Normal Matrix Method Of Attitude Control For Flexible Satellites

Based on the relationship between the normal matrices and stability robustness of control systems, the problem of robust control design is discussed for attitude control of a modern spacecraft, which can be modelled by a central rigid body with several large flexible appendages and moment exchange devices.Under the fact that a normal transfer function matrix can induce a minimum H_∞norm of a system, the character of some special normal matrices, such as Hermite matrix, skew-Hermite matrix, unitary matrix, are studied for the applications on the attitude control of spacecrafts. And the relationships between the normality of 3×3 complex matrices and their elements are discussed for the application of the spacecraft attitude control. Several uncertainty descriptions of the transfer function matrix and the stability robustness criterions for the achievement of H_∞optimal controller by normal matrix under these uncertainty descriptions are introduced separately. Two normal matrix design methods, the Reversed-Frame Normalization ( RFN ) and the Optimization of Parameterized NORmal Matrix ( OPNORM ), are given in a nutshell. And a fact is pointed out that OPNORM is to get a normal, symmetry open-loop transfer function matrix.In the light of the relationships existed between the normal matrix and the stability robustness of a system, the normality of the inverse transfer function matrix, deduced from the hybrid coordinate equations of attitude dynamics of spacecrafts, is analyzed. The analysis indicate that the inverse transfer function matrix is a Hermite matrix in the whole frequency domain and has satisfying normality in the main frequencies when some minor factors such as the vibration damping of flexible appendages and the orbit angle rate are taken into account. This characteristic is of great benefit to the acquirement of a satellite attitude control system, which has a optimum H_∞index, by means of normal matrix methods. Based on the normality of the dynamics transfer function matrix, two kinds of simplest robust controller and their restrictions to the dynamic qualities of the control system and the characteristic of the satellite under the multiplicative perturbation and the inverse-additive perturbation are presented separately. Because it can greatly improve the normality of the close-loop transfer function matrix of the normal attitude control, the scheme for inverse-additive perturbation have a better practicality than that for multiplication perturbation.