A new closed form solution for dynamic stability analysis of rolling airframes having one pair ON-OFF actuator
Abstract
In this paper, the dynamic stability analysis of a rolling airframe actuated by one pair ON-OFF actuator using linear theory is presented via developing a new closed form solution. The effect of discontinuous forcing term on rolling airframe stability is studied. In contrast to tricyclic motion with constant forcing term (constant non-homogeneous term) in which only the amplitude of nutation and precession is affected, it is found that ON-OFF control affects both amplitude and phase of nutation and precession motions. In the case of discontinuous control surface, there are two sources for resonance instability. Finally, through simulation results of closed form solutions, a comparison between airframe’ response to ideal and real ON-OFF command is achieved. The effect of ON-OFF control on angular motion is also evaluated.
Keyword : rolling airframe, one pair ON-OFF actuator, dynamic stability, resonance instability, linear analysis, closed form solution
How to Cite
Karimi, J. (2021). A new closed form solution for dynamic stability analysis of rolling airframes having one pair ON-OFF actuator. Aviation, 25(2), 92-103. https://doi.org/10.3846/aviation.2021.13832
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Dawkins, P. (2011). Differential, equations. Lamar University.
Dormand, J. R., & Prince, P. J. (1980). A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, 6(1), 19–26. https://doi.org/10.1016/0771-050X(80)90013-3
Eikensberry, R. S. (1970, February). Analysis of the angular motion of missile. In Sandia Laboratory, Technical Report SC-CR-70-6051. Sandia National Laboratories.
Koohmaskan, K., Arvan, M. R., Vali, A. R., & Farid, B. (2015). Dynamic stability conditions for a rolling flight vehicle applying continuous actuator. Aerospace Science and Technology, 42, 451–458. https://doi.org/10.1016/j.ast.2015.02.007
Koohmaskan, K., Vali, A. R., Arvan, M. R., & Farid, B. (2016, March). Analysis of two-position and continuous actuators in rolling airframe control. In 13th Conference of Iranian aerospace society (pp. 4–6). Tehran University, Iran (in Persian).
Lestage, A. (2000). Analysis of control and guidance of rolling missiles with a single plane of control fins. In Proceedings of the AIAA Conference on Guidance, Navigation, and Control (pp. 1–11). Denver, CO. AIAA Inc. https://doi.org/10.2514/6.2000-3971
Li, K., Yang, S., & Zhao, L. (2012). Stability of spinning missiles with an acceleration autopilot. Journal of Guidance, Control and Dynamics, 35(3), 774–786. https://doi.org/10.2514/1.56122
Malmgren, A. (1999). Modeling and analysis of rolling missiles with a single control surface plane. In Proceedings of the AIAA Conference on Guidance, Navigation, and Control (pp. 197–204). Portland, Oregon. AIAA Inc. https://doi.org/10.2514/6.1999-3977
Mirzaei, M., & Alishahi, M. M. (2014). Performance investigation of control and guidance system for a spinning flight vehicle with dithering canard. Journal of Modares Mechanical Engineering, 14(7), 169–175 (in Persian).
Mohammadi, B., Arvan, M. R., & Koohmaskan, Y. (2016, February). Dither in a rolling airframe flight vehicle with a twoposition actuator: An amplitude distribution approach. Transactions of the Institute of Measurement and Control, 39(8), 1205–1215. https://doi.org/10.1177/0142331216631190
Murphy, C. H. (1963, July). Free flight motion of symmetric missiles. Ballistic research laboratories, Report No. 1216. Ballistic Research Laboratory. https://doi.org/10.21236/AD0442757
Murphy, C. H. (1981). Symmetric missile dynamic instabilities. Journal of Guidance, Control and Dynamics, 4(5), 464–471. https://doi.org/10.2514/3.56099
Murphy, C. H. (1971). Response of an asymmetric missile to spin varying through resonance. AIAA Journal, 9(11), 2197–2201. https://doi.org/10.2514/3.50025
Nicolaides, J. D. (1953, June). On the free flight motion of missiles having slight configurational asymmetries. Ballistic research laboratories, Report No. 858, AD 26405. Ballistic Research Laboratory. https://doi.org/10.21236/AD0026405
Nobahari, H., & Mohammadkarimi, H. (2012). Multiple-input describing function technique applied to design a single channel ON–OFF controller for a spinning flight vehicle. Journal of Aerospace Engineering, 226(6), 631–645. https://doi.org/10.1177/0954410011414521
Shampine, L. F., & Reichelt, M. W. (1997). The MATLAB ODE Suite. SIAM Journal on Scientific Computing, 18(1), 1–22. https://doi.org/10.1137/S1064827594276424
Vaughn, H. R. (1968, February). A detailed development of the tricyclic theory. In Sandia laboratory, Technical Report SC-M-67-2933. Sandia National Laboratories.
Yan, X., Yang, S., & Zhang, C. (2010). Coning motion of spinning missiles induced by the rate loop. Journal of Guidance, Control and Dynamics, 33(5), 1490–1499. https://doi.org/10.2514/1.48041
Yan, X., Yang, S., & Xiong, F. (2011). Stability limits of spinning missiles with attitude autopilot. Journal of Guidance, Control and Dynamics, 34(1), 278–283. https://doi.org/10.2514/1.51627
Zipfel, P. H. (2007). AIAA Education Series (2nd ed.). Modeling and simulation of aerospace vehicles dynamics. AIAA. https://doi.org/10.2514/4.862182
Zhou, W., Yang, S., & Dong, J. (2013). Coning motion instability of spinning missiles induced by hinge moment. Aerospace Science and Technology, 30(1), 239–245. https://doi.org/10.1016/j.ast.2013.08.008
Zhou, W., Yang, S., & Zhao, L. (2014, January). Limit circular motion of spinning projectiles induced by backlash of actuators. In AIAA Atmospheric Flight Mechanics Conference (pp. 494–505). National Harbor, Maryland, American Institute of Aeronautics and Astronautics Inc. https://doi.org/10.2514/6.2014-0886