Micro-scale robot deposition system control method based on afd time-frequency iterative learning

Abstract

The application relates to a micro-scale robot depositing system control method based on AFD time-frequency iteration learning, which comprises the following steps: S1, an iteration learning dynamics model establishment step; S2, an initialization step; S3, a tracking error adaptive Fourier decomposition AFD time-frequency distribution calculation step; S4, a feedforward signal adaptive Fourier decomposition time-frequency distribution calculation step; S5, a critical frequency determination step; S6, a learning filter amplitude-frequency characteristic calculation step; S7, a robust filter amplitude-frequency characteristic calculation step; S8, an iteration learning system input calculation step; S9, an iteration learning number judgment step; and S10, a tracking trajectory output step. The application combines the AFD-based time-frequency analysis method, the ILC method with an advanced phase and the L-Q filter frequency band width adjustment method, and realizes high-precision control of the micro-scale robot depositing system.

Description

Technical Field

[0001] This invention relates to the field of iterative learning control technology, and more specifically, to a control method for a microscale robot deposition system based on AFD time-frequency iterative learning. Background Technology

[0002] Among numerous motion control systems, feedforward control offers significant advantages for achieving high-performance trajectory tracking and precise tracking accuracy. For example, it is used in nanoscale imaging and measurement in atomic force microscopy, control of the return mechanism in bearing manufacturing systems, and photolithography scanning in semiconductor manufacturing processes. However, feedforward control in practical applications requires a high-quality model of the controlled system, and obtaining accurate system model information in industrial production is often challenging, and in some cases, impossible. Against this backdrop, Iterative Learning Control (ILC) has emerged as a feedforward control strategy for optimizing the performance of systems repeatedly performing the same task. ILC utilizes error information obtained from past learning cycles to generate feedforward control signals for subsequent iterations, thereby improving the performance of the current learning cycle. Unlike other feedforward control methods, ILC can learn effective information from previous iterations to predict and compensate for external signals, such as repetitive disturbances. Moreover, the external signals received by ILC do not need to be known or measurable; they only need to be repeated in the iterations. However, transient tracking lag may occur when the feedforward controller responds to inputs and external disturbances. While feedforward control can eliminate this hysteresis, it is typically only applicable to known or measurable signals, such as the desired reference trajectory, and has limitations in dealing with external disturbances. Due to its simplicity and ease of implementation, ILC is widely used in various fields, such as 3D printing, multi-agent systems, intelligent air conditioning, and high-speed trains.

[0003] In microscale robotic deposition (MRD) systems, robotic arms are used for precise deposition of "ink" to construct complex micro-sized parts in 3D. High-precision XYZ-axis positioning of the robotic arm's end effector is crucial for achieving high-precision workpiece manufacturing. However, for high-precision control of MRD systems, in addition to traditional control methods, the ILC method has attracted significant interest from researchers. Through ILC, MRD systems can iteratively learn to gradually reduce deposition errors, thereby achieving higher deposition accuracy. This is critical for the manufacturing of micro-scale parts, as the small size and precision requirements mean that deposition errors can significantly impact manufacturing quality. Therefore, in MRD systems, ILC has emerged as a potential high-precision control method, promising to significantly improve the control accuracy of micro-scale parts.

[0004] However, in practical applications, current ILC methods still face the challenge of balancing convergence and robustness. While convergence can be addressed using methods such as norm-optimized ILC and adaptive ILC, maintaining robustness while achieving high-precision manufacturing remains a significant challenge. Furthermore, microscale robotic deposition systems often involve complex nonlinear and time-varying properties, further increasing the difficulty of ILC methods. In this context, introducing signal processing methods can be a beneficial complement. By analyzing sensor signals during the robotic arm's motion and deposition process, useful information about the system's dynamic characteristics can be obtained, thereby improving the performance of ILC control. This will provide more possibilities for high-precision control of microscale robotic deposition systems.

