Stabilization of the strongly damping inertia wheel pendulum by a nested saturation functions

The stabilization of the strongly damping inertia wheel pendulum around its unstable equilibrium point is presented in this paper. The fact that this system can be rewritten approximately as a chain of integrators with and nonlinear perturbation suggests the use of a nested saturation based controller for making all state variables converge to zero. The proposed control strategy makes the closed-loop system globally asymptotically and locally exponentially stable around the unstable inverted vertical position, even when the physical damping is presented in the model.