Recently, magnetic bearings have been applied to many rotating machines such as turbo-molecular pumps, cooling gas compressor, flywheel energy storage systems. And high-power density is the future development trend of these machines, which demands that the rotor characterizes slender and high rotating speed and operates above the critical speeds. However, it is a big challenge for a flexible rotor to pass the bending critical speeds and operate above the critical speeds steadily and reliably. Based on above reasons, this article presented the design, modeling, and analysis framework of a flexible rotor test rig with active magnetic bearing (AMB). Special attention was paid to the flexible rotor dynamic model development, dynamic analysis, and model-based robust control design. First, the main structure features were illustrated in detail, including the key dimensions and parameters of the AMB components and rotor. Then models of components including power amplifier and displacement sensor were developed. The finite element method based on Timoshenko beam theory was applied to the rotor dynamics model. The dynamic analysis of the rotor is the foundation of the controller design. Hence, modal analysis had been done, obtaining rotor dynamic properties via synthesis of natural frequency, mode shapes, and Campbell plots. Reduced order model was obtained for controller design convenience. A robust H N controller was designed based on the system model and controller performance was validated with numerical simulation. The results indicate that the controller has good vibration suppression performance and makes the flexible rotor pass the first bending critical speed.
Aiming at how to specify the fundamental trade-off between robust stability and nominal performance of mixed H 2 /H N control as well as lack of experimental studies on vibration control for the maglev actuator in microgravity vibration isolation system, a mixed H 2 /H N output feedback controller based on the linear matrix inequality method is designed and analyzed. This article establishes a state-space realization for a one-dimensional vibration isolation system and the Hnorm performance indices are identified and calculated. Furthermore, the curves of threshold values and true values of H N and H 2 norms are plotted to specify the relationship between the system's robust stability and nominal performance. Therefore, the threshold value of system's H N norm is identified through repeated simulations, and the state-space realization of optimal controller with minimum H 2 norm under the constraints of H N norm threshold value is obtained. The vibration control experimental apparatus of one-dimensional control system is designed and manufactured to test the actual application of mixed H 2 /H N controller for the maglev actuator. The result presents that the designed mixed H 2 /H N control has a better performance in suppressing acceleration vibration and has a higher attenuation amplitude than cascade proportional-integral-derivative control at each corresponding frequency, which proves the practicability and effectiveness of the design method.
The resonance vibration control of flexible rotor supported on active magnetic bearings (AMB) is a challenging issue in the industrial applications. This work addresses the application of robust control method to the resonance vibration control for AMB flexible rotor while passing through the critical speed. This model-based method shows great superiority to handling flexible mode vibration, which can guarantee robust stability and performance when encountering modal perturbation. First, the designed flexible rotor-AMB test rig is briefly introduced. Then the system modeling is described in detail including flexible rotor, power amplifier, displacement sensors and magnetic actuator and rotordynamics are analyzed. Model validation is carried out by sine sweeping test. Finally, the -synthesis controller is designed. The simulation and experimental results indicate that the designed -synthesis controller, which shows great robustness to modal perturbation, can effectively suppress the resonance vibration of flexible rotor and achieve supercritical operation.
In modern industries, high-speed motors and generators have received great attention, and they are widely used in micro turbine, centrifugal compressor, blower, etc. However, the resonance vibration of flexible rotor will become a challenging issue when the rotor has to operate above the first bending critical speed. In this paper, a phase compensation method is proposed to improve the damping level of the flexible rotor around the first bending critical speed. The dynamic characteristics of the flexible rotor are analyzed, and the modal frequency is obtained. The rotor finite element model is verified by the modal test. Based on Proportion-Integration-Differentiation (PID) controller, the phase of the control system is shaped with different general filters to improve the damping level of the flexible rotor around the first bending critical speed. The simulation and experimental results indicate that the first bending mode damping of rotor is obviously enhanced by phase compensation. The phase compensation method can effectively suppress the resonance vibration of the rotor and make the rotor smoothly pass the first bending critical speed, achieving supercritical operation.
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