In the current spectral simulation method based on a digital micromirror device （DMD）， the spectral simulation units have different bias properties and nonlinear modulation； thus， a spectral simulation method for multi-color temperature modulation is lacking. This paper presents a fuzzy proportional-integral-derivative （PID） control-based stellar spectral simulation method. First， the DMD working matrix， spectral modulation weight matrix， spectral distribution function matrix， and target spectrum matrix are constructed. Next， a spectral distribution function fitting algorithm based on a genetic algorithm-optimized backpropagation （BP） neural network is studied. The BP neural network algorithm and the basic elements of the genetic algorithm are designed and used to achieve spectral distribution function fitting in the peak wavelength region of 400-800 nm. Then， a spectral simulation algorithm based on fuzzy PID control is proposed. The fuzzy set and affiliation function are selected， and the fuzzy inference and defuzzification rules are formulated. The fuzzy PID controller is simulated and analyzed， and the results indicate that the overshoot of fuzzy PID control is reduced by 90.7% and the regulation time is shortened by 69.4% compared with those of PID control. Finally， the simulation accuracy of the color temperature spectral distribution curve in the range of 3000-11 000 K is verified via experiments. According to the results， the spectral simulation error is better than ±4.21%. Compared with the PID control， the maximum spectral simulation accuracy of fuzzy PID control at 3 000， 6 500， and 11 000 K is increased by factors of 2.31， 1.71， and 2.02， respectively. The proposed method can increase the spectral simulation accuracy， providing the theory and foundation for the development of high-precision star-sensitive devices.