Time-varying iterative learning feedforward control system and method based on wavelet transform

Abstract

The invention belongs to the field of precision motion control and intelligent control algorithms, and relates to a time-varying iterative learning feedforward control system and method based on wavelet transform. The system comprises an addition and subtraction arithmetic unit, a first memory, a time-varying robust filter Q (f, t) based on wavelet transform, a learning filter L (z), a first addition arithmetic unit, a second memory, a second addition arithmetic unit, a feedback controller C (z) and a controlled object P (z). According to the method, trajectory tracking error signals are repeatedly collected, the coherent power spectrum and the energy contribution distribution of the trajectory tracking error signals are extracted through wavelet transform, then a time-varying robust filter Q (f, t) is constructed, and repetitive error components are accurately extracted. The feed-forward control quantity is iteratively updated based on the repetitive error component, non-repetitive error amplification can be effectively inhibited, and the trajectory tracking precision is remarkably improved. The method is suitable for servo systems needing high-precision repetitive trajectory tracking, such as a photoetching machine workpiece table, a precision motion platform and an ultra-precision machining system.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision motion control and intelligent control algorithm technology, specifically relating to a time-varying iterative learning feedforward control system and method based on wavelet transform. This invention can be widely applied to servo systems that require repetitive trajectory tracking tasks and have stringent requirements for tracking accuracy, such as lithography machine stages, precision motion platforms, and ultra-precision machining systems. Background Technology

[0002] With the rapid development of integrated circuit manufacturing and high-end equipment technology, ultra-precision motion systems are widely used in fields such as lithography machines, magnetic levitation platforms, and CNC machine tools. Taking the lithography machine stage as an example, it needs to achieve nanometer-level trajectory tracking accuracy under high speed and high acceleration during the exposure process. The acceleration and deceleration phases of the stage determine the system settling time, while the tracking error in the constant speed phase directly affects the overlay accuracy. To improve overall performance, motion systems typically adopt a two-degree-of-freedom control structure with feedback and feedforward. Among them, Iterative Learning Control (ILC), as a feedforward learning strategy for repetitive systems, is widely used in precision positioning and trajectory tracking tasks.

[0003] While standard ILC algorithms eliminate repeatability errors, they can also amplify non-repeatability errors, especially in the presence of external disturbances, friction, or noise, leading to learning instability or decreased convergence accuracy. To balance the learning of repeatability errors with the suppression of non-repeatability errors, traditional ILC often employs robust filters with fixed bandwidth. Q(z) However, this filter belongs to the linear time-invariant (LTI) structure, which cannot adapt to the spectral differences of the error signal in the acceleration, constant speed and deceleration segments, and therefore it is difficult to obtain the global optimal performance.

[0004] Existing methods attempt to improve performance through piecewise iterative learning or by introducing time-varying filters. However, the former is subject to learning mutations and stability risks, while the latter, although using different cutoff frequencies at different times, still has limited filtering effects. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a time-varying iterative learning feedforward control system and method based on wavelet transform. The system acquires trajectory tracking error signals through repeated runs, performs wavelet transform analysis to extract the coherent power spectrum and energy contribution distribution, and combines these two parameters to construct a time-varying robust filter for accurately extracting the repetitive error components during the iteration process. The feedforward control quantity is iteratively updated based on these repetitive error components, thereby effectively suppressing the amplification of non-repetitive error components and significantly improving trajectory tracking accuracy.

