The time-modulated Fourier transform spectrometer completes spectral detection through the scanning mirror movement. To satisfy the t of low-speed and high-precision scanning, a linear quadratic optimal controller with minimum relative performance error is proposed. The ratio of the tracking error weighting factor Q and the energy consumption weighting factor R in the optimal controller is optimized by simulation, and when the ratio is 1:2, the speed instability of the scanning mirror in the uniform speed section is 2‰.
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