Parameter Reduction in Estimated Model Sets for Robust Control

This paper proposes two techniques for reducing the number of uncertain parameters in order to simplify robust controller design and to reduce conservatism inherent in robust controllers. The system is assumed to have a known structure with parametric uncertainties that represent plant dynamics variation. An original set of parameters is estimated by nonlinear least-squares (NLS) optimization using noisy frequency response functions. Utilizing the property of asymptotic normality for NLS estimates, the original parameter set can be reparameterized by an affine function of the smaller number of uncorrelated parameters. The correlation among uncertain parameters is detected by the principal component analysis in one technique and optimization with a bilinear matrix inequality in the other. Numerical examples illustrate the usefulness of the proposed techniques.