Limitations of Nonlinear Controls For a Curved and Offset Beam and Ball

Abstract

The problem of stabilizing the position of a ball on a straight beam is a common element of laboratory courses in control. Replacing the straight beam with a circular beam and moving the center of rotation off of the beam produces a harder control problem. This experiment was developed here at UMCP by Sheng, Renner, and Levine [1]. They designed and implemented a stabilizing controller based on a linearized model of the plant and an LQR optimal regulator. Here, the set of initial states that is stabilizable is explored. Also, nonlinear controls based on ideas from feedback linearization and backstepping are developed.