for getting better results. In our paper, the LQR parameters weight matrices Q and R which were tuned using the Genetic Algorithm. The simulations of the control problem are designed using MATLAB script code and MATLAB Simulink on an inverted pendulum model. The results show that the Genetic Algorithm is suitable for tuning the parameters to give an optimal response. The control problem of the inverted pendulum was solved successfully.