A Hamiltonian viewpoint in the modeling of switching power converters

Escobar, G.; Schaft, A.J. van der; Ortega, Roméo

doi:10.1016/s0005-1098(98)00196-4

Cited by 212 publications

(132 citation statements)

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“…These systems have instead bilinear averaged dynamics. In general, it is easier to analyze these systems with Lagrangian and Hamiltonian methods, e.g., Ortega, Loria, Nicklasson, and Sira-Ramirez (1988), Escobar, van der Schaft, and Ortega, (1999).…”

Section: Article In Pressmentioning

confidence: 99%

Subtleties in the averaging of a class of hybrid systems with applications to power converters

Iannelli¹,

Johansson²,

Jönsson³

et al. 2008

Control Engineering Practice

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High-frequency dither signals are commonly used to implement modulation schemes in power electronics converters. These systems represent an interesting class of hybrid systems with external excitation. They have a rich dynamical behavior, which cannot be easily understood intuitively. Despite the common use of averaging techniques in power electronics, it was only recently proved that a dithered hybrid system can be approximated by an averaged system under certain conditions on the dither signal. Averaging and averaged models for various types of power converters are analyzed in the paper. It is shown that the averaged nonlinearity depends on the dither shape and that dither signals with Lipschitz-continuous averaged nonlinearities can be used to adapt the equivalent gain of power converters. Practical stability of the original dithered system can be inferred by analyzing a simpler averaged system. The main contribution of the paper is to show that the averaged and the dithered systems may have drastically different behavior if the assumptions of the recently developed averaging theory for dithered hybrid systems are violated. Several practical experiments and simulation examples of power electronics converters are discussed. They indicate that the conditions on the dither signal imposed by the averaging theory are rather tight. r

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Section: Article In Pressmentioning

confidence: 99%

Subtleties in the averaging of a class of hybrid systems with applications to power converters

Iannelli¹,

Johansson²,

Jönsson³

et al. 2008

Control Engineering Practice

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“…Many switching circuits already fall directly in the class of networks considered in the paper like the well-knownČuk, Boost and Flyback circuits [9]. Moreover, surprisingly many other piecewise linear networks, which do not seem to fit the framework at first sight, can be built from these elements as well (see e.g.…”

Section: Modelling Switched Electrical Circuitsmentioning

confidence: 99%

“…The Boost circuit (see e.g. [9]) consists of a capacitor C with electric charge q, an ideal diode D, a battery (voltage source) E, an inductor L with magnetic flux φ, a resistor R, and an ideal switch S. The voltage-current characteristics of the ideal diode and switch are depicted in Figure 2. These type of circuits, usually called step-up converters, are used to obtain a voltage at the resistance load that is higher than the voltage E of the input source.…”

Section: Modelling Switched Electrical Circuitsmentioning

confidence: 99%

Modelling, Well-Posedness, and Stability of Switched Electrical Networks

Heemels

Camlibel

Schaft

et al. 2003

Hybrid Systems: Computation and Control

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Abstract. A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolved.

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“…Energy-based control and stability analysis have been extensively studied for a wide range of physical systems, which include robotic manipulators [10,15], surface vehicles [11], space crafts [26], mechanical systems [27,2], and electrical systems [20,9], etc. While much research work in the area of robotics leads to a good understanding of this approach, its recent successful applications to power systems require new problem formulations and new insights into this approach [14,28].…”

Section: Introductionmentioning

confidence: 99%

“…The Hamiltonian function, the sum of potential energy (excluding gravitational potential energy) and kinetic energy in physical systems, is a good candidate of Lyapunov functions for many physical systems, which makes it very easy for stability analysis and control design for the systems. Up to now, the port-controlled Hamiltonian approach has been used in various control problems [17,9,23]. In particular, it has been successfully applied to the control of power systems in a series of works [3,24,14,28].…”

Section: Introductionmentioning

confidence: 99%

Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

Wang

Cheng

2007

Systems & Control Letters

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The key in applying energy-based control approach is to be able to express the system under consideration as a dissipative Hamiltonian system, i.e., to obtain Dissipative Hamiltonian Realization (DHR) for the system. In general, the precise DHR form is hard to obtain for nonlinear dynamic systems. When a precise DHR does not exist for a dynamic system or such a precise realization is difficulty to obtain, it is necessary to consider its approximate realization. This paper investigates approximate DHR and construction of local Lyapunov functions for time-invariant nonlinear systems. It is shown that every nonlinear affine system has an approximate DHR if linearization of the system is controllable. Based on the diagonal normal form of nonlinear dynamic systems, a new algorithm is established for the approximate DHR. Finally, we present the concept of kth degree approximate Lyapunov function, and provide a method to construct such a Lyapunov function. Example studies show that the methodology presented in this paper is very effective.

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A Hamiltonian viewpoint in the modeling of switching power converters

Cited by 212 publications

References 10 publications

Subtleties in the averaging of a class of hybrid systems with applications to power converters

Subtleties in the averaging of a class of hybrid systems with applications to power converters

Modelling, Well-Posedness, and Stability of Switched Electrical Networks

Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

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