Nonlinear Control of Inertia Wheel Pendulum via Exact Feedback Linearization

This paper presents the development and implementation of a real-time state-to-state feedback linearization controller for an inertia wheel pendulum. Based on the nonlinear model of the plant, a mathematical proof of existence of such controller is first given, then a non-trivial local diffeomorphism is found that puts the system in the normal form, and finally the latter is employed to design a nonlinear control law that performs state-to-state exact feedback linearization to maintain the inertia wheel pendulum in the vertical upward position. Details guaranteeing reproducibility of results are provided, both for simulation and real-time implementation.