Port-Hamiltonian systems on discrete manifolds

This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by the coboundary operators. This finite-dimensional Dirac structure, as discrete analogue of the canonical Stokes-Dirac structure, allows for the formulation of finite-dimensional port-Hamiltonian systems that emulate the behaviour of the open distributed-parameter systems with Hamiltonian dynamics.Comment: MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modellin

Nordic Electricity Congestion's Arrangement as a Model for Europe: Physical Constraints or Operators' Opportunity

Nordic Electricity Congestion's Arrangement as a Model for Europe: Physical Constraints or Operators' Opportunit

Definition of Power Converters

The paper is intended to introduce power conversion principles and to define common terms in the domain. The concepts of sources and switches are defined and classified. From the basic laws of source interconnections, a generic method of power converter synthesis is presented. Some examples illustrate this systematic method. Finally, the commutation cell and soft commutation are introduced and discussed.Comment: 29 pages, contribution to the 2014 CAS - CERN Accelerator School: Power Converters, Baden, Switzerland, 7-14 May 201

Bounded Disturbance Amplification for Mass Chains with Passive Interconnection

This paper introduces the problem of passive control of a chain of N identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The problem arises in the design of multi-storey buildings which are subjected to earthquake disturbances, but applies in other situations, for example vehicle platoons. The paper studies the scalar transfer functions from the disturbance to a given intermass displacement. It is shown that these transfer functions can be conveniently represented in the form of complex iterative maps and that these maps provide a method to establish boundedness in N of the H-infinity norm of these transfer functions for certain choices of interconnection impedance

3 sampled-data control of nonlinear systems

This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research

Structure-Preserving Discretization of a Coupled Heat-Wave System, as Interconnected Port-Hamiltonian Systems

The heat-wave system is recast as the coupling of port-Hamiltonian subsystems (pHs), and discretized in a structure-preserving way by the Partitioned Finite Element Method (PFEM) (Cardoso-Ribeiro, 2021). Then, depending on the geometric configuration of the two domains, different asymptotic behaviours of the energy of the coupled system can be recovered at the numerical level, assessing the validity of the theoretical results of (Zhang and Zuazua, 2007)