Robust Control Of Relative Orbital Maneuvering

The spacecraft relative orbital maneuvering is affected by the various forms of perturbations caused by the complexity of space environment. This paper designs the corresponding robust controllers both for the spacecraft relative motion systems of the nearly circular reference orbits and the relative motion system of the elliptical orbits.The mathematical models of spacecraft relative motion are described, which are the TH equation and the CW equation. In this basis, the major factors of perturbations affecting the relative motion are analyzed, and the relative acceleration caused by the Earth oblateness J2 perturbation is expressed. Meanwhile the relationship between atmospheric drag and perturbation of orbital average angular velocity is established.The robust controllers for the spacecraft relative motion systems of the nearly circular reference orbits is designed from three aspects, which are the perturbation of parameter, perturbation of acceleration, and the optimal quadratic performance index. Firstly, considering relative motion parameter perturbation which is the average angular velocity of the target spacecraft's orbit under the action of atmospheric drag, this model is based on PD state feedback tracking control theory and the method of eigenstructure assignment, and the closed-loop system eigenvalues of the coefficient matrix condition number is selected as the performance index. Then, robust controller is designed by optimizing the index. Numerical simulation shows the effectiveness of the controller. Secondly, for the relative motion system under the acceleration perturbation, the H2 norm of the error transfer function is expressed by introducing the parameterization controller into the perturbed system, and robust controller of disturbance inhibition is designed by minimizing the index of H2 norm. Finally, perturbation optimal controlling problem is transformed into the corresponding H2 control problem for the optimal quadratic performance index of the perturbed system. Furthermore, the original index is transformed into the expression of free vectors and closed-loop poles by taking advantage of Jordan standard of the closed-loop system coefficient matrix. The problem of designing robust optimal controller is solved by optimizing the integrated performance index. The closed-loop system in the binary formation flying around plane projection elliptical orbit mission mode is simulated.For the spacecraft relative motion system of the elliptical reference orbits, the original LPV model is transformed into the corresponding interval system. Then, the controller is designed by the method of robust eigenstructure assignment. Finally, the closed-loop system of relative motion is numerical simulated.