Dr. Gary J. Balas
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Browsing Dr. Gary J. Balas by Author "Doyle, John C."
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Item Identification of Flexible Structures for Robust Control(Institute of Electrical and Electronic Engineers, 1989-06) Balas, Gary J.; Doyle, John C.This article documents our experience with modeling and identification of an experimental flexible structure for the purpose of control design, with the primary aim being to motivate some important research directions in this area. Initially, a multi-input/multi-output model of the structure is generated using the finite element method. This model is inadequate for control design, due to its large variation from the experimental data. Next, Chebyshev polynomials are employed to fit the data with single-input/multli-output (SIMO) transfer function models. Combining these SIMO models leads to a multi-input/multi-output (MIMO) model with more modes than the original finite element model. To find a physically motivated model, an ad hoc model reduction technique which uses a priori knowledge of the structure is developed. The ad hoc approach is compared with balanced realization model reduction to determine its benefits. Descriptions of the errors between the model and experimental data are formulated for robust control design. Plots of select transfer function models and experimental data are included.Item Robustness and Performance Trade-Offs in Control Design for Flexible Structures(Institute of Electrical and Electronic Engineers, 1994-12) Balas, Gary J.; Doyle, John C.Linear control design models for flexible structures are only an approximation to the “real” structural system. There are always modeling errors or uncertainty present. Descriptions of these uncertainties determine the trade-off between achievable performance and robustness of the control design. In this paper it is shown that a controller synthesized for a plant model which is not described accurately by the nominal and uncertainty models may be unstable or exhibit poor performance when implemented on the actual system. In contrast, accurate structured uncertainty descriptions lead to controllers which achieve high performance when implemented on the experimental facility. It is also shown that similar performance, theoretically and experimentally, is obtained for a surprisingly wide range of uncertain levels in the design model. This suggests that while it is important to have reasonable structured uncertainty models, it may not always be necessary to pin down precise levels (i.e., weights) of uncertainty. Experimental results are presented which substantiate these conclusions.