Abstract
Optimal control problems are considered for transient magnetizationprocesses arising from electromagnetic flow measurement. The magneticfields are generated by an induction coil and are defined in 3D spatial domains thatinclude electrically conducting and nonconducting regions. Taking the electrical voltagein the coil as control, the state equation for the magnetic field and the electrical currentgenerated in the induction coil is a system of integro-differential evolution Maxwell equations.The aim of the control is a fast transition of the magnetic field inthe conduction region from an initial polarization to the opposite one.First-order necessary optimality condition and numerical methods of projected gradient type arediscussed for associated optimal control problems. To deal with the extremely long computingtimes for this problem, model reduction by standard proper orthogonal decomposition is applied.Numerical tests are shown for a simplified geometry and for a 3D industrial application.
Highlights
We extend our investigations in [20] on optimal magnetization problems arising from industrial applications in flow measurement
If the magnetic field changes in time, an electrical potential is measured the velocity of the fluid did not change
We model the magnetization process by a linear parabolic-elliptic evolution Maxwell system that is complemented by an integro-differential equation accounting for the induction law in the coils
Summary
We extend our investigations in [20] on optimal magnetization problems arising from industrial applications in flow measurement. An electrical potential is measured at selected points inside the tube. This volume flow measurement is performed differentially with a pulsed magnetic field to suppress noise and offset voltages as efficiently as possible, see Fig. 1.1. If the magnetic field changes in time, an electrical potential is measured the velocity of the fluid did not change. By controlling the electrical voltage in the induction coils, magnetic fields should be switched very fast from a given steady magnetic field to the one with opposite polarization. We aim at minimizing the L2-distance of the magnetic
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