The invention relates to a fractional order self-sustaining electromechanical seismograph system acceleration stability control method with constraints, and belongs to the field of seismic exploration. The fractional order self-sustaining electromechanical seismograph system acceleration stability control method comprises the following steps of: S1, carrying out system modeling, which is implemented by establishing a mathematical model of a fractional order self-sustaining electromechanical seismograph system according to a Newton's second law and a Kirchhoff's law, and defining constraint conditions; S2, and designing an acceleration stability controller, wherein the design is implemented by constructing an acceleration feedforward controller and an optimal feedback controller, the acceleration feedforward controller is integrated by a molding behavior function based on a fractional order inversion method, a fuzzy wavelet neural network and a tracking differentiator, and the optimal feedback controller is formed by fusing a fuzzy wavelet neural network and an adaptive dynamic programming strategy. According to the fractional order self-sustaining electromechanical seismograph system acceleration stability control method, the boundness of all signals of a closed-loop system is ensured, the safe operation of the system under the constraint condition is ensured, and meanwhile, chaotic oscillation can be suppressed and a minimum cost function can be realized.