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A procedure is developed to deal with performance and robustness issues in the design of multiple-input multiple-output compensators for lightly damped flexible structures. The procedure is based upon representing errors in the plant design model as structured uncertainties, and applying a modified linear quadratic Gaussian design method. The cost function in the regulator problem and the process noise model in the estimator problem are varied in a manner that reflects specific parameter uncertainty including frequency, damping, or modal displacement errors. Numerical examples dealing with the control of a large flexible space antenna with uncertain frequencies demonstrate the application of the method.

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Approximate expressions are developed for internally balanced singular values corresponding to the modes of mechanical systems with gryoscopic forces, light damping, and small circulatory forces. The singular values involve input and output coupling, modal frequency, and modal damping, and they serve as a guide for model reduction by modal truncation. The derivation of these singular values is based on perturbation analysis, and the satisfaction of a frequency separation condition is required to insure their validity. Nomenclature A= system matrix B-input matrix C = output matrix A 0 = system matrix for conservative forces A l = system matrix for nonconservative forces T = transformation matrix W c = system controllability grammian WQ = system observability grammian W c^ = controllability grammian for two-mode subsystem € = small parameter associated with nonconservative forces a, = ith balanced singular value d t = ith approximate balanced singular value a>j = ith system frequency C/.. = ith system damping ratio Q = diagonal matrix of system frequencies

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