The traditional PID (Proportional-Integral-Differential) method, when used to control turbo shaft engine acceleration gives dynamic performance that is, in our opinion, not quite satisfactory.

With the development of science and technology, the performance of turbine shaft aeroengine is constantly improved, its power turbine rotor is developing towards high speed and large length-to-diameter ratio, specified operating speed is generally over bending critical speed, structure is becoming more and more complex.

The convergence problems of solving the nonlinear equations of aero turbine engines were study in detail,the common non-convergence cases were given and the mechanism was analyzed,based on Newton method,an advanced solutions for overcoming the common non-convergence problems was presented:variable step Newton method(VSN).