Abstract
We develop a method to simplify the partial differential equations (PDEs) associated to the potential energy for interconnection and damping assignment passivity based control (IDA-PBC) of a class of underactuated mechanical systems. Solving the PDEs, also called the matching equations, is the main difficulty in the construction and application of the IDA-PBC. With the proposed method, a simplification to the potential energy PDE is achieved through a particular parametrization of the closed-loop inertia matrix that appears as a coupling term with the inverse of original inertia matrix. The results are applied to the Quanser rotary inverted pendulum and illustrated through numerical simulations.
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