Abstract-Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency synchronous step-down dc-dc converter. The specifications are defined such that good performance only can be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

The bubbly flow and mixing conditions for gas stirring in a 50t ladle were investigated by using physical modelling and mathematical modelling. In the physical modelling, the effect of the porous plugs’ configurations on the tracer homogenization was studied by using a saturated NaCl solution to predict the mixing time and a color dye to show the mixing pattern. In the mathematical modelling, the Euler–Lagrange model and species transport model were used to predict the flow pattern and tracer homogenization, respectively. The results show that, for a ±5% homogenization degree, the mixing time with dual plugs using a radial angle of 180° is shortest. In addition, the mixing time using a radial angle of 135° decreases the most with an increased flow rate. The flow pattern and mixing conditions predicted by mathematical modelling agree well with the result of the physical modelling. For a ±1% homogenization degree, the influence of the tracer’s natural convection on its homogenization pattern cannot be neglected. This is especially true for a ‘soft bubbling’ case using a low gas flow rate. Overall, it is recommended that large radial angles in the range of 135°~180° are chosen for gas stirring in the present study when using dual porous plugs.

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