A control method for an AFM, a storage medium, and an electronic device

Abstract

The application relates to the technical field of imaging control of AFM, and provides a control method for AFM, a storage medium and electronic equipment. The method comprises the following steps: time-domain simulation modeling and discrete Fourier transform are carried out on the surface topography of a sample, and the frequency peak spread width and the center frequency offset of a frequency spectrum are extracted; an IIR high-pass filter is designed according to the parameters, so that the transition band of the IIR high-pass filter covers the frequency drift range near the scanning base frequency; the IIR high-pass filter is converted into a comb notch filter through variable replacement, the pure delay module in the Z-axis repetitive control framework is replaced, an improved repetitive controller is formed, and the improved repetitive controller is embedded in parallel with the Z-axis baseline feedback controller. The application overcomes the defect that the traditional repetitive controller is sensitive to frequency deviation, suppresses the error amplification problem at the non-periodic frequency, effectively improves the Z-axis topography tracking precision and the contact force control stability under the condition of high-speed scanning, and realizes high-fidelity imaging of high-speed AFM.

Description

Technical Field

[0001] This invention relates to the field of imaging control technology for AFM, and in particular to a control method, storage medium, and electronic device for AFM. Background Technology

[0002] In constant-force mode imaging using atomic force microscopy (AFM), the Z-axis controller needs to drive the probe to track the sample surface morphology in real time to maintain a constant contact force. With the increasing demand for high-efficiency detection in fields such as nanofabrication and life sciences, high-speed AFM imaging has become an important development direction, placing higher demands on the control accuracy and bandwidth of triaxial nanopositioning platforms.

[0003] In traditional AFM imaging control, the X and Y axes typically employ a proportional-integral (PI) controller combined with a feedforward strategy to track the grid scan trajectory, while the Z axis uses PI control to maintain a constant force mode. However, under high-speed scanning conditions, the triangular wave and ramp trajectories that the X and Y axes need to track exhibit significant periodicity. PI controllers, limited by bandwidth, cannot effectively suppress periodic tracking errors. Simultaneously, the high-speed periodic motion of the fast axis (X-axis) is coupled to the slow axis (Y-axis) through mechanical structures, introducing periodic cross-coupling disturbances. To address these issues, existing research has introduced Conventional Repetitive Control (CRC) into the X and Y axis control of AFM. Based on the internal model principle, CRC uses a pure delay module in the control loop to generate high gain at the scanning fundamental frequency and its harmonics, exhibiting excellent suppression capabilities against strictly periodic disturbances.

[0004] For Z-axis control, some researchers have attempted to apply traditional repetitive controllers to tapping or constant-force modes in AFM imaging to improve the control accuracy of probe deflection angle errors. However, the pure delay module of the traditional repetitive controller only provides high gain at a single frequency point, including the fundamental frequency and its integer harmonics, making it highly sensitive to frequency deviations. In actual AFM scanning, the Z-axis needs to track the unknown sample surface morphology signal. Due to factors such as sample tilt, surface irregularities, and non-ideal scanning, this morphology signal is not a strictly periodic signal; its spectrum exhibits broadening of frequency peaks and a shift in center frequency (i.e., a "quasi-periodic" signal). When the signal frequency experiences a slight drift, the gain of the traditional repetitive controller drops sharply. More seriously, the traditional repetitive controller suffers from error amplification at non-harmonic frequencies, leading to amplified tracking errors of non-periodic frequency components and causing imaging distortion. Summary of the Invention

[0005] To address one of the aforementioned technical problems, the present invention adopts the following technical solution:

[0006] According to one aspect of the present invention, a control method for AFM is provided, comprising the following steps:

[0007] A time-domain simulation model of the surface morphology of the sample to be tested is performed, and a discrete Fourier transform is performed on the simulation signal to extract the frequency peak broadening and center frequency offset of the sample morphology spectrum.

[0008] Based on the extracted frequency peak broadening width and center frequency offset, an infinite impulse response high-pass filter is parametrically designed. The passband frequency, stopband frequency, passband gain, and stopband gain are set according to the broadening width and offset, ensuring that the filter's transition band covers the frequency drift range near the scanning fundamental frequency determined by the XY-axis scanning frequency.

[0009] The infinite impulse response high-pass filter is converted into a comb notch filter by variable substitution, where the parameters of the variable substitution are determined by the ratio of the sampling frequency to the scanning fundamental frequency of the real-time control system.

[0010] In the repetitive control framework of the Z-axis of an atomic force microscope, a comb-shaped notch filter is used to replace the pure delay module, forming an improved repetitive controller.

[0011] An improved repetitive controller is embedded in parallel with the baseline feedback controller of the Z-axis to drive the controlled object corresponding to the Z-axis to track the surface morphology of the sample, thereby improving imaging quality.

[0012] According to a second aspect of the present invention, a non-transitory computer-readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the above-described control method for AFM.

[0013] According to a third aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described control method for AFM.

[0014] This invention has at least one of the following beneficial effects:

[0015] Firstly, it effectively overcomes the shortcomings of traditional repetitive controllers that are highly sensitive to frequency deviations, significantly improving the tracking capability for quasi-periodic signals.

[0016] Traditional repetitive controllers incorporate a pure delay module in the control loop. This module provides high gain only at a single frequency point, including the fundamental frequency and its integer multiples, making it highly sensitive to frequency deviations. Once the actual topographic signal experiences frequency drift due to factors such as sample tilt or surface irregularities, the control gain drops sharply, and tracking performance deteriorates severely.

[0017] This invention extracts the frequency peak broadening and center frequency offset of the morphology spectrum by performing time-domain simulation modeling on the sample surface morphology and performing Discrete Fourier Transform on the simulation signal. Based on the extracted broadening and offset, an IIR high-pass filter is parametrically designed to precisely match its passband frequency, stopband frequency, passband gain, and stopband gain with the aforementioned frequency domain characteristics, ensuring that the filter's transition band covers the entire frequency drift range near the scanning fundamental frequency determined by the XY-axis scanning frequency. Then, this IIR high-pass filter is converted into a comb-shaped notch filter through variable substitution, where the substitution parameters are determined by the ratio of the sampling frequency to the scanning fundamental frequency of the real-time control system. Finally, in the Z-axis repetitive control framework, this comb-shaped notch filter replaces the original pure delay module. With the above design, the comb-shaped notch filter can form a low-sensitivity region with a certain width in the vicinity of the scanning fundamental frequency and its harmonics, so as to maintain a strong error suppression capability when the frequency shifts. When the frequency of the sample morphology signal drifts near the scanning fundamental frequency, the controller can still maintain a high gain because the drift is covered by the transition band, thus effectively solving the problem of the tracking performance of traditional pure delay modules dropping sharply due to frequency shift.

[0018] Secondly, suppress the error amplification problem of traditional repetitive controllers at non-periodic frequencies.

