Regulation control of underactuated mechanical systems based on a new matching equation of port-controlled hamiltonian systems

We consider the control of Port-Controlled Hamiltonian (PCH) systems, which are a generalization of Euler-Lagrange Systems. A new matching equation for PCH systems is developed so that interconnection damping assignment passivity-based control (IDA-PBC) can be extended to the regulation of some underactuated PCH systems whosekinetic energy must be modified. A simple underactuated mechanical system (the inertial wheel pendulum) is used to demonstrate the effectiveness of the proposed method.