A power-based perspective of mechanical systems

This paper is concerned with the construction of a power-based modeling framework for a large class of mechanical systems. Mathematically this is formalized by proving that every standard mechanical system (with or without dissipation) can be written as a gradient vector field with respect to an indefinite metric. The form and existence of the corresponding potential function is shown to be the mechanical analogue of Brayton and Moser's mixed-potential function as originally derived for nonlinear electrical networks in the early sixties. In this way, several recently proposed analysis and control methods that use the mixed-potential function as a starting point can also be applied to mechanical systems.

A power-based perspective in modeling and control of switched power converters [Past and Present]

Nonlinear passivity-based control (PBc) algorithms for switched converters have proven to be an interesting alternative to most linear, control techniques. A possible drawback though of PBC is that it relies on a (partial) system inversion. This usually results in indirect regulations schemes to control non-minimum phase outputs. Recently, a new control paradigm for nonlinear electrical circuits has been presented using the mixed-potential as a control-Lyapunov function. On-going research aims at extending the paradigm to switched power converters in order to avoid the system inversion problem.

A Novel Passivity Property of Nonlinear RLC Circuits

Arbitrary interconnections of passive (possibly nonlinear) resistors, inductors and capacitors define passive systems, with port variables the external sources voltages and currents, and storage function the total stored energy. In this paper we identify a class of RLC circuits (with convex energy function and weak electromagnetic coupling) for which it is possible to ‘add a differentiation’ to the port terminals preserving passivity—with a new storage function that is directly related to the circuit power. To establish our results we exploit the geometric property that voltages and currents in RLC circuits live in orthogonal spaces, i.e., Tellegen’s theorem, and heavily rely on the seminal paper of Brayton and Moser published in the early sixties