This thesis is concerned with multi-objective optimization of magnetic levitation systems. To assist with this process, a new algorithm for processing step response signals was developed. By varying the algorithm’s time step depending on the characteristics of the curve, it achieves increased signal processing speed, which is confirmed by numerical tests. The algorithm is also applicable to fractional-order dynamical systems for which an explicit formula for the inverse Laplace transform of a general type of transfer functions was derived. Accurate determination of magnetic fields of 3D objects is an important part of modeling of levitation systems. This work formulates and solves the problem of finding the stationary magnetic field of a 3D object at any point in space based on known values of the magnetic field near the surface of a magnetized object. For a multilayered solenoid, new compact analytical formulas of the lifting force and its derivatives were derived. Using these expressions, the optimal coil geometries, acquired with several nonsmooth minimum search methods, were compared.
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