Nanomanufacturing and Metrology

, Volume 1, Issue 1, pp 58–65 | Cite as

The Method for Restraining Laser Drift Based on Controlling Mirror

  • Shujie Liu
  • Shixin Zhang
  • Yubin Huang
  • Yayong Wang
  • Kuangchao Fan
Original Articles

Abstract

Based on piezoelectric ceramics (PZT), a feedback control method for compensating beam drift is proposed in this paper. The actuator can control the pitch and yaw angle of the light simultaneously, and its structure is very simple. The angular drift of laser is detected and separated in the designed optical path. The influence of interference noise is suppressed by moving average filter, and then, the beam drift is compensated through controlling mirror by PZT to suppress its influence on the stability of alignment measurement. The real-time control is realized by using proportional–integral–derivative (PID). The method of relay feedback is used to realize automatic tuning of PID parameters. Compensated by this method, the drift of quadrant photodiode detector (QPD1) in X and Y directions was reduced by 87 and 44%, respectively; that of QPD2 was reduced by 29.7 and 28.6%, respectively; and that of QPD3 was reduced by 78 and 70.3%, respectively. So the laser angular drift in the measuring optical path is well suppressed.

Keywords

Laser alignment Beam drift Feedback control Moving average filter PID 

1 Introduction

In ultra-precision machining and measuring equipment, the laser beam is often used as a measurement benchmark with its good single orientation, high brightness and high stability. However, in the propagation process, the light emitted from the laser often causes drift, including laser beam drift, angular drift and random drift [1, 2]. The main causes of laser beam drift include the temperature distortion of laser resonator and the inhomogeneous refractive index of air along the beam propagation path and its random variation. In order to improve the direction stability of laser beam, a lot of beam alignment methods with different applications have been proposed by researchers. In the laser alignment system for long-distance measurement, the spatial lines of interference and diffraction fringes generated by wave plates, phase plates and double slits are used as reference lines, using the characteristics of their insensitivity to drift for alignment. The typical methods include phase plate diffraction alignment and double-beam compensation alignment. Laser alignment technology, such as laser direction stabilization and single-mode fiber alignment, is widely used in ultra-precision machining equipment and measuring equipment. Although the alignment precision is high, those methods are of great difficulty. Generally, the environment of the laser alignment system is better, and the main reason of the laser beam drift is the temperature distortion of the laser resonator [3, 4].

In long-distance measurement, angular drift has more serious influence on measurement accuracy [5]. Based on the above, this paper proposes a method to automatically suppress the angular drift at the exit of laser, which provides a stable measuring reference for the laser measurement system. The purpose of this paper is to control the angular drift of the measuring light by using feedback control.

2 Optical Path Design and Analysis of Test Principle

As shown in Fig. 1a, the reflection occurs at the PZT adjustment unit after the laser beam is ejected. The reflected light is divided into two parts by a spectroscope. A part of the light is emitted along the original path for measuring light, and the other enters the detecting unit to monitor the laser angular drift in real time. The center of the photosensitive surface of the QPD (quadrant photodiode detector) is located at the focus of the convex lens. The angular drift of the beam is obtained after the light is passed through the convex lens. When the beam produces angular drift of the spot on the photosensitive plane of the QPD deviates from the central position of the four-quadrant detector, the offset reflects the angular drift of the laser and the angular is a spatial quantity, which can be divided into angular drift in the direction of X-axis drift and angular drift in the direction of Y-axis as shown in Fig. 1b. QPD2 and QPD3 consist of measurement units, and in this paper they are used to detect the state of light drift after controlled. The purpose of this paper is to use feedback control to reduce the angular drift of the measurement light by detecting the light angle drift from the detecting unit.
Fig. 1

Light path and testing schematic diagram

Figure 2 shows the three-dimensional diagram of the control unit. The PZT1 and PZT2 independently drive the point of a and the point of b on the movable plate and make the movable plate rotate around the point of b in order to control the pitch angle and yaw angle of the mirror on the movable plate.
Fig. 2

Three-dimensional diagram of the control unit

3 Principles of Mean Filter and Feedback Compensation

3.1 Analysis of Mean Filter

How to extract the drift component accurately and effectively from the weak detection signal which containing a large number of interfering noises is the key problem of the control part [6, 7, 8]. In this paper, the moving average filtering algorithm is adopted to extract the odd continuous sampling values from the actual measurement signals, and average values of them are taken to replace the original sampling values in order to filter out high-frequency noise. Its algorithm is as follows:
$$ y_{s} (i) = \frac{1}{2N + 1}(y(i + N) + y(i + N - 1) + \cdots + y(i - N)) $$
(1)
here ys(i) is the filtered signal value; i is the sampling signal sequence; 2N + 1 is the sampling length.
A set of actually testing data are taken as an example to illustrate the filtering algorithm for suppressing the random interference noise and extracting the useful signals as shown in Fig. 3. In the experiment, the sampling interval is 0.5. In Fig. 4 which is the local enlarged drawing of Fig. 3, the signal of n = 5 is the smoothest so we can think of it as the signal without random noise approximately. So the signal-to-noise ratio (SNR) can be computed and is shown in Table 1.
Fig. 3

Filtering analysis of laser drift data. a N = 0. b N = 1. c N = 2. d N = 3. e N = 4. f N = 5

Fig. 4

Local enlarged drawing of Fig. 3

Table 1

Signal-to-noise ratios of signals shown in Fig. 4

N

0

1

2

3

4

SNR

31.7142

32.1368

35.1188

37.3410

38.9847

With the analysis above, the original signals of n = 0 contains a lot of high-frequency random noise; n = 1 represents 3 point average filter, in which high-frequency random noise is decreased a little; and n = 2 represents 5-point average filter, in which the high-frequency noise has been obviously reduced. Then, the number of continuous sampling points average filter is increased, but the smoothness of the signal is not obvious, and more computer storage units will be occupied, which will reduce the real-time performance of the feedback control system. After comprehensive consideration, the average filter values of n = 2 are used instead of the actual sampling value.

3.2 The PID Control Process and Relay Feedback Auto-Tuning of PID Controllers

The error of e(t) is obtained by comparing the given value of x(t) and measured value of r(t). After the e(t) is calculated by the PID controller, the control value of u(t) is obtained which is used to drive the PZT adjustment unit and then change the direction vector of the reflected light in order to compensation of angular drift. In [9] engineering, the formula above is often represented as
$$ u\left( t \right) = K_{\text{p}} e\left( t \right) + \frac{{K_{\text{p}} }}{{T_{{\rm i}} }}\int_{0}^{t} {e\left( t \right)} + K_{\text{p}} T_{\text{d}} \frac{\text{d}}{{{\text{d}}t}}e\left( t \right) $$
(2)
here Kp, Ti and Td are, respectively, proportional gain, integral time constant and differential time constant in the PID controller. In this paper, a digital incremental algorithm of PID is used to implement feedback control.
$$ \begin{aligned} \Delta u\left( k \right) & = u\left( k \right) - u\left( {k - 1} \right) \\ & = K_{\text{p}} \left\{ {e\left( k \right) - e\left( {k - 1} \right) + \frac{T}{{T_{i} }}e\left( k \right) + \frac{{T_{\text{d}} }}{T}\left[ {e\left( k \right) - 2e\left( {k - 1} \right) + e\left( {k - 2} \right)} \right]} \right\} \, \\ & = K_{\text{p}} \left[ {Ae\left( k \right) - Be\left( {k - 1} \right) + Ce\left( {k - 2} \right)} \right] \\ \end{aligned} $$
(3)

From the formula above, we can see that the algorithm is simple and does not need to accumulate, but only needs to keep the three sampling values of e(t) at present and in the past. It is easy to obtain better control results. After proper weighting calculation of the three sampling values, the output increment of the controller can be obtained. Through adjusting the weighting coefficients, it is easy to realize parameter optimization and we can obtain a good control quality and precision. During the period of auto-tuning, the nonlinear control of relay characteristic is added into the closed-loop control to make the controlled process produce the limit cycle oscillation. The characteristic parameters (the critical proportionality coefficient Ku and the critical oscillation period Tu) of the mathematical model of the dynamic process are obtained from the curve of limit cycle oscillation, and then, the corresponding PID parameters are calculated by the Z–N tuning table of PID parameter. After the auto-tuning process is finished, the system will automatically switch to the PID control mode [10, 11, 12].

