In comparison to the ± 1-deg attitude pointing requirement for the baseline system, the pitch-axis performance is well within specifications. In addition, it was determined in the structural analysis study that the structure will experience localized bending of 1 deg when excited by end forces of 667 lb. Consequently, control forces about the Y axis of 0.11 lb should not affect the system's performance. A verification of these results was obtained from a digital simulation of the control dynamics of the baseline SSPS structure and control system. Figures 21a through 2If, respectively, show time-history plots of the spacecraft's attitude, control force, and generalized modal velocities, and modal displacements for the first and second anti-symmetrical modes. To determine the influence of structural flexibility, a digital simulation was also performed of the SSPS rigid-body dynamics only. Results are shown in Figures 22a and 22b. A comparison of these two sets of time-history responses reveals that structural flexibility decreases the system's damping ratio and increases its attitude error. As a result of this flight control performance evaluation about the pitch axis, we concluded that the baseline structure can be considered to be stiffer than necessary for maintenance of the ±1.0 deg pointing accuracy. In response to this observation a parametric study was performed in which attitude control performance sensitivity was measured as a function of changes in structural stiffness. The results of this study are shown in Figure 23 through 28 in which A0 /0„v A0„/T. v, T„ , y cy y ay k Fcv/Td , K. and K„ are, respectively, shown as a function of the frequency of the system's lowest vertical anti-symmetrical bending mode frequency. These figures show the results for damping ratios ranging from 0.25 to 1.0 and also consider undamping control frequencies which are factors of 5 and 10 less than the corresponding fundamental bending mode frequency. As expected these results indicate that the system attitude error and response time increases as the structural stiffness (frequency) decreases. Figure 29 consolidates these pitch mode results by relating structural frequency (stiffness) and attitude error to structural weight. As indicated, a decrease in structural frequency (stiffness) results in a decrease in structural weight, but an increase in attitude error. However, although a 25% change in frequency; (stiffness) decreases the structural weight by 50%, the pitch-axis attitude error is still well within the baseline system requirements. b. Roll Mode SSPS roll dynamics have been defined to be rotation about the spacecraft's X axis in the Y-Z plane as indicated in Figure 30.
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