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Abstract

Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.

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Authors and Affiliations

Marco Reit
Michael Berens
Wolfgang Mathis
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Abstract

In the field of power and drive systems, electrical AC machines are mostly modeled using a set of explicit ordinary differential equations in a state space representation. It is shown, that by using other equation types for simulation, algebraic constraints arising from aggregating several machines to a more complex system can directly be considered. The effects of different model variants on numerical ODE/DAE solvers are investigated in the focus of this work in order perform efficient simulations of larger systems possessing electrical AC machines.

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Authors and Affiliations

Michael Popp
Patrick Laza
Wolfgang Mathis

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