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In order to achieve the fast response of turboshaft engine combined with torsional vibration, a predictive controller of helicopter/engine based on the least mean square adaptive torsional vibration suppression is proposed and designed. First, in order to make up for the insufficiency of conventional notch filter on torsional vibration suppression with changeable frequency under variable rotor speed, an adaptive one based on least mean square is presented in the process of helicopter autorotation downward. Then, based on the least mean square adaptive filter, a predictive controller based on the support vector regression is proposed to compensate for the dynamic control performance in helicopter autorotation recovery process. It is shown that least mean square adaptive filter can suppress all low-order torsional vibrations with amplitude less than 15% in comparison with the notch filter, which proves the more remarkable ability of adaptive torsional vibration suppression. Meanwhile, the droop of power turbine speed can be reduced to less than 0.3% with the steady-state error no more than 0.01% by adopting the predictive controller based on least mean square adaptive torsional vibration suppression. The fast response and high-quality control of turboshaft engine has been realized.