Design of high-precision laser direct writing digital servo filter

Laser direct writing technology is an ultra-precision processing technology that has been widely used in recent years. This technology uses a laser beam with variable intensity to perform regular high-precision scanning on the surface of the substrate. During the scanning process, the photolithography substrate moves with the carrier platform. Therefore, the quality of the photolithography element depends on the positioning accuracy of the carrier platform and the stability of the movement, and the rapidity of the photolithography element depends on the responsiveness of the system.
The motion controller based on digital servo is the key to the ultra-precision positioning system. Since the digital servo filter is the core of the digital servo motion controller, the design of the digital servo filter will affect the positioning accuracy of the system. The digital
servo filter refers to the closed-loop control and regulation of the system using digital technology, and all control adjustments are implemented in software. The full softwareization of the regulator enables many control ideas and means in control theory to be applied. At the same time, it is easy to use software to complete the liberalization of parameters and the self-diagnosis function of faults, which greatly improves the control performance of the system, thereby overcoming the shortcomings of the analog closed-loop servo system, such as the difficulty in separating the signal and noise of weak signals, the difficulty in improving the control accuracy, the susceptibility to mechanical friction and temperature, and the zero drift error of the position loop control.

1 Servo control system structure and analysis
1.1 Servo control system structure
The hardware structure of the entire servo control system is shown in Figure 1. The upper device consists of a DSP processor and a D/A conversion module, and the servo unit consists of a Yaskawa servo driver. The entire system is a closed-loop servo motor control system. The DSP processor generates a digital pulse signal of a trapezoidal motion curve, which directly drives the D/A converter to generate an analog voltage through a designed digital filter, and drives the servo motor through the servo unit. The position and speed signals in the actual motion are fed back by the motor to the optical encoder, and the photoelectric encoder generates a digital signal, which is then transmitted to the DSP for collection and processing.

1.2 System Analysis
The key to this solution is to solve the problems of viscous friction between the motor shaft and the load and external interference to the motor and converter. Due to the existence of friction ring and external interference, the dynamic and static performance of the system is greatly affected, mainly manifested as creeping at low speed, large static error or limit cycle oscillation in steady state. In order to meet the requirements of laser direct writing, the system must also have the characteristics of fast response speed, short positioning time, and high steady-state accuracy. If the starting speed is too slow or overshoots, and the stop time is too long, the system will have strong oscillation and high noise.

2 Design of digital filter
2.1 Design of digital servo filter model
After a large number of experiments and analysis of the system, it was found that the use of PID control method for position deviation control can improve accuracy and step response; adding speed and acceleration feedforward compensation control method can improve the steady-state accuracy of the system; adding friction compensation can overcome the influence of friction. Therefore, this solution is not designed to be a composite control system that uses position error for closed-loop control and uses given position signal for open-loop control.
Then the system control output is U(t)=Up(t)+Uva(t)+Uf(t), where Up(t) is the PID controller, Uva(t) is the speed and acceleration compensation controller, and Uf(t) is the friction compensation controller.

The control law of the PID servo filter is shown in Figure 2.

In Figure 2, Kp is the proportional gain, Ki is the integral gain, Kd is the differential gain, Kvff is the velocity feedforward gain, Kaff is the acceleration feedforward gain, Kf is the viscous friction coefficient, En is the position deviation, Vt is the velocity at time t, At is the acceleration at time t, and the output B static error is mainly used to compensate for the influence of gravity on the control axis. The analog quantity corresponding to the filter output is limited by the output saturation controller.

2.2 Parameter Adjustment
In the position PID regulator, the size of the proportional gain Kp determines the rapidity of the system, and the role of the integral gain Ki is to eliminate the static error of the system. The role of the differential gain Kd is to increase damping and reduce oscillation. The adjustment process is to adjust Kp first, then adjust Ki, and then adjust Kd. When setting the Ki gain for the first time, if Ki is set to a non-zero value, it will cause a sudden "jump". To avoid this, it is necessary to set the integral limit (saturation controller of the integral part) to 0, set Ki to the expected value, and then set the integral limit to the expected integral limit. This clears all previous integral values, so that the integral starts to operate smoothly from the previous point. Then adjust Kvff and Kaff to improve the steady-state accuracy of the system. Finally, adjust Kf to overcome the influence of friction.
Adjust Kvff in the startup phase. If Kaff is too large, the speed will be too fast and cause position overshoot. Adjust Kvff in the deceleration phase. If Kaff is too small, the positioning time will be too long. According to the optimal control concept, if the system starts at maximum acceleration, moves at maximum speed, and brakes at maximum deceleration, it can reach the coordination point in the shortest time without overshoot. Therefore, the parameters should be set according to the three stages of start-up, uniform speed, and deceleration.

3 MATLAB design and simulation
3.1 Simulation module design
According to the design principle, the deviation counting module in Figure 1 is equivalent to a PID controller with feedforward compensation, and is designed as the corresponding part in Figure 2, and the D/A converter is equivalent to discrete data through a zero-order holder; the Yaskawa servo drive is equivalent to the speed loop and current loop; the output signal is observed using a simulation oscilloscope. Therefore, the entire servo three-loop PID simulation principle is shown in Figure 3.

Among them, rin(k) is the position input signal at sampling time K. In order to simulate the actual effect, the input rin(k) is set to an irregular position signal, and the input command is a sine superposition signal; drin(k) is the speed input signal at sampling time K; ddrin(k) is the acceleration input signal at sampling time K, and drin(k+1)=(rin(k+1)-rin(k))/ts, ddrin(k+1)=(drin(k+1)-drin(k))/ts.
3.2 Simulation waveform
For high-precision laser direct writing, its performance mainly depends on the stability of speed, responsiveness and accuracy of position. Therefore, in the simulation of Figure 3, the control system parameters should be adjusted multiple times according to the actual situation, and after analysis and comparison, a tracking diagram with stable speed and accurate position is obtained, and its simulation waveform is shown in Figure 4.

Figure 4(a) shows the speed tracking result. The set speed and the actual speed coincide. The speed is stable and controlled within 0.1%. There is a sudden "jump" in speed near time 0, which is due to the lack of adjustment of the integral limit. Therefore, in actual situations, the integral limit (saturation controller) should be set to 0, Ki should be set to the expected value, and then the integral limit should be set to the expected integral limit.
Figure 4(b) shows the position tracking result. The actual output position coincides with the set target position. The position positioning is highly accurate and the accuracy is controlled within 0.1%.
The simulation results show that under friction conditions, there is no "flat top" phenomenon in position tracking and no "dead zone" phenomenon in speed tracking. The position tracking has high positioning accuracy and the speed tracking has high steady-state accuracy.

4 Software Implementation
The servo unit module is designed by the servo driver, and its parameter adjustment can be set in the servo driver. Please refer to the driver user manual for details. The PID digital filter + feedforward composite control system is implemented by DSP2812. The operation process is: first generate the MATLAB language of the PID composite simulation module into the C language in CCS, then transplant it into the CCS software, and modify it according to the PID control formula principle combined with the software design process.

5 Conclusions
The servo control system structure is introduced, the friction link and actual requirements in the system are analyzed, and then the servo PID digital filter is designed according to the control principle. The digital filter is verified to have stable speed through MATLAB simulation; the position tracking error converges to zero. And experience on adjusting control parameters is obtained from it. The final actual results show that the input and output time difference of the entire system is less than 100 Ls; there is no noise and oscillation; the positioning accuracy error is controlled within the range of ±1μm.