H - INFINITY FULL-STATE FEEDBACK CONTROL FOR A BALL-BALANCING ROBOT

Abstract

The main purpose of this paper is to present the H - infinity controller
proposed to control the ball - balancing robot. In this paper, a method of
building state-space models is presented. The state - space model is built on
three separate planes xy, yz and zx by applying Lagrange equations for each
plane. Lagrange equation is the relationship between kinetic, potential, and non
- potential force, the model of this system is found by solving this equation. The
H - infinity controller is designed for two planes yz, zx. Because the state - space
model in yz and zx are the same, the H - infinity controller is only designed for
one plane. The H - infinity controller is approached by Linear matrix inequalities
(LMIs) to optimize the cost function. For the xy plane, the state - space model is
different, therefore the PID controller is used. The simulation results performed
on MATLAB/Simulink are fully presented in this paper. With the PID controller for
the xy plane, a minor test is done to examine the response of this controller.