PDH frequency tracking method based on system identification and fuzzy PID control scheme

Abstract

The present invention discloses a PDH frequency tracking method based on system identification and fuzzy PID control scheme. It includes: obtaining the frequency tracking error signal of the PDH system constructed based on the optical fiber resonant cavity, processing the signal, and extracting the error signal reflecting the laser frequency and the resonant frequency of the resonant cavity; further based on the system identification theory, taking the signal in the error linear interval as the output, taking the input voltage signal of the laser PZT as the input, performing system identification on the controlled module composed of the laser PZT and the frequency discrimination system composed of the resonant cavity, the bandpass filter, the mixer, and the low-pass filter, and obtaining the transfer function of the module; based on the system identification result, taking the module as the controlled module, taking the PZT control voltage signal that can make the error signal 0 as the theoretical input, and building a new PDH frequency tracking system; combining the fuzzy PID control scheme, by reasonably designing the membership function and the fuzzy rules, the PID parameters of the new PDH frequency tracking system are optimized and adjusted. The present invention can solve the problems of low tracking accuracy and poor long-term stability caused by the difficulty in obtaining the transfer function of the control module in the traditional PDH scheme.

Description

Technical Field

[0001] The present invention belongs to the technical field of precision instrument manufacturing and precision test and measurement, and more specifically, to a laser frequency tracking method and device based on PDH (Pound-Drever-Hall) technology of system identification and fuzzy PID (fuzzy Fussy Proportional-Integral-Derivative, referred to as fuzzy PID) control scheme. Background Art

[0002] With the development of photonic technology and precision manufacturing technology, optical resonant cavity, as an important optical device in modern optical applications, has a wide range of application value in research fields such as laser physics, quantum optics, laser spectroscopy, and precision measurement. In these applications, the resonant frequency of the resonant cavity reflects key information. Therefore, in many complex optical systems, it is necessary to lock the resonant frequency of the laser and the optical cavity. This process usually requires the generation of an error signal that is proportional to the difference between the laser frequency and the optical cavity resonant frequency, and controls the frequency tracking and locking through a servo control system. However, due to factors such as equipment errors and environmental influences, the laser cannot achieve stable tracking of the resonant frequency of the resonant cavity. Therefore, it is critical to research and develop a technology that enables the laser to accurately track the resonant frequency over a large range.

[0003] Domestic and foreign scholars have conducted a lot of research on the problem that the laser frequency is difficult to accurately track and lock the resonant frequency of the resonant cavity. The accurate tracking and locking of the resonant cavity frequency, which has key applications in many fields such as optical metrology and optical sensing, is in the blank area of ​​the existing technology. New technologies and methods are urgently needed to further improve the frequency tracking and locking accuracy. Among them, PDH technology, as the most widely used frequency stabilization technology, has been realized after the continuous efforts of many researchers. However, there are still many problems with PDH technology, which hinders the application and functionalization of PDH technology. In traditional PDH systems, the resonant frequency of the resonant cavity is usually used as a reference, and the PZT actuator of the laser is driven by a PID servo circuit to track the resonant cavity, while the frequency discrimination module is the controlled object. However, this scheme has many problems. First, the resonant frequency is easily affected by environmental factors such as temperature and vibration. Second, the PZT used as an actuator and its related circuits have significant delays. Finally, traditional schemes often regard the frequency discrimination mechanism as a linear mechanism and ignore the influence of noise. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of existing methods and devices. In order to achieve the tracking and locking of the resonant frequency of the laser to the resonant cavity in the field of high-end equipment manufacturing, a PDH frequency tracking method based on system identification theory and fuzzy PID is proposed. The system identification is used to identify the transfer function of the controlled object in the new control scheme, and a new control loop is built. The PID parameters are adjusted in combination with fuzzy control to achieve high-precision tracking of the laser to the resonant cavity.