[0006] A time-varying iterative learning feedforward control system based on wavelet transform includes: an adder / subtractor, a first memory, and a time-varying robust filter based on wavelet transform. Q(f, t) Learning filter L(z) First adder, second memory, second adder, feedback controller C(z) and the controlled object P(z) ; The input terminals of the adder and subtractor are respectively connected to the reference trajectory. r(t) and the controlled object P(z) The output terminal is used to perform subtraction to generate trajectory tracking error. e k (t) ; The output of the adder / subtractor is connected to the feedback controller. C(z) The input terminals of the first memory and the input terminals of the second memory. The output of the first memory is connected to a time-varying robust filter based on wavelet transform. Q(f, t) The input terminal; The wavelet transform-based time-varying robust filter Q(f, t) The output is connected to a learning filter. L(z) The input terminal; The input terminals of the first adder are respectively connected to the learning filter. L(z) The output terminal of the second memory is connected to the input terminal of the second memory and is used to update the iterative feedforward control signal. f k+1 (t) ; The output of the first adder is connected to the input of the second memory, and is used to update the iterative feedforward control signal. f k+1 (t) ; The input terminals of the second adder are respectively connected to the feedback controller. C(z) The output terminals of the first and second memory are connected to the controlled object. P(z) The input terminal is used to generate the total control signal. u k (t) ; Furthermore, the learning filter L(z) The design method is as follows: A parameterized model of the controlled object is established using physical analysis or system identification methods. P(z) According to the feedback controller used C(z) Calculate the process sensitivity function of the closed-loop system T = P / (1 + PC)A stable learning filter is designed using the direct inverse mode method, zero phase error tracking method, or zero amplitude error tracking method to approximate the inverse of the process sensitivity function as closely as possible.

[0007] Furthermore, the time-varying robust filter based on wavelet transform... Q(f, t) The construction method includes the following steps: Step 2-1), for the controlled object P(z) Multiple repeated trajectory tracking experiments were conducted, and multiple sets of trajectory tracking error signals were collected. e i (t) ; Step 2-2), for each group of trajectory tracking error signals e i (t) Preprocessing was performed separately to obtain e i _extended(t) ; Steps 2-3), for e i _extended(t) Perform wavelet transform analysis separately; Steps 2-4): For the time-frequency distribution matrix obtained by wavelet transform, remove the edge regions affected by boundary effects, and retain only the central effective time-frequency region that is not affected by distortion, as its corresponding wavelet time-frequency distribution matrix. W i (f, t) ; Steps 2-5), based on multiple sets of wavelet time-frequency distribution matrices W i (f, t) Calculate its coherent power spectrum Coh(f, t) This allows us to obtain the frequency distribution of repeatability errors at different times; Steps 2-6), combined with coherent power spectrum Coh(f, t) With energy contribution distribution dCPS(f, t) Construct a time-varying robust filter.

[0008] Furthermore, a coherent power spectrum in steps 2-5) Coh(f, t) The calculation method uses the squared modulus of the sum of the energies of each group as the numerator and the sum of the squared moduli of the energies of each group as the denominator:

[0009] in Wi(f, t) Let i be the wavelet time-frequency distribution matrix of the i-th group. f For frequency, t For time, n This represents the number of experimental groups.

[0010] Furthermore, one energy contribution distribution in steps 2-5) dCPS(f, t) The construction method includes the following steps: Step 2-5-1), for multiple sets of wavelet time-frequency distribution matrices Wi(f, t) The average wavelet time-frequency matrix is ​​obtained by summing and taking the mean. W_average(f, t) ; Step 2-5-2), calculate the average wavelet time-frequency matrix along the frequency direction. W_average(f, t) The cumulative energy distribution is obtained by calculating the cumulative power spectrum along the frequency axis. CPS(f, t) ; Steps 2-5-3), this cumulative power spectrum CPS(f, t) Differentiating along the frequency direction yields the energy contribution distribution of errors at different times and frequencies. dCPS(f, t) ; Furthermore, one of the steps in steps 2-6) involves a combined coherent power spectrum. Coh(f, t) With energy contribution distribution dCPS (f, t) The specific steps for constructing a time-varying robust filter are as follows: Step 2-6-1), for the coherent power spectrum Coh(f, t) With energy contribution distribution dCPS(f, t) Normalization yields Coh norm (f, t) and dCPS norm (f, t) ; Step 2-6-2), Coh norm (f, t) and dCPS norm (f, t) By proportionally weighting and merging, a composite weighted matrix is ​​obtained. M (f, t) :

[0011] in, α and β This is an adjustable weighting coefficient used to adjust the weight ratio between repeatability characteristics and energy contribution.