[0019] The pure delay module in a traditional repetitive controller not only generates high gain at the fundamental frequency and harmonics, but also generates unexpected gain amplification at non-harmonic frequencies, which amplifies the tracking error of non-periodic frequency components and causes imaging distortion.

[0020] This invention replaces the pure delay module with a comb-shaped notch filter derived from an IIR high-pass filter. The frequency response characteristics of this comb-shaped notch filter are essentially inherited from the IIR high-pass filter upon which it is based: the high-pass filter has extremely low gain in the frequency band below its stopband frequency, a characteristic determined by the set stopband frequency and stopband gain. After conversion to a comb-shaped notch filter through variable substitution, the low-gain characteristic of the original single stopband region is periodically replicated to all frequency positions outside the fundamental frequency and harmonics—that is, at any non-periodic frequency, the comb-shaped notch filter exhibits a low-gain response equivalent to the stopband of the high-pass filter, thus automatically returning to a lower gain level. An improved repetitive controller containing this comb-shaped notch filter is embedded in parallel within the Z-axis baseline feedback controller, making it less prone to additional gain amplification at frequency points outside the fundamental frequency and harmonics, fundamentally suppressing the amplification of non-periodic frequency components, thereby ensuring image fidelity.

[0021] Thirdly, it provides a systematic and parameterizable design process, effectively improving Z-axis topography tracking accuracy and contact force control stability under high-speed scanning conditions.

[0022] This invention establishes a complete design process, from sample morphology spectral analysis to parametric design of IIR high-pass filters, then to constructing comb-shaped notch filters through variable substitution, and finally replacing the pure delay module and embedding it in parallel with a Z-axis baseline controller to drive the Z-axis controlled object. Designers can quantitatively set various parameters of the IIR filter based on the spectral characteristics of the actual sample morphology, ensuring precise matching between the controller's frequency characteristics and the actual frequency domain characteristics of the controlled signal. This overcomes the limitations of traditional repetitive controllers that rely on trial and error, significantly improving the controller's design efficiency and engineering operability. Furthermore, because this improved repetitive controller is robust to frequency drift and does not amplify aperiodic frequency errors, the Z-axis controlled object can stably track the sample surface morphology under high-speed scanning conditions, effectively maintaining a constant contact force between the probe and the sample, thereby achieving high-speed AFM imaging while ensuring imaging quality. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A flowchart of a control method for AFM provided in an embodiment of the present invention.

[0025] Figure 2 The diagram shown illustrates the basic principle of high-speed AFM constant force mode imaging involved in this invention.

[0026] Figure 3 The diagram shows the overall design flow of the three-axis repeating controller proposed in this invention.

[0027] Figure 4 This is to simulate the morphology and its time-domain curves and frequency-domain characteristic spectral lines; among which, Figure 4 (a) is a simulated surface morphology image of the sample with tilted stripes; Figure 4 (b) is its local time-domain trajectory curve; Figure 4 (c) is the frequency domain characteristic spectrum obtained after discrete Fourier transform. Figure 4 (d) is a simulated surface morphology image of the tilted grid sample; Figure 4 (e) is its local time-domain trajectory curve; Figure 4 (f) is its frequency domain characteristic spectral line.

[0028] Figure 5 This is a block diagram of a three-axis repetitive controller; where, Figure 5(a) is a block diagram of a traditional repetitive controller for the X-axis; Figure 5 (b) is a block diagram of a traditional repetitive controller for the Y-axis; Figure 5 (c) is a block diagram of the improved Z-axis repetitive controller.

[0029] Figure 6 The frequency domain characteristics of the system sensitivity function under different controllers are shown.

[0030] Figure 7 The images show the imaging results of the tilted groove-shaped sample at different scan rates of 10Hz, 25Hz, and 50Hz; among them, Figure 7 (a)-(c) show the imaging results using a baseline integration controller at scan frequencies of 10Hz, 25Hz and 50Hz, respectively; Figure 7 (d)-(f) show the imaging results using the traditional repetitive control strategy, respectively; Figure 7 (g)-(i) are the imaging results using the triaxial repetitive control strategy proposed in this invention, respectively; Figure 7 (j)-(l) are the sample morphology cross-sectional curves corresponding to the marked sections of each figure.

[0031] Figure 8 The images show the results of the grid sample at different scan speeds of 10Hz, 25Hz, and 50Hz; among them, Figure 8 (a)-(c) show the imaging results using a baseline integration controller at scan frequencies of 10Hz, 25Hz and 50Hz, respectively; Figure 8 (d)-(f) show the imaging results using the traditional repetitive control strategy, respectively; Figure 8 (g)-(i) are the imaging results using the triaxial repetitive control strategy proposed in this invention, respectively; Figure 8 (j)-(l) are the sample morphology cross-sectional curves corresponding to the marked sections of each figure.

[0032] Figure 9 This is a schematic diagram of the deflection of a cantilever beam; where, Figure 9 (a)-(c) are the cantilever beam deflection section curves of the inclined groove sample under three control strategies (baseline integral controller I, conventional repetitive controller CRC, and the three-axis repetitive controller IMRC of this invention); Figure 9 (d)-(f) are the deflection section curves of the cantilever beam under the three corresponding control strategies for the square column sample.

[0033] Figure 10 This is a schematic diagram illustrating the amplitude-frequency response characteristics and variable substitution transformation of an infinite impulse response high-pass filter; where, Figure 10 (a) is a high-pass IIR filter A schematic diagram of the amplitude-frequency response characteristic curve; Figure 10 (b) is a high-pass IIR filter with variable substitution. A schematic diagram of the resulting comb filter characteristic curve. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] As a first possible embodiment of the present invention, such as Figure 1 As shown, a control method for AFM is provided. The basic principle of AFM constant force mode imaging is: a Z-axis piezoelectric actuator drives the probe to move in the vertical direction, maintaining a constant contact force between the probe and the sample. The deflection signal of the probe reflects the height change of the sample surface morphology, such as... Figure 2 As shown, the Z-axis controlled object consists of a piezoelectric actuator and a cantilever beam probe system connected in series, and its dynamic characteristics exhibit a slightly damped resonance mode. Under high-speed scanning conditions, the topography signal that the Z-axis needs to track is not a strictly periodic signal, but rather a "quasi-periodic signal" exhibiting spectral peak broadening and center frequency shift characteristics. In traditional repetitive control (CRC), the pure delay element only provides high gain at a single frequency point, and the suppression effect drops sharply when the frequency shifts, and the error is amplified at non-periodic frequencies. Therefore, this embodiment designs the following improved repetitive control method for Z-axis control requirements. This method can effectively address the frequency shift problem of the sample topography signal, avoid the amplification of errors at non-periodic frequencies by traditional repetitive control, and thus improve the topography tracking accuracy and contact force control stability of the Z-axis under high-speed scanning conditions. The method specifically includes:

[0036] S1: Perform time-domain simulation modeling of the surface morphology of the sample to be tested, and perform discrete Fourier transform on the simulation signal to extract the frequency peak broadening width and center frequency offset of the sample morphology spectrum.

[0037] The purpose of this step is to provide a frequency domain basis for the subsequent parameterized design of the Infinite Impulse Response (IIR) filter. In actual AFM scanning, the surface morphology of the sample under test is unknown, and samples with different morphological characteristics exhibit significant differences in their spectral distribution. By performing time-domain simulation modeling on the standard sample under test (e.g., a striped sample or a grid sample placed at an angle), the signal characteristics of the Z-axis reference trajectory during the actual scanning process can be simulated.

[0038] Performing a Discrete Fourier Transform (DFT) on the simulated signal transforms the time-domain topography signal to the frequency domain, thereby obtaining the spectral distribution information of the sample topography. For example... Figure 4 As shown in (a)-(f), the time-domain simulation and spectral distribution information of the morphology of the tilted square and tilted stripe samples are presented. According to the frequency domain characteristic spectral lines in the figures, unlike the ideal periodic signal which exhibits isolated frequency components at the fundamental frequency and its harmonics, the spectrum of the actual sample morphology is characterized by the broadening of the frequency peaks and the shift of the center frequency, i.e., a "quasi-periodic signal". The frequency peak broadening refers to the width of the main lobe of the spectrum, reflecting the degree of dispersion of the frequency components of the morphology signal; the center frequency shift refers to the shift of the actual spectral peak frequency relative to the ideal scanning fundamental frequency. These two parameters are the core basis for the subsequent design of the passband and stopband frequencies of the IIR filter, directly determining the frequency domain coverage of the comb-shaped notch filter.

[0039] S2: Based on the extracted frequency peak broadening width and center frequency offset, a parameterized infinite impulse response high-pass filter is designed; the passband frequency, stopband frequency, passband gain and stopband gain are set according to the broadening width and offset, so that the transition band of the filter covers the frequency drift range near the scanning fundamental frequency determined by the XY axis scanning frequency.

[0040] like Figure 3 The overall design flow of the three-axis repetitive controller shown includes four main steps: Step 1 is to analyze surface features and design a multi-axis control strategy; Step 2 is to decompose frequency domain features and design an IIR filter; Step 3 is to convert the IIR filter into an improved repetitive controller; and Step 4 is to use the three-axis repetitive controller for high-speed AFM imaging. The core of this step is to convert the frequency domain features extracted in S1 into the design parameters of the IIR filter, i.e., the corresponding... Figure 3 Step two. The high-pass IIR filter is not used to filter out low-frequency signals, but rather serves as the core for generating the subsequent comb-shaped notch filter. By adjusting the passband and stopband frequencies, the final comb-shaped notch filter can be controlled to form a low-sensitivity region of a certain width near the fundamental frequency and its harmonics, thus maintaining strong error suppression capability even when the frequency shifts.

[0041] When the frequency of the sample morphology signal drifts due to factors such as changes in scanning speed, sample tilt, or surface irregularities, the controller can maintain high-gain tracking capability as long as the drifted frequency still falls within the low-sensitivity region. Therefore, the passband frequency setting should cover the frequency peak broadening width extracted in S1, and the stopband frequency setting should cover the possible range of center frequency offset, so that the filter's transition band can completely cover the frequency drift range near the scanning fundamental frequency.

[0042] Specifically, the infinite impulse response high-pass filter adopts a Butterworth-type structure, and its transfer function is... satisfy:

[0043]

[0044] in, The unit delay operator represents the delay of one sampling period; The filter order; The coefficients of the numerator polynomial, The coefficients of the denominator polynomial are calculated using the passband frequency, stopband frequency, passband gain, and stopband gain of the Butterworth filter according to the standard filter design formula; and the first term coefficient of the numerator is... Normalization is performed to obtain Gain normalization is performed on the coefficients of the numerator polynomial to ensure that the passband gain of the infinite impulse response high-pass filter does not exceed a preset gain threshold (usually less than 1), thereby avoiding excessive gain in the repetitive control branch that could affect system stability.

[0045] The amplitude-frequency response curve of the above high-pass IIR filter is as follows: Figure 10 As shown in (a), the horizontal axis represents frequency (Hz) and the vertical axis represents amplitude. The curve shows the passband frequency. With stopband frequency Positional relationship: at frequencies lower than Within the stopband range, the filter significantly attenuates signal components, especially at frequencies higher than [specific frequencies]. The passband filter allows signal components to pass through at higher gain. and The gain gradually transitions within the transition band. The positional relationship between the passband frequency and the stopband frequency defines the width of the low-sensitivity region of the subsequent comb notch filter at the fundamental frequency, which is directly determined by the frequency domain features extracted by S1.

[0046] Butterworth-type filters are characterized by a maximally flat amplitude-frequency response within the passband, with no ripple, making them suitable as the core for generating comb-shaped notch filters. In the transfer function described above, the denominator polynomial coefficients... The value of is determined by frequency transformation of the denominator polynomial of the Butterworth normalized prototype filter; the coefficients of the numerator polynomial The result is determined by the bilinear transformation of the passband gain and stopband gain of the high-pass filter.

[0047] The first term coefficient of the numerator The purpose of normalization is to control the amplitude of the passband gain, preventing excessively large passband gain from amplifying the tracking error signal and thus causing system saturation or instability. After normalization to 1, the passband gain is determined by the ratio of the remaining numerator coefficients to the denominator coefficients. The passband gain should not exceed a preset gain threshold (usually less than 1) to avoid excessive gain in the repetitive control branches, which could affect system stability. The specific value needs to be determined based on the gain characteristics of the controlled object and the system stability margin.

[0048] S3: The infinite impulse response high-pass filter is converted into a comb notch filter through variable substitution. The parameters of the variable substitution are determined by the ratio of the sampling frequency of the real-time control system to the scanning fundamental frequency.

[0049] Variable substitution This is the core operation for extending a single notch / high-pass filter into a multi-notch / multi-bandpass filter that simultaneously possesses the same frequency response characteristics at the fundamental frequency and all its harmonics. This refers to the number of delay periods, which is the number of sampling points contained within each fundamental frequency period. The sampling frequency of the real-time control system. This is for scanning the fundamental frequency.

[0050] The physical meaning of this replacement is: to perform a frequency response adjustment on the original filter in the frequency domain. The compression factor doubles, making the original filter more efficient at the normalized frequency. The response characteristics at that point appear in the new filter. Such positions, thus at the base frequency and its harmonics The frequency response forms a comb shape. The comb-shaped filter characteristic curve of the high-pass IIR filter after the above variable substitution is shown below. Figure 10 As shown in (b), that is, originally at the frequency and The stopband and passband boundary characteristics at a certain point, after variable substitution, appear as follows: and At, and in The positions repeat periodically, thus at the fundamental frequency A comb-shaped notch filter is formed at its harmonics. The amplitude-frequency response characteristics.

