An electrical interpretation of mechanical systems via the pseudo-inductor in the BraytonMoser equations Rinaldis, Alessandro de; Scherpen, Jacquelien M.A. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract-In this paper an analogy between mechanical and electrical systems is presented, where, in contrast to the traditional analogy, position dependence of the mass inertia matrix is allowed. In order to interpret the mechanical system in an electrical manner, a pseudo-inductor element is introduced to cope with inductor elements with voltage-dependent electromagnetic coupling. The starting point of this paper is given by systems described in terms of the Euler-Lagrange equations. Then, via the introduction of the pseudo-inductor, the BraytonMoser equations are determined for the mechanical system.

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In the present work we are interested on the derivation of power-based passivity properties for a certain class of non-linear mechanical systems. While for (non)-linear mechanical systems, it is of common use to adopt a storage function related to the system's energy in order to show passivity and stabilize the system on a desired equilibrium point(e.g., IDA-PBC (Ortega et al., 1998)), we want here to obtain similar properties related to the system's power. The motivation arises from the idea that in some engineering applications(satellite orbit motion, aircraft dynamic,etc...)seems more sensible to cope with the power flowing into the system instead of the energy that for stabilization purposes, means to consider the systems's equilibrium the state for which the energy flow-rate(i.e.,system's power)is minimal. In this respect, we recall first the power-based description for a certain class of (non)-linear mechanical systems given in (de Rinaldis and Scherpen, 2005) and then we give sufficient conditions to obtain power-based passivity properties, provided a suitable choice of port-variables. We conclude with the example of the inverted pendulum on the cart.