## 3 Laser Processing Control Method for MCR Frequency Modulation  
### Workflow of Laser Processing Control System for MCR Frequency Modulation  
The automatic operation process of the laser processing control system for MCR frequency modulation is depicted in Figure 3. It mainly includes the following steps: (1) Parameters are set. (2) The carrier platform moves to the feeding and discharging position. The wafer of the MCRs is sucked tightly by a vacuum pump under the carrier platform after positioning is completed. (3) The left and right top pins return to the starting positions, and the carrier platform is transported to the machining position by the carrying device. (4) Each MCR is in contact with the frequency detection probe for frequency detection. (5) The laser performs frequency modulation on the MCRs. (6) After the frequency modulation of the current MCR is completed, the carrier platform automatically transports the wafer to the next row for processing until all 16 rows of the MCR are processed. (7) After the frequency modulation of all the MCRs are completed, the carrier platform descends, the vacuum pump of the suction cup is closed and the moving device moves the carrier platform to the reclaiming and discharging position. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Performance Requirements** & **Evaluating Indicator** & **Index Value** \\ \hline Reliability & Fault alarm rate, \(\tau\) (Times/Week) & \(\tau<1\) \\ Over-frequency rate & Over-frequency rate of laser processing for frequency modulation, \(\upmu\) & \(\mu<1.56\%\) \\ Efficiency & Frequency modulation time of single row of MCRs, \(t\)(s) & \(t<320\) s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance requirements and indexes of laser processing control system for MCR frequency modulation. In the automatic operation of laser processing for MCR frequency modulation, each row of MCRs needs laser frequency modulation multiple times to achieve the target frequency value. The frequency modulation completion time of each MCR may be different. Therefore, in the frequency modulation process of each row of MCRs, the frequency modulation detailed process is depicted in Figure 4. According to the detected frequency and the set range of processing, the MCRs are divided into rejects, workable products and qualified products. The reject is the MCR of which the frequency cannot be adjusted to reach the target frequency range. The workable product is the MCR of which the frequency can be adjusted to reach the target frequency range. The qualified product is the MCR of which the frequency is within the target frequency range. The reject will be marked as the defective product, and frequency modulation operation will not be performed. According to the difference between the detected current frequency and the target frequency, workable MCRs will be laser-processed to modulate their frequencies. After each round of laser frequency modulation, frequency detection will be carried out again. According to the detected frequency, the workable MCR will be processed again until the maximum number of processing times is reached. After reaching the maximum number of processing times, the last frequency detection will be carried out and the unqualified products will be marked as rejects. Motion Control Method of Laser Processing Carrier Platform for MCR Frequency Modulation 3.2.1. Linear Motor Mathematical Model of Laser Processing Carrier Platform for MCR Frequency Modulation  
In the laser processing control system for MCR frequency modulation, the positions of laser and frequency monitoring probe are fixed, so only when the MCR wafer moves to the target position can the laser processing for frequency modulation be carried out. In order to ensure motion accuracy, the platform is driven by the linear motor. In order to simplify the analysis of the linear motor, it is assumed that the permanent magnets in the linear motor are uniformly distributed, and the effects of eddy current and magnetic circuit saturation hysteresis loss are ignored.