Abstract
Rotorcraft stability is an inherently multidisciplinary area, including aerodynamics of rotor and fuselage, structural dynamics of flexible structures, actuator dynamics, control, and stability augmentation systems. The related engineering models can be formulated with increasing complexity due to the asymmetric nature of rotorcraft and the airflow on the rotors in forward flight conditions. As a result, linear time-invariant (LTI) models are drastic simplifications of the real problem, which can significantly affect the evaluation of the stability. This usually reveals itself in form of periodic governing equations and is solved using Floquet’s method. However, in more general cases, the resulting models could be non-periodic, as well, which requires a more versatile approach. Lyapunov Characteristic Exponents (LCEs), as a quantitative method, can represent a solution to this problem. LCEs generalize the stability solutions of the linear models, i.e., eigenvalues of LTI systems and Floquet multipliers of linear time-periodic (LTP) systems, to the case of non-linear, time-dependent systems. Motivated by the need for a generic tool for rotorcraft stability analysis, this work investigates the use of LCEs and their sensitivity in the stability analysis of time-dependent, comprehensive rotorcraft models. The stability of a rotorcraft modeled using mid-fidelity tools is considered to illustrate the equivalence of LCEs and Floquet’s characteristic coefficients for linear time-periodic problems.
Highlights
Before providing the detailed rotorcraft model and its stability analysis using Lyapunov Characteristic Exponents (LCEs), the proposed procedure was verified against analytical solution
This work presented the use of Lyapunov Characteristic Exponents (LCEs) for the estimation of the stability properties of time-dependent rotorcraft models
Time-variance was introduced by changing the properties of one of the lead-lag dampers, resulting in a time-periodic system
Summary
Rotorcraft use rotating blades to generate the loads required for flight, i.e., lift, propulsion, and control, as needed to take-off and land vertically, as well as hover [1]. They can fulfill many roles that fixed-wing aircraft cannot perform as effectively, such as search and rescue, if they can at all. Rotors should have a long enough span to enable the efficient lifting, propulsion, and control of the vehicle [2] These three fundamental functions significantly affect each other, and lead to cross-couplings, which result in more complex flight physics compared to fixed-wing aircraft [3]
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