Stabilization of the cart-pendulum system using normalized quasi-velocities

A globally stabilizing controller in terms of the normalized quasi-velocities (NQV) for the cart-pendulum system is considered in this note. Introducing the NQV vector together with generalized coordinates leads to first-order differential equations with the identity mass matrix of the system. The proposed NQV controller, based on an energy approach, ensures balancing the inverted pendulum and bringing it to its upper equilibrium position. At the same time the cart displacement tends to zero. Some differences between the modified controller and the classical one given by Lozano et al. (2000) were discussed too.