SUMMARYThis paper considers the use of matrix models and the robustness of a gradient-based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data-dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean-square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well-known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non-causal controller dynamics. The results are compared with recently published results for robust inverse-model-based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high-frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation.
Acoustic black holes (ABHs) are geometric structural features that provide a potential lightweight damping solution for flexural vibrations. In this article, a parametric study of an ABH on a beam has been carried out to assess how practical design constraints affect its behaviour, thus providing detailed insight into design trade-offs. The reflection coefficient of the ABH has been calculated for each taper profile, parameterised via the tip-height, taper-length, and power-law, and it has been shown to exhibit spectral bands of low reflection. These bands have been related to the modes of the ABH cell and become more closely spaced in frequency as the ABH parameters are suitably varied. This suggests that ABH design should maximise the modal density to minimise the broadband reflection coefficient; however, the minimum level of reflection is also dependent on the power-law and tip-height. Consequently, broadband reflection values have been used to show that optimum power-law and tip-height settings exist that achieve a balance between maximum modal density and minimum level of reflection. Additionally, at discrete frequencies, in cases where tip-height and taper-length are practically constrained, the power law can be tuned to maximise performance. Finally, an experimental study is used to validate the results.
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