A method for high frequency perturbation rejection based on repetitive sampling in a tilting mirror system

Abstract

The application discloses a high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system, mainly used for real-time high-frequency disturbance signal tracking control, reducing the visual axis error, and especially aiming at the high-frequency disturbance signal which is difficult to suppress due to limited sensor sampling. The method comprises the following steps: identifying aliasing of unknown signals and obtaining frequency information of actual disturbances through a sampling scheme with a variable sampling period; then, the actual high-frequency signal component exceeding the Nyquist frequency of the sensor is recovered through a repeated sampling algorithm; finally, a multi-rate parallel repeated control scheme is designed to compensate and suppress the high-frequency disturbance signal exceeding the closed-loop bandwidth. The method can effectively solve the aliasing of the high-frequency disturbance signal when the image sensor sampling is limited, and the problem that the tracking control is difficult to realize, and the anti-interference ability of the system is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of tracking control, and particularly relates to a high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system, which is mainly used for disturbance suppression of a line-of-sight stability in a tilting mirror control system to improve high-frequency disturbance suppression performance of the system. BACKGROUND

[0002] The tilting mirror has advantages of high bandwidth, fast response, small size, etc. and is widely used in fields of laser communication, telescope systems, astronomical instruments, etc. However, according to the sampling theorem, an image sensor with a limited sampling frequency is difficult to obtain an actual signal beyond the Nyquist frequency, which directly leads to difficulty of the tilting mirror control system in effective trajectory tracking and disturbance suppression.

[0003] Common methods such as non-uniform sampling, compressed sensing and sub-Nyquist sampling algorithms use advanced technologies to accurately capture and reconstruct high-frequency signals while maintaining or reducing the sampling rate. These technologies ensure signal integrity and accurate reconstruction through algorithm optimization, making it possible to sample at a lower Nyquist sampling rate and providing new solutions for various practical application scenarios. However, the original purpose of these methods is to recover the true signal under certain conditions including frequency, amplitude, phase and other information, which requires high real-time performance. In addition, the optimization algorithm used in reconstructing the original signal is complex and computationally intensive, which will bring heavy computational pressure and burden to the digital control system. SUMMARY

[0004] To solve the above technical problems, the application provides a high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system, which adopts a repeated sampling method based on closed-loop error and a parallel repeated control scheme to effectively suppress high-frequency disturbance, simplify the process of high-frequency signal recovery, and has good real-time tracking performance and significant disturbance suppression effect.

[0005] To achieve the above purpose, the technical scheme adopted by the application is as follows:

[0006] A high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system, which comprises the following steps:

[0007] Step one, a tilting mirror closed-loop feedback control system is built, and the proportional-integral controller parameters are adjusted so that the disturbance information from the base and the optical path is reflected in the closed-loop error, thereby adapting to the stability and effectiveness requirements of the tilting mirror control system, and making the system closed loop have low-frequency disturbance suppression effect.

[0008] Step two, at the closed-loop error end, a variable period sampling method is applied to identify error signal spectrum information under different sampling results, and the frequency information of the actual disturbance of the unknown signal is calculated by comparing the identified error signal spectrum information.

[0009] Step three, on the closed-loop error side, a repeated sampling method is applied to restore the spectrum components of the actual high-frequency disturbance exceeding the sensor Nyquist frequency;

[0010] Step four, on the basis of closed-loop feedback control, a parallel repetitive controller is designed on the closed-loop error side to compensate and suppress the high-frequency disturbance signals restored by repeated sampling.

[0011] Further, the application of the variable-period sampling method to identify the error signal spectrum information under different sampling results comprises:

[0012] Step 11, sampling at the original sampling frequency of the sensor The closed-loop error signal is sampled, and the Fourier transform is performed on the sampled signal to obtain the aliasing signal frequency generated by under-sampling , and determine the aliasing frequency set ;

[0013] Step 12, design a new sampling frequency , satisfying , where m is a parameter to be designed, and the aliasing signal frequency generated after secondary sampling is . Determine the corresponding another aliasing frequency set , when , then prove , is the true frequency of the disturbance signal. When , continue to the next step;

[0014] Step 13, take the intersection of the two aliasing frequency sets , and the disturbance signal frequency value range set , defined as the true frequency set of the disturbance signal . When the true frequency set has only one element, then the one element is determined as the true frequency of the disturbance signal; if there is more than one element in the true frequency set , repeat step 12 to determine another aliasing frequency set , take the intersection of the true frequency set and , and update the set until there is only one frequency element in .

[0015] Further, in order to simplify the calculation process and reduce the calculation complexity, the application of the repeated sampling algorithm to restore the spectrum components of the actual high-frequency signal exceeding the sensor Nyquist frequency comprises: according to the result of M times re-sampling derived as , where and are the DFT results of M times up-sampling and M points rectangular sequence respectively, k represents the sampling time.

