Application of chaos methods to helicopter vibration reduction using Higher Harmonic Control
Sarigul-Klijn, Martinus M.
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Chaos is a discipline used in understanding complex nonlinear dynamics. The geometric and topological methods of Chaos theory are applied, for the first time, to the study of flight test data. Data analyzed is from the McDonnell Douglas OH-6A Higher Harmonic Control (HHC) test aircraft. HHC is an active control system used to suppress helicopter vibrations. Some of the first practical applications of Chaos methods are demonstrated with the HHC data. Although helicopter vibrations are mostly periodic, evidence of chaos was found. The presenc3e of a strange attractor was shown by computing a positive Lyapunov exponent and computing a non-integer fractal correlation dimension. Also, a broad band Fourier spectrum and a well defined attractor in pseudo phase space are observed. A limit exists to HHC vibration reduction due to the presence of chaos. A new technique based on a relationship between the Chaos methods (the Poincare section and Van der Pol plane) and the vibration amplitude and phase was discovered. This newly introduced technique results in the following: 1) it gives the limits of HHC vibration reduction, 2) it allows rapid determination of best phase for a HHC controller, 3) it determines the minimum HHC controller requirement for any helicopter from a few minutes duration of flight test data (for the OH-6A, a scheduled gain controller for HHC appears to be adequate for steady level flight), 4) it shows that the HHC controller transfer matrix is linear and repeatable when the vibrations are defined in the "Rotor Time Domain" and that the matrix is nonlinear and nonrepeatable when the vibrations are defined in the "Clock Time Domain." This technique will reduce future HHC flight test requirements. Further, the technique does not require the helicopter to be equipped with HHC. These methods may be applicable to other vibration control and flight testing problems.
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