The above results indicate that for each degree that the vehicle is commanded to point from its nominal zero position about the X axis the attitude error for the baseline spacecraft is 2.5 x IO-5deg. However, this quantity should nominally be zero, since the nominal orientation of the spacecraft requires 0CX = 0. The second term listed about indicates that, in the presence of disturbance torques Tdx the system's roll-axis pointing error would be 4.2 x IO-9 rad/ft-lb. Consequently, for a constant-gravity gradient torque of 89,700.0 ft-lb, the roll-axis, steady-state pointing error would be 0.00037 rad (0.0212 deg). To counter this constant disturbance torque, the above relationships indicate that a steady-state control thrust of 5.5 lb is required at each end of the roll-axis acting in opposite directions. When compared to the ±1 deg baseline system pointing requirements for the roll-axis, it is evident that the presently designed baseline structure and control system are well within the performance specifications. Furthermore, a control thrust of 5.5 lb is far below the maximum 667-lb limit placed on the end thruster by the results of the structural analysis [Reference 36]. The results of this flight control performance evaluation were verified using a digital simulation of the control dynamics of the SSPS. Figures 33a through 33e show time-history response plots for the spacecraft's roll attitude, control thrust profile, and generalized bending mode dynamics in the presence of a 89,700-ft-lb disturbance torque. A similar set of time-history plots is shown in Figure 34 for the roll-axis, rigid-body dynamics. A comparison of these sets of dynamic responses shows that the influence of structural flexibility is to decrease the system's damping ratio and increase the attitude error. On the basis of this flight control performance analysis about the roll axis, it was concluded that the baseline structure and control system were well within the design specifications. Consequently, a parametric study was performed to determine the influence of structural stiffness upon the system's attitude error. The resulting set of curves are presented in Figures 35 through 40 in which the frequency of the lowest anti-symmetric roll bending mode is, respectively, plotted against As noted, these plots consider a family of systems damping ratios ranging from 0.25 to 1.0 as well as two sets of undamped natural frequencies corresponding to values which are factors of 5 and 10 below the lowest anti-symmetrical bending modes of the roll axis. The results of this roll mode parametric study indicate that the system's roll axis attitude error and response time increase as the roll axis fundamental bending frequency (stiffness) decreases. Figure 41 cross-plots structural weight and roll attitude error against bending mode frequency. The results shown in this plot indicate that a 25% decrease in the baseline structural frequency results in a 50% reduction in structural weight, while the baseline pointing accuracy is still well within required accuracy.
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