Local linear dynamics assignment in IDA-PBC for underactuated mechanical systems

The problem of finding a set of design parameters in the well-known IDA-PBC approach for a class of nonlinear underactuated mechanical systems to realize desired time behavior of the closed loop Port-Hamiltonian system in a transparent way is considered. Using a local coordinate transformation, the effect of the homogeneous solution of the potential energy matching PDE is isolated. By comparison of desired local linear dynamics with the parametrized linearization of the closed loop dynamics a set of linear equations for the IDA-PBC design parameters is derived. Besides the possibility to assign predefined dynamics the definiteness check of the potential energy can be omitted. With an Acrobot-type mechanical system the design steps are illustrated and simulations validate the performance of the approach.