Optimization of Soyuz 2-1V launch-vehicle engine thrust control based on the principle of minimum control

The author developed a principle of minimum control, which is aimed to minimize energy consumption necessary for control, and applied it for synthesis of a discrete optimal closed-loop system controlling engine thrust vector magnitude of a Soyuz 2-1v launch-vehicle as a particle. The problem is solved with the following simplifications: assumption of the Earth’s figure sphericity, use of analytic dependences of atmospheric density and sound velocity variation with altitude, and drag coefficient variation with trajectory. To model centre-of-mass motion, the author used finite-difference equations. It is assumed that it is possible to force and throttle the engine thrust of both stages given conservation of their specific thrust. A launch from the Plesetsk cosmodrome is simulated. The motion is considered to be two-dimensional in polar coordinate system. The article includes the results of the launch-vehicle motion simulation. It also shows that application of this principle of minimum control results in increase in injection orbit altitude for the same payload.