Dimitri Jeltsema

Port-Hamiltonian Systems Theory: An Introductory Overview

An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel developments and relationships with other formalisms. Port-Hamiltonian systems theory yields a systematic framework for network modeling of multi-physics systems. Examples from different areas show the range of applicability. While the emphasis is on modeling and analysis, the last part provides a brief introduction to control of port-Hamiltonian systems.

Technical Communique: 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.

Lyapunov-Based Control Scheme for Single-Phase Grid-Connected PV Central Inverters

A Lyapunov-based control scheme for single-phase single-stage grid-connected photovoltaic central inverters is presented. Besides rendering the closed-loop system globally stable, the designed controller is able to deal with the system uncertainty that depends on the solar irradiance. A laboratory prototype has been built as a proof of concept for the proposed control technique. A nonlinear passive adaptive controller has been programmed in a field-programmable gate array.

Multidomain modeling of nonlinear networks and systems

Many physical systems, including mechanical, electrical, electromechanical, fluid, and thermal systems, can be modeled by the Langrangian and Hamiltonian equations of motion. A key aspect of the Langrangian and Hamiltonian frameworks is the role of energy storage. In this paper, equations regarding Langrangian and Hamiltonian are discussed and compared to the Brayton-Moser equations. A practical advantage of the BM framework is that the system variables are directly expressed in terms of easily measurable quantities, such as currents, voltages, velocities, forces, volume flows, pressures, or temperatures. The Langrangian, and Hamiltonian formulation normally involve generalized displacement and momenta, which in many cases cannot be measured directly.

Brief paper: Power-based control of physical systems

It is well known that energy-balancing control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, the alternative paradigm of power shaping was introduced in Ortega, Jeltsema, and Scherpen (2003) -where, as suggested by its name, stabilization is achieved shaping a function akin to the power instead of the energy function. In this paper we extend this technique to general nonlinear systems. The method relies on the solution of a PDE, which identifies the open-loop storage function. We show through some physical examples, that the power-shaping methodology yields storage functions which have units of power. To motivate the application of this control technique we illustrate the procedure with two case studies: a tunnel diode circuit and a two-tanks system.

Lagrangian modeling of switching electrical networks

In this paper, a general and systematic method is presented to model topologically complete electrical networks, with or without multiple or single switches, within the Euler–Lagrange framework. Apart from the physical insight that can be obtained in this way, the framework has proven to be useful for the application of passivity-based control techniques, which on a case by case basis already has shown to be useful for the control of power converters within the class of switching electrical networks. The switches are assumed to be ideal, and pulse-width modulation is taken into account. Magnetic coupling of inductive elements is also included in the framework.

Multidomain Modeling of Nonlinear Networks and Systems ENERGY- AND POWER-BASED PERSPECTIVES

Many physical systems, including mechanical, electrical, electromechanical, fluid, and thermal systems, can be modeled by the Langrangian and Hamiltonian equations of motion. A key aspect of the Langrangian and Hamiltonian frameworks is the role of energy storage. In this paper, equations regarding Langrangian and Hamiltonian are discussed and compared to the Brayton-Moser equations. A practical advantage of the BM framework is that the system variables are directly expressed in terms of easily measurable quantities, such as currents, voltages, velocities, forces, volume flows, pressures, or temperatures. The Langrangian, and Hamiltonian formulation normally involve generalized displacement and momenta, which in many cases cannot be measured directly.

A power-based description of standard mechanical systems

This paper is concerned with the construction of a power-based modeling framework for 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 analog of Brayton and Mosers 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.

A dual relation between port-Hamiltonian systems and the Brayton-Moser equations for nonlinear switched RLC circuits

In the last decades, several researchers have concentrated on the dynamic modeling of nonlinear electrical circuits from an energy-based perspective. A recent perspective is based on the concept of port-Hamiltonian (PH) systems. In this paper, we discuss the relations between the classical Brayton-Moser (BM) equations-stemming from the early sixties-and PH models for topologically complete nonlinear RLC circuits, with and without controllable switches. It will be shown that PH systems precisely dualize the BM equations, leading to possible advantages at the level of controller design. Consequently, useful and important properties of the one framework can be translated to the other. Control designs for the PH model cannot be directly implemented since they require observation of flux and charges, which are not directly available through standard sensors, while the BM models require only observation of currents and voltages. The introduced duality allows to pull back PH designs to the space of currents and voltages. This offers the possibility to exchange several different techniques, available in the literature, for modeling, analysis and controller design for RLC circuits. Illustrative examples are provided to emphasize the duality between both frameworks.

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

Abstract 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