A composite controller can achieve stable suppression of high-bandwidth beam jitter of large-aperture tilt mirrors. The composite control method comprises multiple control links in series or parallel, and the controller is large-scale. There are many jitter analysis results for a single high-frequency narrowband; however, the correction of complex-frequency beam jitter requires further consideration of the mutual amplification and traction between multiple control links in the composite controller. Therefore, parameter matching is a challenging problem in the design of composite controllers. Accordingly, in this study, a parameter optimization method is proposed based on stochastic parallel gradient descent assistance to achieve high-bandwidth and high-precision control of large-aperture tilt mirrors using a composite controller.

To minimize the beam jitter residual variance, the power spectrum characteristics of the open-loop beam jitter to be corrected are first analyzed, and a composite controller is designed accordingly, including a proportional integral (PI) controller and dual two-order filter. Subsequently, the residual variance of the beam jitter is selected as the cost function to optimize the parameters of the composite controller using the stochastic parallel gradient descent method. Finally, after several iterations, optimal adjustment of the control performance of the composite controller is achieved. After parameter optimization, the correction and residual variance suppression abilities of the composite controller are verified using the Bode diagram and power spectrum density.

For the beam jitter signal of the multifrequency narrowband power spectral density function (Fig. 4), the design of multiple controller links includes a PI controller, 30-Hz, 70- Hz, 146-Hz dual two-order filters, 70-Hz advanced phase compensation, and resonance elimination model. The initial parameters of each link of the composite controller are designed accordingly (Table 1). The composite controller corresponding to the initial parameters suppresses the residual variance from 117.48 μrad² to 84.58 μrad², with a residual variance suppression ratio of only 28%, and has a significant amplification effect on the high-frequency jitter. After 1000 iterations using the stochastic gradient descent method, the transfer function of beam jitter suppression in multiple controller links with the optimized parameters is obtained (Table 2). The jitter residual variance of a single tilting mirror closed-loop beam is suppressed from 117.48 μrad² to 44.35 μrad², and the residual variance suppression ratio reaches 62.2%. Furthermore, jitter is significantly suppressed near the low-frequency broadband and 30 Hz, 70 Hz, and 146 Hz narrowbands (Fig. 9). An optical test platform is set up (Fig. 10) to verify the effectiveness of the optimization parameters. The beam jitter composite controller with optimized parameters can effectively suppress the jitter of 30 Hz and 70 Hz and low-frequency broadband. The jitter at 146 Hz is partially suppressed, and there is a certain amplification at high frequency. The magnification factor is small and does not exceed 6 dB. The beam jitter residual variance is suppressed from 200.05 μrad² to 93.93 μrad². Compared with the composite control algorithm with initial parameters, under the same correction conditions, the beam jitter suppression performance of a single large-aperture tilt mirror is improved by 34.2 percentage points after optimization by the proposed stochastic gradient parallel descent auxiliary method.

The experimental results show that the residual variance-suppression ratio of the high-bandwidth beam jitter of a single large-aperture tilt mirror is 53.1%, which is comparable to that of the traditional method based on two tilt mirrors. This method can effectively reduce the complexity of the system and contribute to the high-bandwidth and high-precision control of beam jitter by large-aperture tilt mirrors. Furthermore, it can contribute to an optimization and evaluation method for the design of beam jitter controllers.