Towards Power-Based Control Strategies for a Class of Nonlinear Mechanical Systems

Abstract

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 general 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 [1]), 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) achieve its minimum. In this respect, we recall first the power-based description for a certain class of (non)-linear mechanical systems given in [2] 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.