[0005] The specific scheme of the present invention is that we set a PZT control voltage signal that is not easily affected by the environment and can make the discrimination error zero as a reference signal, replacing the traditional resonant frequency that is easily affected by the environment. Secondly, we constructed a new control loop, using PZT and discrimination modules as control objects, and using system identification theory to achieve high-precision identification of the transfer function of the control object by constructing reasonable orders and delay times; finally, based on the above work, the system was built, combined with the fuzzy PID control scheme, and the traditional PID parameters were parameterized.

[0006] To achieve the above object, according to one aspect of the present invention, a novel PDH frequency tracking method based on system identification and fuzzy PID control scheme is proposed, comprising the following steps:

[0007] (1) Using lasers, electro-optic modulators, fiber resonators, photodetectors, and a data processing module consisting of a bandpass filter, a mixer, and a low-pass filter implemented based on FPGA, combined with a traditional PID control scheme and laser PZT, a traditional PDH frequency tracking system is built to obtain an error signal reflecting the laser frequency and the resonant frequency of the resonant cavity, wherein the resonant cavity, the photodetector, and the data processing module implemented by FPGA together constitute a frequency discrimination module;

[0008] (2) extracting the laser PZT input voltage signal and the error signal obtained in step (1) to perform system identification, that is, performing system identification on the whole composed of the PZT and the frequency discrimination module to obtain the transfer function of the module;

[0009] (3) The whole composed of PZT and frequency discrimination module in step (2) is regarded as the controlled system, and the PZT voltage that can make the error signal 0 is used as the theoretical input value to construct a new PID feedback loop, build a new PDH frequency tracking system, and obtain the PID parameters of the system;

[0010] (4) Based on the fuzzy control theory, the PID parameters obtained in step (3) are adjusted to complete the three steps of fuzzification, fuzzy rule formulation, and defuzzification respectively, so as to build a more accurate PDH frequency tracking system.

[0011] In order to improve the accuracy of the PDH frequency tracking system, the coupling ratio of the optical fiber resonant cavity in step (1) is selected as 99:1 to obtain higher resonant cavity finesse, and the material of the resonant cavity is selected as polarization-maintaining fiber to avoid mode splitting caused by scattering noise.

[0012] Step (2) is specifically as follows: first, determine that the input signal of the system identification module is the input voltage of the laser PZT, and the output signal is the data of the error signal obtained in step (1) within the linear interval; secondly, divide the input signal and the output signal into two uniform parts according to time, use the first half for system identification, and the second half for result verification; then, determine the order range of the module based on prior knowledge, and estimate whether the module contains a delay link; then, evaluate the order range based on the ARMAX fourth-order model, determine the order range again, and analyze the zero-pole distribution and delay time range under different order models; finally, calculate the models of different orders and delay times respectively, and calculate their fitting efficiency.

[0013] For a single-input single-output system, the equation of the ARMAX model in step (1) is shown in formula (1):

[0014]

[0015] Among them, y(t) represents the output at time t, u(t) represents the input at time t, and n a is the number of extreme points, n b is the number of zeros plus 1, n k is the input delay, and e(t) is the white noise interference.

[0016] Step (3) is specifically as follows: without changing the hardware system, define new theoretical input values ​​and determine new controlled modules. Then, the PID parameters of the system will change with the changes of the system, thus forming a new PDH system.

[0017] In step (4), the fuzzification mainly completes the mapping of the system input and output signals from the basic domain to the fuzzy domain. Specifically, the input and output of the fuzzy PID parameter tuning system are first determined, where the input is the error e and the error change rate ec, and the output is Δk p , Δk i , Δk d, that is, a two-input and three-output system. Secondly, determine the basic domain of each parameter, determine the fuzzy domain of each parameter, and finally set the expression of the fuzzy subset of the input value and output value of the fuzzy controller to seven linguistic variables, namely negative large [NB], negative medium [NM], negative small [NS], zero [ZO], positive small [PS], positive medium [PM], positive large [PB], and complete the mapping from the basic domain to the fuzzy domain; then complete the selection of the membership function and calculate the membership. Combined with the characteristics of the PDH system, the membership functions of NM, NS, ZO, PS, and PM all select triangular membership functions, and their expressions are shown in formula (2). At the same time, in order to ensure the stability when the parameters change. The membership function of NB is selected as Z type, and its expression is shown in formula (3). The membership function of PB is selected as S type, and its expression is shown in formula (4).

