On Control Moments Construction for Uniaxial Reorientation Problem of Rigid Body under Disturbances

Abstract

The problem of uniaxial reorientation of an asymmetric rigid body is solved by means of external control moments. The given geometric restrictions are imposed on the control moments. External uncontrolled interference is taken into account, the statictical descriptions of which is not available. It is assumed that the control moments of external forces are "applied" to the main central axes of inertia connected with the body. The control process is modeled be a nonlinear conflict-controlled system of ordinary differential equations, including dynamic Euler equations and kinematic equations in Poisson variables. The control moments are formed according to the feedback principle as nonlinear functions (discontinuous) of the phase variables of the considered conflict-controlled system. The choise of such functions is determined by the following circumstances: 1) the solution of the original nonlinear reorientation problem can be reduced to the solution of linear antagonistic game problems (with an unfixed end time); 2) in the absence of interference, the control momets are time-suboptimal; 3) reorientation is achieved by one spatial turn without additional restrictions on the nature of the resulting movement (such as a flat turn, etc.). Solutions of the closed control system are understood in the Filippov sense. An estimate of admissible levels of external un controlled interference depending on the given restrictions on the control moments is indicated, the conclusion of which is based on the indicated interpretation of the solutions. This estimate is a sufficient condition under which a guaranteed solution of the reorientation problem is provided in finite time by means of proposed constructions of control moments. An iterative algorithm is given for finding the control moment parameters that determine the guaranteed reorientation time.