TY - JOUR
T1 - Linear Time-Invariant Approximations of Nonlinear Time-Periodic Systems
AU - Saetti, Umberto
AU - Horn, Joseph F.
N1 - Funding Information:
This research was partially funded by the U.S. Government under Agreement No. W911W6-21-2-0002. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Aviation Development Directorate or the U.S. Government. The Rotorcraft Aircrew System Concepts Airborne Laboratory (RASCAL) flight data used in this research/investigation were provided to the Pennsylvania State University under the U.S. Army/Navy/NASA Vertical Lift Research Center of Excellence, Agreement No. W911W6-17-2-0003.
Publisher Copyright:
© 2023 Vertical Flight Society.
PY - 2023/1
Y1 - 2023/1
N2 - This paper discusses the development of a numerical method for the approximation of the nonlinear time-periodic rotorcraft flight dynamics with higher order linear time-invariant (LTI) models. The method relies on a per-rotor revolution perturbation scheme, which is of particular importance for the linearization of simulation models that do not allow for per-time-step perturbations, and for those output measures that necessitate the solution of partial differential equations and thus require several time steps to be computed. The paper demonstrates the application of the proposed methodology to obtain high-order LTI models capable of predicting vibrations for a generic utility helicopter. Simulations are used to validate the response of the linearized models against those from nonlinear simulations and from competing approaches in the literature. The proposed method is shown to predict accurately the nonlinear response for the case shown and for small amplitude maneuvers. Frequency-domain validation is also performed to compare the linear models derived with the proposed method with those obtained with harmonic decomposition, a competing approach based on a per-time-step perturbation scheme. Interestingly, the proposed algorithm yields nearly identical numerical results compared to harmonic decomposition, suggesting that the two methods are in fact equivalent but rely on different formulations.
AB - This paper discusses the development of a numerical method for the approximation of the nonlinear time-periodic rotorcraft flight dynamics with higher order linear time-invariant (LTI) models. The method relies on a per-rotor revolution perturbation scheme, which is of particular importance for the linearization of simulation models that do not allow for per-time-step perturbations, and for those output measures that necessitate the solution of partial differential equations and thus require several time steps to be computed. The paper demonstrates the application of the proposed methodology to obtain high-order LTI models capable of predicting vibrations for a generic utility helicopter. Simulations are used to validate the response of the linearized models against those from nonlinear simulations and from competing approaches in the literature. The proposed method is shown to predict accurately the nonlinear response for the case shown and for small amplitude maneuvers. Frequency-domain validation is also performed to compare the linear models derived with the proposed method with those obtained with harmonic decomposition, a competing approach based on a per-time-step perturbation scheme. Interestingly, the proposed algorithm yields nearly identical numerical results compared to harmonic decomposition, suggesting that the two methods are in fact equivalent but rely on different formulations.
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U2 - 10.4050/JAHS.68.012006
DO - 10.4050/JAHS.68.012006
M3 - Article
AN - SCOPUS:85158839761
SN - 0002-8711
VL - 68
JO - Journal of the American Helicopter Society
JF - Journal of the American Helicopter Society
IS - 1
M1 - 012006
ER -