Control Design of Active Magnetic Bearings for Rotors Subjected to Destabilising Seal Forces - Theory & Experiment

Abstract

The use of Active Magnetic Bearings (AMBs) in industrial applications has increased over recent decades as the technology has grown more mature, further aided by advancements and decreasing prices of the electronic components. AMBs are well suited to turbo-machinery applications offering several advantages over traditional types of bearings, including: no mechanical contact, no lubrication, low maintenance, low vibration level, high rotational speed and low energy consumption. These advantagesmake AMBs especially useful in challenging environments, for instance in subsea turbomachinery applications for oil and gas production, where reliability, low maintenance and high speed are of great importance. Annular seals are a key component in turbomachinery. They prevent internal flow leakage from high pressure to low pressure regions and improve the overall machine efficiency; in many applications, however, they also affect the system rotor-dynamic properties significantly. For this reason, the seal characteristics must be included in the rotor-dynamic stability analysis. Unfortunately, in many cases the seal forces are hard to model due to complex geometries of the seal and multiphase fluids. At present, there is no generally accepted method for determination of dynamic seal forces. Therefore, large uncertainties must be expected when modelling dynamic seal forces and consequently also in rotor-dynamic stability analysis. This thesis focuses on i) closed loop identification of uncertain AMB parameters, ii) closed loop identification of unknown stiffness and damping coefficients of a dynamicseal model and iii) the design of AMB controllers to handle dynamic seal forces. Controllers that can guarantee stability and performance in the presence of uncertainseal forces are of special interest. The main original contribution of the thesis is the framework for design of model based controllers for AMB systems subjected to uncertainand changing dynamic seal forces. An identification method has been developed, and experimentally validated, to obtain precise models of Linear Fractional Transformation (LFT) form for synthesising H1, μ and Linear Parameter Varying (LPV) controllers. The seal parameters and AMB dynamics are identified on-site without any need ofspecial equipment. A perturbed model of the combined AMB, rotor and seal system is constructed usingFinite Element Methods (FEM), modal reduction and LFT. It describes the dynamicbehaviour due to parametric uncertainties/changes of the damping and stiffness coefficient sof the seal and the uncertainties in the stiffness of the AMBs. Using different types of excitation signals, i.e. stepped sine, impulse and Pseudo Random Binary Sequence(PRBS), and optimisation in the time domain, the above mentioned parameters areidentified. Inserting the identified parameters in the known model structure results inaccurate models, which - when simulated - fit experimental data well. The perturbedmodel is further used for the robust controller synthesis to describe the uncertaintiesin seal forces and for LPV control synthesis, to compensate for known changes in seal forces due to changes in operating conditions. A rotor dynamic test facility with a rigid rotor, two radial AMBs and one annular test seal is used for i) closed loop identification of parameters in the AMB-rotor model, ii) identification of dynamic seal forces, iii) implementation of AMB controllers to compensate for dynamic seal forces. The stability and performance of the designed controllers are examined and compared to a reference decentralised PID controller. Controllers based on identified nominal seal models are shown to provide good compensation for the destabilising dynamic seal forces. Furthermore, significant performance improvement is shown when using a robust controller, which can handle changes in operational pressures better, in comparison to a nominal model based controller. Simulations using both type of model based controllers match experiments well.