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.

Differentiation and Passivity for Control of Brayton-Moser Systems

This article deals with a class of resistive-inductive-capacitive (RLC) circuits and switched RLC (s-RLC) circuits modeled in the Brayton-Moser framework. For this class of systems, new passivity properties using a Krasovskii-type Lyapunov function as storage function are presented, where the supply rate is function of the system states, inputs, and their first time derivatives. Moreover, after showing the integrability property of the port-variables, two simple control methodologies called output shaping and input shaping are proposed for regulating the voltage in RLC and s-RLC circuits. Global asymptotic stability is theoretically proved for both the proposed control methodologies. Moreover, robustness with respect to load uncertainty is ensured by the input shaping methodology. The applicability of the proposed methodologies is illustrated by designing voltage controllers for dc-dc converters and dc networks