[0005] In summary, microscale robotic deposition systems, as a high-precision manufacturing technology, face complex control challenges. ILC, as a method of feedforward control, shows potential in improving system performance, but the balance between convergence and robustness still needs to be addressed. Meanwhile, the introduction of signal processing methods may also provide new avenues for improving control performance. Summary of the Invention

[0006] The purpose of this invention is to improve upon existing methods and provide a control method for microscale robot deposition systems based on AFD time-frequency iterative learning. By combining AFD-based time-frequency analysis, ILC method with leading phase, and LQ filter bandwidth adjustment method, high-precision control of microscale robot deposition systems is achieved, with good convergence and robustness.

[0007] The present invention adopts the following technical solution:

[0008] A control method for a microscale robot deposition system based on AFD time-frequency iterative learning includes:

[0009] S1, Steps for establishing an iterative learning dynamics model;

[0010] An iterative learning dynamics model for the microscale robotic deposition system is established as follows:

[0011] (1);

[0012] (2);

[0013] in, , Indicates the motor running time as The corner position at that time; Indicates the motor running time as Rotational speed at time; , Indicates the motor running time as The corner position at that time; Indicates the motor running time as Rotational speed at time; This indicates that the microscale robotic deposition system is in the first... Trajectory control dynamics output during each iteration of learning; This indicates that the microscale robotic deposition system is in the first... Trajectory control dynamics input during each iteration of learning; This indicates that the microscale robotic deposition system is in the first... High-frequency structural resonance generated during subsequent learning iterations; , and Let represent the system eigenvalue matrices of the microscale robotic deposition system; , This indicates the maximum operating cycle of the microscale robotic deposition system;

[0014] S2, Initialization steps;

[0015] set up The maximum number of iterations is The initial input for the iterative motion of the microscale robotic deposition system along one axis is set as follows: ; The iterative learning dynamic model of the microscale robotic deposition system is obtained System output at time ,as well as Initial iterative learning to control tracking error and initial feedforward signal ;in This represents the desired tracking trajectory for the one-axis motion of a microscale robotic deposition system. Indicates the first The system output at the next iteration; where... Indicates the learning filter, , Indicates the inverse Z-transform; Indicator Learning Filter In the initial bandwidth Amplitude-frequency characteristics at time;

[0016] S3, Steps for calculating the time-frequency distribution of the adaptive Fourier decomposition (AFD) of tracking error;

[0017] calculate Adaptive Fourier decomposition time-frequency distribution ;

[0018] ;

[0019] in, , express The instantaneous signal amplitude; ; yes Adaptive Fourier decomposition of the first The decomposition terms of the order of magnitude; It is the maximum decomposition order; yes Basis functions for adaptive Fourier decomposition. yes orthogonal system of order; yes The constant term of adaptive Fourier decomposition; Indicates the real part; Indicates the inner product;

[0020] calculate instantaneous phase ,as follows:

[0021] ;

[0022] in, ; Indicates to Complex coefficients within the unit circle during the m-th decomposition of adaptive Fourier decomposition; Indicates to Take the mold; express The complex argument; The complex coefficients inside the unit circle at the i-th decomposition of AFD; Indicates to Take the mold. express The complex argument;

[0023] calculate The time-frequency distribution is ;

[0024] in, , Represents the modulus of a complex number; It is the Dirac function;

[0025] S4, the steps for calculating the time-frequency distribution of the adaptive Fourier decomposition of the feedforward signal;

[0026] calculate AFD time-frequency distribution , ;

[0027] in, , express The instantaneous signal amplitude; Indicates feedforward signal The signal components of the m-th adaptive Fourier decomposition; yes Basis functions for adaptive Fourier decomposition; yes The constant term of the adaptive Fourier decomposition; calculation instantaneous phase for:

[0028] ;

[0029] in, ; Indicates to Complex coefficients within the unit circle during the m-th decomposition of adaptive Fourier decomposition; Indicates to Take the mold; express The complex argument; The complex coefficients inside the unit circle at the i-th decomposition of AFD; Indicates to Take the mold. express The complex argument;

[0030] calculate Time-frequency distribution ;

[0031] in, ;

[0032] S5, Critical Frequency Determination Steps;

