Atomic force microscope control method and system, medium and terminal

Abstract

The invention relates to the technical field of atomic force microscopes, in particular to an atomic force microscope control method and system, a medium and a terminal. The control method comprises the following steps: calculating an error signal e and an error change rate ec through a signal acquisition step; regulatory factors alpha e, beta and alpha ec are obtained through a domain of discourse regulation step; fuzzy control is carried out on control parameters Kp, Ki and Kd of the PID controller; and the control parameters Kp, Ki and Kd of the PI lambda D controller are subjected to optimization control through an optimization output step so as to act on the atomic force microscope. Through the steps, variable universe fuzzy control and fractional order PID are combined, rolling time domain optimization is added, and accurate control over the scanning process of the atomic force microscope is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of atomic force microscopy, and particularly to a control method and system, a medium, and a terminal for an atomic force microscope. Background Art

[0002] As a high-precision microscopic imaging tool, the Atomic Force Microscope (AFM) has been widely used in fields such as materials science, biomedicine, and nanomanufacturing. However, with the development of science and technology, the performance requirements of AFM have been continuously improved, especially in high-speed imaging and high-precision processing. The traditional PID (Proportional-Integral-Derivative) control technology faces performance bottlenecks in AFM, especially during high-speed operation and complex sample scanning, where the imaging quality is difficult to reach an ideal level.

[0003] During the operation of AFM, the scanning core component is a displacement stage based on a piezoelectric ceramic. Due to its high precision and easy controllability, piezoelectric ceramics are widely used in precision instruments such as AFM and scanning tunneling microscopes. However, piezoelectric ceramics have non-linear characteristics such as hysteresis characteristics, creep characteristics, and vibration characteristics. These characteristics make the working principle of analyzing the piezoelectric ceramic displacement platform very complex, and at the same time, they will also cause positioning errors and affect the imaging quality. Especially in different scanning modes, different characteristics often jointly cause greater errors in AFM. In addition, repetitive movements are required during the sample scanning process, but the traditional PID control technology has deficiencies in repetitive movement control, resulting in poor quality or even errors in the surface topography images of the samples.

[0004] Therefore, how to improve the control technology to achieve better image signal tracking and higher imaging quality has become a key issue in the current development of AFM technology. Summary of the Invention

[0005] To solve at least one deficiency in the control technology of the atomic force microscope in the above-mentioned prior art, the present invention provides a control method for an atomic force microscope, including the following steps: Signal acquisition step; acquiring a reference signal and an output signal for controlling the atomic force microscope; calculating an error signal e and an error change rate ec based on the reference signal and the output signal; Domain adjustment step; inputting the error signal e and the error change rate ec into a domain regulator for variable domain, and the domain regulator obtains adjustment factors α e 、β、α ec ; Fuzzy control step; inputting the error signal e, the error change rate ec, and the adjustment factors α e 、β、αec They are respectively input into the fuzzy controller, and the fuzzy controller outputs the change amounts ΔK p 、ΔK i 、ΔK d of the control parameters of the PID controller through the processes of fuzzification, fuzzy logic inference, and defuzzification, and obtain the control parameters K p 、ΔK i 、ΔK d of the PID controller through the change amounts ΔK p 、K i 、K d ; Optimized output step; by respectively obtaining the fractional orders of the integral term and the differential term of the PID controller, to obtain PI λ D µ controller; and optimize the control parameters K λ D µ of the PI p 、K i 、K d controller through the rolling horizon algorithm for optimal control, to obtain the optimized control quantity, and apply the optimized control quantity to the atomic force microscope.

[0006] In some embodiments, in the domain adjustment step, the domain adjuster respectively obtains the adjustment factors α e 、β、α ec through the processes of fuzzification, fuzzy logic inference, and defuzzification. The specific steps include: The domain adjuster fuzzifies the error signal e and the error change rate signal ec by using the membership function defined by the combination of trimf and gaussmf; defines the fuzzy subsets of the domain adjuster, and performs fuzzy logic inference by using the Mamdani fuzzy inference method and defuzzification by using the centroid method to obtain the adjustment factors α e 、β、α ec ; the adjustment factors α e 、α ec respectively adjust the input through their corresponding quantization factors Ke and Kec, and the adjustment factor β adjusts the output through its corresponding proportionality factor Ku.

