Dissipativity preserving balancing for nonlinear systems — A Hankel operator approach

In this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system. We discuss an approach that allows us to apply the theory of balancing based upon Hankel singular value analysis. In order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified, asymptotically stable, system. Then Hankel singular value theory can be applied and the axis singular value functions of the modified system equal the nonlinear extensions of “similarity invariants” obtained from the required supply and available storage of the original system. Furthermore, we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations. The obtained relations are used to perform model order reduction based on balanced truncation, yielding dissipative reduced order models for the original systems. A second order electrical circuit example is included to illustrate the results.     

Power-based control: Canonical coordinate transformations,integral and adaptive control

Power-based modeling was originally developed in the early sixties to describe a large class of nonlinear electrical RLC networks, in a special gradient form. Recently this idea has been extended for modeling and control of a larger class of physical systems. In this paper, first, coordinate transformations are introduced for systems described in this framework, such that the physical structure is preserved. Such a transformation can provide new insights for both analysis and control design. Second, power-based integral and adaptive control schemes are presented. Advantages of these schemes are shown by their application on standard mechanical systems.     

Cryogenic mechatronic design of the HIFI Focal Plane Chopper

This paper discusses the cryogenic mechatronic development of the Focal Plane Chopper (FPC) mechanism in the Heterodyne Instrument for the Far Infrared (HIFI) which is one of the science instruments on board the Herschel space telescope. The extreme cryogenic environment, in which the mechanism has to operate, places a number of constraints on the mechatronic design of the instrument. The paper gives an overview of cryogenic design issues applicable to the development of the FPC and provides solutions to the problems encountered.     

A cyclodissipativity characterization of power factor compensation of nonlinear loads under nonsinusoidal conditions

Recently, it has been established that power factor (PF) improvement for nonlinear loads with nonsinusoidal source voltage is equivalent to imposing the property of cyclodissipativity to the source terminals. Using this framework, the classical capacitor and inductor compensators were interpreted in terms of energy equalization. The purpose of this brief note is to extend this approach in three directions. In the result reported in the literature, the supply rate is a function of the load, which is usually unknown, stymieing the applicability of the technique for compensator synthesis. Our first contribution is a new cyclodissipativity condition, which is also equivalent to PF improvement, but whose supply rate is now function of the compensator. Second, we consider general lossless linear compensators, instead of only capacitive or inductive compensators. As a result, we show that the PF is improved if and only if a certain equalization condition between the weighted powers of inductors and capacitors of the load is ensured. Finally, we exhibit the gap between the ideal compensator, namely the one that achieves unitary PF, and the aforementioned equalization condition. This result naturally leads to the formulation of a problem of optimization of the parameters of the compensator. Copyright © 2011 John Wiley & Sons, Ltd.     

Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems

Simplicial Dirac structures as finite analogues of the canonical Stokes–Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input–output finite-dimensional port-Hamiltonian systems that emulate the behavior of distributed-parameter port-Hamiltonian systems. This paper elaborates on the matrix representations of simplicial Dirac structures and the resulting port-Hamiltonian systems on simplicial manifolds. Employing these representations, we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port-Hamiltonian systems on simplicial manifolds.