[0016] Further, a multi-rate parallel repetitive control is designed to improve the high-frequency disturbance suppression capability of the closed-loop system, and the controller is designed as , which is a proportional-integral controller and a repetitive controller two parts, wherein the repetitive controller , N is an integer order of the repetitive controller, is a fractional order of the repetitive controller, is a delay compensation factor;

[0017] When the value of is close to 1, the repetitive controller can effectively reduce the water bed amplification phenomenon at non-periodic frequencies, and avoid destroying the stability of the system in the high-frequency region;

[0018] is a delay compensation link, and is designed as , which is used to realize the delay compensation of the high-frequency part and improve the stability performance of the closed-loop control in the high-frequency part;

[0019] The fractional order delay filter designed as a all-pass type can effectively solve the problem of too large disturbance frequency fluctuation in the high-frequency part, and is used for suppressing the disturbance at any characteristic frequency point.

[0020] Further, the method can realize the trajectory tracking and disturbance suppression of signals exceeding the sensor Nyquist frequency, and effectively reduce the closed-loop error.

[0021] Compared with the prior art, the present application has the following advantages:

[0022] (1) The control method can effectively improve the disturbance suppression capability of the system exceeding the Nyquist frequency under the condition of limited sensor sampling;

[0023] (2) The control method performs high-frequency signal identification and recovery work at the closed-loop error end, and effectively deals with the disturbance from the base and the optical link;

[0024] (3) The control method uses a parallel repetitive control scheme to improve the control performance of the sensitivity function, and has better stability and robustness;

[0025] (4) The control structure of the present application is simple, the calculation complexity is low, and it is easy to realize. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1This is a schematic diagram illustrating the implementation principle of a high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system according to the present invention.

[0027] Figure 2 This is a schematic diagram of repeated sampling in this invention;

[0028] Figure 3 This is a schematic diagram of the multi-rate parallel repetitive control principle of the present invention;

[0029] Figure 4 A comparison chart of the closed-loop error of the system after adding repeated sampling control. Detailed Implementation

[0030] The present invention will be described below with reference to the accompanying drawings and specific embodiments. Those skilled in the art can understand the effects and advantages of the present invention based on the content disclosed in this specification.

[0031] like Figure 1 As shown, the tilting mirror control system consists of a perturbed tilting mirror, a controlled tilting mirror, a target (simulated by a laser in this invention), an image sensor, and a resampling control module. During system operation, the image sensor provides the closed-loop system with the line-of-sight error, and the control output drives the deflection of the controlled tilting mirror to keep the target centered. Furthermore, the perturbed tilting mirror can simulate high-frequency disturbances from the optical link, and the resampling control module is used to identify, recover, and suppress high-frequency disturbances exceeding the sensor's Nyquist frequency. The figure also shows the implementation principle of a high-frequency disturbance suppression method based on resampling in a tilting mirror system proposed in this invention, and its implementation steps are as follows:

[0032] Step 1: Build a tilt mirror closed-loop feedback control system and adjust the proportional-integral controller parameters so that all disturbance information from the base and optical path is reflected in the line-of-sight error, thereby meeting the requirements of stability and effectiveness of the tilt correction system and enabling the closed loop of the system to have low-frequency disturbance suppression effect.

[0033] Step 2: At the closed-loop error end, apply the variable period sampling method to identify the error signal spectrum information under different sampling results, compare the identified error signal spectrum information, and calculate the frequency information of the actual disturbance of the unknown signal.

[0034] Step 3: At the closed-loop error end, apply the resampling method to recover the actual high-frequency disturbance spectrum components that exceed the sensor's Nyquist frequency;

[0035] Step 4: Based on the closed-loop feedback control, design a parallel repetitive controller at the closed-loop error end to compensate for and suppress the high-frequency disturbance signal recovered by repeated sampling.

[0036] like Figure 2Figure 1 shows the proposed under-sampling sequence, the re-sampling process and the re-sampling result. Figure 1 represents the convolution. Wherein is the aliasing frequency due to under-sampling, is the actual frequency, is the aliasing frequency after M times re-sampling. As can be seen from the figure, after re-sampling, the aliasing signal of under-sampling can recover part of the original signal spectrum components in the frequency domain. The recovered original signal spectrum components are in accordance with the result of the rectangular sequence DFT of the re-sampling result performs peripheral line distribution, is the digital angular frequency.