[0033] Set time-frequency distribution energy amplitude and time-frequency distribution energy amplitude ;

[0034] Solve the inequalities and Determine tracking error and feedforward signal The critical frequency; if ,but ;if ,but ;in, Indicator Learning Filter No. The bandwidth of the next iteration; Indicates a robust filter No. The bandwidth of the next iteration; This represents the system signal frequency learned in the k-th iteration;

[0035] S6, Learn the steps for calculating the amplitude-frequency response of a filter;

[0036] Computational learning filter Amplitude-frequency characteristics ,as follows:

[0037] ;

[0038] in, ; ; It is the sampling frequency;

[0039] S7, Steps for calculating the amplitude-frequency response of a robust filter;

[0040] Computational robust filter Amplitude-frequency characteristics ,as follows:

[0041] ;

[0042] in, ; ;

[0043] S8, the system input computation steps for iterative learning;

[0044] The calculation is performed using an iterative learning control law with a leading phase. The system input for the next iteration of learning ,as follows:

[0045] ;

[0046] in, yes The frequency domain representation, i.e. ; It is the Z-transform. For complex variables, For frequency, The sampling period is It is the imaginary unit; ; ; and These are robust filters and learning filters. and These represent the bandwidth of the filter;

[0047] right Performing the inverse Z-transform, we obtain ,Right now ,in Indicates the inverse Z-transform;

[0048] S9, the step for determining the number of iterations in learning;

[0049] make Repeat steps S3-S9 until the number of iterations is satisfied. ;

[0050] S10, Tracking trajectory output step;

[0051] Will get Substituting the iterative learning dynamics models (1) and (2) of the established microscale robot deposition system, the dynamic output of the desired tracking trajectory is obtained. .

[0052] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0053] (1) The present invention provides a control method for microscale robot deposition system based on AFD time-frequency iterative learning, which uses a novel time-frequency analysis method of adaptive Fourier decomposition (AFD). This analysis method simultaneously characterizes the feedforward input signal of ILC from the time dimension and the frequency dimension, and obtains the non-negative instantaneous frequency, thus ensuring the completeness of the feedforward input signal analysis.

[0054] (2) The present invention provides a control method for a microscale robot deposition system based on AFD time-frequency iterative learning, which uses the ILC algorithm with leading phase. This algorithm can compensate for system delay and has no amplitude attenuation, which can reduce noise amplification effect and improve convergence speed.

[0055] (3) The present invention provides a control method for a microscale robot deposition system based on AFD time-frequency iterative learning, which uses the LQ filter bandwidth adjustment algorithm. When the system consists of low-frequency repetitive signals, the bandwidth of the filter is dynamically reduced by real-time measurement of the tracking error signal, thereby improving the convergence speed of ILC. Conversely, when the system includes high-frequency signals, the algorithm dynamically increases the filter bandwidth to improve the robustness of ILC. Attached Figure Description

[0056] Figure 1 This is a flowchart of a microscale robot deposition system control method based on AFD time-frequency iterative learning according to an embodiment of the present invention;

[0057] Figure 2 This is a schematic diagram of the axial motion of the microscale robotic deposition system according to an embodiment of the present invention;

[0058] Figure 3 This is a classic circuit structure diagram for iterative learning control of a microscale robot deposition system;

[0059] Figure 4 This is a schematic diagram of the LQ filter bandwidth adjustment algorithm according to an embodiment of the present invention;

[0060] Figure 5 This is a schematic diagram of the reference trajectory of the microscale robotic deposition system according to an embodiment of the present invention;

[0061] Figure 6 The initial ILC tracking error in the embodiment of the present invention Graph showing the relationship between time t and ...

