Lumped Approximation of a Transmission Line with an Alternative Geometric Discretization

An electromagnetic one-dimensional transmission line represented in a distributed port-Hamiltonian form is lumped into a chain of subsystems which preserve the port-Hamiltonian structure with inputs and outputs in collocated form. The procedure is essentially an adaptation of the procedure for discretization of Stokes-Dirac structures presented previously, that does not preserve the port-Hamiltonian structure after discretization. With some modifications essentially inspired on the finite difference paradigm, the procedure now results in a system that preserves the collocated port-Hamiltonian structure along with some other desirable conditions for interconnection. The simulation results are compared with those presented previously.

On Factorization, Interconnection and Reduction of Collocated Port-Hamiltonian Systems

Based on a geometric interpretation of nonlinear balanced reduction some implications of this approach are analyzed in the case of collocated port-Hamiltonian systems which have a certain balance in its structure. Furthermore, additional examples of reduction for this class of systems are presented.

An electrical interpretation of mechanical systems via the pseudo-inductor in the Brayton-Moser equations

In this paper an analogy between mechanical and electrical systems is presented, where, in contrast to the traditional analogy, position dependence of the mass inertia matrix is allowed. In order to interpret the mechanical system in an electrical manner, a pseudo-inductor element is introduced to cope with inductor elements with voltage-dependent electromagnetic coupling. The starting point of this paper is given by systems described in terms of the Euler-Lagrange equations. Then, via the introduction of the pseudo-inductor, the Brayton-Moser equations are determined for the mechanical system. © 2005 IEEE.

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.

Energy-Storage Balanced Reduction of Port-Hamiltonian Systems

Supported by the framework of dissipativity theory, a procedure based on physical energy to balance and reduce port-Hamiltonian systems with collocated inputs and outputs is presented. Additionally, some relations with the methods of nonlinear balanced reduction are exposed. Finally a structure-preserving reduction method based on singular perturbations is shown.

Passive compensation of nonlinear robot dynamics

In this paper, we derive a coordinate-free formulation of a passive controller that makes a mechanical system track reference curves in a potential field. Contrary to conventional reference tracking, we do not specify a single time-varying trajectory that the system has to track. Instead, we specify a whole curve that the system has to stay on at all times. Using tools from differential geometry, we first derive a controller that makes the system move along arbitrary (smooth enough) reference curves while keeping the kinetic energy constant. We then apply the results to the case of movement in an artificial potential field, in which case, the reference curves are completely determined by the potential field and cannot be chosen arbitrarily. Simulation then shows the performance of the controller on a benchmark robot with two degrees of freedom