[0037] As shown in Figure 2, the re-sampling control principle diagram of the proposed method is shown. The dashed line is low-rate sampling, and the dotted line is high-rate sampling, Figure 3 represents the discrete model of the system, and represent the discrete transfer functions of the proportional-integral controller and the repetitive controller, respectively, represents re-sampling, and (kT) and (kMT) represent the discrete signals with sampling interval time T and MT, is the down-sampler, r( ), e( ), u( ) and y( ) represent the input signal, error signal, control signal and output signal of the closed-loop system, respectively, represents the system delay: caused by image sensor delay, analog / digital conversion and driver hysteresis, etc. In order to analyze the characteristics of the system, the delay part is unified into the high-rate sampling. According to the block diagram, the sensitivity transfer function can be derived as:

[0038] (1)

[0039] Further simplify the sensitivity transfer function. It is known that at high frequencies, formula (1) can be divided into two parts: the proportional-integral control part and the repetitive control part . Among them the control performance of is limited by the delay link of the system, which directly limits the effective control bandwidth of the proportional-integral control algorithm, and it is difficult to effectively suppress high-frequency disturbances. Therefore, by optimizing to improve the high-frequency trajectory tracking and disturbance rejection performance of the sensitivity function. The repetitive controller designed in the present application has the time delay compensation characteristic and the fractional order time delay filter performance , and the repetitive control sensitivity function is , which satisfies and is a fractional order time delay filter, at this time , when , , an infinite gain can be obtained, which is of great significance for achieving disturbance rejection and trajectory tracking at any characteristic frequency point. In addition, as increases to approach but not equal to 1, approaches 1, that is, 0 dB, effectively reducing the water bed amplification of the conventional repetitive control in the non-periodic frequency part.

[0040] In order to demonstrate the improvement effect of the disturbance rejection ability of the parallel repetitive control algorithm beyond the sensor Nyquist frequency, a parallel control structure is added and the corresponding controller is designed, and a position tracking experiment is carried out. As shown in Figure 4 , the position error comparison chart before and after adding the repetitive sampling and the repetitive controller is shown. In order to verify the effectiveness of the repetitive measurement result, a high-speed sensor is added to collect the actual measurement result, and when the two results are consistent, the effectiveness of the method can be explained. From Figure 4 , it can be seen that due to the direct limitation of the actual high-frequency signal tracking performance by the limited sensor sampling, the system closed-loop error is too large without adding the repetitive controller (w / o: shown by the dashed line), and it is difficult to achieve trajectory tracking; after adding the repetitive controller (w: shown by the solid line), the closed-loop error is greatly reduced in the actual sampling result and the repetitive sampling result, which can explain that the method is effective for tracking control beyond the sensor Nyquist frequency.

[0041] The above specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system, characterized in that, The method includes the following steps: Step 1: Build a tilting mirror closed-loop feedback control system and adjust the proportional-integral controller parameters so that the disturbance information from the base and optical path is reflected in the closed-loop error. Step 2: At the closed-loop error end, apply the variable period sampling method to identify the error signal spectrum information under different sampling results, compare the identified error signal spectrum information, and calculate the actual disturbance frequency information of the unknown signal. Step 3: At the closed-loop error end, apply the resampling method to recover the actual high-frequency disturbance signal that exceeds the Nyquist frequency of the sensor; Step 4: Based on closed-loop feedback control, design a parallel repetitive controller at the closed-loop error end to compensate for and suppress the actual high-frequency disturbance signal recovered by the repetitive sampling method, including: Design a multi-rate parallel repetitive controller. These are proportional-integral controllers. and repeat controller Two parts; Among them, the repetitive controller N is the integer order of the repetitive controller. For the fractional order of the repeating controller, As the delay compensation factor; when When the value is close to 1, the repetitive controller It can reduce the amplification phenomenon of waterbeds at non-periodic frequencies; This is a delay compensation stage used to compensate for delays in the high-frequency components. Designed as an all-pass fractional-order delay filter, it is used to suppress disturbances at arbitrary characteristic frequency points.

2. The high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system according to claim 1, characterized in that, The application of the variable-period sampling method to identify the error signal spectrum information under different sampling results includes: Step 11: Using the sensor's original sampling frequency The closed-loop error signal is sampled, and a Fourier transform is performed on the sampled signal to obtain the frequency of the aliasing signal caused by undersampling. Determine the set of aliasing frequencies ; Step 12: Design a new sampling frequency. ,satisfy Where m is the parameter to be designed, the frequency of the aliasing signal generated after secondary sampling is obtained as Determine the corresponding set of other aliasing frequencies. ,when Then it is proven , The true frequency of the disturbance signal; when If so, proceed to the next step; Step 13: Take two sets of aliasing frequencies , and the set of frequency ranges for disturbance signals The intersection of these two sets is defined as the true frequency set of the disturbance signal. When the real frequency set If there is exactly one element, then that element is determined to be the true frequency of the disturbance signal; if the true frequency set... If there is more than one element, repeat step 12 to determine another set of aliasing frequencies. Then take the real frequency set and The intersection, and update Gather, until There is one and only one frequency element.

3. The high-frequency disturbance suppression method based on repeated sampling in a tilting mirror system according to claim 1, characterized in that, The application of the resampling method to recover the actual high-frequency disturbance signal exceeding the sensor's Nyquist frequency includes: The resampling result obtained from the derivation is: ,in , and These are the DFT results for M-fold repeated sampling, upsampling, and M-point rectangular sequences, respectively, where k represents the sampling time.

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