PREDICTABLE CONTROL OF DISTURBED ROCKET MOTION IN ONE PLANE
Рубрика:
| AVDIEIEV, VV |
| Space Sci. & Technol. 2026, 32 ;(4):03-11 |
| https://doi.org/10.15407/knit2026.04.003 |
| Мова публікації: English |
Анотація: During the fl ight, the parameters of the rocket as a control object change, since they depend on the trajectory point and fuel
consumption. Th e indicators of the system for stabilizing its disturbed motion, in particular the stability margin and the requirements for the power of the executive device, are determined in a limited vicinity of individual trajectory points using algorithms developed for linear, stationary systems, which necessitates the introduction of safety factors in the hardware. In available sources, the development of methods for obtaining the above indicators that would not depend on the trajectory point is not given due attention. Th e work aims to develop methodological support for constructing an algorithm for controlling the disturbed motion of a rocket, when used in a certain trajectory section, the time-varying stabilization system becomes stationary, as a result of which the stability margin on the roots plane of the characteristic polynomial (ChP) and the requirements for the power of the actuator do not depend on the trajectory point. Th e mathematical model for controlling the rocket’s disturbed motion in one plane is formulated as a set of linear diff erential equations with variable parameters. In the vicinity of a certain trajectory point, these parameters are treated as constants, allowing the equation to be transformed according to Laplace, yielding transfer functions and analytical expressions for the ChP coeffi cients, which include the values of the model parameters of the control object predicted along the selected trajectory interval and the coeffi cients of the control law. Th is yields a system of algebraic equations, from which the dependence of the control law’s coeffi cients on the trajectory point is determined. Using the example of a time-varying rocket motion stabilization system, the possibility of obtaining those dynamic characteristics independent of the trajectory point, which are determined by the given location of the ChP roots on the complex plane, is shown. |
| Ключові слова: control law, rocket motion control, time-varying system |
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Avdieiev V. (2020). Determination of model parameters of rocket stabilization system in fl ight. Int. Sci. Tech. J. Probl. Control
and Inform., 66(6), 78—92. doi: 10.34229/1028-0979-2021-6-8
Deng L., Shu Z., Chen T. (2025). Robust PMC with event-triggered learning for unknown linear time-varying systems.
Automatica, 179, 112434. https://doi.org/10.1016/j.automatica.2025.112434
Dong J., Zhou B. (2025). Stability and stabilization of discrete-time linear time-varying systems via Lyapunov diff erence
equations and inequalities. Systems and Control Lett., 204, 106203. https://doi.org/10.1016/j.sysconle.2025.106203
Kawano Yu. (2020). Converse stability theorems for positive linear time-varying systems. Automatica, No. 122, 109193. https://
doi.org/10.1016/ j.automatica.2020.109193
Kessler N., Fagiano L. (2026). On the design of linear time varying model predictive control for trajectory stabilization.
Automatica, 183, 112577. https://doi.org/10.1016/j.automatica.2025.112577
Mate S., Jaju P., Bhartiya S., Nataraj P. S. V. (2023). Semi-Explicit Model Predictive Control of Quasi Linear Parameter Varying
Systems. Eur. J. Control, 69, 100750. https://doi.org/10.1016/j.ejcon.2022.100750
Mullhaupt Ph., Buccieri D., Bonvin D. (2007). A numerical suffi ciency test for the asymptotic stability of linear time-varying
systems. Automatica, 43, Issue 4, 631—638. https://doi.org/10.1016/j.automatica.2006.10.014
Seiler P., Moore R. M., Meissen Ch., Arcak M., Packard A. (2019). Finite horizon robustness analysis of LTV systems using
integral quadratic constraints. Automatica, No. 100, 135—143. https://doi.org/10.1016/j.automatica.2018.11.009
Shao X., Wang H., Zhang H. P. (2015). Enhanced trajectory linearization control based advanced guidance and control for
hypersonic reentry vehicle with multiple disturbances. Aerospace Science and Technology, No. 46, 523—536. https://doi.
org/10.1016/j.ast.2015.09.003
Snyder S., Zhao P., Hovakimyan N. (2021). Adaptive control for linear parameter-varying systems with application to a VTOL
aircraft . Aerospace Sci. and Technol., No. 112, 106621. https://doi.org/10.1016/j.ast.2021.106621
Stenin A., Timoshin Yu., Drozdovych I. (2019). Walsh Functions in Linear-Quadratic Optimization Problems of Linear Nonstationary
Systems. Probl. Control and Inform., 51(4), 43—57. https://doi:10.1615/JAutomatInfScien.v51.i8.40
Tian B., Zong Q., Wang J., et al. (2013). Quasi-continuous high-order sliding mode controller design for reusable launch
vehicles in reentry phase. Systems and Control Lett., No. 28.1, 198—207. https://doi.org/10.1016/j.ast.2012.10.015
Timchenko V. (2023). Optimization of programmed trajectories of moving object’s stabilization based on control systems of
variable structure. Int. Sci. Tech. J. Probl. Control and Inform., 67(3), 61—76. https://doi:10.34229/2786-6505-2022-3-5
Xie X., Lam J., Fan C., et al. (2022). A polynomial blossoming approach to stabilization of periodic time-varying systems.
Automatica, No. 141, 110305. https://doi.org/10. 1016/j.automatica.2022.110305
Zakwan M., Ahmed S. (2020). Dwell-time based stability analysis and control of LPV systems with piecewise constant
parameters and delay. Systems and Control Lett., 145, 104805. https://doi.org/10.1016/j.sysconle.2020.104805
Zhao T., Zhou B., Michiels W. (2018). Stability analysis of linear time-varying time-delay systems by non-quadratic Lyapunov
functions with indefi nite derivatives. Systems and Control Lett., No. 122, 77—85. https://doi.org/10.1016/j.sysconle.
2018.09.012
Zhou B. (2016). On asymptotic stability of linear time-varying systems. Automatica, No. 68, 266—276. https://doi.org/10.1016/j.
automatica. 2015.12.030
Zhou B. (2021). Lyapunov diff erential equations and inequalities for stability and stabilization of linear time-varying systems.
Automatica, No. 131, 109785. https://doi.org/10.1016/j.automatica.2021.109785
Zhou B., Tian Y., Lam J. (2020). On construction of Lyapunov functions for scalar linear time-varying systems. Systems and
Control Lett., No. 135, P. 104591. https://doi.org/10.1016/j.sysconle. 2019.104591