Numerical simulation of piezoelectric bimorph mirror control strategy applied to synchrotron radiation

In order to improve the control degree of freedom and surface shape accuracy of the piezoelectric bimorph mirror (PBM) in synchrotron radiation, and to solve the problem of abnormal fluctuations of the calculated voltages (overfitting) affected by noise caused by the excessive number of piezoelectric actuation units, the PBM model was established and simulation control was carried out. The 36 sets of piezoelectric response equations were obtained through the finite element simulation, and the mathematical model of surface shape and voltage was constructed. To compensate the mirror surface distortion caused by gravity, the control effects of two voltage solutions using least square method (LSM) and Tikhonov regularization were analyzed and compared by obtained ellipse shape. The results show that after using Tikhonov regularization inversion, the surface shape control error is reduced by 21.7% compared with LSM, and the maximum voltage fluctuation between adjacent electrodes is reduced from 1.019 kV to 0.174 kV, which meet the actual requirements of engineering. The system is robust to tested noise, and has more superior application value than LSM.