Receptance-based robust eigenstructure assignment

The robustness of receptance-based active control techniques to uncertain parameters in fitted transfer function matrices is considered. Variability in assigned closed-loop poles, which arises from uncertain open-loop poles, zeros, and scaling parameters, is quantified by means of analytical sensitivity formulae, which are derived in this research. The sensitivity formulae are shown to be computationally efficient, even for a large number of random parameters, and require only measured receptances, thereby preserving the model-free superiority of receptance-based techniques. An evolution-based global optimisation procedure is used to perform eigenstructure assignment so that the robustness, as defined by a metric, is maximised. The robustness metric is designed to scale the relative importance of each closed-loop pole and their respective real and imaginary parts. The proposed technique is tested numerically on a multi-degree-of-freedom system. It is shown that, in both single- and multiple-input systems, it is possible to increase the robustness by optimally selecting a set of closed-loop poles. However, it is determined that the closed-loop eigenvectors of the system play a significant role in the propagation of uncertainty and hence, since multiple-input systems may independently assign both closed-loop poles and eigenvectors, multiple-input systems are able to reduce the uncertainty propagation to a greater extent. (C) 2020 Elsevier Ltd. All rights reserved.