[0062] Figure 7 The initial ILC tracking error in the embodiment of the present invention AFD TFD distribution map;

[0063] Figure 8 The initial ILC tracking error in the embodiment of the present invention Energy distribution map;

[0064] Figure 9 The initial ILC tracking error in the embodiment of the present invention Short-time Fourier transform (TFD) distribution plot;

[0065] Figure 10 This is an embodiment of the present invention. ILC tracking error Schematic diagram showing the relationship between time t and the change of time t;

[0066] Figure 11 This is an embodiment of the present invention. ILC tracking error AFD TFD distribution map;

[0067] Figure 12 This is an embodiment of the present invention. ILC tracking error Energy distribution map;

[0068] Figure 13 This is an embodiment of the present invention. Figure 12 ILC tracking error The distribution of the short-time Fourier transform (TFD). Detailed Implementation

[0069] The present invention will be further described below through specific embodiments.

[0070] See Figure 1 As shown, the present invention provides a control method for a microscale robot deposition system based on AFD time-frequency iterative learning, comprising:

[0071] S1, the steps for establishing an iterative learning dynamics model.

[0072] Microscale robotic deposition (MRD) systems play a crucial role in the 3D fabrication of miniature, complex parts. They utilize the positioning of a robotic arm to deposit ink materials, enabling precise control over the manufacturing process. As the requirements for precise XYZ axis positioning of the robotic arm actuators increase, manufacturing demands also become more stringent. See also Figure 2 The diagram illustrates the axial movement of an MRD system. In this setup, the proposed ILC algorithm is used to control the axial position (X-axis, Y-axis, or Z-axis) of the MRD system, which is driven by a motor. This configuration enables precise control of axial movement, allowing for accurate and complex deposition of ink materials during the manufacturing process.

[0073] In this embodiment, the iterative learning dynamics model of the microscale robotic deposition system is established as follows:

[0074] (1);

[0075] (2);

[0076] in, , Indicates the motor running time as The corner position at that time; Indicates the motor running time as Rotational speed at time; , Indicates the motor running time as The corner position at that time; Indicates the motor running time as Rotational speed at time; This indicates that the microscale robotic deposition system is in the first... Trajectory control dynamics output during each iteration of learning; This indicates that the microscale robotic deposition system is in the first... Trajectory control dynamics input during each iteration of learning; This indicates that the microscale robotic deposition system is in the first... High-frequency structural resonance generated during subsequent learning iterations; , and Let represent the system eigenvalue matrices of the microscale robotic deposition system; , This indicates the maximum operating cycle of the microscale robotic deposition system.

[0077] S2, Initialization steps.

[0078] set up The maximum number of iterations is The initial input for the iterative motion of the microscale robotic deposition system along one axis is set as follows: ; The iterative learning dynamic model of the microscale robotic deposition system is obtained System output at time ,as well as Initial iterative learning to control tracking error and initial feedforward signal ;in This represents the desired tracking trajectory for the one-axis motion of a microscale robotic deposition system. Indicates the first The system output at the next iteration; where... Indicates the learning filter, , Indicates the inverse Z-transform; Indicator Learning Filter In the initial bandwidth The amplitude-frequency characteristics at that time.

[0079] S3, Steps for calculating the time-frequency distribution of the adaptive Fourier decomposition (AFD) of tracking error.

[0080] calculate Adaptive Fourier decomposition time-frequency distribution , ;

[0081] in, , express The instantaneous signal amplitude; ; yes Adaptive Fourier decomposition of the first The decomposition terms of the order of magnitude; It is the maximum decomposition order; yes Basis functions for adaptive Fourier decomposition. yes orthogonal system of order; yes The constant term of adaptive Fourier decomposition; Indicates the real part; Indicates the inner product;

[0082] calculate instantaneous phase ,as follows:

[0083] ;

[0084] in, ; Indicates to Complex coefficients within the unit circle during the m-th decomposition of adaptive Fourier decomposition; Indicates to Take the mold; express The complex argument; The complex coefficients inside the unit circle at the i-th decomposition of AFD; Indicates to Take the mold. express The complex argument;

[0085] calculate The time-frequency distribution is ;

[0086] in, , Represents the modulus of a complex number; This is the Dirac function.

[0087] S4, the steps for calculating the time-frequency distribution of the adaptive Fourier decomposition of the feedforward signal.

