The National Transport University Bulletin

Abstract

The paper focuses on the propulsion systems of space vehicles. The purpose of the work is to describe mathematical models and approaches to optimizing the operating parameters of space propulsion systems based on a nuclear energy source. The research method is mathematical modeling, optimal control theory, variational calculus. The article discusses approaches to mathematical modeling of promising space propulsion systems based on nuclear energy sources intended for manned interplanetary expeditions. Due to psychological problems, the influence of cosmic radiation, the effects of zero gravity, the implementation of manned expeditions imposes strict requirements, on the one hand, on the time of the maneuver, and on the other hand, on its efficiency, from the point of view of the mass of the payload. It is shown that such requirements can be satisfied by bimodal propulsion systems capable of operating in high and low thrust modes using a common nuclear energy source. High-thrust maneuvers form planet-centric arcs of the trajectory, low-thrust maneuvers are implemented on the heliocentric arc. Mathematical models of high-thrust nuclear rocket engines and low-thrust engines as control objects are considered. It is shown that high-thrust nuclear rocket engines, as control objects, belong to a separate class of engines with limited specific impulse and limited power. Control functions and restrictions imposed on them are defined for this class. The general problem of interplanetary flight optimization with a combination of high and low thrust is formulated as a problem of optimizing the distribution of the ∆v budget between the maneuvers with high and low thrust. At the same time, taking into account the finite-thrust limitation on the high thrust maneuver leads to the formulation of an optimization problem, as a problem of optimal control According to the approach [12], the general optimization problem for interplanetary transfer is formulated as an optimal-control problem for a dynamic system with a discontinuous right-hand side and phase space change. For simplification, it is possible to use the impulse approximation of high thrust active arcs. A model of an ideal engine of limited power is used to simulate low-thrust motion, the use of which allows to separate the dynamic and parametric parts of the optimization problem. It is shown that the method of the transporting trajectory can be used to obtain an analytical solution of the dynamic part of the problem. The implementation of this approach together with the application of impulse approximation of high thrust active arcs reduces the general problem of optimal control to the problem of minimizing a function of several variables. For this problem the independent variables are the components of the spacecraft's velocity vectors on the spheres of influence of the starting and destination planets.

Keywords: