# The Method for Restraining Laser Drift Based on Controlling Mirror

## 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

*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.

*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.

## 3 Principles of Mean Filter and Feedback Compensation

### 3.1 Analysis of Mean Filter

*y*

_{s}(

*i*) is the filtered signal value;

*i*is the sampling signal sequence; 2

*N*+ 1 is the sampling length.

*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.

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

*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

*K*

_{p},

*T*

_{i}and

*T*

_{d}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.

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 *K*_{u} and the critical oscillation period *T*_{u}) 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

*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.

Measured value of QPDs

Index value | Before control | After control | ||||
---|---|---|---|---|---|---|

QPD1 (″) | QPD2 (μm) | QPD3 (″) | QPD1 (″) | QPD2 (μm) | QPD3 (″) | |

| ||||||

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 |

| ||||||

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 |

Interpretation of results

Ratio of before and after control | QPD1 (%) | QPD2 (%) | QPD3 (%) |
---|---|---|---|

| |||

P–P value | 87 | 29.7 | 78 |

Mean value | 97.9 | 59.2 | 83.8 |

Std value | 92.9 | 51.5 | 84.7 |

| |||

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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