[0088] calculate AFD time-frequency distribution , ;

[0089] in, , express The instantaneous signal amplitude; Indicates feedforward signal The signal components of the m-th adaptive Fourier decomposition; yes Basis functions for adaptive Fourier decomposition; yes The constant term of the adaptive Fourier decomposition; calculation instantaneous phase for:

[0090] ;

[0091] in, ; Indicates to Complex coefficients within the unit circle during the m-th decomposition of adaptive Fourier decomposition; Indicates to Take the mold; express The complex argument; The complex coefficients inside the unit circle at the i-th decomposition of AFD; Indicates to Take the mold. express The complex argument;

[0092] calculate Time-frequency distribution ;

[0093] in, .

[0094] S5, Critical Frequency Determination Steps.

[0095] Set time-frequency distribution energy amplitude and time-frequency distribution energy amplitude ;

[0096] Solve the inequalities and Determine tracking error and feedforward signal The critical frequency; if ,but ;if ,but ;in, Indicator Learning Filter No. The bandwidth of the next iteration; Indicates a robust filter No. The bandwidth of the next iteration; This represents the frequency of the system signal during the k-th iteration of learning.

[0097] S6, Learn the steps for calculating the amplitude-frequency response of a filter.

[0098] Computational learning filter Amplitude-frequency characteristics ,as follows:

[0099] ;

[0100] in, ; ; It is the sampling frequency.

[0101] S7, Steps for calculating the amplitude-frequency response of a robust filter.

[0102] Computational robust filter Amplitude-frequency characteristics ,as follows:

[0103] ;

[0104] in, ; .

[0105] S8 represents the system input computation steps for iterative learning.

[0106] The calculation is performed using an iterative learning control law with a leading phase. The system input for the next iteration of learning ,as follows:

[0107] ;

[0108] in, yes The frequency domain representation, i.e. ; It is the Z-transform. For complex variables, For frequency, The sampling period is It is the imaginary unit; ; ; and These are robust filters and learning filters. and These represent the bandwidth of the filter;

[0109] right Performing the inverse Z-transform, we obtain ,Right now ,in This represents the inverse Z-transform.

[0110] The iterative learning algorithm described above is the leading-phase ILC algorithm, and its convergence condition is as follows:

[0111] ;

[0112] That is, if the above conditions are met, the iterative learning control is stable and convergent, where It is the system process sensitivity function.

[0113] S9, the step for determining the number of iterations in learning.

[0114] make Repeat steps S3-S9 until the number of iterations is satisfied. .

[0115] S10, Tracking trajectory output step.

[0116] Will get Substituting the iterative learning dynamics models (1) and (2) of the established microscale robot deposition system, the dynamic output of the desired tracking trajectory is obtained. .

[0117] See Figure 3 The diagram shown is a basic circuit structure diagram for iterative learning control of a microscale robot deposition system. In the diagram, Indicates ILC number The feedforward signal for each iteration of learning, where Mem represents the storage unit. Indicates the first External disturbances to the system during each iteration of learning , and Represent the system's desired tracking trajectory, the first... The ILC tracking error learned in the iteration, the The system output of the next iteration of learning.

[0118] Consider a closed-loop LTI system, where P is the controlled system (microscale robotic deposition system) and C is the feedback system. Define the ILC tracking error as:

[0119] ;

[0120] It can be deduced that:

[0121] ;

[0122] in, The sensitivity function of the system The sensitivity function characterizes the system process. The expression for the ILC learning law is:

[0123] ;

[0124] The goal of iterative learning control is to achieve results within a finite time interval. Seeking suitable input internally This makes the system's tracking error As the number of iterations approaches infinity, we have .

[0125] In classic ILC design, Defined as a learning filter, It is defined as a robust filter. It has a constant cutoff frequency to improve robustness against high-frequency noise suppression and system model bias.

[0126] In the classic ILC design method, the bandwidth of the robust filter Q remains constant with the number of learning iterations. It is worth noting that in existing bandwidth-adaptive ILC designs, the bandwidth of the learning filter L is the same as that of the learning filter in the classic ILC method, remaining constant. This invention provides an LQ filter bandwidth adjustment algorithm that can adjust the bandwidth based on the ILC tracking error. and feedforward signal The bandwidths of the learning filter L and the robust filter Q are adjusted to track the desired trajectory of abrupt changes while filtering out repetitive and non-repetitive interferences in the system.

