Permanent magnet synchronous motor (PMSM) servo system is the control and execution mechanism of spacecraft, and its precise modeling is of great practical significance for improving the performance of the spacecraft. A comprehensive model considering elasticity, backlash, and friction was established based on the structural composition and transmission characteristics of spacecraft. Firstly, an elastic-dead zone model was established based on the transmission characteristics, with two mass elastic and gear backlash dead zones as the main features. Then, an improved LuGre friction model was established that considers the effects of vibration and environmental temperature, and the three models were organically combined. Finally, a method for identifying nonlinear parameters of the system using sinusoidal sweep and the least squares method was proposed, and the accuracy of the constructed model was verified. The experiment shows that the error of the simulation results is consistent with the experimental results. This method can precisely obtain the servo system model, providing theoretical support for control method research.