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Adaptive phasor control of a Duffing oscillator with unknown parameters

: Wantoch, T. von; Röck, H.; Koschmieder, F.; Benecke, W.


Boje, E. ; International Federation of Automatic Control -IFAC-:
19th IFAC World Congress 2014. Proceedings : Cape Town, South Africa, 24 - 29 August 2014
IFAC-PapersOnline, 2014
ISBN: 978-3-902823-62-5
International Federation of Automatic Control (IFAC World Congress) <19, 2014, Cape Town>
Conference Paper
Fraunhofer ISIT ()

Weakly damped electrical and mechanical oscillators that contain a cubic nonlinearity are described mathematically using Duffing's equation. In particular microelectromechanical systems (MEMS) exhibit mechanical structures that are characterized by nonlinear elasticity due to a hardening or softening spring constant. Driving these nonlinear oscillators by sinusoidal excitation with varying frequency and amplitude we observe typical characteristics of nonlinear oscillators in the frequency response as jump phenomena at bifurcation points. Especially in applications with varying physical parameters due to changes in environmental conditions or external disturbances a stable operation in resonance cannot be guaranteed by applying conventional Phase Locked Loops (PLLs). In this work we propose an adaptive phasor control approach that is based on a phasor representation of the linearized Duffing oscillator in order to control the amplitude and phase of the oscillation separately. The Duffing oscillator is linearized adaptively by using a dynamic parameter estimator for the unknown nonlinear spring constant.