SIMULATION OF OPTIMAL CONTROL OF ORBITAL VEHICLE THRUST DURING LAUNCH

Abstract

In 21st century economically feasible and less expensive ways of space exploration and industrialization become the great challenge for mankind. One of the promising approaches is development of modern SSTO (single-stage-to-orbit) and VTOL (vertical-take-off-landing) technologies, leveraging latest achievements in new materials and propulsion systems. The paper presents results of simulation of dynamic systems, moving in central gravitational field, in an environment, where atmospheric drag force has a serious impact on system’s dynamics. Model, proposed in paper, has been analyzed and build, based on Pontrjagin’s principle of optimality. Optimal regular and singular thrust control of engine is analyzed. Research has been conducted on relations between optimal control feasibility and SSTO parameters, including initial acceleration and average (along trajectory) drag coefficient. Impact of drag dependence on Mach number on accuracy of computed optimal trajectory has been considered. One approach to solve the problem has been developed, where impact of proposed optimal control implementation on problem’s optimality criteria is evaluated. The derived formula for calculating optimal control is invariant to conditions on right end of ascent trajectory.