Modelling Electromechanical Systems with Electrical Switching Components Using the Linear Complementarity Problem

Enge, Olaf; Maißer, P.

doi:10.1007/s11044-005-3991-8

Cited by 9 publications

(9 citation statements)

References 12 publications

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“…There are basically three ways to treat electrical systems, called the ux approach, the charge approach and mixed approaches [10]. This distinction is based on what is chosen as the independent variables in the system.…”

Section: Models Of Switches In Electrical Systemsmentioning

confidence: 99%

“…Equation (21) is called the mesh transformation [10] and deÿnes the node-branch incidence matrix of the electrical network as well as the kinematics of the associated mechanical system [7,9,10,19].…”

Section: The Extended Dc-dc Buck Convertermentioning

confidence: 99%

“…In order to show the link between mechanical and electrical modelling in a most comprehensive way, we restrict ourselves to mechanical lumped parameter models with linear kinematics only. The full non-linear approach is found in a di erential geometric setting in Reference [10] for electromechanical systems with diodes, and in References [4,7] for mechanical systems with particular emphasis on general concepts related to set-valued constitutive laws. In the charge approach, the local variables from mechanics and electricity are related to each other according to Table I.…”

Section: Models Of Switches In Electrical Systemsmentioning

confidence: 99%

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Models of non-smooth switches in electrical systems

Glocker

2005

Int. J. Circ. Theor. Appl.

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SUMMARYIdealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expressed in terms of set-valued functions, which allow to formulate the circuit's dynamic behaviour as a di erential inclusion. This approach is demonstrated by the example of the DC-DC buck converter. A di erence scheme, known in mechanics as time stepping, is applied for numerical approximation of the evolution problem. The discretized inclusions are formulated as a linear complementarity problem in standard form, which implicitly takes care of all switching events by its solution. State reduction, which requires manipulation of the set-valued branch relations in order to obtain a minimal model, is performed on the example of the buck converter.

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Section: Models Of Switches In Electrical Systemsmentioning

confidence: 99%

Section: The Extended Dc-dc Buck Convertermentioning

confidence: 99%

Section: Models Of Switches In Electrical Systemsmentioning

confidence: 99%

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Models of non-smooth switches in electrical systems

Glocker

2005

Int. J. Circ. Theor. Appl.

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“…Table 1). For electrical systems there are three common approaches to describe the dynamics of the system: The charge approach, the flux approach and mixed approaches [10]. In the charge approach, the charges g(t) with the associated currents ı(t) are chosen as independent variables…”

Section: Classical Analogymentioning

confidence: 99%

“…The dynamical behaviour is formulated as a differential inclusion and solved numerically using the time-stepping method. A method for the modelling of electro-mechanical systems with variable structure in the electrical subsystem is presented in [10] with the focus on the diode. In the charge approach for electrical systems, the currents and charges are used as variables.…”

Section: Introductionmentioning

confidence: 99%

Non-smooth modelling of electrical systems using the flux approach

Möller

Glocker

2007

Nonlinear Dyn

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The non-smooth modelling of electrical systems, which allows for idealised switching components, is described using the flux approach. The formulations and assumptions used for non-smooth mechanical systems are adopted for electrical systems using the position-flux analogy. For the most important non-smooth electrical elements, like diodes and switches, set-valued branch relations are formulated and related to analogous mechanical elements. With the set-valued branch relations, the dynamics of electrical circuits are described as measure differential inclusions. For the numerical solution, the measure differential inclusions are formulated as a measure complementarity system and discretised with a difference scheme, known in mechanics as time-stepping. For every time-step a linear complementarity problem is obtained. Using the example of the DC-DC buck converter, the formulation of the measure differential inclusions, state reduction and their numerical solution using the time-stepping method is shown for the flux approach.

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