For the baseline spacecraft design, the system's damping ratio was selected to be 0.50, so as to limit the peak oscillations of the system's response. To separate the system's control dynamics from the structural dynamics, an undamped natural frequency for each axis was chosen to be a factor of 10 less than the corresponding lowest anti-symmetrical bending mode frequency.* For the pitch axis this results in an undamped natural frequency of 0.00178 rad/sec. Using Equations (1) and (2) we found the baseline control parameters for the pitch axis to be: With the above set of parameter values, the dynamic performance for the pitch axis of the baseline spacecraft was evaluated using the parametric performance indices defined in Tables 1 and 5 of Reference 35. The results of the pitch axis performance evaluation are summarized below: y These results indicate that for each degree the SSPS is commanded to point about the Y axis, the attitude error would be 0.005 deg. However, since the nominal orientation requires a zero off-set angle the first terms contribute a zero attitude error. However, in attempting to maintain a nominal orientation the spacecraft must counteract disturbance torques which are tending to cause it to move off nominal. The second quantity listed above indicates that, in the presence of disturbance torques, the attitude error for the pitch mode is 3.5 x IO-9 rad/ft-lb. Therefore, for a constant disturbance torque about the Y axis of 4100 ft-lb, the steady-state, off-nominal attitude error is 1.50 x 10-5 rad (86 x IO"5 deg). To counter this disturbance the baseline control system must continuously exert 0.11 lb of thrust in coupled pairs at the extremities of the Y axis (as indicated by the third quantity listed above). In responding to this disturbance, the pitch axis dynamics will decay to within 95% of its steady-state value in 3180 sec.
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