MARGIN OF STABILITY OF THE TIME-VARYING CONTROL SYSTEM FOR ROTATIONAL MOTION OF THE ROCKET
DOI:
https://doi.org/10.15588/1607-3274-2024-3-16Keywords:
rocket motion control, time-varying system, Laplace transformAbstract
Context. The rocket motion control system is time-varying, since its parameters during flight depend on the point of the trajectory and fuel consumption. Stability margin indicators are determined in a limited area of individual points of the trajectory using algorithms that are developed only for linear stationary systems, which leads to the need to enter stock factor in hardware. In the available sources, due attention is not paid to the development of methods for determining the quantitative assessment of the stability margin of the time-varying control system.
Objective is to develop a methodological support for the construction of an algorithm for calculating the stability margin indicators of the time-varying system for controlling the rocket rotational motion in the plane of yawing using the equivalent stationary approximation at a selected trajectory section.
Method. The mathematical model of the control system for the rocket rotational movement in one plane is adopted in the form of a linear differential equation without considering the inertia of the executive device and other disturbing factors. The effect of deviation of parameters from their average values for a certain trajectory section is considered as a disturbance, which makes it possible to transition from a non-stationary model to an equivalent approximate stationary one. The Nyquist criterion is used to estimate the stability margin indicators, which is based on the analysis of the frequency characteristic of an open system, for the determination of which the Laplace transform mathematical apparatus is used. To simplify the transition from functions of time in the differential equation of perturbed motion to functions of a complex variable in the Laplace transform, time-varying model parameters are presented in the form of a sum of exponential functions.
Result. Methodological support was developed for building an algorithm for determining the stability margin of the rocket’s rotary motion control system at a given trajectory section with time-inconstant parameters.
Conclusions. Using the example of the time-varying system for controlling the rocket rotational movement, the possibility of using the Laplace transformation to determine the stability margin indicators is shown.
The obtained results can be used at the initial stage of project work.
The next stage of the research is an assessment of the level of algorithm complexity, considering the inertia of the executive device and the disturbed movement of the mass center.
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