Controlling Non-Minimum Phase Nonlinear Systems - The Inverted Pendulum on a Cart Example

Control design for minimum phase nonlinear systems has been well developed in the literature via the input-output linearization method developed in [Isi89] and elsewhere. Since a minimum phase system has stable internal dynamics, one may only need to design a control for the linear subsystem after performing input-output linearization for such a system. This paper addresses the design of controls for non-minimum phase nonlinear systems that result in stable output regulation or tracking with acceptable closed-loop performance. The approach is based on the decomposition of a system into an input-output subsystem and an internal dynamics. The developed results are applied to the classical inverted pendulum on a cart example. Simulation and experimental results are reported.