On Chaos Methods Applied to Higher Harmonic Control

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. For a given helicopter, 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 is presented. This technique results in the following: 1) it gives the limits of HHC vibration reduction, 2) it allows rapid determination of optimum 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 non-repeatable when the vibrations are defined in the “Clock Time Domain.” The method will reduce future HHC flight test requirements. Determination of the limit of HHC performance and the minimum HHC controller requirement does not require an HHC equipped helicopter, although an instrumentation system is required. These methods may be applicable to other vibration control and flight testing problems