Stability of a two-dimensional airfoil with time-delayed feedback control |
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| Authors: | YH Zhao |
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| Institution: | 1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China;2. Shannxi Key Laboratory for Environment and Control of Flight Vehicle, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China;3. Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK;1. School of aeronautics, Northwestern Polytechnical University, 127 Youyixi Road, Xi?an, Shaanxi 710072, PR China;2. University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, ON, Canada M3H 5T6;3. Mitsubishi Electric Research Laboratories (MERL), Cambridge, MA 201 Broadway, Cambridge, MA, 02139, USA;1. Department of Electrical Engineering, University of California, Los Angeles, CA, United States;2. Department of Mathematics, The Petroleum Institute, Abu Dhabi, United Arab Emirates;3. Department of Statistics, Rice University, 2125 Duncan Hall, 6100 Main, Houston, TX 77005, United States;4. The Boeing Company, Huntsville, AL, United States |
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| Abstract: | This paper presents a systematic study on aeroelastic stability of a two-dimensional airfoil with a single or multiple time delays in the feedback control loops. Firstly, the delay-independent stability region of the aeroelastic system with a single time delay is determined on the basis of the generalized Sturm criterion for polynomials. Then, the stability switches with variations in time delay are analyzed when the system parameters fall out of the delay-independent stability region. Flutter boundaries of the controlled aeroelastic system as time delay varies are predicted in a continuous way by the predictor-corrector technique. Finally, two methods, the polynomial eigenvalue method and the infinitesimal generator method, are introduced to investigate the stability of the controlled aeroelastic system with multiple time delays. Numerical simulations are made to demonstrate the effectiveness of all the above approaches. |
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