[0007] In some embodiments, the fuzzy subsets defined for the domain adjuster are set to {CB, CM, CS, ZO, ES, EM, EB}, which respectively represent {substantial compression, medium compression, slight compression, remain unchanged, slight extension, medium extension, substantial extension}.

[0008] In some embodiments, in the fuzzy control step, the fuzzy controller outputs the control parameter change ΔK of the PID controller through fuzzification, fuzzy logic reasoning and defuzzification processes. p , ΔK i , ΔK d The specific steps include: The fuzzy controller uses the membership function defined by trimf and gaussmf to perform fuzzy processing on the error signal e and the error change rate signal ec to obtain the fuzzy error signal e and the error change rate signal ec; Define the fuzzy subset of the fuzzy controller, and perform fuzzy logic reasoning on the fuzzified error signal e and the error change rate signal ec according to the Mamdani fuzzy reasoning method; The centroid method is used to defuzzify the inference results and obtain the control parameter change ΔK of the PID controller. p , ΔK i , ΔK d .

[0009] In some embodiments, the fuzzy subsets defining the fuzzy controller are set to {NB, NM, NS, ZO, PS, PM, PB}, representing {extremely small, medium small, tiny, medium, slightly large, medium large, extremely large} respectively.

[0010] In some embodiments, the centroid method is based on the centroid of the area enclosed by the membership function curve selected in the fuzzy control process and the horizontal axis of the coordinate as the output value of each variable after defuzzification, and its formula is expressed as follows: , where is the output value of each variable after defuzzification, is the first elements, Represented as an element in the fuzzy set N The membership function value is a triangle, a trapezoid, or a Gaussian shape.

[0011] In some embodiments, the PI is processed by a rolling time domain algorithm. λ D µ The control parameter K of the controller p , K i , K d Perform optimization control to obtain the optimized control quantity, specifically including: adjusting the PI according to the existing model, current state, expected state and future control quantity λ D µ The controller predicts the output-related parameters Np, Nc and rω; and minimizes the deviation between the predicted output-related parameters Np, Nc and rω and the desired state through a cost function to obtain an optimized control amount.

[0012] In some embodiments, it further includes a sampling signal filling step; obtaining a sampling signal controlled by an atomic force microscope, and extracting missing and / or abnormal time points of the sampling signal in a time series; according to the sampling signal, using an interpolation algorithm to fill the missing and / or abnormal time points to obtain an interpolated sampling signal; iteratively optimizing the interpolated sampling signal through a rolling horizon algorithm, and combining the iteratively optimized interpolated signal with the sampling signal to form the output signal to be obtained in the signal acquisition step.

[0013] In some embodiments, it further includes a control quantity filling step; obtaining the optimized control quantity, and extracting missing and / or abnormal time points of the optimized control quantity in a time series; according to the optimized control quantity, using an interpolation algorithm to fill the missing and / or abnormal time points to obtain an interpolated control signal; iteratively optimizing the interpolated control signal through a rolling horizon algorithm, combining the iteratively optimized interpolated control signal with the optimized control quantity to form an actual control signal, and applying the actual control signal to the atomic force microscope.

[0014] In a second aspect, the present invention further provides a control system for an atomic force microscope, including: A signal acquisition module; obtaining a reference signal and an output signal controlled by an atomic force microscope; calculating an error signal e and an error change rate ec according to the reference signal and the output signal; A universe adjustment module; inputting the error signal e and the error change rate ec into a universe regulator for variable universe, and the universe regulator respectively obtains adjustment factors α e 、β、α ec ; A fuzzy control module; respectively inputting the error signal e, the error change rate ec, and the adjustment factors α e 、β、α ec into a fuzzy controller, and the fuzzy controller respectively outputs changes in control parameters of a PID controller ΔK p 、ΔK i 、ΔK d , and obtains control parameters K p 、ΔK i 、ΔK d of the PID controller through the changes in control parameters of PID ΔK p 、K i 、K d ; An optimized output module; respectively obtaining fractional orders of the integral term and the differential term of the PID controller to obtain PI λ Dµ a controller; and optimize the control parameters K λ D µ of the PI-D controller through a receding horizon algorithm to obtain an optimized control quantity, and apply the optimized control quantity to the atomic force microscope. p , K i , K d

[0015] In a third aspect, the present invention further provides a storage medium, which is a non-volatile storage medium or a non-transient storage medium, on which a computer program is stored, and when the computer program is run by a processor, it executes the control method of the atomic force microscope described in the above embodiments.