[0018]

[0019] In step (4), the fuzzy rules transform the fuzzy domain of the system input signal into the fuzzy domain of the system output signal. The formulation of fuzzy rules should be combined with the characteristics of the PDH frequency tracking system.

[0020] In step (4), the defuzzification converts the output signal obtained above from the fuzzy domain back to the precise value. Specific methods include average maximum membership method, weighted average method, area centroid method, etc. In combination with the characteristics of this system, this application selects the area centroid method.

[0021] After completing step (4), the three output parameters obtained are added to the original PID parameters obtained in step (3) to obtain the final PID parameters, and the fuzzy tuning of the PID parameters is completed. The expression of the final PID parameters is shown in formula (5). After the above process, the tuning of the PID parameters in the new PDH system is completed.

[0022] BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flowchart of a novel PDH frequency tracking method based on system identification and fuzzy PID control scheme;

[0024] Figure 2 It is the structure diagram of PDH frequency tracking system;

[0025] Figure 3 It is the system identification flow chart;

[0026] Figure 4 It is a fuzzy control flow chart

[0027] Figure 5 It is the membership function curve of fuzzy PID input parameters;

[0028] Figure 6 It is the membership function curve of fuzzy PID output parameters

[0029] Figure 7 It is the state diagram after the fuzzy rules in PID are three-dimensionalized;

[0030] Figure 8 is the fuzzy PID rule diagram;

[0031] Fig. 9 It is the fuzzy PID fuzzy control query diagram;

[0032] Fig.10 It is a simulation model diagram constructed by the present invention; DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the novel PDH frequency tracking method based on system identification and fuzzy PID control scheme of the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0034] See also Figure 1 The present invention provides a novel PDH frequency tracking method based on system identification and fuzzy PID control scheme, comprising the following steps: firstly, building a traditional PDH system and obtaining an error curve; secondly, using the error curve as an output signal and the control voltage of a laser PZT as an input signal for system identification to obtain the transfer function of the module; then, the laser PZT and the frequency discrimination module together constitute a controlled module, and using the PZT voltage that can make the error signal 0 as the theoretical input value, combined with the traditional PID control scheme, a novel PDH frequency tracking system is built; finally, combining the fuzzy control theory, the traditional PID parameters in the novel PDH frequency tracking scheme are fuzzy tuned to realize a high-precision PDH frequency tracking system.

[0035] See also Figure 2 , which is a structural diagram of the traditional PDH frequency tracking system provided in this application, specifically including a laser, an optical isolator, an electro-optical modulator, an optical fiber resonant cavity, and a data processing module composed of a bandpass filter, a mixer, and a low-pass filter based on FPGA design, wherein ADC is the abbreviation of analog-to-digital converter, which refers to an analog / digital converter and completes the conversion of analog signals to digital signals; DAC is the abbreviation of digital-to-analog converter, which refers to a digital / analog converter and completes the conversion of digital signals to analog signals; DDS is Direct Digital Synthesis, the full name of direct digital frequency synthesis, which completes the control of the electro-optical modulator by FPGA.

[0036] See also Figure 3 , which is a system identification flow chart provided in this application. Specifically, the system identification includes the following steps: first, the actual data is divided into two parts, the first half is used for system identification, and the second half is used for model verification. The type of model is determined based on prior knowledge and input and output data obtained from experiments; secondly, the model order is selected, and the zero poles and delay time are determined; finally, the second half of the data is used for model verification. When the fitting effect is poor, the above steps are repeated. If the fitting effect is good, the model is output.