[0127] See Figure 4 The diagram shows a schematic of the LQ filter bandwidth adjustment algorithm proposed in this invention. In fact, the learning filter... and robust filters These are all FIR Gaussian filters, whose filter coefficients can accurately represent the bandwidth. Unlike traditional methods, the LQ filter proposed in this invention incorporates both time-varying and iterative-varying factors, enabling dynamic adjustment of the filter's bandwidth to suppress system noise amplification.

[0128] To verify the effectiveness of this invention, it was applied to a practical microscale robotic deposition MRD (MRD) system. The learning control method proposed in this invention is used to control the position of the X-axis. Notably, the X-axis is driven by a linear motor with a lubricated bearing slider.

[0129] For a given MRD system, the nominal system is obtained from the frequency response data. Its expression is:

[0130] ,

[0131] Feedback controller is The sampling frequency is 1 kHz. Figure 3 It can be seen that,

[0132] Closed-loop system transfer function of MRD system for:

[0133] ;

[0134] Considering the reference trajectory of the MRD system is , See Figure 5 As shown.

[0135] Set the initial input for iteration of the MRD system as follows: Calculate the initial ILC tracking error during iteration. The relationship of their changes is as follows Figure 6As shown. For Time-frequency analysis of AFD was performed to obtain the corresponding TFD distribution. And the energy distribution map, respectively Figure 7 and Figure 8 As shown. According to The TFD distribution analysis examines the impact of noise, nonlinearity, and other interferences on the performance of the actual system, and designs the bandwidth accordingly. Simultaneously with iteration time and number of iterations A varying L-filter. (By...) Figure 6 and Figure 7 As shown, and Within the time interval, ILC tracking error signal Significant high-frequency energy is present, while in other time periods, most of the energy is contained in the low-frequency region. It is worth noting that the TFD distribution here is based on AFD analysis, and its instantaneous signal is monotonically non-negative, without signal cross-terms, which can be seen from... Figure 6 This has been verified. In contrast, the present invention provides... Figure 9 The simulation results of the short-time Fourier transform are shown. From these, it can be concluded that the intensity using AFD is more concentrated than that using the short-time Fourier transform, and its time-domain and frequency-domain resolution is higher, while the time-frequency characteristics of the time-frequency analysis based on the short-time Fourier transform are not obvious. (Regarding the feedforward signal...) Time-frequency analysis was performed to obtain the TFD distribution. Based on this, a Q-filter is designed with a bandwidth of [missing information]. Satisfying the ILC convergence condition .

[0136] See Figures 10-13 As shown, when the number of iterations... At that time, ILC tracking error signal exist , and It possesses considerable energy at that time, and is composed of Figure 13 It is evident that the results obtained using short-time Fourier transform analysis do not possess good time-domain and frequency-domain resolution. Therefore, if the signal exhibits significant bandwidth variations, switching to a higher bandwidth within a local time interval is necessary. To adapt and The high-frequency components are incorporated into the learning process, thereby improving the convergence performance of ILC.

[0137] The above embodiments are merely illustrative of the present invention and are not intended to limit the invention. Any changes or modifications to the above embodiments based on the technical essence of the present invention will fall within the scope of the claims of the present invention.

