Static Shape Control for Flexible Structures

This paper outlines aspects of modeling, identification, and estimation which are combined in the static shape control of flexible structures. The structural models considered here are specified by possibly interconnected elliptic partial differential equations which model deflections under a suitable range of static loads. Other modeling aspects, such as electromagnetic field analysis for antenna systems, are also considered. Modeling errors as well as observation errors are given a white noise characterization which leads to a second-order analysis of the related statistical errors. The identification techniques are based on the method of maximum likelihood whereby parameter values of the model are determined by the maximization of a suitably defined likelihood functional which incorporates the parameterization of the model with the observation data. Parameter estimates are improved by means of a quasi-Newton iteration in parameter space. The estimation methods are based on the derived conditional mean of the state given the observation data. The resulting estimate is then represented as a least-squares superposition of shape functions which are derived from the structural model. Batch-processing of the data obtained by various sensing strategies yields recursive formulations for the estimate similar to the well-known Kalman gains.

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