Modeling of a Horizontal Active Magnetic Bearing System with Uncertainties in Deterministic Form

In this paper the derivation of mathematical model of a horizontal active magnetic bearing (AMB) system in deterministic form is presented. The system is open-loop unstable and highly coupled due to nonlinearities inherited in the system such as gyroscopic effect and mass imbalance. Based on the equation of motions of the rotor and dynamic equation of electromagnetic coils, the dynamic model of the system with eight inputs is derived and represented in state-space format in which the system matrix is 16times16 in size. By using the upper and lower bounds of the parameter and the state variables of the system, the model is transformed into deterministic form where it can be shown that the system contains mismatched uncertainties in the state and disturbance matrices. This final system model with its numerical values can be used for the design of a class of a dynamic controller for system stabilization