[0037] See also Figure 4 , which is the fuzzy control flow chart provided in this application. Specifically, fuzzy tuning includes the following steps: first, fuzzification of input and output parameters is completed based on the knowledge base, and mapping from basic domain to fuzzy domain is completed; secondly, fuzzy rules are formulated based on the knowledge base and system characteristics, and parameter tuning is completed according to the fuzzy rules; finally, defuzzification from fuzzy domain to basic domain is completed.

[0038] See also Figure 5 , which is a membership function diagram of the input signal in the fuzzy PID parameter tuning provided by the present application. Specifically, after determining the basic domain and fuzzy domain of the input signal, the membership function is selected and the membership function diagram is drawn. The mapping of the input signal from the basic domain to the output domain is completed.

[0039] See also Figure 6 , which is a membership function diagram of the output signal in the fuzzy PID parameter setting provided by the present application. Specifically, after determining the basic domain and fuzzy domain of the output signal, the membership function is selected and the membership function diagram is drawn. The mapping of the output signal from the basic domain to the output domain is completed.

[0040] See also Figure 7 , which is the rule base for fuzzy PID parameter tuning provided by this application. Specifically, based on the system characteristics, fuzzy rules are formulated, the membership functions of input and output parameters, fuzzy domain and other parameters are set, and the formulated 49 fuzzy rules that meet the characteristics of this system are written into the fuzzy rule editor.

[0041] See also Figure 8 After completing the relevant design of input, output and fuzzy rules for the fuzzy PID parameter setting provided by this application, the fuzzy control surface diagram of the system output parameters based on the corresponding rules can be obtained. The changes of the three parameters according to the external conditions have been reflected in detail in the surface diagram, so in the actual experiment, these three surface diagrams can also be used to adjust the PID parameters.

[0042] See also Fig. 9, which is the fuzzy control query device in the fuzzy PID parameter setting provided in this application. After completing the parameter settings related to fuzzification and fuzzy rules, the area centroid method can be selected for defuzzification to obtain a clear value. The fuzzy control query device can also be used to record and query at any time the control output results of the fuzzy PID controller operation under various E and Ec input values.

[0043] See also Fig.10 , which is a software simulation diagram provided in this application, wherein the upper part is the new PDH frequency tracking system based on system identification and fuzzy PID proposed in this paper, and the lower part is the traditional PDH frequency tracking system.

Claims

1. A PDH frequency tracking method based on system identification and fuzzy PID control scheme, characterized in that: The following steps are involved: (1) A PDH frequency tracking system is constructed based on a laser, an electro-optic modulator, a fiber resonant cavity, a photodetector, a programmable gate array (FPGA), a PID control module, and a PZT actuator, wherein the resonant cavity, the photodetector, and a data processing module constructed based on the FPGA convert the optical signal into an electrical signal, and together constitute a frequency discrimination module; a frequency tracking error signal of the PDH system constructed based on the fiber resonant cavity is obtained, and the signal is processed to extract an error signal reflecting the laser frequency and the resonant frequency of the resonant cavity; (2) determining the composition of the controlled module that needs to be system-identified and the input and output signals of the system identification, specifically using the signal within the error linear interval obtained in step (1) as the output signal of the system identification, taking the input voltage signal of the laser PZT as the input, and performing system identification on the whole composed of the laser PZT and the frequency discrimination module; (3) Based on system identification theory and combined with prior knowledge, determine the order of the system to be analyzed and whether to include delay time, and use the optimal result of the system identification as the transfer function of the module; (4) Based on the system identification result obtained in step (3), the result is used as the controlled module, the PZT control voltage signal that can make the error signal zero is used as the theoretical input, and the PDH frequency tracking system is constructed in combination with the PID control scheme; (5) Combining fuzzy control theory, by fuzzifying the input and output signals, formulating fuzzy rules, and defuzzifying, the PID parameters in step (4) are fuzzy optimized and adjusted to optimize the performance of the PDH frequency tracking system and complete the construction of the PDH frequency tracking system.