[0051] The advantage of this transformation is that once the comb-shaped notch filter is obtained through variable substitution... The change of value only requires adjusting the decimation factor of the delay operator, without redesigning the coefficients of the IIR filter, thus achieving efficient reconfiguration of the controller parameters.

[0052] Specifically, the transfer function of the comb-shaped notch filter By using a normalized infinite impulse response high-pass filter variables in Replace with Obtain, among which The delay period is equal to the sampling frequency of the real-time control system. With the scanning fundamental frequency The ratio, i.e. The following conditions must be met:

[0053]

[0054] in, unit delay operator The delayed operator after double extraction represents The delay of one sampling period; The unit delay operator The delayed operator after double extraction represents The delay of one sampling period; and Meaning and transfer function The corresponding coefficients in the text have the same meaning; The value of can be, for example, 500; and the transfer function that replaces the delay module is:

[0055]

[0056] in, This is a phase compensation term calculated based on the Zero Phase Error Tracking Control (ZPETC) method, used to compensate for the phase lag introduced by the comb-shaped notch filter. To compensate for the delay index, its value can be, for example, 5; Let be the transfer function of the comb-shaped notch filter.

[0057] transfer function It replaces the pure delay element in traditional repetitive controllers The introduction of this notch pattern results in a lower sensitivity region of a certain width at the fundamental and harmonic frequencies after the original IIR high-pass filter is comb-spread, while maintaining high-pass characteristics at non-fundamental and non-harmonic frequencies. This notch pattern effectively attenuates the components of the error signal corresponding to the fundamental and harmonic frequencies, while preventing the amplification of errors at other frequency components.

[0058] This is a forward phase compensation term used to compensate for the comb-shaped notch filter. and subsequent inverse compensator Phase lag introduced in the control loop. Because the controlled object in the AFM exhibits phase lag within the scanning frequency band, without phase compensation, positive feedback may occur near the fundamental frequency, leading to system instability. The ZPETC method uses forward compensation to make the phase response in the band of interest approximately zero, thereby ensuring stable insertion of the improved repetitive controller.

[0059] S4: In the repetitive control framework of the Z-axis of the atomic force microscope, the comb-shaped notch filter is used to replace the pure delay module to form an improved repetitive controller.

[0060] The core of traditional repetitive controllers is the internal model principle: by introducing a pure delay element into the control loop. This is used to establish the internal mode of a periodic signal, thereby generating high gain at the fundamental frequency and its harmonics. However, the gain characteristic of a pure delay element is a frequency-selective spike, which is very sensitive to frequency shifts.

[0061] This step uses the design in S3. By replacing the pure delay element in traditional repetitive control, an improved repetitive control (IMRC) is formed. The replaced control loop has a flat gain passband at the fundamental frequency and harmonics (instead of a sharp single frequency peak), and at the same time, it has the ability to suppress error components at non-fundamental frequency and non-harmonic frequencies (instead of amplifying them), thus overcoming the two inherent defects of traditional repetitive control.

[0062] Specifically, the improved repetitive controller includes: a low-pass filter, a comb-shaped notch filter, a phase compensator, a stable inverse compensator, a first summing node, and a second summing node; the input of the stable inverse compensator is connected to the error signal of the Z-axis control loop, and the output of the stable inverse compensator is connected to the first input of the first summing node; the input of the phase compensator is connected to the forward control signal of the Z-axis controlled object, and its output is connected to the second input of the first summing node to compensate for the phase delay introduced by the stable inverse compensator; the output of the first summing node is connected to the input of the comb-shaped notch filter, and the output of the comb-shaped notch filter is connected to the input of the low-pass filter; the output of the low-pass filter is connected to the first input of the second summing node, the second input of the second summing node is connected to the output of the baseline feedback controller, and the output of the second summing node is used to drive the Z-axis controlled object.

[0063] The above structure is as follows Figure 5 As shown in (c). In the figure, the reference input signal is The probe deflection feedback signal is The two are subtracted at the comparison node to obtain the error signal, which is then fed into two parallel branches:

[0064] The first branch is the baseline feedback controller. This is used to ensure the basic stability of the system.

[0065] The second branch is an improved repetitive controller. In the improved repetitive controller branch, the error signal is sent to the stable inverse compensator. The forward control signal of the Z-axis controlled object is sent to the phase compensator (shown in the figure). express), Output and The output, after being superimposed by the first summing node, is then sequentially passed through a comb notch filter. Low-pass filter The processed output is sent to the second summing node, which then feeds back the baseline to the controller. The output of the filter is superimposed with the output of the low-pass filter to drive the Z-axis controlled object. .

[0066] It should be noted that, Figure 5 (c) This is the core improved module of the present invention, and its function is equivalent to that of a comb-shaped notch filter. It is used to create a low-sensitivity region at the fundamental frequency and its harmonics, and to maintain low gain at non-periodic frequencies. A stable inverse compensator, used to compensate for the dynamic characteristics of the controlled object; This is a phase compensator, whose input is the forward control signal of the Z-axis controlled object, used to compensate for the stabilizing inverse compensator. The introduced phase delay, after being superimposed by the first summing node, is input together to... In this embodiment With the diagram They all have the same meaning, representing the compensation delay index. The connection relationship of the above modules constitutes a "plug-in" controller structure.

[0067] low-pass filter Its function is to limit the operating frequency band of repetitive control and filter out high-frequency noise and disturbances caused by unmodeled dynamics. In this embodiment, A non-causal finite impulse response (FIR) filter structure is adopted, and its order n and cutoff frequency are set according to the robust stability conditions of the closed-loop system.

[0068] Comb notch filter The functionality of this feature has been detailed in S3. Phase compensator Used to compensate for the phase lag of the stable inverse compensator and the controlled object in the frequency band of interest.

[0069] Stable inverse compensator This is the stable inverse model of the controlled object along the Z-axis. Its transfer function is calculated using the ZPETC method based on the identified model of the controlled object, and is used to compensate for the amplitude and phase frequency characteristics of the controlled object. Specifically, for the controlled object... The ZPETC method addresses the non-minimum phase zeros (i.e., zeros outside the unit circle) that exist in the system. It eliminates the phase error caused by these non-minimum phase zeros by designing a stable inverse filter, thereby compensating for the dynamic characteristics of the controlled object without violating system stability.

[0070] The summing node superimposes the output of the baseline feedback controller and the output of the improved repetitive controller to jointly drive the controlled object. The baseline feedback controller ensures the basic stability of the system, while the improved repetitive controller provides high-gain tracking performance at the fundamental frequency and harmonics.

[0071] The cutoff frequency of the low-pass filter is set to the scanning fundamental frequency. Several times (e.g., 5 times) is used to filter out high-frequency noise; the transfer function of the stable inverse compensator is the controlled object model. stable inverse Used to compensate for the amplitude and phase frequency characteristics of the controlled object; phase compensator Phase compensation term in comb notch filter The synergistic effect ensures the stability of the system across the entire frequency band.