[0012] Steps 2-6-3), for the composite weighted matrix M(f, t) Segmented binarization is performed, and the entire trajectory process is divided into an acceleration segment, an establishment period, a constant speed segment, and a deceleration segment based on the acceleration curve of the reference trajectory. Furthermore, in step 2-6-3), the composite weighted matrix... M(f, t) The specific process for segmented binarization is as follows: The entire trajectory process is divided into an acceleration phase, a setup phase, a constant velocity phase, and a deceleration phase based on the acceleration curve of the reference trajectory, and thresholds are set for each phase. threshold The portion greater than the threshold is set to 1, and the portion less than the threshold is set to 0.

[0013] A time-varying iterative learning method based on wavelet transform, executed by the aforementioned system, specifically includes the following steps: S1. Initialization: Set the initial feedforward control signal. f 0 (t) Set to 0 and store in the second memory; S2. Under the action of the feedforward control signal, a trajectory tracking experiment is conducted, and the first memory records the trajectory tracking error signal. e k (t) ; S3, Track tracking error signal e k (t) Preprocessing is performed to obtain e k _extended(t) ; S4, to e k _extended(t) Perform wavelet transform analysis; S5. For the time-frequency distribution matrix obtained by wavelet transform, remove the distorted regions at both ends affected by boundary effects, and retain only the central effective region as its corresponding wavelet time-frequency distribution matrix. W j (f, t) ; S6. Calculate the wavelet time-frequency distribution matrix of the current iteration error. W j (f, t) With time-varying robust filters Q(f, t) Performing the Hadamard product yields F(f, t) ; S7, to F(f, t) Reconstructing the tracking error signal using inverse wavelet transform yields a signal with high repeatability and energy. e_sel (t) ; S8 e_sel(t) The first signal is generated after the learning filter is applied; S9, the first adder will process the first signal and the previous feedforward control signal stored in the second memory. f k (t) The new feedforward control signal is obtained by performing a summation operation. fk+1 (t) And store it in the second memory; S10, in the new feedforward control signal f k+1 (t) Under the influence of the system, a new trajectory tracking experiment is conducted, and the first memory records the new trajectory tracking error. e k+1 (t) ; S11. Determine whether the trajectory tracking error signal meets the iterative convergence requirement. If the L2 norm of the difference between two trajectory tracking errors is less than the set threshold... δ hour:

[0014] S12, i.e., the iterative learning has converged, and the current feedforward control signal is the desired feedforward control signal. Otherwise, the iterative learning has not converged, and S3 is repeated until the iterative convergence requirement is met.

[0015] Furthermore, the method for preprocessing a signal as described in S3 includes the following steps: S31. Extend the tracking error signal at both ends using either mirror expansion or periodic expansion. pad_length Length, to reduce edge effects; S32. Verify the extension length by performing an inverse wavelet transform on the extended signal and comparing it with the middle segment of the original signal. pad_length Does it meet the requirements?

[0016] The beneficial effects of this invention compared to the prior art are as follows: (1) This invention has time-varying adaptability. Through a time-varying processing mechanism based on wavelet time-frequency analysis results, this invention enables the system to respond differently to the error signal characteristics of different time periods. During the acceleration and deceleration phase, priority is given to enhancing the learning and compensation of repetitive errors, thereby improving the iterative convergence accuracy; during the uniform speed phase, the amplification of non-repetitive errors is suppressed, while the suppression of low-frequency repetitive errors is also taken into account, so as to realize dynamic optimization control under time-varying conditions.

[0017] (2) The present invention has accurate repeatability feature extraction by fusing coherent power spectra. Coh(f, t) With energy contribution distribution dCPS(f, t) Information to construct time-varying robust filters Q(f, t) This enables high-precision extraction and differentiation of repeatability errors. (3) The system of the present invention has high iterative stability. It adopts a continuous and smooth time-varying robust filtering strategy to replace the traditional segmented iterative learning method, which avoids the problem of discontinuity of feedforward control signal caused by sudden change in filtering characteristics, thereby significantly improving the iterative stability and overall dynamic performance of the system. Attached Figure Description

[0018] Figure 1 The block diagram of a time-varying iterative learning feedforward control system based on wavelet transform is shown. Figure 2 The flowchart shows a time-varying iterative learning method based on wavelet transform. Figure 3 The controlled object in the embodiments of the present invention P(z) The Bird diagram; Figure 4 This is a reference trajectory curve diagram used in the trajectory tracking task in this embodiment of the invention; Figure 5 The time-varying filter constructed in the embodiments of the present invention Q(f, t) Time-frequency graph; Figure 6 This is a graph showing the trajectory tracking error curves of the method of the present invention and the standard iterative learning control method after the termination of iteration, given a reference trajectory in an embodiment of the present invention. Figure 7 This is a graph showing the change of the trajectory tracking error 2-norm / N of the method of the present invention and the standard iterative learning control method with the number of iterations, given a reference trajectory in an embodiment of the present invention. Detailed Implementation

[0019] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples; it should be noted that the following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0020] In this embodiment, the structural block diagram of a time-varying iterative learning control system based on wavelet time-frequency analysis is as follows: Figure 1 As shown, it includes: an adder / subtractor, a first memory, and a time-varying robust filter based on wavelet transform. Q(f, t) Learning filter L(z) First adder, second memory, second adder, feedback controller C(z) and the controlled object P(z) ; The input terminals of the adder and subtractor are respectively connected to the reference trajectory. r(t) and the controlled object P(z) The output terminal; The output of the adder / subtractor is connected to a feedback controller. C(z) The input terminals of the first memory and the input terminals of the second memory. The output of the first memory is connected to a time-varying robust filter based on wavelet transform. Q(f, t) The input terminal; The wavelet transform-based time-varying robust filter Q(f, t) The output is connected to a learning filter.L(z) The input terminal; The input terminals of the first adder are respectively connected to the learning filter. L(z) The output terminal of the second memory is connected to the input terminal of the second memory. The input terminals of the second adder are respectively connected to the feedback controller. C(z) The output terminals of the first and second memory are connected to the controlled object. P(z) The input terminal; In this embodiment, the Bode diagram of the controlled object is as follows: Figure 3 As shown.

[0021] In this embodiment, the feedback controller is designed as a PID controller, which makes the closed-loop stability of the servo control system stable.

[0022] In this embodiment, the sampling period of the servo control system is 0.0002s.

[0023] In this embodiment, the reference trajectory used for the trajectory tracking task is as follows: Figure 4 As shown.

[0024] Before conducting the actual trajectory tracking task, given a reference trajectory, five sets of error signals were obtained by repeatedly conducting experiments on the controlled object. e i (t) ; In this embodiment, five sets of error signals are used. e i (t) Mirroring and expanding at both ends, the expansion length pad_length The length is three times that of the error signal to reduce edge effects; Continuous wavelet transform was performed on the five preprocessed error signals to remove edge regions affected by boundary effects, retaining only the central effective time-frequency region unaffected by distortion, which served as its corresponding wavelet time-frequency distribution matrix. W i (f, t) ; Calculate its coherent power spectrum Coh(f, t) The numerator is the square of the modulus of the sum of the energies of each group, and the denominator is the sum of the squares of the moduli of the energies of each group:

[0025] Five sets of wavelet time-frequency distribution matrices W i (f, t) The average wavelet time-frequency matrix is ​​obtained by summing and averaging. W_average (f, t) ; Calculate the average wavelet time-frequency matrix along the frequency direction W_average(f, t)The cumulative energy distribution is obtained by calculating the cumulative power spectrum along the frequency axis. CPS(f, t) ; This cumulative power spectrum CPS(f, t) Differentiating along the frequency direction yields the energy contribution distribution of errors at different times and frequencies. dCPS(f, t) .

