In practical terms of model identification for optical infrared telescope servo system, the measured states often contain noise. In order to improve accuracy of modeling, a sparse identification method based on Spark Identification of Nonlinear Dynamics with Control (SINDYc) algorithm was proposed. For the telescope servo system, theoretical analysis and numerical simulation of the SINDYc algorithm were carried out. The state variable curves of the telescope servo system model under different noise levels were compared, and the determination coefficient curve of the identification model under different noise levels was fitted. Based on the antarctic telescope experimental platform, sine and square wave signals were designed as excitation signals for model identification experiments, and the modeling accuracy of the SINDYc algorithm was experimentally verified. The prediction results of the numerical simulation model show that the identification accuracy of SINDYc algorithm is above 0.99 when the noise level is below 20%. When the noise level is below 10%, the maximum deviation is within 5% of the signal amplitude. The identification experimental data show that the accuracy of model prediction is 0.9857 and 0.9952 under the excitation of two different signals. The effectiveness and accuracy of the sparse identification method based on the SINDYc algorithm are confirmed by numerical simulation and experimental validation. The obtained model by this identification method can provide a good analytical model for the analysis and controller design of future large-aperture optical infrared telescope control systems.