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Unformatted text preview: Ball and Beam I. PHYSICAL DESCRIPTION A ball is placed on a beam, see figure below, where it is allowed to roll with 1 degree of freedom along the length of the beam. A lever arm is attached to the beam via a servo gear. As the servo gear turns ( ), the lever changes the angle of the beam ( ) . When the angle is changed from the vertical position, gravity causes the ball to roll along the beam. A controller will be designed for this system so that the balls position can be manipulated. For this problem, assume that the ball rolls without slipping and friction between the beam and ball is negligible. II. EQUATION OF MOTION The equation of motion for the ball is given by J X 2 + m .. r + mg sin mr . 2 = 0 . Linearization of this equation about the beam angle, = 0 , gives the following linear approximation of the system: J X 2 + m .. r = mg. The equation which relates the beam angle to the angle of the gear can be approximated by the linear relationship...
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This note was uploaded on 08/23/2011 for the course EML 4312 taught by Professor Dixon during the Spring '07 term at University of Florida.
- Spring '07