Nonlinear Modeling and Control of the Magnetic Bearings

A nonlinear modeling and control method for magnetic bearings is proposed, that tales into account the core material’s nonlinear high flux behavior for the first time. A combination of the generalized Lur’e method and linear matrix inequalities is used during the modeling and control design process. The nonlinear modeling makes it possible to operate an existing industrial Active Magnetic Bearing (AMB) system with larger electric currents and thus achieve a larger maximum load capacity than existing AMB modeling and control practices allow. As a result, existing industrial AMBs can be tuned to become more resilient when dealing with external disturbances. In addition, smaller and lighter AMBs can be designed using the proposed method, which enables them to achieve of the same maximum force requirement of present-day larger AMB systems at a fraction of the size and cost.

The proposed control method is verified by experimental data drawn from a balance beam test rig designed for this project and very good correlation was obtained between the experimental data and theoretical predictions.
In comparison to classical control design, a significantly improved transient response and a significantly higher dynamic load capacity was achieved through the use of the proposed modeling and control design.
The control synthesis based on the nonlinear model with a generalized sector condition offered little or no performance improvement over the control synthesis based on the nonlinear model with a regular sector condition for the problem considered. Despite this fact, using the generalized sector condition was proven to be necessary in order to guarantee a less conservative design compared to classical control design.
The uncertainty descriptions developed in this work were appropriate and because of the use of the generalized sector condition, guaranteed not to be overly conservative.

While the nonlinear behavior of the magnetic bearings due to the material magnetization has been studied and modeled previously, the extra load capability within the nonlinear region has not been optimally used in the control strategies. A combined approach for modeling and control of magnetic bearing that counts on the extra load capability within the nonlinear magnetization region is proposed in this work. Various optimized controllers with different objectives are designed using the extra load capability for the first time on this dissertation.