[0016] In a fourth aspect, the present invention further provides a terminal, including a memory and a processor, where a computer program capable of running on the processor is stored on the memory, and when the processor operates the computer program, it executes the control method of the atomic force microscope described in the above embodiments.

[0017] Based on the above, compared with the prior art, the control method of the atomic force microscope provided by the present invention combines variable universe fuzzy control and fractional-order PID, and adds receding horizon optimization to achieve precise control of the scanning process of the atomic force microscope. At the same time, it effectively avoids problems such as the difficulty in selecting the universe of the controller when the input error change range is large and the reduction of the decision-making speed due to too many rules in traditional fuzzy control.

[0018] Other features and beneficial effects of the present invention will be described in the subsequent description, and some of them will become obvious from the description or be understood by implementing the present invention. The objectives and other beneficial effects of the present invention can be achieved and obtained through the structures specifically pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained without creative efforts; in the following description, the positional relationships in the drawings, unless otherwise specified, are all based on the directions shown by the components in the drawings.

[0020] Figure 1 is a logic diagram of the existing traditional PID control; Figure 2 ​​Figure 3 Control logic diagram of the control method of an atomic force microscope provided by an embodiment of the present invention; Figure 4 Schematic diagram of the variation of the universe of discourse adjustment; Figure 5 Tracking comparison diagram of triangular waves under different control methods; Figure 6 Partial enlarged view of the tracking comparison of triangular waves under different control methods; Figure 7 Error comparison diagram of triangular waves under different control methods; Figure 8 Tracking comparison diagram of sine waves under different control methods; Figure 9 Partial enlarged view of the tracking comparison of sine waves under different control methods; Figure 10 Error comparison diagram of sine waves under different control methods. Specific embodiments

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention; the technical features designed in different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0022] In the description of the present invention, it should be noted that all terms (including technical terms and scientific terms) used in the present invention have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs, and should not be construed as limiting the present invention; it should be further understood that the terms used in the present invention should be understood as having a meaning consistent with their meaning in the context of this specification and the relevant art, and should not be understood in an idealized or overly formal sense, unless clearly defined as such in the present invention.

[0023] Currently, the main research methods for improving AFM control technology to achieve better image signal tracking and higher imaging quality include control methods based on a three-layer BP neural network combined with a PID controller, control methods based on a cascade structure combined with a PID controller, control methods based on fuzzy control combined with a PID controller, etc. However, in the existing technology, the PID controller based on a three-layer BP neural network has a good control effect on control systems without an accurate mathematical model, but lacks the proof of a complete theoretical system and the algorithm is time-consuming and laborious. The PID controller based on a cascade structure adds a secondary control quantity loop to the main control quantity loop, doubling the workload, etc.

[0024] The control accuracy of the traditional PID algorithm is relatively low, and complex control systems are in fractional-order form. If only integer-order differential equations are used to describe such systems, it is difficult to accurately express the essential characteristics of the systems. Moreover, AFM needs to be controlled in the x, y, and z directions. For a PID controller, the number of parameters to be tuned will reach nine, and this process will surely be time-consuming and laborious, and it may not necessarily achieve the optimal control effect. For the control method based on fuzzy control combined with a PID controller, there are still the following problems: for example, when the input error change range is large, it is difficult to select the controller's universe of discourse, and too many rules lead to a decrease in the decision-making speed, etc. Moreover, although fuzzy control has a good control effect, there are obvious drawbacks in the selection of the universe of discourse and the determination of membership functions, and the process is quite cumbersome and requires a large amount of experiments and data to be obtained more accurately.