[0026] For coherent power spectrum CPS(f, t) With energy contribution distribution dCPS(f, t) After normalization, the components are weighted proportionally and then merged to obtain a composite weighted matrix. M(f, t) :

[0027] For composite weighted matrices M(f, t) Segmented binarization is performed, dividing the entire trajectory process into acceleration, establishment, uniform velocity, and deceleration segments based on the acceleration curve of the reference trajectory. Thresholds are set for each segment. threshold The portion of the data above the threshold is set to 1, and the portion below the threshold is set to 0, thus obtaining the time-varying robust filter. Q (f, t) :

[0028] In this embodiment, the time-varying robust filter Q(f, t) like Figure 5 As shown.

[0029] In this embodiment, the learning filter L(z) The design method is as follows: A parameterized model of the controlled object is established using the system identification method. P(z) According to the feedback controller used C(z) Calculate the process sensitivity function of the closed-loop system T = P / (1 + PC) A stable learning filter is designed using the direct inverse mode method to approximate the inverse of the process sensitivity function as closely as possible.

[0030] Specifically, given a reference trajectory, the specific steps of the time-varying iterative learning method based on wavelet transform are as follows: Step 1: Initialization, set the initial feedforward control signal. f 0 (t) Set to 0 and store in the second memory; Step two: Under the action of the feedforward control signal, a trajectory tracking experiment is conducted, and the first memory records the trajectory tracking error signal. e k (t) ; Step 3: Process the trajectory tracking error signal e k (t) Preprocessing is performed to obtaine k _extended(t) ; Step four, for e k _extended(t) Perform wavelet transform analysis; Step 5: For the time-frequency distribution matrix obtained by wavelet transform, remove the distorted regions at both ends affected by boundary effects, and retain only the central effective region as its corresponding wavelet time-frequency distribution matrix. W j (f, t) ; Step 6: Calculate the wavelet time-frequency distribution matrix of the current iteration error. W j (f, t) With time-varying robust filters Q(f, t) Performing the Hadamard product yields F(f, t) ; Step seven, for F(f, t) Reconstructing the tracking error signal using inverse wavelet transform yields a signal with high repeatability and energy. e_ sel(t) ; Step 8, e_sel(t) The first signal is generated after the learning filter is applied; Step nine: The first adder will use the first signal and the previous feedforward control signal stored in the second memory. f k (t) The new feedforward control signal is obtained by performing a summation operation. f k+1 (t) And store it in the second memory; Step 10, in the new feedforward control signal f k+1 (t) Under the influence of the system, a new trajectory tracking experiment is conducted, and the first memory records the new trajectory tracking error. e k+1 (t) ; Step 11: Determine whether the trajectory tracking error signal meets the iterative convergence requirement. If the L2 norm of the difference between two trajectory tracking errors is less than the set threshold... δ hour:

[0031] Step 12, which is the convergence of iterative learning, outputs the current feedforward control signal as the desired feedforward control signal; otherwise, the iterative learning has not converged, and Step 3 is repeated until the iterative convergence requirement is met. In this embodiment, the specific method for determining iterative convergence is that the L2 norm of the difference between two trajectory tracking errors is less than a set threshold. δ When the iterative learning converges.

[0032] In this embodiment, the threshold δ Take 1×10 -6 In other embodiments, the specific value can also be adjusted according to actual needs.

[0033] The application effect of the method of the present invention in this embodiment is as follows: Figure 6 As shown, compared with existing iterative learning control methods, given a reference trajectory, the method of this invention can provide differentiated responses to error signal characteristics in different time periods. During the acceleration and deceleration phases, it prioritizes enhancing the learning and compensation of repeatability errors, thereby improving the iterative convergence accuracy; during the constant speed phase, it suppresses the amplification of non-repeatability errors while also suppressing low-frequency repeatability errors.

