Design and application of models reference adaptive control (MRAC) on ball and beam

Abstract

This paper presents the implementation of an adaptive control approach to the ball and beam system (BBS). The dynamics of a BBS are non-linear, and in the implementation, the uncertainty of the system's parameters may occur. In this research, the linear state-feedback model reference adaptive control (MRAC) is used to synchronize the states of the BBS with the states of the given reference model. This research investigates the performance of the MRAC method for a linear system that is applied to a non-linear system or BBS. In order to get a faster states convergence response, we define the initial condition of the feedback gains. In addition, the feedback gains are limited to get less oscillation response. The results show the error convergence is improved for the different sets of the sinusoidal reference signal for the MRAC with modified feedback gains. The ball position convergence improvement of MRAC with modified feedback gains for sinusoidal reference with an amplitude of 0.25, 0.5, and 0.75 are 35.1 %, 36 %, and 52.4 %, respectively.