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A moving-bank multiple model estimator/controller (MMAE/MMAC) based on linear system, quadratic cost, and Gaussian noise (LQG) assumptions is used to quell unwanted vibrations in a simulated large flexible space structure. The structure, known as the Space Integrated Controls Experiment (SPICE), exists at Phillips Laboratory, Kirtland Air Force Base, New Mexico. The structure consists of a large platform and a smaller platform connected by a tripod of flexible legs. The purpose of the control system is to maintain a very precise line-of-sight (LOS) vector through the center of the spacecraft. Kalman filtering, used to estimate the position and velocity of the bending modes of the structure, and LQG control techniques are the primary design tools used in the MMAE/MMAC algorithms. Implementing a parallel bank of filters increases robustness when uncertainties exist in the system model, here specifically allowing adaptation to uncertain and changing undamped natural frequencies of the bending modes of the structure. A moving-bank algorithm is utilized to reduce the computational loading. The MMAE/MMAC design provides a well-suited method of estimating variations in the vector of undamped natural frequencies and quelling vibrations in the structure. The MMAE/MMAC was able to track numerous parameter changes and jumps while providing adequate control for the structure.