Engineering and Applied Sciences Journal

Optimal Control Problem of Spacecraft Spatial Reorientation Taking into Account Loading of Construction Using Quaternions and The Combined Criterion of Quality

Abstract

Mikhail Valerâ??evich Levskii

Quaternion solution of the problem on optimal control of a spatial turn of a spacecraft (as rigid body) from an arbitrary initial into an assigned final angular position taking into account the degree of loading of the construction is considered. The solved problem differs in use of new criteria of optimality. Optimization of control process is based on the combined functional of quality that combines in a given proportion time spent on spacecraft rotation and the integral of quadratic form relative to angular velocity (this quadratic form reflects dynamical loads on spacecraft construction). The proposed control method for spacecraft rotation improves conditions of turn in sense of minimum loading of spacecraft construction. Analytical solution of optimal control problem is obtained on the base of maximum principle with use of quaternionic models of the solid body motion controlled. The properties of optimal motion of a spacecraft are revealed in an explicit form, the structure of optimal control is specified. It was shown that degree of spacecraft construction loading during reorientation maneuver does not exceed the required value which is determined by coefficients of the minimized functional; and time of rotation is minimum also (as it is possible under given value of dynamical loading). To construct optimal control program, formalized equations and calculation formulas are written. Analytical equations and relations are presented for finding optimal control. Key relationships determining optimal values of the parameters of control algorithm for spacecraft turning are described. Numerical example and results of mathematical modeling that confirm the practical feasibility of the developed method for control of spacecraft reorientation are given. Important implication of the investigated problem of spacecraft optimal control is caused that often, allowable loading of spacecraft board and its elements of construction becomes significant restriction (constraints) for spacecraft motion with respect to center of mass (particularly for scientific spacecrafts and small spacecrafts which have sensitivity to loads). Solution to the problem of spatial reorientation in closed form is obtained for case of symmetric loading of spacecraft construction. 

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