Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • NSF Public Access
  • Search Results
  • Aerodynamic-Dynamic Interactions and Multi-Body Formulation of Flapping Wing Dynamics: Part II - Trim and Stability Analysis
Title: Aerodynamic-Dynamic Interactions and Multi-Body Formulation of Flapping Wing Dynamics: Part II - Trim and Stability Analysis
Flapping ight dynamics constitutes a multi-body, nonlinear, time-varying system. The two major simplifying assumptions in the analysis of apping ight stability are neglecting the wing inertial e ects and averaging the dynamics over the apping cycle. The challenges resulting from relaxing these assumptions naturally invoke the geometric control theory as an appropriate analysis tool. In this work, a reduced-order model (extracted from the full model derived in the rst part of this work) for the longitudinal apping ight dynamics near hover is considered and represented in a geometric control framework. Then, combining tools from geometric control theory and averaging, the full dynamic stability as well as balance analyses of hovering insects are performed.  more » « less
Award ID(s):
1709746
PAR ID:
10049021
Author(s) / Creator(s):
;
Date Published:
Journal Name:
AIAA Guidance, Navigation, and Control Conference
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, AIAA Guidance, Navigation, and Control Conference)
    Flapping ight dynamics constitutes a multi-body, nonlinear, time-varying system. The two major simplifying assumptions in the analysis of apping ight stability are neglecting the wing inertial e ects and averaging the dynamics over the apping cycle. Relaxing the rst assumption invokes a multi-body formulation of the equations of motion. In this work, the full, multi-body, equations of motion governing the longitudinal apping ight dynamics near hover are considered. The aerodynamic loads are represented through a relatively simple analytical model that accounts for the dominant contributions; e.g., leading edge vortex and rotational e ects. The dynamic and aerodynamic models are coupled together to account for mutual interactions. 
    more » « less
  2. ; (, AIAA Guidance, Navigation, and Control Conference)
    Because of the wing oscillatory motion with respect to the body, the ight dynam- ics of biological yers as well as their man-made mimetic vehicles, apping-wing micro- air-vehicles (FWMAVs), are typically represented by multi-body, nonlinear time-periodic (NLTP) system models whose balance and stability analyses are quite challenging. In this work, we consider a NLTP system model for a two-degree-of-freedom FWMAV that is con ned to move along vertical rails. We combine tools from chronological calculus, geo- metric control, and averaging to provide a mathematically rigorous analysis for the balance of FWMAVs at hover; that is, relaxing the single-body and direct averaging assumptions that are commonly adopted in analyzing balance and stability of FWMAVs and insects. We also use optimized shooting to numerically capture the resulting periodic orbit and verify the obtained results. Finally, we provide a combined averaging-shooting approach for the balance and stability analysis of NLTP systems that (i) unlike typical shooting methods, does not require an initial guess; (ii) provides more accurate results than the analytical av- eraging approaches, hence relaxing the need for intractable high-order averaged dynamics; and (iii) allows a deeper scrutiny of the system dynamics, in contrast to numerical shooting methods. 
    more » « less
  3. ; (, Journal of Nonlinear Science)
    Flapping flight dynamics is quite an intricate problem that is typically represented by a multi-body, multi-scale, nonlinear, time-varying dynamical system. The unduly simple modeling and analysis of such dynamics in the literature has long obstructed the discovery of some of the fascinating mechanisms that these flapping-wing creatures possess. Neglecting the wing inertial effects and directly averaging the dynamics over the flapping cycle are two major simplifying assumptions that have been extensively used in the literature of flapping flight balance and stability analysis. By relaxing these assumptions and formulating the multi-body dynamics of flapping-wing microair- vehicles in a differential-geometric-control framework, we reveal a vibrational stabilization mechanism that greatly contributes to the body pitch stabilization. The discovered vibrational stabilization mechanism is induced by the interaction between the fast oscillatory aerodynamic loads on the wings and the relatively slow body motion. This stabilizationmechanism provides an artificial stiffness (i.e., spring action) to the body rotation around its pitch axis. Such a spring action is similar to that of Kapitsa pendulum where the unstable inverted pendulum is stabilized through applying fast-enough periodic forcing. Such a phenomenon cannot be captured using the overly simplified modeling and analysis of flapping flight dynamics. 
    more » « less
  4. ; (, Physics of Fluids)
    Geometric control theory is the application of differential geometry to the study of nonlinear dynamical systems. This control theory permits an analytical study of nonlinear interactions between control inputs, such as symmetry breaking or force and motion generation in unactuated directions. This paper studies the unsteady aerodynamics of a harmonically pitching–plunging airfoil in a geometric control framework. The problem is formulated using the Beddoes–Leishman model, a semi-empirical state space model that characterizes the unsteady lift and drag forces of a two-dimensional airfoil. In combination with the averaging theorem, the application of a geometric control formulation to the problem enables an analytical study of the nonlinear dynamics behind the unsteady aerodynamic forces. The results show lift enhancement when oscillating near stall and thrust generation in the post-stall flight regime, with the magnitude of these force generation mechanisms depending on the parameters of motion. These findings demonstrate the potential of geometric control theory as a heuristic tool for the identification and discovery of unconventional phenomena in unsteady flows. 
    more » « less
  5. ; (, Automatica)
    This paper provides a rigorous derivation for what is known in the literature as the Lie bracket approximation of control-affine systems in a more general and sequential framework for higher-orders. In fact, by using chronological calculus, we show that said Lie bracket approximations can be derived, and considered, as higher-order averaging terms. Hence, the theory provided in this paper unifies both averaging and approximation theories of control-affine systems. In particular, the Lie bracket approximation of order (n) turns out to be a higher-order averaging of order (n + 1). The derivation and formulation provided in this paper can be directly reduced to the first and second order. Lie bracket approximations available in the literature. However, we do not need to make many of the assumptions that were needed/provided in the literature and show that they are in fact natural corollaries from our work. Moreover, we use our results to show that important and useful information about control-affine extremum seeking systems can be obtained and used for significant performance improvement, including a faster convergence rate influenced by higher-order derivatives. We provide multiple numerical simulations to demonstrate both the conceptual elements of this work as well as the significance of our results on extremum seeking with comparison against the literature. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Text Encoded Conversion
  • XML
  • Save / Share this Record
  • Send to Email