Research On Normal Matrix Methodology Of Attitude Control For Spacecraft

Spacecraft rely heavily on the effectiveness of complex onboard control systems.Currently, the structures of spacecraft are more and more complex, and the performancerequirements are higher and higher. These challenge the designing of spacecraft attitudecontrol systems. The present thesis is focused on the application issues of the normalmatrix design approach on the attitude control of spacecraft.The researches are based on the spacecraft that can be regarded as a central rigid-body with stored angular momentum and some ?exible appendages attached. Firstly, thesystem's dynamical model is derived, and the characteristics of the normal matrix, diago-nally dominant, and the distribution of poles and zeros of the linearized dynamical modelin frequency domain are analyzed carefully. Based on these analysis results, the normalmatrix control problems are considered for the attitude stabilization of rigid and ?exiblespacecraft, and for the attitude maneuver of spacecraft. A comparison is made betweentwo uncertainty descriptions: the multiplicative perturbation and inverse-additive pertur-bation. The inside-the-loop input shaping is studied and applied to the attitude stabiliza-tion of ?exible spacecraft. The feedback linearization is employed in the designing ofnormal matrix control law for large angle attitude maneuvering, and the nonlinear H∞normal matrix control law is designed by using the Hamilton-Jacobi-Isaacs inequality forthe attitude tracking problem.The research on the characteristics of spacecraft dynamics show that, (i) the dy-namics model of spacecraft is generally not the normal matrix, and the main factors thataffect the normality are the ?exible motions and the coupling between the products ofinertia, stored angular momentum, and the orbit velocity. (ii) The transmission zeros arestill the constrained modal frequencies of ?exible appendages regardless of the storedangular momentum, but the unconstrained modal frequencies are no longer the systempoles. The system poles are determined by a odd-dimension eigenvalue problem of gen-eralized gyroscopic system when the stored angular momentum occur. (iii) The inertiatensor of a rigid body in any centroid body-fixed coordinate is a diagonally dominant ma-trix if the maximum and minimum principle moments of inertia meet a given condition.Therefore, the transfer function matrix of spacecraft dynamics are generally regarded asa diagonally dominant matrix.For the normal matrix control of spacecraft attitude stabilization, the usage of the inverse-additive perturbation can bring more advantages to the system than that of themultiplicative perturbation. With the uncertainty descriptions of the inverse-additive per-turbation, the improvement of the system's normality is more convenient, and only partof the parameters in the control law are included in the normal-matrix design condition,therefore the others are freed and can be used in the trade-off among performance re-quirements of the three loops.Like the traditional input shaping, the inside-the-loop input shaper can suppressthe vibrations, has robustness to the alteration of the vibration frequencies, and can si-multaneously suppress the vibrations of the design frequency and its odd-number timesfrequencies. But unlike traditional input shaping, the inside-the-loop input shaper cannot suppress the vibration of a single odd, for example, 3 or 5, times frequency. TheLMI criteria of asymptotic and robust stability are derived for the inside-the-loop inputshaping system, which is regarded as a special case of multi-delay system with delays ofmultiple relationship. The relationships among the modal frequencies in the multi-modesystem can be used in the saving of the shaping time of inside-the-loop input shaper andthe reduction of the input shaper effectively. The system's robustness can be improvedby inserting the inside-the-loop input shaper into the attitude control loops of the ?exiblespacecraft besides the vibration suppression.For the applications of the normal matrix design methodology to nonlinear attitudemaneuver control problems, the normal matrix control approach are combined with thefeedback linearlization. The normal matrix control law is derived for the large angle at-titude maneuver problem, and both the inside-the-loop input shaper, for the suppressionof the ?exible vibrations, and the outside-the-loop input shaper, for the reduction of therigid oscillation, are employed to promoting the precision and response speed of the sys-tem. For the attitude tracking problem, the normal matrix control law is designed basedon the attitude error dynamics model, and the control law is proved to be a nonlinear H_∞control law for the nonlinear attitude tracking problem.The computer simulation results demonstrate the validity and effectiveness of thetheoretic analysis and design results in the present dissertation.