[0072] The cutoff frequency setting of the low-pass filter determines the bandwidth of the repetitive control. If the cutoff frequency is too low, it cannot cover enough harmonic orders, affecting the suppression effect on higher harmonic disturbances; if the cutoff frequency is too high, it may introduce high-frequency noise and unmodeled dynamics, leading to system instability. Typically, setting the cutoff frequency to 5 to 10 times the scanning fundamental frequency can effectively cover the main harmonic components.

[0073] The design of a stable inverse compensator is crucial for achieving accurate tracking. Its transfer function is based on the controlled object model obtained from system identification and solved using the ZPETC method. The phase compensator and the phase compensation term in the comb-shaped notch filter are also discussed. Using the same compensation index This creates a consistent phase lead along the signal path, thus offsetting the phase lag introduced by the comb notch filter and the stable inverse compensator.

[0074] Specifically, the Z-axis controlled object consists of a Z-axis piezoelectric actuator and a cantilever beam probe system connected in series with it.

[0075] In AFM constant force mode imaging, the Z-axis piezoelectric actuator and the cantilever probe system are not two independent objects, but rather a series dynamic system. The piezoelectric actuator receives a control voltage signal and generates a displacement output, which drives the cantilever probe to move in the vertical direction; the change in the contact force between the probe and the sample surface is reflected by the deflection of the cantilever beam, and the deflection signal of the cantilever beam serves as a feedback signal.

[0076] Therefore, the transfer function of the controlled object along the Z-axis The frequency response characteristics of the Z-axis, from control input to feedback output, should be included, encompassing both the electromechanical dynamics of the piezoelectric actuator and the mechanical dynamics of the cantilever beam probe system. During system identification, a sweep frequency excitation signal must be applied to the entire Z-axis series system, and the probe deflection signal must be collected as the output response to obtain an accurate model of the controlled object on the Z-axis.

[0077] S5: An improved repetitive controller is embedded in parallel into the baseline feedback controller of the Z-axis to drive the controlled object corresponding to the Z-axis to track the surface morphology of the sample, thereby improving the imaging quality.

[0078] Parallel embedded structure is a typical implementation of repetitive controllers. The baseline feedback controller (such as a proportional-integral controller or a proportional-integral-derivative controller) is responsible for ensuring the basic stability and initial tracking performance of the system, while the improved repetitive controller is superimposed on the output of the baseline controller as a plug-in module.

[0079] The advantages of this parallel structure are: the insertion of the improved repetitive controller does not affect the original stability and design parameters of the baseline controller; when the repetitive controller causes abnormal output due to frequency mismatch or other reasons, the baseline controller can still maintain the stable operation of the system, thereby ensuring the safety and robustness of the system.

[0080] like Figure 6 As shown in the figure, by comparing the amplitude-frequency curves of the sensitivity function corresponding to the Baseline Integrator Controller (Baseline), the Traditional Repetitive Controller (CRC), and the Improved Repetitive Controller (IMRC) of this invention, it can be seen that: the Baseline Integrator Controller has limited disturbance suppression capability at the fundamental frequency; the Traditional Repetitive Controller has an extremely sharp low sensitivity peak at the fundamental frequency, and the sensitivity increases sharply with frequency shift, and there is a gain "bulge" at non-periodic frequencies; while the Improved Repetitive Controller has a flat low sensitivity passband near the fundamental frequency, and maintains a low sensitivity level at non-periodic frequencies, verifying the robustness of this invention to frequency shift and its ability to suppress non-periodic frequency gain.

[0081] Under stable operating conditions, the improved repetitive controller provides additional high gain at the fundamental frequency and harmonics, further reducing tracking errors and thus achieving high-precision topography tracking.

[0082] This method also includes S6: optimizing the parameters of the infinite impulse response high-pass filter through system sensitivity function analysis, specifically including the following steps:

[0083] System sensitivity function The sensitivity function characterizes the propagation properties from disturbance input to system tracking error and is a core indicator for evaluating the disturbance suppression capability of a control system. A smaller amplitude of the sensitivity function indicates a stronger ability to suppress disturbances. In repetitive controller design, analyzing the frequency domain characteristics of the sensitivity function allows for a quantitative evaluation of the controller's disturbance suppression performance at different frequencies.

[0084] This step establishes a sensitivity function model from disturbance to tracking error and transforms the controller parameter optimization problem into an IIR filter parameter adjustment problem, providing a theoretical basis for systematic parameter design.

[0085] The first step is to establish a mechanism from the disturbance. To tracking error System sensitivity function The following conditions must be met:

[0086]

[0087] in, The transfer function of the baseline feedback controller, which can be, for example, a PI controller, with a proportional gain... and integral coefficient Tuning is performed based on the frequency domain characteristics of the controlled object; The transfer function of the Z-axis controlled object is obtained by system identification based on the dynamic characteristics of the piezoelectric actuator and cantilever beam probe system. To replace the transfer function of the delay module, The unit delay operator Delay operator after multiple extraction;

[0088] The approximate expression for the sensitivity function described above is based on a low-pass filter. Utilization within the passband This was obtained under the given conditions. This approximation simplifies the expression of the sensitivity function, making the IIR filter parameters... Design and system sensitivity function A direct analytical relationship was established between them.

[0089] It is a comb notch filter The function, and Directly from a high-pass IIR filter This is obtained through variable substitution. Therefore, by adjusting the high-pass IIR filter... By changing the frequency domain parameters (passband frequency, stopband frequency, order, etc.), the system sensitivity function can be directly altered. The frequency domain shape allows for quantitative adjustment of the system's ability to suppress disturbances.

[0090] Baseline feedback controller The tuning can be performed using standard frequency domain tuning methods, based on the controlled object. The amplitude-frequency and phase-frequency characteristics are used to determine the proportional coefficient that meets the stability margin requirements. and integral coefficient .

[0091] The second step is to adjust the passband frequency of the infinite impulse response high-pass filter (e.g., adjust it to the scanning fundamental frequency). (0.8 times), to change the width of the low-sensitivity region (i.e., the flat bottom) of the comb notch filter, thereby adjusting the system's robustness to frequency drift;

[0092] The passband frequency determines the width of the low-sensitivity region formed by the comb-type notch filter at the fundamental frequency. The wider the passband frequency, the greater the tolerance range of the filter to frequency shifts, and the stronger the system's robustness to changes in scan speed and frequency drift of sample morphology.

[0093] However, an excessively wide passband frequency can cause the edge of the low-sensitivity region to extend into the non-harmonic frequency region, resulting in higher gain for frequency components that are not originally part of the fundamental frequency or harmonics, thus affecting the system's ability to suppress aperiodic frequencies. Therefore, the setting of the passband frequency needs to strike a balance between frequency offset robustness and aperiodic frequency suppression capability.

[0094] When the passband frequency is set to the scanning fundamental frequency Within the range of 0.5 to 2 times, it is possible to ensure a certain level of robustness while avoiding excessive impact on the gain characteristics of non-periodic frequencies. The specific value should be quantitatively determined based on the frequency peak broadening width extracted from S1.