[0025] In view of this, the present invention provides a control method for an atomic force microscope to effectively solve the above problems. On the basis of the Figure 1 shown classical PID control, the concept of fractional order is added to form a fractional-order PID control, that is, PI λ D µ controller; and then combined with fuzzy control to adaptively adjust PI λ D µParameters of the controller; among them, the setting of the universe of discourse directly affects the adjustment performance of the controller. The variation range of the trajectory tracking error of the AFM is often very large. If a fuzzy self-tuning PID controller with a constant universe of discourse is used alone, in order to adapt to its large error range, the fuzzy universe of discourse has to be selected large enough. After the error converges to a certain range, the fuzzy logic reasoning will no longer work. On the other hand, if the fuzzy universe of discourse is selected to be relatively small, then its set value will not change in the initial stage, that is, when the error is large, the controller loses sensitivity to the error change. One way to solve this contradiction is to subdivide the fuzzy universe of discourse. However, this will lead to a sharp increase in the fuzzy rules, resulting in a fuzzy rule explosion, so that the computational amount is too large to be applied in the actual system. Therefore, the embodiment of the present invention applies the idea of variable universe of discourse to the design of the fuzzy fractional-order PID controller. At the same time, by adding a receding horizon control (RHC) algorithm to the obtained predicted value, the control error is further reduced, making the adjustment of the proposed control strategy simpler, effectively reducing the tracking error, and improving the control performance. Finally, a new control method for the atomic force microscope proposed by the present invention is formed, that is, the AFM control algorithm based on variable universe of discourse fuzzy predictive fractional-order PID (VD-FPFOPID).

[0026] The following combines different embodiments and the accompanying drawings of the specification to describe and explain the technical solutions of the present invention in detail through various specific implementation manners.

[0027] Embodiment 1 Please refer to Figure 2 , the control method of the atomic force microscope provided in this embodiment includes the following steps: Signal acquisition step; acquiring a reference signal and an output signal for the control of the atomic force microscope; calculating an error signal e and an error change rate ec according to the reference signal and the output signal.

[0028] Specifically, the output signal y of the atomic force microscope can be detected by a detection mechanism, and the output signal y is subtracted from the reference signal r to calculate the error signal e and the error change rate ec, where e = y - r, ec = e(t) - e(t - 1), e(t) is the error signal at the current moment, and e(t - 1) is the error signal at the previous moment.

[0029] Universe of discourse adjustment step; inputting the error signal e and the error change rate ec into a universe of discourse regulator for variable universe of discourse, and the universe of discourse regulator respectively obtains adjustment factors α e , β, α ec .

[0030] Specifically, when implementing Figure 3As shown in the figure, let the initial setting domain of the input variable error be \(X = [-E, E]\), and the new domain after variable domain transformation is denoted as \(X' = [-\alpha E, \alpha E]\). Here, \(\alpha\) is the domain scaling factor, and \(X'\) is the adjusted domain. Among them, the purpose of variable domain processing is to dynamically adjust the domains of the error signal and the error change rate according to the operating state of the system to improve the adaptive ability of the controller.

[0031] In the process of fuzzifying the error signal \(e\) and the error change rate \(ec\), fuzzy logic inference, and defuzzification, it specifically includes converting the error signal \(e\) and the error change rate \(ec\) into fuzzy language variables and mapping them to predefined fuzzy sets. Among them, fuzzification includes the determination of the domain and the selection of the membership function. The quantity obtained by fuzzification can be represented as a definite numerical value, that is, the membership degree, in the computer. The membership degree is a value between 0 and 1. The closer it is to 1, the more in line with the actual situation, and the closer it is to 0, the less in line with the actual situation. Then, according to the fuzzified error signal \(e\) and the error change rate \(ec\), and the pre-set fuzzy rules, fuzzy logic inference is carried out. The fuzzy rules are used to determine how to adjust the adjustment factor \(\alpha\) according to the error and the error change rate. e 、\(\beta\), \(\alpha\) ec Finally, the result of fuzzy logic inference is converted back to a specific numerical value, that is, the adjustment factor \(\alpha\) is obtained. e 、\(\beta\), \(\alpha\) ec Among them, the defuzzification process can use the center average method, the maximum membership degree method, the centroid method, or other suitable defuzzification techniques. In the defuzzification process, the adjustment factor \(\alpha\) e 、\(\alpha\) ec are respectively adjusted for the input through their corresponding quantization factors \(Ke\), quantization factor \(Kec\), and the adjustment factor \(\beta\) is adjusted for the output through its corresponding proportionality factor \(Ku\). Through this design, flexible adjustment and precise adjustment can be carried out according to different input and output requirements to ensure the accuracy and reliability of the output results. It can make the system show better performance when processing complex signals to optimize the response speed, stability, and robustness of the system. At the same time, it can also effectively improve the control accuracy of the atomic force microscope.