4 Experimental Results and Analysis

In order to verify the feasibility of the proposed scheme, an experimental system for detection of laser drift and feedback compensation control is built, as shown in Fig. 5. In the experiment, QPD1 detects the laser drift and sends it to the PID controller as feedback to realize the closed-loop feedback compensation of the beam drift. QPD2 and QPD3 are used to check the beam stability of measured light after control. The sampling period is 0.5 s, the recording data interval is 4 s, and the continuous acquisition time is 3.5 h. Figure 5 shows the results of the measured beam drift before and after feedback control.
Fig. 5

Diagram of experimental installation. a Schematic diagram of feedback control experiment. b Overall diagram of experimental installation. c Enlarged drawing of the part A

As shown in Fig. 6, the measured beam drift is well suppressed after control.
Fig. 6

Comparison of plots between before control and after control

In order to quantify the results before and after the control, the drift statistic is used to reflect the control effect. Tables 2 and 3 show the percentage decline of the indicators after the control. As we can see, using the peak value of QPDs to evaluate the control effect of beam drift is more stringent and reasonable. The peak value of QPDs decreased after feedback control. The drift of QPD1 in X and Y directions is reduced by 87 and 44%, respectively; that of QPD2 is reduced by 29.7 and 28.6%, respectively; and that of QPD3 is reduced by 78 and 70.3%, respectively.
Table 2

Measured value of QPDs

Index value

Before control

After control

QPD1 (″)

QPD2 (μm)

QPD3 (″)

QPD1 (″)

QPD2 (μm)

QPD3 (″)

X direction

 P–P value

11.162

4.647

62.214

1.451

3.266

13.655

 Mean value

4.607

1.846

29.836

− 0.097

− 0.753

− 4.835

 Std value

2.863

0.956

19.599

0.203

0.464

2.989

Y direction

 P–P value

3.050

4.143

24.489

1.707

2.957

7.262

 Mean value

0.966

− 1.593

12.706

0.070

0.430

− 1.007

 Std value

0.629

0.792

6.481

0.258

0.340

0.978

Table 3

Interpretation of results

Ratio of before and after control

QPD1 (%)

QPD2 (%)

QPD3 (%)

X direction

 P–P value

87

29.7

78

 Mean value

97.9

59.2

83.8

 Std value

92.9

51.5

84.7

Y direction

 P–P value

44

28.6

70.3

 Mean value

92.8

73

92

 Std value

59

57

85

5 Conclusion

In this paper, the active suppression method based on PZT is used to suppress the angular drift at the laser emitting end. It can improve the accuracy of the long-distance measurement because the angular drift has been suppressed before the laser enters the measuring light path. The relay feedback technique is used in the auto-tuning of PID parameters, which will ensure the control parameters can be easily obtained. The method can be applied to the measurement of five degrees of freedom in machine tools, which will provide a stable laser beam for measuring optical path and improve the measurement accuracy.

Notes

Acknowledgements

The authors gratefully acknowledge the financial support of China National Key Research and Development Plan Project (No. 2017YFF0204801) and Special Fundamental Research Funds for Central Universities of China (No. DUT17GF214).

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Copyright information

© International Society for Nanomanufacturing and Tianjin University and Springer Nature 2018

Authors and Affiliations

  • Shujie Liu
    • 1
  • Shixin Zhang
    • 1
  • Yubin Huang
    • 1
  • Yayong Wang
    • 1
  • Kuangchao Fan
    • 1
    • 2
  1. 1.School of Mechanical EngineeringDalian University of TechnologyDalianChina
  2. 2.Department of Mechanical EngineeringNational Taiwan UniversityTaipeiChina

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