Applying a Genetic Algorithm to Optimize Linear Quadratic Regulator for Ball and Beam System

The paper presents a Genetic Algorithm (GA) used to optimally tune parameters of a Linear Quadratic Regulator for balancing a ball and beam system at its equilibrium position. GA is an optimal search technique using the principle of Genetics and Natural Selection. It is commonly used to generate high-quality solutions to optimize and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Linear Quadratic Regulator (LQR) is a type of optimal control based on state-space representation. The combination between LQR and GA helps to find the optimal feedback gain vectors which are joined with the all states of the ball and beam system. Simulation results show that the proposed combination is able to keep the ball and beam system at its equilibrium state.