Rational Approximation of the Analytical Model of Nonlaminated Cylindrical Magnetic Actuators for Flux Estimation and Control

Consideration of Hysteresis, Saturation, Fringing and Leakage Fluxes in the Frequency-Dependent Analytical Model of Nonlaminated Cylindrical Actuators

“…The same formula also applies approximately for the core elements of class 3 in Fig. 2 with c = ( 2 2 − 2 1 )/ 2 as defined in [1]. In the following section V, we will use this example to demonstrate the expansion of any transcendental solution with the hysteresis angle hyst to model the frequency-dependent impact of the hysteresis.…”

“…As a consequence, there emerges a desire for high-stiffness magnetic bearings with a disturbance suppression Δ DS > 120 dB, which will match the stiffness of their mechanical counterparts (Δ DS ≈ 160 dB) to some degree. This is especially challenging for magnetic thrust bearings as well as other solid-core actuators, as eddy current flow inside the iron core and the resultant magnetic skin effect [1] is usually not avoidable. The three-dimensional flux propagation renders a laminated core, as common in radial bearings, ineffective.…”

“…It relies on typical parameters like the stiffness and the damping , which are equal to ball, oil and air bearings, and therefore keep the initial start-up of the magnetic bearing simple and comprehensible. For this reasons we presented an alternative control approach in our previous work [1], maintaining the cascaded structure and its practical advantages. Instead of the measurable coil current, we control the actual force-generating flux density as shown in Fig.…”

“…Section II gives a brief introduction into the existing eddy-current model, on which the flux density estimator is based on. For a deeper understanding of the physics and the mathematical modeling based on fractionalorder systems, we like to refer to our previous work [1]. In section III we will first delve briefly into the historic modeling of hysteresis before focusing on the identification of the loaddependent hysteresis angle hyst in section IV.…”

“…Cylindrical actuators and magnetic bearings were first considered by [13] and [14], respectively, leading to the almost complete model by Zhu et al [4]. In our previous work [1] we presented a full historical review of eddy current models, a study on their physical impact as well as final model refinements. Due to this extensive groundwork we will introduce only the most essential equations here.…”