[0034] In this embodiment, given a reference trajectory, the trajectory tracking error is 2. The curve of norm / N changing with the number of iterations is as follows: Figure 7 As shown.

[0035] The above description is merely a specific embodiment of the present invention, but it should be noted that the scope of protection of the present invention is not limited thereto; any modifications, changes and substitutions made by those skilled in the art within the technical scope disclosed in the present invention without departing from the principles and spirit of the present invention should be included within the scope of protection of the present invention.

Claims

1. A time-varying iterative learning feedforward control system based on wavelet transform, characterized in that, include: Adder / subtractor, first memory, time-varying robust filter based on wavelet transform Q(f,t) Learning filter L(z) First adder, second memory, second adder, feedback controller C(z) and the controlled object P(z) ; The input terminals of the adder and subtractor are respectively connected to the reference trajectory. r(t) and the controlled object P(z) The output terminal is used to perform subtraction to generate a trajectory tracking error signal. e k (t) ; The output of the adder / subtractor is connected to a feedback controller. C(z) The input terminals of the first memory and the input terminals of the second memory. The output of the first memory is connected to a time-varying robust filter based on wavelet transform. Q(f,t) The input terminal; The wavelet transform-based time-varying robust filter Q(f,t) The output is connected to a learning filter. L(z) The input terminal; The input terminals of the first adder are respectively connected to the learning filter. L(z) The output terminal of the second memory is connected to the input terminal of the second memory and is used to update the iterative feedforward control signal. f k+1 (t) ; The input terminals of the second adder are respectively connected to the feedback controller. C(z) The output terminals of the first and second memory are connected to the controlled object. P(z) The input terminal is used to generate the total control signal. u k (t) .

2. The time-varying iterative learning feedforward control system based on wavelet transform as described in claim 1, characterized in that, The time-varying robust filter based on wavelet transform Q(f,t) The construction method includes the following steps: Step 2-1), for the controlled object P(z) Multiple repeated trajectory tracking experiments were conducted, and multiple sets of trajectory tracking error signals were collected. e i (t) ; Step 2-2), for each group of trajectory tracking error signals e i (t) Preprocessing was performed separately to obtain e i _extended(t) ; Steps 2-3), for e i _extended(t) Perform wavelet transform analysis separately; Steps 2-4): For the time-frequency distribution matrix obtained by wavelet transform, remove the edge regions affected by boundary effects, and retain only the central effective time-frequency region that is not affected by distortion, as its corresponding wavelet time-frequency distribution matrix. W i (f,t) ; Steps 2-5), based on multiple sets of wavelet time-frequency distribution matrices W i (f,t) Calculate its coherent power spectrum Coh(f,t) This allows us to obtain the frequency distribution of repeatability errors at different times; Steps 2-6), combined with coherent power spectrum Coh(f,t) With energy contribution distribution dCPS(f,t) Construct a time-varying robust filter.

3. The time-varying iterative learning feedforward control system based on wavelet transform as described in claim 2, characterized in that, A coherent power spectrum in steps 2-5) Coh(f,t) The calculation method uses the squared modulus of the sum of the energies of each group as the numerator and the sum of the squared moduli of the energies of each group as the denominator: in W i (f,t) For the first i Group wavelet time-frequency distribution matrix, f For frequency, t For time, n This represents the number of experimental groups.

4. A time-varying iterative learning feedforward control system based on wavelet transform as described in claim 2, characterized in that, One type of energy contribution distribution in steps 2-5) dCPS(f,t) The construction method includes the following steps: Step 2-5-1), for multiple sets of wavelet time-frequency distribution matrices Wi(f,t) The average wavelet time-frequency matrix is ​​obtained by summing and taking the mean. W_average(f,t) ; Step 2-5-2), calculate the average wavelet time-frequency matrix along the frequency direction. W_average(f,t) The cumulative energy distribution is obtained by calculating the cumulative power spectrum along the frequency axis. CPS(f,t) ; Steps 2-5-3), this cumulative power spectrum CPS(f,t) Differentiating along the frequency direction yields the energy contribution distribution of errors at different times and frequencies. dCPS(f,t) .