[0095] The third step is to adjust the stopband frequency and order of the infinite impulse response high-pass filter (for example, the stopband frequency can be adjusted to the scanning fundamental frequency). 5 times, order It can be set to 4) to change the gain of the comb notch filter at non-periodic frequencies, thereby adjusting the system's ability to suppress non-periodic frequency gain.

[0096] The stopband frequency determines how quickly and to what extent a comb notch filter recovers its baseline gain level at frequencies far from the fundamental frequency and its harmonics. The lower the stopband frequency (the closer it is to the passband frequency), the stronger the filter's gain suppression capability for non-periodic frequencies, but the steeper the transition band, which may cause undesirable gain fluctuations in the filter within the transition band.

[0097] The higher the stopband frequency (the further away from the passband frequency), the lower the gain of the filter at non-periodic frequencies over a wider frequency range, but the transition band is relatively smooth. Filter order. The order determines the steepness of the transition band: the higher the order, the steeper the transition band, and the faster the transition between the passband and the stopband, but the computational complexity also increases accordingly.

[0098] By adjusting the combination of stopband frequency and order, a balance can be struck between non-periodic frequency suppression capability and filter design complexity. Typical stopband frequencies range from 3 to 10 times the scanning fundamental frequency, and typical order ranges from 2 to 8.

[0099] Fourth, repeat steps two and three until robustness and suppression capability reach a preset balance. Steps two and three adjust two conflicting performance metrics of the system: frequency drift robustness (passband width) and aperiodic frequency suppression capability (stopband gain). These two metrics have a trade-off relationship, and neither can be optimized simultaneously.

[0100] Therefore, it is necessary to iteratively adjust the three parameters—passband frequency, stopband frequency, and order—and evaluate the system sensitivity function after each adjustment. The frequency response was analyzed, and the gain flatness near the fundamental frequency and the degree of gain suppression at non-periodic frequencies were observed until both met the preset design specifications.

[0101] This parameter optimization method based on sensitivity function analysis transforms the controller design problem into a quantifiable and iterative systematic process, overcoming the limitations of traditional empirical trial-and-error methods.

[0102] As a second possible embodiment of the present invention, a three-axis coordinated repeatability control method for atomic force microscopy is provided. Based on the first embodiment, this method further configures conventional repeatability controllers for the X and Y axes respectively, and clarifies the three-axis frequency coordination relationship and the acquisition method of feedback signals for each axis, thereby constituting a complete three-axis differentiated control scheme, effectively improving the overall performance of high-speed scanning imaging. Specifically:

[0103] In AFM scanning imaging systems, the control tasks and signal characteristics of the three axes differ fundamentally. The X-axis, as the fast axis, performs periodic smooth triangular wave scanning, and its reference trajectory is a strictly periodic signal; The axis, acting as a slow axis, performs a step-by-step ramp scan, and its reference trajectory is also a strictly periodic signal; while The surface morphology of the sample that the axis needs to track is a quasi-periodic signal, and its spectrum exhibits broadening and shifting characteristics.

[0104] To address the different control requirements of the three axes, this embodiment proposes differentiated control strategies: for shaft and The axis employs a traditional repetitive controller, leveraging its excellent tracking performance for strictly periodic signals; The axes employ an improved repetitive controller from the first embodiment, leveraging its robust tracking performance for quasi-periodic signals. This differentiated three-axis configuration enables frequency coordination across the three axes while ensuring optimal control performance for each axis, thereby improving the overall imaging accuracy and stability of the high-speed AFM imaging system.

[0105] For atomic force microscopy shaft and Each axis is equipped with a traditional repeater controller; Traditional repeating controllers for axes are used to track smooth triangular wave scan trajectories; Traditional repeating controllers for axes are used to track ramp scan trajectories and suppress [the effects of] [the following]. The pair caused by axis motion The cross-coupling periodic perturbation of the axis; and the comb notch filter (i.e., in the first embodiment) The fundamental frequency of the comb-shaped notch filter within the improved repetitive controller for the X and Y axes and the scanning frequency. Maintain consistency to achieve triaxial frequency coordination.

[0106] The structure of the traditional repetitive controller for the X and Y axes described above is as follows: Figure 5 (a) and Figure 5 As shown in (b), the two structures are basically the same, with Figure 5 (a) is used as an example to illustrate: The reference input signal in the figure is The displacement feedback signal is The two are subtracted at the comparison node to obtain the error signal, which is then fed into two parallel branches: the first branch is the baseline feedback controller. The first branch is used to ensure the basic stability of the system; the second branch is a traditional repetitive controller, which includes a pure delay element. FIR low-pass filter Stable reverse compensator and phase compensator Among them, the pure delay stage Used to generate high gain at the fundamental frequency and its harmonics to suppress periodic disturbances, the outputs of the two branches are superimposed by a summing node to drive the X-axis controlled object. To generate actual displacement output . Figure 5 (b) The shaft structure is similar.

[0107] The Y-axis ramp signal advances a fixed displacement at the end of each scan line, gradually covering the X-axis scan area. High-speed X-axis motion generates cross-coupled perturbations on the Y-axis through mechanical and electromagnetic coupling. These perturbations manifest as periodic signals with the same frequency as the X-axis scan. Traditional repeating controllers for axes can suppress cross-coupling disturbances while tracking ramp commands.

[0108] Comb notch filter in an improved repetitive controller for the Z-axis At base frequency The bandpass characteristic is formed at its harmonics, and its fundamental frequency is consistent with the XY axis scanning frequency, which means that The improved repeating controller for the axis only High-gain tracking is provided at the fundamental frequency and harmonics of the X and Y axes, and is strictly synchronized with the scanning period of the X and Y axes, thereby ensuring frequency coordination for Z-axis topography tracking while achieving high-precision planar scanning.

[0109] In addition, the actual displacements of the X and Y axes are measured by an interferometric displacement sensor and used as feedback signals; the deflection signal of the atomic force microscope probe is used as the feedback signal for the Z axis.

[0110] Interferometric displacement sensors (such as laser interferometers based on the Michelson interferometry principle) have nanometer-level or even sub-nanometer-level displacement measurement resolution, which can accurately measure the actual displacement output of XY-axis piezoelectric actuators. This avoids the influence of nonlinear effects such as hysteresis and creep in piezoelectric actuators on displacement accuracy, and provides accurate feedback signals for high-precision closed-loop control of the XY-axis.

[0111] The Z-axis uses the deflection signal of the AFM probe as the feedback signal, which reflects the change in contact force between the cantilever beam probe and the sample surface. In constant force mode, the control system adjusts the vertical position of the Z-axis piezoelectric actuator to keep the probe deflection signal near a preset value, thereby ensuring a constant contact force between the probe and the sample.

