The use of complex variables and frequency characteristics for stability analysis of magnetically suspended flywheels

Magnetic bearings are capable of providing a long life and contact-free operation of high-speed flywheel rotors, and it is necessary to obtain the system stability information at different rotation speeds. To reduce the system order, this article adopts complex variables to build the system dynamic model, and the frequency characteristics of the controlled plant lead to a simple system stability judging method which can directly derive the stable speed range. After the in-depth analysis of the positive and negative frequency characteristics of the controlled plant influenced by rotation speeds, some stability conclusions based on linear controllers with cross feedback are developed, which also reveal limitations of linear controllers to stabilize the magnetically suspended flywheel systems and lead to some novel definitions of relative stability margin. Simulations and experimental results demonstrate the effectiveness and superiority of the proposed stability analysis method.