Stabilizing the Damped Inverted Pendulum Cart System by Means of a Cascade Chain of Integrators

In this work, we introduce a smooth control law to stabilize the damped inverted pendulum cart, assuming that the pendulum is initialized in the upper-half plane, and the linear viscous force is known. To this end suitable nonlinear transformations to express the system as if it were a four order chain of integrator and perturbed by a nonlinear function that diminished in the origin. Then, a convenient control law consisted of saturation functions for the system in its new form is designed. The corresponding stability analysis were carried out with several Lyapunov functions. The effectiveness of the obtained control law was assessed with numerical simulations.