An Energy-Balancing Perspective of Interconnection and Damping Assignment Control of Nonlinear Systems

Stabilization of nonlinear feedback passive systems is achieved assigning a storage function with a minimum at the desired equilibrium. For physical systems a natural candidate storage function is the difference between the stored and the supplied energies—leading to the so-called Energy-Balancing control, whose underlying stabilization mechanism is particularly appealing. Unfortunately, energy-balancing stabilization is stymied by the existence of pervasive dissipation, that appears in many engineering applications. To overcome the dissipation obstacle the method of Interconnection and Damping Assignment, that endows the closed-loop system with a special—port-controlled Hamiltonian—structure, has been proposed. If, as in most practical examples, the open-loop system already has this structure, and the damping is not pervasive, both methods are equivalent. In this brief note we show that the methods are also equivalent, with an alternative definition of the supplied energy, when the damping is pervasive. Instrumental for our developments is the observation that, swapping the damping terms in the classical dissipation inequality, we can establish passivity of port-controlled Hamiltonian systems with respect to some new external variables—but with the same storage function.

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.

Gradient System Modelling of Matrix Converters with Input and Output Filters

Due to its complexity, the dynamics of matrix converters are usually neglected in controller design. However, increasing demands on reduced harmonic generation and higher bandwidths makes it necessary to study large-signal dynamics. A unified methodology that considers matrix converters, including input and output filters, as gradient systems is presented.

Characterizing Inductive and Capacitive Nonlinear RLC Circuits: A Passivity Test

Linear time-invariant RLC circuits are said to be inductive (capacitive) if the current waveform in sinusoidal steady-state has a negative (resp., positive) phase shift with respect to the voltage. Furthermore, it is known that the circuit is inductive (capacitive) if and only if the magnetic energy stored in the inductors dominates (resp., is dominated by) the electrical energy stored in the capacitors. In this paper we propose a framework, based on passivity theory, that allows to extend these intuitive notions to nonlinear RLC circuits.

On Brayton and Moser’s Missing Stability Theorem

In the early sixties Brayton and Moser proved three theorems concerning the stability of nonlinear electrical circuits. The applicability of each theorem depends on three different conditions on the type of admissible nonlinearities in circuit. Roughly speaking, this means that the theorems apply to either circuits that contain purely linear resistors or conductors—combined with linear or nonlinear inductors and capacitors, or to circuits that contain purely linear inductors and capacitors—combined with linear or nonlinear resistors and conductors. This brief note presents a generalization of Brayton and Moser’s stability theorems that also includes the analysis of circuits that contain nonlinear resistors, conductors, inductors and/or capacitors at the same time