Identifying parameters in active magnetic bearing system using LFT formulation and Youla factorization

In this paper, a method for identifying uncertain parameters in a rotordynamic system composed of a flexible rotating shaft, rigid discs and two radial active magnetic bearings is presented. Shaft and disc dynamics are mathematically described using a Finite Element (FE) model while magnetic bearing forces are represented by linear springs with negative stiffness. Bearing negative stiffness produces an unstable rotordynamic system, demanding implementation of feedback control to stabilize the rotordynamic system. Thus, to identify the system parameters, closed-loop system identification techniques are required., The main focus of the paper relies on how to effectively identify uncertain parameters, such as stiffness and damping force coefficients of bearings and seals in rotordynamic systems. Dynamic condensation method, i.e. pseudo-modal reduction, is used to obtain a reduced order model for model-based control design and fast identification., The paper elucidates how nodal parametric uncertainties, which are easily represented in the full FE coordinate system, can be represented in the new coordinate system of the reduced model. The uncertainty is described as a single column vector of the system matrix A of the full FE model while it is represented as several elements spread over multiple rows and columns of the system matrix of the reduced model. The parametric uncertainty, for both the full and reduced FE model, is represented using Linear Fractional Transformation (LFT). In this way the LFT matrices represent the mapping of the uncertainties in and out of the full and reduced FE system matrices. Scaling the LFT matrices easily leads to the amplitudes of the uncertainty parameters., Youla Parametrization method is applied to transform the identification problem into an open-loop stable problem, which can be solved using standard optimization methods., An example shows how to decouple and identify an uncertainty in the linear bearing stiffness of a reduced FE rotordynamic system.