4 June 1999 Control system design for structural systems under statistical parametric uncertainty
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This paper presents a statistical approach to the controller design process for structural systems represented by uncertain models. The plant model uncertainty is here accounted for in terms of first- and second-order statistics of uncertain parameters. The basic idea is to make the closed-loop system stability as robust as possible to statistical variations of uncertain plant model parameters. First, an approximate expression for the root variance of an uncertain polynomial is derived as a function of second-order statistics of the polynomial coefficients. The expression is specialized to the case of an SISO closed-loop system characteristic polynomial, where the uncertainty is due to statistical variability of model parameters. Uncertainty cost functions intended to represent the uncertainty of the closed-loop pole locations are then constructed. By parameterizing the set of controllers that yield a desired characteristic polynomial, the uncertainty cost function minimization is converted into a constrained optimization problem. This scheme is illustrated with an SISO seismic control system previously studied in the literature. By comparing the predicted closed-loop pole variance to numerical results obtained from Monte Carlo simulations, it is concluded that the expression developed here provides excellent approximation, with the advantage of being an analytical expression that is suitable for use in multi-objective optimization design algorithms.
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Ruben Huerta-Ochoa, Ruben Huerta-Ochoa, Stanley H. Johnson, Stanley H. Johnson, } "Control system design for structural systems under statistical parametric uncertainty", Proc. SPIE 3667, Smart Structures and Materials 1999: Mathematics and Control in Smart Structures, (4 June 1999); doi: 10.1117/12.350078; https://doi.org/10.1117/12.350078

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