[0032] In the domain adjustment step, the adjustment factors \(\alpha\) e 、\(\beta\), \(\alpha\) ec are respectively used to adjust the domains of the error signal \(e\) and the error change rate \(ec\). Specifically, \(\alpha\) e is used to adjust the domain range of the error signal \(e\), \(\beta\) is used to adjust the domain ranges of the proportional, integral, and differential parameters of the PID controller, and \(\alpha\) ec is used to adjust the domain range of the error change rate \(ec\). According to the obtained adjustment factors \(\alpha\) e 、\(\beta\), \(\alpha\) ec, adaptively adjust the parameters of the fractional-order PID controller to optimize the performance of the controller and improve the robustness and control accuracy of the control system.

[0033] Fuzzy control steps; input the error signal e, the error change rate ec, and the adjustment factors α e , β, α ec into the fuzzy controller respectively. The fuzzy controller outputs the change amounts ΔK of the control parameters of the PID controller through the processes of fuzzification, fuzzy logic inference, and defuzzification p , ΔK i , ΔK d , and obtain the control parameters K of the PID controller through the change amounts ΔK of the control parameters of the PID p , ΔK i , ΔK d . p , K i , K d .

[0034] In specific implementation, first perform fuzzification processing on the obtained error signal e, error change rate ec, and adjustment factors α e , β, α ec respectively. The fuzzification process includes mapping the exact value of each input quantity to a predefined fuzzy set, and each input quantity will be assigned a membership degree indicating the degree to which it belongs to each fuzzy set. Then use fuzzy rules for inference. These fuzzy rules are formulated based on expert knowledge and experience and are used to determine how to adjust the parameters of the PID controller according to the input fuzzy sets. Finally, convert the output quantity obtained from the fuzzy logic inference back to the exact change amounts ΔK of the control parameters of the PID controller p , ΔK i , ΔK d . The defuzzification process can adopt the centroid average method, the maximum membership degree method, the center of gravity method, or other appropriate defuzzification techniques. Then use the change amounts ΔK of the control parameters obtained from defuzzification p , ΔK i , ΔK d to update the control parameters K of the PID controller p , K i , K d . Its update formula is: , , ; where K p , K i , K d are the proportional coefficient, integral coefficient, and differential coefficient updated by the PID controller respectively, , , They are the initial proportional coefficient, integral coefficient, and derivative coefficient of the PID controller, respectively.

[0035] Optimize the output step; by obtaining the fractional orders of the integral term and derivative term of the PID controller respectively to get the PI λ D µ controller; and use the receding horizon algorithm to optimize the control parameters K λ D µ of the controller, p K i K d K

[0036] Specifically, when implementing, preferably construct a PI λ D µ controller. Since the PI λ D µ controller has two more tuning parameters λ and µ than the integer-order PID controller, therefore, the application of the PI λ D µ controller has a wider adjustment range than the traditional integer-order PID controller, and can make the control parameters K p K i K d K p K i K d input to the PI λ D µ controller, and then in each control period, use the receding horizon algorithm (RHC) to optimize the control parameters K λ D µ of the controller. p K i K d K

[0037] In this embodiment, the receding horizon algorithm is an optimization technique based on model prediction. It adjusts the prediction horizon Np, control horizon Nc, and weight coefficient rω to make the system approach the desired state as much as possible in a future time period to adapt to the dynamic changes of the system. Its optimization process includes the following steps: a) According to the current state and desired state of the system, establish an optimization problem, and the goal is to minimize the cost function, which reflects the weights of the control error and control action. b) Apply an optimization algorithm (such as the gradient descent method, sequential quadratic programming, etc.) to solve the optimization problem to obtain the optimized control parameters K p K i K d Kp ’, K i ’, K d ’ is updated to PI λ D µ in the controller. Specific relevant formulas can be reasonably set according to actual needs and will not be elaborated here.

