Development of a methodology to model the dynamic properties of UAVS and high-order control systems

• G. S. Vasilyev Universidad del Zulia http://orcid.org/0000-0003-1681-5223
• O. R. Kuzichkin Belgorod State University, Belgorod, 308015, Russia http://orcid.org/0000-0003-0817-223X
• I. A. Kurilov Vladimir State University, Vladimir, 600000, Russia http://orcid.org/0000-0003-1901-7411
• D. I. Surzhik Vladimir State University, Vladimir, 600000, Russia http://orcid.org/0000-0002-0101-3503

Resumen

When modeling the dynamic properties of an unmanned aerial vehicle (UAV) and an automatic control system (ACS), it is often necessary to take into account factors such as the lack of rigidity of the aircraft structure, the influence of control and destabilizing factors, which leads to an increase in the order of the model under study. The known numerical and analytical methods do not allow us to obtain general solutions for the variable parameters of the high-order system under study, and at the same time provide the required amount of error and computational costs. A method is developed to model the dynamic properties of UAVs and high-order control systems based on the spectral method, the linear approximation by parts of the input control actions and the spectrum of the system's output signal. An example of using the technique to model the dynamic properties of different orders ACS UAVs (from 1 to 10) with different types of inertia is considered. Based on the analysis of errors in the calculation of the transition process, the effectiveness of the method for analyzing high-order systems is shown based on the required computational costs.

Citas

Byard, R. W., & McLain, T. W. (2015). Small unmanned aerial vehicles: theory and practice. Moscow: TECHNOSPHERA.

Chen, C. T. (1998). Linear system theory and design. Oxford University Press, Inc.

Chrysos, M. (1995). An extension of the Filon method for the accurate numerical integration of rapidly varying functions. Journal of Physics B: Atomic, Molecular and Optical Physics, 28(11), L373.

Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proc. Camb. Phil. Soc, 43(1), 50–67.

doi:10.1017/S0305004100023197..

Dech, G. (1971). Guide to the Practical Application of the Laplace Transform. Moscow: Nauka, 1971. – 288 p.

Ditkin, V. A., & Prudnikov, A. P. (1961). Integral transformations and operational calculus. - Moscow: Fizmatgiz,. – 524 p.

Dwight, G. B. (1977). Tables of integrals and other mathematical formulas. - Moscow: Nauka. 244 p.

Godunov, S. K., Ryaben'kii, V. S. (1962). Introduction to the theory of difference schemes. - Moscow: Fizmatgiz.

Hairer, E., & Wanner, G. (1996). Solving ordinary differential equations II: Stiff and different-algebraic problems, second edition, Springer Verlag, Berlin, ISBN 3-540-60452-9.

Hazewinkel, M., ed. (2001) [1994], "Residue of an analytic function", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4.

Krylov, V. I. (1968). Reference book on the numerical reversal of the Laplace transform. - Minsk,. – 296 p.

Kuriki, Y., & Namerikawa, T. (2013). Formation control of UAVs with a fourth-order flight dynamics. 52nd IEEE Conference on Decision and Control, Firenze, 6706-6711

Kurilov, I. A., Romashov, V. V., Zhiganova, E. A., Romanov, D. N., Vasilyev, G. S., Kharchuk, S. M., & Surzhik, D. I. (2014). Methods of analysis of radio devices based on the functional approximation. Electronic and telecommunications systems, (1), 13.

Lambert, J. D. (1991). Numerical methods for ordinary differential systems: the initial value problem. John Wiley & Sons, Inc.

Lebedev A. A., & Chernobrovkin L. S. (1973). Flight dynamics of unmanned aerial vehicles. – Study book for universities. - Moscow: Mashinostroenie, – 616 p.

Makarov, I.M., & Mensky, B.M. (1978). Tables of inverse Laplace transformations and inverse z-transformations. Fractional-rational images. Moscow: Higher school, – 247 p.

Moiseev, V. S. (2013). Applied theory of control of unmanned aerial vehicles: monograph. Kazan: GBU «Republican Center for Monitoring the Quality of Education»(Series «Modern Applied Mathematics and Informatics»).–768 p.

Polivanov, K. M. (1972). Theoretical foundations of electrical engineering, 1. - Moscow: Energia,. - 240 p.

Shostak R. Ya. (1972). Operational calculus. Training manual for higher education institutions. Ed. 2nd. - M.: Higher school, – 280 p.

Vasilyev, G. S., Kurilov, I. A., Kharchuk, S. M., & Surzhik, D. I. (2013, September). Analysis of dynamic characteristics of the nonlinear amplitude-phase converter at complex input influence. In 2013 International Siberian Conference on Control and Communications (SIBCON) (pp. 1-4). IEEE.

Vasilyev, G., Kurilov, I., & Kharhuk, S. (2011, September). Research of static characteristics of converters of signals with a nonlinear control device. In 2011 International Siberian Conference on Control and Communications (SIBCON) (pp. 93-96). IEEE.