Arbitrary amplitude periodic solutions for parametrically excited systems with time delay |
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Authors: | Attilio Maccari |
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Institution: | (1) Technical Institute Cardano, Via Alfredo Casella 3, 00013 Mentana, RM, Italy |
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Abstract: | Periodic solutions for parametrically excited system under state feedback control with a time delay are investigated. Using
the asymptotic perturbation method, two slow-flow equations for the amplitude and phase of the parametric resonance response
are derived. Their fixed points correspond to limit cycles (phase-locked periodic solutions) for the starting system. In the
system without control, periodic solutions (if any) exist only for fixed values of amplitude and phase and depend on the system
parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical
requirements. On the contrary, it is demonstrated that, if the vibration control terms are added, stable periodic solutions
with arbitrarily chosen amplitude and phase can be accomplished. Therefore, an effective vibration control is possible if
appropriate time delay and feedback gains are chosen. |
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Keywords: | Vibration control Parametric resonance Time delay |
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