Controller comparison and mathematical modelling of ball and beam system

Abstract

The present project shows a comparison between three control techniques applied in the ball and beam system. In the ball and beam system problem, a bar is rotated using a motor and this rotation makes a sphere roll over the bar until it reaches the desired position.  The mathematical modeling was done writing the dynamic equations on the state space, and the non-linear state equations were represented as a plant system using Simulink. The applied control techniques were state-feedback controller, linear quadratic regulator (LQR) and neural network based NARMA controller. The three techniques were applied for continuous and discrete signals and were tested with and without state observer. Several simulations were carried out using Matlab and Symulink, and results shown that the system can be stabilized by all the controllers with slight differences, state-feedback was faster and NARMA model was smoother and required a smaller input.