[0112] This feedback signal configuration fully considers the differences in physical characteristics of each axis control task: the XY axis focuses on position accuracy, so a high-precision displacement sensor is used as feedback; The focus of the axis is on constant contact force, so the probe deflection signal, which directly reflects the contact force, is used as feedback.

[0113] To verify the effectiveness of the technical solutions provided in the first and second embodiments above, this section provides specific experimental verification data and comparative analysis results. Specifically:

[0114] This embodiment demonstrates a systematic experimental verification on a self-built triaxial nanopositioning experimental platform. The experimental platform employs a series-parallel hybrid configuration triaxial nanopositioning system with a working stroke of [missing information]. The X and Y axes are driven by normal stress electromagnetic actuators, while the Z axis is driven by a piezoelectric ceramic actuator. shaft and The actual displacement of the axis is measured using an interferometric displacement sensor, and the feedback signal of the Z-axis is obtained from the probe deflection signal of a commercial AFM scanning head. The system sampling frequency is set to 10kHz.

[0115] Before the experiment, the triaxial system was first identified in the frequency domain, and the linear dynamic transfer function models of each axis were obtained, providing a basis for the design of controller parameters. The experiment used standard slotted grating samples (period spacing...) (Feature height 100nm) and square columnar grating sample (period spacing) The feature height (100nm) was used as the test object, and the imaging areas were respectively and The image resolution is Pixels. Experiment in The imaging performance of the baseline PI controller, the conventional repetitive controller, and the triaxial repetitive controller proposed in this invention were tested at three scanning frequencies of 50Hz.

[0116] In the XY axis control performance verification, pure baseline tests were conducted respectively. The tracking performance of the controller and its embedded traditional repetitive control structure were compared. Experimental results show that at a scan frequency of 50Hz, the traditional repetitive control strategy reduces the X-axis tracking error by more than [percentage missing]. The Y-axis tracking error was reduced by more than This verifies the efficient suppression capability of traditional repetitive control structures for strictly periodic disturbances along the X and Y axes.

[0117] The above data was obtained by comparing the root mean square tracking error (RMSE) of pure baseline PI control and the embedded traditional repetitive control. The RMSE metric is defined as follows:

[0118]

[0119] in This represents the actual output displacement. For reference trajectory instructions, This represents the total number of sampling points. This metric reflects the proportion of tracking error to the travel of the reference trajectory, and can objectively evaluate the tracking accuracy under different control strategies.

[0120] In the Z-axis IMRC performance verification, a slotted grating sample was used (the sample rotated approximately around the Z-axis). Introducing a frequency drift effect artificially results in imaging results such as... Figure 7 As shown. At a scanning frequency of 50Hz, from Figure 7 The baseline integrator imaging results shown in (a)-(c) exhibit blurred topography and loss of detail; from Figure 7 As shown in (d)-(f), the imaging results of the traditional repetitive control strategy are acceptable at 10Hz and 25Hz, but significant morphological distortion occurs at 50Hz. This is due to the performance degradation of the pure delay element caused by the frequency shift resulting from the tilted placement. Figure 7 As shown in (g)-(i), the imaging results of the three-axis repetitive control strategy of the present invention can be seen that, It maintained clear shape contours and sharp edge features at all three scanning frequencies of 50Hz. Figure 7 The cross-sectional curves shown in (j)-(l) further confirm its robustness under frequency offset conditions. Quantitative analysis shows that at a scanning frequency of 50Hz, the IMRC method reduces the mean absolute error of the topography from that of the traditional CRC method. Down to The decline exceeded .

[0121] Mean absolute error (MAE) is defined as the percentage of the average absolute deviation between the reconstructed topography value and the true value relative to the total height of the topography. This metric reflects the fidelity of the imaged topography. Placing the sample at an angle causes the scanning direction to be non-perpendicular to the sample fringe direction, resulting in a deviation in the scanning trajectory period relative to the controller's preset scanning period, thus artificially simulating a frequency shift in the topography signal.

[0122] Under the above conditions, the performance of traditional CRC degrades due to the sensitivity of the pure delay element to frequency offset, while IMRC maintains high topography reconstruction accuracy because the comb notch filter has a low-sensitivity region near the fundamental frequency.

[0123] In the imaging verification of the square cylindrical grating sample, the imaging results are as follows: Figure 8 As shown, the rectangular cylindrical sample exhibits a significant height difference between the plane and the cylinder, placing stringent demands on the Z-axis controller's response speed and overshoot-free tracking capability. From Figure 8 As shown in the baseline integral controller imaging results (a)-(c), there is a significant rounding effect and tracking lag at the edges of the square pillars; from Figure 8 As shown in (d)-(f), the imaging results of the traditional repetitive control strategy reveal ringing and overshoot at the edge of the square pillar during 50Hz scanning; from Figure 8 As shown in (g)-(i), the imaging results of the three-axis repetitive control strategy of the present invention show that the edges of the square pillars are steep, the top plane is flat, and the bottom transition is clean, which is highly consistent with the morphology of the 10Hz low-speed reference. Figure 8The cross-sectional curves shown in (j)-(I) also quantitatively verify its excellent shape preservation ability. The root mean square error of the morphology results obtained by the IMRC method at a scanning speed of 50Hz and the low-speed baseline PI at 10Hz is only [missing information]. The root mean square error of the contact force is only .

[0124] The above The root mean square error of the morphology is relative to the total height of the sample, 100 nm, indicating that the deviation between the morphology reconstructed by the IMRC method at 50 Hz high-speed scanning and the morphology at 10 Hz low-speed reference is extremely small, verifying the high-fidelity imaging capability of the IMRC method at high-speed scanning.

[0125] The root mean square error of contact force is This indicates that the probe deflection signal can remain stable near the set value when tracking rapid changes in morphology at high speed, and the fluctuation of the contact force is very small, effectively avoiding sample scratches or probe wear caused by excessive contact force.

[0126] In the contact force stability verification, the cantilever beam deflection is as follows: Figure 9 As shown. Figure 9 middle, Figure 9 (a)–(c) show the deflection section curves of the cantilever beam under three control strategies for the inclined groove sample. Figure 9 (d)-(f) show the deflection cross-sectional curves of the rectangular prism sample under the corresponding three control strategies. As can be seen from the figures: the baseline integral controller exhibits the largest deflection signal fluctuation amplitude during high-speed scanning, with even momentary detachment or overshoot occurring at abrupt changes in the edge of the rectangular prism sample; the traditional repetitive controller improves deflection fluctuation in most areas, but significant deflection oscillations still exist at abrupt changes in the edge of the rectangular prism; while the deflection curve of the three-axis repetitive control strategy of this invention remains stable near the set value, with the fluctuation amplitude maintained within the set value throughout the entire scanning stroke. Within this range, the contact force between the probe and the sample remains constant. At a scan rate of 50 Hz, the IMRC method effectively suppresses the maximum deflection error of both slotted and rectangular prism grating samples within a certain range. the following.