Claims

1. A control method for a microscale robot deposition system based on AFD time-frequency iterative learning, characterized in that, include: S1, Steps for establishing an iterative learning dynamics model; An iterative learning dynamics model for the microscale robotic deposition system is established as follows: (1)； (2)； in, , Indicates the motor running time as The corner position at that time; Indicates the motor running time as Rotational speed at time; , Indicates the motor running time as The corner position at that time; Indicates the motor running time as Rotational speed at time; This indicates that the microscale robotic deposition system is in the first... Trajectory control dynamics output during each iteration of learning; This indicates that the microscale robotic deposition system is in the first... Trajectory control dynamics input during each iteration of learning; This indicates that the microscale robotic deposition system is in the first... High-frequency structural resonance generated during subsequent learning iterations; , and Let represent the system eigenvalue matrices of the microscale robotic deposition system; , This indicates the maximum operating cycle of the microscale robotic deposition system; S2, Initialization steps; set up The maximum number of iterations is The initial input for the iterative motion of the microscale robotic deposition system along one axis is set as follows: ; The iterative learning dynamic model of the microscale robotic deposition system is obtained System output at time ,as well as Initial iterative learning to control tracking error and initial feedforward signal ;in This represents the desired tracking trajectory for the one-axis motion of a microscale robotic deposition system. Indicates the first The system output at the next iteration; where... Indicates the learning filter, , Indicates the inverse Z-transform; Indicator Learning Filter In the initial bandwidth Amplitude-frequency characteristics at time; S3, Steps for calculating the time-frequency distribution of the adaptive Fourier decomposition (AFD) of tracking error; calculate Adaptive Fourier decomposition time-frequency distribution ; ； in, , express The instantaneous signal amplitude; ; yes Adaptive Fourier decomposition of the first The decomposition terms of the order of magnitude; It is the maximum decomposition order; yes Basis functions for adaptive Fourier decomposition. yes orthogonal system of order; yes The constant term of adaptive Fourier decomposition; Indicates the real part; Indicates the inner product; calculate instantaneous phase ,as follows: ； in, ; Indicates to Complex coefficients within the unit circle during the m-th decomposition of adaptive Fourier decomposition; Indicates to Take the mold; express The complex argument; The complex coefficients inside the unit circle at the i-th decomposition of AFD; Indicates to Take the mold. express The complex argument; calculate The time-frequency distribution is ; in, , The modulus of a complex number; It is the Dirac function; S4, the steps for calculating the time-frequency distribution of the adaptive Fourier decomposition of the feedforward signal; calculate AFD time-frequency distribution , ; in, , express The instantaneous signal amplitude; Indicates feedforward signal The signal components of the m-th adaptive Fourier decomposition; yes Basis functions for adaptive Fourier decomposition; yes The constant term of the adaptive Fourier decomposition; calculation instantaneous phase for: ； in, ; Indicates to Complex coefficients within the unit circle during the m-th decomposition of adaptive Fourier decomposition; Indicates to Take the mold; express The complex argument; The complex coefficients inside the unit circle at the i-th decomposition of AFD; Indicates to Take the mold. express The complex argument; calculate Time-frequency distribution ; in, ; S5, Critical Frequency Determination Steps; Set time-frequency distribution energy amplitude and time-frequency distribution energy amplitude ; Solve the inequalities and Determine tracking error and feedforward signal The critical frequency; if ,but ;if ,but ;in, Indicator Learning Filter No. The bandwidth of the next iteration; Indicates a robust filter No. The bandwidth of the next iteration; This represents the system signal frequency learned in the k-th iteration; S6, Learn the steps for calculating the amplitude-frequency response of a filter; Computational learning filter Amplitude-frequency characteristics ,as follows: ； in, ; ; It is the sampling frequency; S7, Steps for calculating the amplitude-frequency response of a robust filter; Computational robust filter Amplitude-frequency characteristics ,as follows: ； in, ; ; S8, the system input computation steps for iterative learning; The calculation is performed using an iterative learning control law with a leading phase. The system input for the next iteration of learning ,as follows: ； in, yes The frequency domain representation, i.e. ; It is the Z-transform. For complex variables, For frequency, The sampling period is It is the imaginary unit; ; ; and These are robust filters and learning filters. and These represent the bandwidth of the filter; right Performing the inverse Z-transform, we obtain ,Right now ,in Indicates the inverse Z-transform; S9, the step for determining the number of iterations in learning; make Repeat steps S3-S9 until the number of iterations is satisfied. ; S10, Tracking trajectory output step; Will get Substituting the iterative learning dynamics models (1) and (2) of the established microscale robot deposition system, the dynamic output of the desired tracking trajectory is obtained. .

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