Passivity based stabilization of linear mechanical systems with dissipation in unactuated degrees of freedom



A well-known problem in nonlinear controller design for underactuated mechanical systems using the Interconnection and Damping Assignment (IDA-PBC) technique is physical dissipationf in unactuated degrees of freedom. For certain equilibria the definiteness requirements on the virtual energy of the port-Hamiltonian (pH) target system and the closed loop dissipation matrix can not be satisfied simultaneously. At the GAMM Meeting 2012 we presented a modification of the nonlinear pH target system, where particularly the total energy function is augmented by a cross term between coordinates and momenta. For the sake of brevity in this short communication we focus on the case of linear mechanical systems. In particular, it is shown how the generalized pH target structure is derived from the solution of a Lyapunov equation for the closed loop system. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)