Nonlinear Dynamics

, Volume 94, Issue 4, pp 2335–2346 | Cite as

Synthesis of oscillators for exact desired periodic solutions having a finite number of harmonics

  • René BartkowiakEmail author
  • Christoph Woernle
Original Paper


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.


Oscillator synthesis Algebraic curve Limit cycle Exact solution Potential function 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Chair of Technical Mechanics/DynamicsUniversity of RostockRostockGermany

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