Stabilization of a Cart-Inverted Pendulum with Interconnection and Damping Assignment Passivity-Based Control Focusing on the Kinetic Energy Shaping

Interconnection and damping assignment passivity-based control (IDA-PBC) is a nonlinear control method which stabilize a system shaping its total energy and utilizing passivity. In previous studies, IDA-PBC is shown to be a powerful method to stabilize underactuated mechanical systems. However, the transient performances tend to be slow. In this study, to improve the slow responses and realize fast transient ones, the IDA-PBC is applied for a cart-inverted pendulum and free parameters in a closed-loop inertia matrix which have not been used in the previous studies are utilized. This means modifying the kinetic energy more actively. On the other hand, the additional use of the free parameters makes the selection of them more complicated because several assumptions must be satisfied to derive an IDA-PBC controller. To deal with this problem, we also propose a systematic method to select them graphically from a simple two dimensional region. Finally, we show that the transient performances of the IDA-PBC can be as fast as the LQR with the active modification of the kinetic energy. The IDA-PBC with suitable parameters also theoretically estimates as large domain of attraction as the upper half plane preserving the fast transient performances.