integral compensation. The procedure for accomplishing the design of the optimal robust control is as follows: • Step 1- Develop a model that includes the rigid body dynamics, the gravity gradient dynamics, the rotational dynamics of any controllers that are included, the flexible dynamics through a large finite element model of the structure, and any significant thermal/structural interactions. • Step 2- Reduce the dimension of the model. This is a key step since the validity of the robustness results depends on the minimization of spillover which takes place at this step. Order reduction techniques include methods based on singular perturbation, variable time scale, or modal truncation based on cost of control. ® Step 3“ Design the control system using the model of step 2 and a performance measure for the quality of control that penalizes motions in regions of the structure where loads nust be reduced, and also gives the overall rigid body control performance that is required (pointing of the microwave antenna to some specified angle, for example). • Step 4- Verify the design of step 2 on a larger dimension version of the dynamic model than was used to develop the design. This is necessary because the only way one can evaluate the spill-over effect is with a dynamic model that is of larger dimension than the design model. • Step 5“ Repeat steps 2,3, and 4 until the design has the desired level of robustness for typical parameter uncertainties in the structural and control actuator dynamics. The effectiveness of this approach as a design technique relies on the fact that any infinite dimensional system may be evaluated on a sufficiently large finite dimensional approximation, as long as the control system has a specified high frequency characteristic. In the case of optimal designs, this characteristic is the roll off of the control,at the higher frequencies, that is at least 20 db/ decade. An Example Figure 2 shows a structure that was used to evaluate the design proceedure described above. This structure was an earlier version of a space construction base that was developed by Grumman for JSC. The controller was asked to reduce the motion of the solar array, while stabilizing an unstable gravity gradient orientation. In addition the pointing of the overall system was to be insured. The actuators consisted of only the rigid body actuators which were three orthogonal control moment gyroscopes mounted close to the shuttle attachment point at the bottom of the mast that carries the solar array and construction boom. The control sehsors were a set of 52 strain sensors (26 strain gages configured in such a way that both strain and strain rate were sensed), plus the normal complement of rigid body sensors (attitude and rate in each axis). The resulting design is extremely robust, and the verification on the higher dimension model has been formulated as a 16 mm movie that shows precisely how the control operation helps damp the solar array vibration while maintaining rigid body control despite the unstable gravity gradient torques.
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