Synthesis of oscillators for exact desired periodic solutions having a finite number of harmonics |
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Authors: | René Bartkowiak Christoph Woernle |
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Institution: | 1.Chair of Technical Mechanics/Dynamics,University of Rostock,Rostock,Germany |
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Abstract: | The synthesis of autonomous oscillators with exact desired periodic steady-state solution is described in this contribution. The vector field of the oscillator differential equation is built up with a conservative and a dissipative part. Both parts are synthesized using an algebraic function describing the desired limit cycle. The desired periodic motion is restricted by a finite numbers of harmonics, whereby the amplitude and the phase shift of every harmonic can be freely chosen, depending on the specific application. Afterwards the synthesis of a periodically driven oscillator with an exact desired periodic response is described. For this purpose, the differential equation of the autonomous oscillator is extended by a state-dependent compensation term that equals the excitation at the steady-state solution. Here the freely definable amplitudes and phase angles of the oscillator motion are restricted by the existence and stability conditions for synchronization. |
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