Approximate feedback linearization: the cart-pole example

An existing nonlinear design methodology developed by Krener (1984, 1987), approximate feedback linearization, is applied to the control of underactuated single-input-single-output nonlinear systems. A computational approach to test for the order of linearization as well as a method to compute the approximate output function is derived. A method to simplify the dynamics using partial precompensation which uses the constraint equations of motion is presented. This approach is applied to a simple example. Simulation results showed a substantial improvement in the operating range of the linear controller by using this approach