Control of Limit Cycle Oscillations
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Limit cycles are defined as periodic motions in mechanical systems. Self excited systems like Van der Pol oscillators are characterized by asymptotically stable limit cycles due to steady energy dissipation. On the other hand, conservative systems show marginally stable limit cycles without energy dissipation. However, such motions are very sensitive to disturbances and, therefore, less helpful in engineering. By adding control to conservative systems asymptotic stable, weakly dissipative limit cycles can be found. It is shown how limit cycle oscillations can be adapted to prescribed motions in manufacturing processes reducing energy consumption. For this purpose the shooting method is employed, harmonic and arbitrary prescribed motions are considered.
Key wordsControl limit cycle energy consumption shooting method
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