模糊PID控制的恒星光谱模拟

Simulation of stellar spectrum controlled by fuzzy PID

针对目前基于数字微镜(Digital Micromirror Device,DMD)的光谱模拟中,光谱模拟单元具有不同偏态性质且存在非线性调制等特点,提出了一种适用于多种色温调制的基于模糊PID控制的恒星光谱模拟方法。构造了DMD工作矩阵、光谱调制权重矩阵、光谱分布函数矩阵以及目标光谱矩阵,建立了基于DMD的光谱模拟数学模型;然后,研究了基于遗传算法优化BP神经网络的光谱分布函数拟合算法,在400~800 nm的峰值波长内实现了光谱分布函数拟合;提出了一种基于模糊PID控制的光谱模拟算法,选择模糊集合与隶属度函数,制定了模糊推理以及解模糊化规则。仿真分析了模糊PID控制器性能,结果表明与PID控制相比,模糊PID控制的超调量减小90.7%,调节时间缩短了69.4%。最后,实验验证了3000~11000 K色温光谱分布曲线的模拟精度,结果表明:光谱模拟误差优于±4.21%;相较于PID控制,模糊PID控制在3000,6500以及11000 K色温的最大光谱模拟精度分别提高了2.31倍,1.71倍和2.02倍。所提出的方法可以进一步提升光谱模拟精度,为高精度星敏感器的地面标定提供理论与技术基础。

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 3000-11000 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 3000,6500,and 11000 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.