Limit cycle of low spinning projectiles induced by the backlash of actuators

Limit cycles with large amplitudes are harmful to the performances of spinning projectiles. In this paper, the backlash of the gear drives outside the control loop of the actuator that may lead to a stable limit cycle of low spinning projectiles in the free flight phase, which means the input command of the canard is zero, is investigated. The backlash nonlinearity is simplified as a relay model and is represented by the describing function method. Both the sufficient condition for the existence of a stable limit cycle and the equations to calculate the amplitude and frequency of the motion are obtained and then validated by numerical simulations. Meanwhile, the effects of the backlash in the controlled phase are studied as well. It is noted that the harmful impact of the backlash in the controlled phase is much less than that in the free flight phase.