Optimal Control for the Electroplating Process Based on the Supplementary Cathode and Bipolar Electrode

The article describes the main approaches (including technical parameters and equipment) to taking into account the changes and correction of the electrolyte components of the bath with the supplementary cathodes and bipolar electrodes in the electroplating processing of products. A voltage change on the anode is proposed as a manipulated variable for the galvanic process as a control object for the electroplating bath. The task of optimal control of the electroplating process by the criterion of distribution of uniformity on the surface of the coating thickness of the product is set. A mathematical model is formulated of the dynamics of the distributed coordinates for the contact criterion of the uniformity coverage with the control action in the form of changes of the anode voltage, taking into account the structural and technological assumptions. This is based on the Faraday's law, Ohm's law of the differential form and a partial differential equation of a parabolic type describing the distribution built in the amount of the electroplating bath. An algorithm was invented for solving the equations of the mathematical model of the electroplating process, which considers the task as a quasi-static one and based on the modifications of the direct Ritz method for the search function of the anode voltage in the class of the polynomials of various degrees. A comparison is proposed of the relative values of the refinement criteria of the unevenness produced during the transition to a higher polynomial degree in order to obtain the required accuracy solutions for determination of the degree of the polynomial control. An example is described of solving the problem of chrome electroplating of V-shape parts in the electroplating bath with two side cathodes and one bipolar electrode. This example describes the function of the anode voltage in the form of the polynomials of the zero, first and second degrees. A rational solution describing the anode voltage changes as the polynomials of the first degree is shown. The further increase in the degree doesn't give a significant gain in the unevenness of the coverage criterion, however, it ensures a significant increase of the duration of the search optimization. Thus, the obtained feature of the voltage change on the anode does not depends strongly on time, so, the change of the concentration of the electrolyte components is reduced slightly during a short period of coating. However, when analyzing a longer period, the process under a constant stress might lead to significant losses in the expected distribution of the coating thickness.

оптимальное управление, объект управления, математическая модель, дополнительные катоды, биполярные электроды, модифицированный метод Ритца, гальванический процесс, неравномерность толщины покрытия, концентрация компонентов электролита, optimal control, control object, mathematical model, supplementary cathodes, bipolar electrodes, modified Ritz method, electroplating process, anode voltage, unevenness of the coating thickness, concentration of the electrolyte components

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