ОПТИМІЗАЦІЯ ВИТРАТ ПАЛИВА В ЗАДАЧІ СТАБІЛІЗАЦІЇ КУТОВОГО ПОЛОЖЕННЯ ОСЕСИМЕТРИЧНОГО КОСМІЧНОГО АПАРАТУ

Context. The problem of maintaining the angular orientation of a spacecraft is critical, especially when subjected to impulsive external disturbances that cause sharp deviations in angular velocities. The relevance of solving this problem is determined by the limited fuel supply on board, particularly for the class of spacecraft designed to provide artificial gravity, where precise and efficient control is paramount.Objective. The main objective of this work is to minimize the consumption of energy resources (fuel) for the stabilization of the angular position of a specific class of spacecraft. This goal is achieved through the sequential execution of two interrelated tasks: 1) damping sharp deviations in the spacecraft’s angular velocities; 2) stabilizing the final angular position.Method. A two-stage approach is proposed. To solve the first task (damping), optimal control is synthesized using a combinationof Pontryagin’s maximum principle and the phase plane method. This allows for the creation of optimal switching curves that divide the phase plane into regions with corresponding optimal control values. To solve the second task (stabilization), a modal approach based on a proposed method of indeterminate coefficients is used, which ensures the specified dynamic characteristics of the transient stabilization processes.Results. Modeling of the dynamics of the spacecraft’s angular motion was carried out. The simulation results confirm the high effectiveness of using the proposed combined approach for solving the problem of stabilizing the angular position of the spacecraft after significant external disturbances.Conclusion. The joint application of Pontryagin’s maximum principle with the phase plane method for fuel-efficient damping of angular velocities, followed by the implementation of an optimal stabilization law based on the proposed method of indeterminate coefficients, represents an effective procedure for controlling the orientation and stabilization of a spacecraft with minimal fuel consumption