Limited torque spinup of an unbalanced rotor on an elastic support

Consider an oscillator with an embedded unbalanced rotor which starts from rest and spins up under the influence of a motor with limited torque. For the case of a constant torque which is small relative to the size of the unbalance, the rotor speed will stall near the resonant frequency of the oscillator-this is referred to as “capture”. For larger constant torque, the rotor will spin up through resonance without stalling-this is referred to as “pass-through”. For the constant torque capture case, the authors develop a feedback control strategy which exploits unstable dynamic behavior near resonance in order to drive the system to a state favorable for pass-through-a state which cannot be reached using constant torque. Numerical verification shows that using this feedback strategy as opposed to constant torque, the motor needs approximately one tenth of the torque capability to achieve marginal pass-through