2. The PDH frequency tracking method based on system identification and fuzzy PID control scheme according to claim 1, characterized in that: In the process of obtaining the error signal of the laser frequency and the resonant cavity resonant frequency in step (1), the modulation coefficient of the electro-optic modulator is firstly designed to control the energy of the modulated laser signal to be concentrated on the carrier and the positive and negative first-order sidebands; then, the material properties of the optical fiber resonant cavity and the construction scheme are reasonably selected to obtain the resonant cavity transmission spectrum, and the photoelectric detector is used to obtain the error signal reflecting the laser frequency and the resonant cavity resonant frequency; further, the data processing module composed of a bandpass filter, a mixer, and a low-pass filter built by FPGA is used to obtain the error signal in the linear range.

3. The PDH frequency tracking method based on system identification and fuzzy PID control scheme according to claim 2 is characterized in that: The process of obtaining the transfer function based on the system identification theory in step (2) includes the following steps: first, determining the module that needs to be identified, which is composed of a laser PZT and a frequency discrimination module; second, determining that the input signal and output signal of the system identification are: the input voltage signal of the laser PZT and the error signal in the obtained linear interval; finally, combining prior knowledge, determining that the order of the module is no higher than the third order and includes a delay time.

4. The PDH frequency tracking method based on system identification and fuzzy PID control scheme according to claim 3 is characterized in that: Step (3) is as follows: use the impulse algorithm to calculate the unit impulse response of the system, use the autoregressive moving average model with additional input to calculate its fourth-order model, and judge whether the system is linear based on the above results; secondly, estimate the order range of the system in combination with prior knowledge, and select the transfer function model for identification, and continue to calculate until the optimal model is selected.

5. The PDH frequency tracking method based on system identification and fuzzy PID control scheme according to claim 4 is characterized in that: The expression of the autoregressive algorithm in step (4) is as shown in Formula 1: Among them, y(t) is the output value over time, n a Number of system poles, n b Add 1 to the number of zero points in the system, n k The number of input samples that occur before the input affects the output (also called the dead time of the system), where u(t) is the input signal and e(t) is the noise.

6. The PDH frequency tracking method based on system identification and fuzzy PID control scheme according to claim 5, characterized in that: In step (5), the input and output signals are fuzzified as follows: first, the basic domain is determined: combining database experience and multiple experimental results, the error input signal E, the error input change rate Ec, and the range of the output signal are determined; secondly, the fuzzy domain is determined, which are negative large [NB], negative medium [NM], negative small [NS], zero [ZO], positive small [PS], positive medium [PM], and positive large [PB], which are used to complete the mapping of the input signal and the output signal from the basic domain to the fuzzy domain; finally, the membership function is reasonably selected based on the characteristics of the signal and the membership of each fuzzy domain is calculated.

7. The PDH frequency tracking method based on system identification and fuzzy PID control scheme according to claim 6, characterized in that: Since the internal length of the laser is adjusted, the fuzzy rules in step (5) should be formulated in combination with the characteristics of the PDH system. Considering the system as a two-input and three-output system, 49 fuzzy rules are formulated.

8. The PDH frequency tracking method based on system identification and fuzzy PID control scheme according to claim 7, characterized in that: In step (5), the defuzzification method selects the area centroid method to complete the conversion of the output signal from the fuzzy domain to the basic domain.

9. A PDH frequency tracking system based on system identification and fuzzy PID control scheme, using the PDH frequency tracking method of claim 1, characterized in that: It includes three modules: the first module is used to complete the acquisition of the original signal of the frequency tracking error. The module is composed of a laser with a band of 1550nm, an electro-optical modulator, a fiber resonant cavity, and a photodetector; the second module uses FPGA to build a frequency discrimination module composed of a bandpass filter, a mixer, and a low-pass filter; the third module is a feedback module composed of a PID control module and a laser PZT. The PID control module controls the laser PZT based on the error signal obtained by the second module to achieve the laser tracking of the resonant frequency of the resonant cavity.

Images