Flywheel system which uses magnetic bearing is modeled as follows. The rotor shaft is assumed to be rigid body and magnetic bearing which suspend the rotor shaft is changed to spring and damper.
10 electro magnets are needed for the system. The equation of motion is derived by above model and control problem is solved using optimal control theory and suboptimal control theory.
Computer simulation is done and the results are as follows. The results show that the settling time is very fast $(3×10^{-3} -5×10^{-3}$ sec) because of high stiffness in the feedback system. By decreasing unbalance stiffness from -500N/mm to -300N/mm axially, -320.283N/mm to -220.283 N/mm radially, settling time increased from $3×10^{-2}$ sec to $4×10^{-2}$ sec. By decreasing weighting matrix for input, the feedback system becomes underdamped system.