[0127] The maximum tracking error is defined as:

[0128]

[0129] This metric reflects the percentage of the instantaneous maximum deviation during tracking relative to the total travel distance. This metric is crucial for assessing contact force safety during high-speed scanning: if the maximum deflection error exceeds a certain threshold (typically a set value)... This means that a momentary collision or detachment may occur between the probe and the sample, leading to sample damage or measurement failure. The IMRC method stably controls the maximum deflection error within a certain range. The following verification demonstrates that this method maintains good sample safety while ensuring image quality.

[0130] Based on the above experimental results, the triaxial repetitive control strategy achieved high-precision grating scanning imaging at a scanning frequency of 50 Hz. Its imaging quality was highly consistent with that of the 10 Hz low-speed baseline controller, which fully demonstrates the effectiveness and superiority of the proposed control strategy in high-speed atomic force microscopy imaging.

[0131] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0132] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0133] In an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0134] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely in hardware, entirely in software (including firmware, microcode, etc.), or in a combination of hardware and software, collectively referred to herein as “circuit,” “module,” or “system.”

[0135] An electronic device according to this embodiment of the invention. The electronic device is merely an example and should not be construed as limiting the functionality or scope of the embodiments of the invention.

[0136] Electronic devices are manifested in the form of general-purpose computing devices. Components of an electronic device may include, but are not limited to: at least one processor, at least one memory, and buses connecting different system components (including memory and processor).

[0137] The memory stores program code that can be executed by a processor, causing the processor to perform the steps described in the "Exemplary Methods" section above, according to various exemplary embodiments of the present invention.

[0138] The storage may include readable media in the form of volatile storage, such as random access memory (RAM) and / or cache memory, and may further include read-only memory (ROM).

[0139] The storage may also include programs / utilities having a set (at least one) of program modules, including but not limited to: an operating system, one or more applications, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0140] A bus can represent one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus that uses any of the various bus architectures.

[0141] The electronic device can also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable a user to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be performed via input / output (I / O) interfaces. Furthermore, the electronic device can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via a network adapter. The network adapter communicates with other modules of the electronic device via a bus. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0142] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible embodiments, various aspects of the present invention may also be implemented as a program product comprising program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of the present invention described in the "Exemplary Methods" section above.

[0143] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0144] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0145] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0146] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0147] Furthermore, the accompanying drawings are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes shown in the above drawings do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0148] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0149] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A control method for AFM, characterized in that, Includes the following steps: The surface morphology of the sample to be tested is modeled in the time domain and the discrete Fourier transform is performed on the simulation signal to extract the frequency peak broadening and center frequency offset of the sample morphology spectrum. Based on the extracted frequency peak broadening width and center frequency offset, an infinite impulse response high-pass filter is parametrically designed; wherein the passband frequency, stopband frequency, passband gain and stopband gain are set according to the broadening width and offset, so that the transition band of the filter covers the frequency drift range near the scanning fundamental frequency determined by the XY axis scanning frequency. The infinite impulse response high-pass filter is converted into a comb notch filter by variable substitution, wherein the parameter of the variable substitution is determined by the ratio of the sampling frequency of the real-time control system to the scanning fundamental frequency; In the repetitive control framework of the Z-axis of an atomic force microscope, the comb-shaped notch filter is used to replace the pure delay module to form an improved repetitive controller; The improved repeating controller is embedded in parallel with the baseline feedback controller of the Z-axis to drive the controlled object corresponding to the Z-axis to track the surface morphology of the sample, thereby improving the imaging quality.

2. The method according to claim 1, characterized in that, The infinite impulse response high-pass filter adopts a Butterworth-type structure, and its transfer function is... satisfy: ； Where k is the filter order. The coefficients of the numerator polynomial, The coefficients of the denominator polynomial; The unit delay operator; and the numerator first term coefficient Normalization is performed to ensure that the passband gain is less than 0.

8.

3. The method according to claim 2, characterized in that, The transfer function of the comb notch filter By using a normalized infinite impulse response high-pass filter Replace the variable z in the text with The value is obtained, where N is the number of delay cycles and is equal to the ratio of the sampling frequency of the real-time control system to the scanning base frequency; The following conditions must be met: ； in, and The delay operator is the unit delay operator after being decimated by N times and kN times; and the transfer function replacing the pure delay module is... ,in The phase compensation term is calculated based on the zero-phase-error tracking control method. To compensate for the delay index.

4. The method according to claim 1, characterized in that, The improved repetitive controller includes: a low-pass filter, a comb notch filter, a phase compensator, a stable inverse compensator, a first summing node, and a second summing node; The input terminal of the stable inverse compensator is connected to the error signal of the Z-axis control loop, and the output terminal of the stable inverse compensator is connected to the first input terminal of the first summing node; The input terminal of the phase compensator is connected to the front control signal of the Z-axis controlled object, and the output terminal of the phase compensator is connected to the second input terminal of the first summing node; The output of the first summing node is connected to the input of the comb notch filter, and the output of the comb notch filter is connected to the input of the low-pass filter. The output of the low-pass filter is connected to the first input of the second summing node, the second input of the second summing node is connected to the output of the baseline feedback controller, and the output of the second summing node is used to drive the Z-axis controlled object.

5. The method according to claim 4, characterized in that, The Z-axis controlled object consists of a Z-axis piezoelectric actuator and a cantilever beam probe system connected in series with it.

6. The method according to claim 3, characterized in that, Optimizing the parameters of the infinite impulse response high-pass filter through system sensitivity function analysis includes the following steps: The first step is to establish the system sensitivity function from the disturbance to the tracking error. ; The following conditions must be met: ； in, ; Let be the transfer function of the baseline feedback controller. The transfer function of the Z-axis controlled object; The second step is to adjust the passband frequency of the infinite impulse response high-pass filter to change the width of the flat bottom of the comb notch filter, thereby adjusting the system's robustness to frequency drift. The third step is to adjust the stopband frequency and order of the infinite impulse response high-pass filter to change the gain of the comb notch filter at non-periodic frequencies, thereby adjusting the system's ability to suppress non-periodic frequency gains. Fourth, repeat steps two and three until the robustness and the inhibition ability reach a preset balance.

7. The method according to claim 1, characterized in that, Conventional repeatability controllers were configured for the X and Y axes of the atomic force microscope: Traditional repeat controllers for the X-axis are used to track smooth triangular wave scan trajectories; Traditional repetitive controllers for the Y-axis are used to track ramp scan trajectories and suppress cross-coupled periodic disturbances on the Y-axis caused by X-axis motion. The fundamental frequency of the comb-shaped notch filter is consistent with the scanning frequency of the XY axis.

8. The method according to claim 7, characterized in that, The actual displacements of the X and Y axes are measured using an interferometric displacement sensor as feedback signals; the deflection signal of the atomic force microscope probe is used as the feedback signal for the Z axis.

9. A non-transitory computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a control method for AFM as described in any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a control method for AFM as described in any one of claims 1 to 8.

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