DESIGN OF AN APPROXIMATE CONTROL LAW USING INPUT-STATE LINEARIZATION FOR THE BALL ON A PLATE SYSTEM

This paper demonstrates an approximate frill state feedback linearizing control law for the nonlinear ball on a plate system. It is shown that true full state feedback is not possible due both to the centrifugal acceleration terms and the nonlinear coupling between both coordinate axis. In an effort to make the system feedback linearizable, the dynamics corresponding to the centrifugal acceleration and the nonlinear coupling are simply treated as nonlinear disturbances to the original dynamics. The derived approximate full state feedback linearizing control law is evaluated via simulation of the original dynamics illustrating that the nonlinear disturbances are indeed small, and that the system controlled by the approximate control law is capable of more effective position and trajectory tracking than the standard Jacobian linearization.