Modeling and shape control of a segmented-mirror telescope

The Advanced Structure/Control Integrated Experiment (ASCIE) is an optical telescope consisting of seven hexagonal segments mounted on a light-weight flexible truss. The position and the attitude of the six peripheral segments are actively controlled by 18 electromagnetic actuators to keep the segments optically aligned. 24 inductance sensors are used to measure the relative displacements between the segments. Optical performance requires keeping the piston displacement errors within 50 namometers and the tilt errors within.1 arcsecond relative to the central segment.; Disturbability, controllability/observability and static fidelity analyses are used to eliminate modes from the Finite Element Model while keeping enough of the dynamic and static characteristics of the system for evaluation and control design purposes. New optimal and aggregation based algorithms are introduced for matching impulse and step responses. When a feedthrough term is allowed in the reduced order model and when the step responses are matched, the aggregation technique returns the same model as a modal truncation technique which would treat the neglected modes as quasi-steady. The control design model contains 30 modes. The first 20 modes are tightly clustered within the projected control bandwidth. The other 10 modes are in the cross-over region. 20 neglected modes that can be potentially destabilized by spillover are less than a decade away from the control bandwidth.; A systematic norm-preserving procedure is developed to take advantage of the six fold symmetry of the ASCIE and to decompose the control design model into input/output decoupled subsystems. Two subsystems are formed: one with 22 modes, 12 controls and 12 measurements, the other with 8 modes, 6 controls and 6 measurements. The decomposition reduces by a factor of 3 the CPU time needed to compute the control logic.; Worst case control design methods that trade performance, parameter stability margins, and spillover margins are used to synthesize the control laws. New macros that can be incorporated in standard software control packages have been developed to facilitate the implementation of these design methods (block-diagram-based interconnection of multivariable systems). To avoid the spillover instability, 60dB/decade of roll-off are needed for a control bandwidth of 10-12 Hz. (Abstract shortened with permission of author.)...