Contributions to the dynamics of helicopters with active rotor controls
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This dissertation presents an aeromechanical closed loop stability and response analysis of a hingeless rotor helicopter with a Higher Harmonic Control (HHC) system for vibration reduction. The analysis includes the rigid body dynamics of the helicopter and blade flexibility. The gain matrix is assumed to be fixed and computed off-line. The discrete elements of the HHC control loop are rigorously modeled, including the presence of two different time scales in the loop. By also formulating the coupled rotor-fuselage dynamics in discrete form, the entire coupled helicopter-HHC system could be rigorously modeled as a discrete system. The effect of the periodicity of the equations of motion is rigorously taken into account by converting the system into an equivalent system with constant coefficients and identical stability properties using a time lifting technique. The most important conclusion of the present study is that the discrete elements in the HHC loop must be modeled in any HHC analysis. Not doing so is unconservative. For the helicopter configuration and HHC structure used in this study, an approximate continuous modeling of the HHC system indicates that the closed loop, coupled helicopter-HHC system remains stable for optimal feedback control configurations which the more rigorous discrete analysis shows can result in closed loop instabilities. The HHC gains must be reduced to account for the loss of gain margin brought about by the discrete elements. Other conclusions of the study are: (i) the HHC is effective in quickly reducing vibrations, at least at its design condition, although the time constants associated with the closed loop transient response indicate closed loop bandwidth to be 1~rad/sec on average, thus overlapping with FCS or pilot bandwidths, and raising the issue of potential interactions; (ii) a linearized model of helicopter dynamics is adequate for HHC design, as long as the periodicity of the system is correctly taken into account, i.e., periodicity is more important than nonlinearity, at least for the mathematical model used in this study; and (iii) when discrete and continuous systems are both stable, and quasisteady conditions can be guaranteed, the predicted HHC control harmonics are in good agreement.