| Kamil Aida-Zade, Vugar Hashimov Optimal placement of vibration damping stabilizers for a two-dimensional slab |
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| Abstract. The purpose of this work is to offer a method for synthesizing control actions on the vibration stabilization process of a homogeneous slab. It has been proposed that aggregated pointwise strikes on the slab at the starting time moment produced the vibrations. Depending on the observed states of the slab in the measurement locations, values of the stabilizing effects on the slab from stabilizers installed at its different locations are assigned. It is suggested to apply linear feedback considering the results of current measurements to allow to synthesize control actions. The following parameters are optimized in the problem formulation that is being considered: 1) linear feedback parameters; 2) the coordinates of the slab's stabilizer locations; 3) the coordinates of the locations where the slab's state is measured. Optimal control of a system with distributed parameters can be reduced to a parametric control synthesis problem. For a numerical solution, it is proposed to apply first-order optimization methods. In the space of optimized parameters, you can use the gradient components formulas of the target functional of the problem. The paper will present the influence of measurement errors in controlled points on the process of slab stabilization will be analyzed and the results of numerical experiments will be presented. |
| Keywords: vibrations of a two-dimensional slab, synthesis of the control, lumped source, measurement point, loaded differential equation, gradient projection method |
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| DOI: https://doi.org/10.54381/itta2024.07 |