Hamiltonian perspective on compartmental reaction–diffusion networks

Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction–diffusion system is a distributed-parameter port-Hamiltonian system on a compact spatial domain. Motivated by the need for computer-based design, we offer a spatially consistent discretization of the PDE system and, in a systematic manner, recover a compartmental ODE model on a simplicial triangulation of the spatial domain. Exploring the properties of a balanced weighted Laplacian matrix of the reaction network and the Laplacian of the simplicial complex, we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points. The paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction–diffusion networks.     

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.     

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.