5. A time-varying iterative learning feedforward control system based on wavelet transform as described in claim 2, characterized in that, In steps 2-6), one of the combined coherent power spectra... Coh(f,t) With energy contribution distribution dCPS(f,t) The specific steps for constructing a time-varying robust filter are as follows: Step 2-6-1), for the coherent power spectrum Coh(f,t) With energy contribution distribution dCPS(f,t) Normalization yields Coh norm (f,t) and dCPS norm (f,t) ; Step 2-6-2), Coh norm (f,t) and dCPS norm (f,t) By proportionally weighting and merging, a composite weighted matrix is ​​obtained. M(f, t) : in, α and β These are adjustable weighting coefficients used to adjust the weight ratio between repeatability characteristics and energy contribution. Steps 2-6-3), for the composite weighted matrix M(f,t) Perform piecewise binarization to generate a time-varying robust filter. Q(f, t) .

6. The time-varying iterative learning feedforward control system based on wavelet transform as described in claim 5, characterized in that, In step 2-6-3), the composite weighting matrix is... M(f,t) The specific process for segmented binarization is as follows: The entire trajectory process is divided into an acceleration phase, a setup phase, a constant velocity phase, and a deceleration phase based on the acceleration curve of the reference trajectory, and thresholds are set for each phase. threshold The portion greater than the threshold is set to 1, and the portion less than the threshold is set to 0. 。 7. A time-varying iterative learning method based on wavelet transform, characterized in that, This method is executed by the system described in claims 1-6, and specifically includes the following steps: S1. Initialization: Set the initial feedforward control signal. f 0 (t) Set to 0 and store in the second memory; S2. Under the action of the feedforward control signal, a trajectory tracking experiment is conducted, and the first memory records the trajectory tracking error signal. e k (t) ; S3, Track tracking error signal e k (t) Preprocessing is performed to obtain e k _extended(t) ; S4, to e k _extended(t) Perform wavelet transform analysis; S5. For the time-frequency distribution matrix obtained by wavelet transform, remove the distorted regions at both ends affected by boundary effects, and retain only the central effective region as its corresponding wavelet time-frequency distribution matrix. W j (f,t) ; S6. Calculate the wavelet time-frequency distribution matrix of the current iteration error. W j (f,t) With time-varying robust filters Q(f,t) Performing the Hadamard product yields F(f,t) ; S7, to F(f,t) Reconstructing the tracking error signal using inverse wavelet transform yields a signal with high repeatability and energy. e_sel(t) ; S8 e_sel(t) The first signal is generated after the learning filter is applied; S9, the first adder will process the first signal and the previous feedforward control signal stored in the second memory. f k (t) The new feedforward control signal is obtained by performing a summation operation. f k+1 (t) And store it in the second memory; S10, in the new feedforward control signal f k+1 (t) Under the influence of the system, a new trajectory tracking experiment is conducted, and the first memory records the new trajectory tracking error. e k+1 (t) ; S11. Determine whether the trajectory tracking error signal meets the iterative convergence requirement. If the L2 norm of the difference between two trajectory tracking errors is less than the set threshold... δ hour: If the iterative learning converges, the current feedforward control signal is the desired feedforward control signal. Otherwise, if the iterative learning has not converged, step S3 is repeated until the iterative convergence requirement is met.

8. The time-varying iterative learning method based on wavelet transform as described in claim 7, characterized in that, The signal preprocessing method described in S3 includes the following steps: S31. Extend the tracking error signal at both ends using either mirror expansion or periodic expansion. pad_length Length, to reduce edge effects; S32. Verify the extension length by performing an inverse wavelet transform on the extended signal and comparing it with the middle segment of the original signal. pad_ length Does it meet the requirements?

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