Algorithm for solving optimal open-loop terminal control problem for spacecraft rendezvous with account of constraints on the state

The paper proposes an algorithm for solving the optimal open-loop terminal control problem of two spacecraft rendezvous with constraints on their states. A system of nonlinear differential equations that describes the dynamics of the active (maneuvering) spacecraft relative to the passive spacecraft (station) in the central gravitational field of the Earth in the orbital coordinate system of coordinates related to the passive spacecraft center-of-mass is considered as an initial model. The obtained nonlinear model of the active spacecraft dynamics is linearized relative to the specified reference state trajectory of the passive spacecraft, and then it is discretized and reduced to linear recurrence relations. Mathematical formalization of the spacecraft rendezvous problem under consideration is carried out at a specified final moment of time for the obtained discrete-time controlled dynamical system. The quality of solving the problem is estimated by a convex functional taking into account the geometric constraints on the active spacecraft states and the associated control actions in the form of convex polyhedral-compacts in the appropriate finite dimensional vector space. We propose a solution of the problem of optimal terminal control over the approach of the active spacecraft relative to the passive spacecraft in the form of a constructive algorithm on the basis of the general recursive algebraic method for constructing the availability domains of linear discrete controlled dynamic systems, taking into account specified conditions and constraints, as well as using the methods of direct and inverse constructions. In the final part of the paper, the computer modeling results are presented and conclusions about the effectiveness of the proposed algorithm are made.

MOMENTAL METHOD FOR CALCULATING FORCES IN CYLINDRICAL SHELLS OF ORBITAL FACILITIES

The article is devoted to the torque method, according to the principles of which it is possible to determine the loads arising in the thin-walled shell of the hulls of orbital vehicles from the action of the internal pressure uniformly distributed over the area, normally oriented to the middle surface of the shell. In this case, the load on the shell consists of normal forces (longitudinal and circumferential), a transverse force that causes radial displacements in the shell, and a bending moment in the longitudinal plane of the object. The specified bending moment can occur during the manifestation of inertial forces (for example, the Coriolis force) during the transition of the orbital vehicle in height from one orbit to another in vertical directions normal to the orbit (rotational movements); the same rotary movements can cause inertial forces to appear when maneuvering spacecraft and rocket units at the same height (in conventionally horizontal directions). To determine the above loads and radial displacements of the shell, a mathematical algorithm is proposed based on the principles of the moment calculation method according to the scheme of an infinitely long shell, which is typical for orbital vehicle housings.

Steering law design for a magnetically suspended control and sensitive gyro cluster considering rotor tilt saturation

To effectively reject the influence of rotor tilt saturation in a magnetically suspended control and sensitive gyro cluster, an adaptive nonlinear pseudo-inverse steering law is developed in this study. Based on the working principle of a Lorentz force magnetic bearing–rotor system in a single magnetically suspended control and sensitive gyro, the dynamical model of a rigid spacecraft equipped with a magnetically suspended control and sensitive gyro cluster is established. Because of the monotonicity and symmetric properties of the chosen nonlinear function, an adaptive nonlinear weighting matrix is incorporated with the pseudo-inverse steering law for the magnetically suspended control and sensitive gyro cluster. The steering law adjusts the weighting matrix elements according to saturation penalty functions so that the rotors generate control torques consistent with the limited rotor tilting domain. The effectiveness and superiority of this steering law are verified by numerical simulations. The simulation results demonstrate that the proposed steering law not only imposes control torques on the carrier spacecraft with three degrees of freedom but also avoids rotor tilt saturation, ensuring rapid attitude control of agile maneuvering spacecraft.