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## Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives

#### Uğur Özdemir [1] , Mehmet Serif Kavsaoglu [2] , Zafer Oznalbant [3] , Unver Kaynak [4]

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The longitudinal stability analysis of an aircraft is performed by the investigation of root locations of its transfer function’s denominator (the characteristic equation). However, this transfer function is obtained by linearizing aircraft dynamic model at a certain operation point (altitude and speed). However, aircraft have varying stability derivatives, therefore dynamic behavior, for different flight phases such as take-off, cruise, and landing. Thus, the stability investigation of the characteristic equation can be said to be valid only for a certain flight condition. In reality, stability derivatives have varying values depending on flight conditions. Therefore, an analysis including all possible values of stability derivatives in the flight envelope is required to guarantee stability. In this study, two most varying stability derivatives in the transfer function were taken as uncertain parameters. Gridding these two parameters to check the stability of the UAV for all possible flight conditions can be thought as a method, but it is very time-consuming, and it cannot assure the stability theoretically. A new simple approach, guaranteeing stability under the uncertainty of two stability derivatives, is developed by using the Edge and Bialas theorems. Here, the problem of the investigation of the stability under the uncertainty of two stability derivatives is reduced to the analysis of four polynomials. Thus, the stability characteristics of an airplane for a given flight envelope can be easily determined by just looking at the eigenvalues of the matrices obtained from these four polynomials.
Stability Analysis, Edge Theorem, Bialas Theorem, UAV, Flight Dynamics
• Yechout T.R., Morris S.L., Bossert D.E., and Hallgren W.F. Introduction To Aircraft Flight Mechanics: Performance, Static Stability, Dynamic Stability And Classical Feedback, AIAA, 2003.
• Blakelock J.H., Automatic Control of Aircraft and Missiles, 1st edition, John Wiley & Sons, New York, 1965.
• Roskam J., Airplane Flight Dynamics And Automatic Controls, DARcorporation, USA, 2003.
• Oznalbant Z., Kavsaoglu M. S., and Cavcar M., Design, Flight Mechanics and Flight Demonstration of a Tiltable Propeller VTOL UAV”, presented at 16th AIAA Aviation Technology, Integration and Operations Conference, AIAA Aviation Forum, 2016.
• Sadraey M. H., Design of a Nonlinear Robust Controller for a Complete Unmanned Aerial Vehicle Mission, Ph.D. Thesis, University of Kansas, 1995.
• Soylemez M. T., Pole Assignment for Uncertain Systems, Research Studies Press (RSP), Baldock, UK, 1999.
• Ackerman J., Robust Control: The Parameter Space Approach, Springer, New York, London, 2002.
• Bialas S., A Necessary And Sufficient Condition For The Stability Of Convex Combinations Of Stable Polynomials Or Matrices, Bull. Polish Academy of Sciences, vol. 33, no. 9-10, pp.473-480, 1988.
• Bialas S., and Garloof J., Convex Combination Of Stable Polynomials, J. of the Franklin Inst., vol. 319, no.3, pp. 373-377, 1985.
Primary Language en Engineering Articles Author: Uğur Özdemir Author: Mehmet Serif Kavsaoglu Author: Zafer Oznalbant Author: Unver Kaynak
 Bibtex @research article { estubtda515780, journal = {Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering}, issn = {2667-4211}, address = {Eskişehir Teknik Üniversitesi}, year = {2018}, volume = {19}, pages = {831 - 843}, doi = {10.18038/aubtda.405179}, title = {Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives}, key = {cite}, author = {Özdemir, Uğur and Kavsaoglu, Mehmet Serif and Oznalbant, Zafer and Kaynak, Unver} } APA Özdemir, U , Kavsaoglu, M , Oznalbant, Z , Kaynak, U . (2018). Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, 19 (4), 831-843. DOI: 10.18038/aubtda.405179 MLA Özdemir, U , Kavsaoglu, M , Oznalbant, Z , Kaynak, U . "Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives". Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 19 (2018): 831-843 Chicago Özdemir, U , Kavsaoglu, M , Oznalbant, Z , Kaynak, U . "Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives". Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 19 (2018): 831-843 RIS TY - JOUR T1 - Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives AU - Uğur Özdemir , Mehmet Serif Kavsaoglu , Zafer Oznalbant , Unver Kaynak Y1 - 2018 PY - 2018 N1 - doi: 10.18038/aubtda.405179 DO - 10.18038/aubtda.405179 T2 - Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering JF - Journal JO - JOR SP - 831 EP - 843 VL - 19 IS - 4 SN - 2667-4211- M3 - doi: 10.18038/aubtda.405179 UR - https://doi.org/10.18038/aubtda.405179 Y2 - 2018 ER - EndNote %0 Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives %A Uğur Özdemir , Mehmet Serif Kavsaoglu , Zafer Oznalbant , Unver Kaynak %T Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives %D 2018 %J Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering %P 2667-4211- %V 19 %N 4 %R doi: 10.18038/aubtda.405179 %U 10.18038/aubtda.405179 ISNAD Özdemir, Uğur , Kavsaoglu, Mehmet Serif , Oznalbant, Zafer , Kaynak, Unver . "Longitudinal Stability Analysis of a UAV under the Uncertainty of Two Stability Derivatives". Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 19 / 4 (December 2019): 831-843. https://doi.org/10.18038/aubtda.405179