Synthesis of oscillators for exact desired periodic solutions having a finite number of harmonics
| Autor: | René Bartkowiak, Christoph Woernle |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
0209 industrial biotechnology Differential equation Applied Mathematics Mechanical Engineering Mathematical analysis Aerospace Engineering Ocean Engineering 02 engineering and technology 01 natural sciences 010305 fluids & plasmas Periodic function 020901 industrial engineering & automation Amplitude Control and Systems Engineering Limit cycle Harmonics 0103 physical sciences Dissipative system Harmonic Algebraic function Electrical and Electronic Engineering |
| Zdroj: | Nonlinear Dynamics. 94:2335-2346 |
| ISSN: | 1573-269X 0924-090X |
| DOI: | 10.1007/s11071-018-4492-7 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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