[0038] For example, in the control of an atomic force microscope, Np can be set to the next 10 sampling periods, Nc to 5 sampling periods, and rω is dynamically adjusted according to the error and the rate of change of the error. In this way, RHC can recalculate the optimal control quantity within each sampling period, thus achieving real-time optimal control of the system. The cost function is a core component of RHC, and its goal is to minimize the deviation between the predicted output and the desired state. In the PI λ D µ controller optimization process, the cost function usually includes the square term of the error and the square term of the control quantity to balance the control accuracy and the magnitude of the control quantity. Specifically, in the control of an atomic force microscope, the cost function can be set to the sum of the squares of the errors plus the square of the control quantity, and the weight coefficient is adjusted according to the dynamic characteristics of the system. By minimizing the cost function, RHC can obtain the optimal control quantity, enabling the system to approach the desired state as closely as possible within the future prediction time domain. This optimal control method can not only improve the control accuracy of the system but also effectively reduce the fluctuation of the control quantity, thereby enhancing the stability and robustness of the system. In the specific implementation process, the optimization process of RHC is usually achieved through numerical optimization algorithms such as the gradient descent method or the interior point method. These algorithms can quickly find the optimal solution with limited computing resources, thus meeting the requirements of real-time control. For example, in the control of an atomic force microscope, the optimization process of RHC can be completed within each sampling period to ensure the real-time update of the control quantity. In this way, RHC can achieve efficient control in complex dynamic systems and provide strong support for the application of PI λ D µ controller.

[0039] Finally, according to the optimized PI λ D µ controller parameters, calculate the control quantity u(t), which is the controller's response to the current state of the system. Apply the calculated optimized control quantity u(t) to the atomic force microscope to achieve precise and stable control of it.

[0040] In this embodiment, through the above-mentioned fractional-order PI λ D µCombined with the rolling horizon algorithm on the controller, it can reduce the limitations of traditional integer-order controllers when dealing with the characteristics of piezoelectric ceramics, especially the control accuracy in the hysteresis region and creep region, effectively improve the control accuracy and response speed of the atomic force microscope, enhance the robustness of the system at the same time, and is applicable to complex nano-operation and control scenarios.

[0041] In an optional embodiment, in the universe of discourse adjustment step, the universe of discourse regulator obtains the adjustment factors α e , β, α ec through the processes of fuzzification, fuzzy logic inference and defuzzification, and the specific steps are as follows: First, the universe of discourse regulator fuzzifies the error signal e and the error change rate signal ec by using the membership function defined by combining trimf and gaussmf. Trimf is a triangular membership function, suitable for defining clear boundary ranges, while gaussmf is a Gaussian membership function, which can better describe fuzzy boundaries. By combining these two functions, the fuzzy characteristics of the error signal and the error change rate signal can be described more accurately. For example, the initial universe of discourse of the error signal e is X = [-E, E], which is divided into multiple fuzzy subsets through trimf, such as "substantial compression", "medium compression", "light compression", etc., and gaussmf is used to describe the transition regions of these subsets to ensure the smoothness of fuzzification.

[0042] Second, define the fuzzy subsets of the universe of discourse regulator. In this embodiment, the fuzzy subsets are preferably set as {CB, CM, CS, ZO, ES, EM, EB}, representing {substantial compression, medium compression, light compression, remain unchanged, light expansion, medium expansion, substantial expansion} respectively, corresponding to different universe of discourse adjustment strategies. The division of these fuzzy subsets enables the universe of discourse regulator to dynamically adjust the control strategy according to the actual state of the system, avoiding control rigidity or response lag caused by a fixed universe of discourse. For example, when the error signal e is large, the system may select the "substantial compression" subset to narrow the universe of discourse range and improve the control accuracy; when the error signal e is small, the system may select the "light expansion" subset to expand the universe of discourse range and enhance the stability of the system. The definition of such fuzzy subsets makes the universe of discourse adjustment more flexible and adaptable, and can dynamically adjust the universe of discourse range according to the actual error situation to effectively meet the control requirements under different working conditions and ensure the stable operation of the system in various complex environments.

[0043] Next, the Mamdani fuzzy inference method is preferably used for fuzzy logic inference in this embodiment. The fuzzy inference method is based on fuzzy rules, maps the fuzzified error signal and error change rate signal to fuzzy subsets, and obtains the corresponding adjustment factors through inference. For example, when the error signal e belongs to the "medium amplitude compression" subset and the error change rate ec belongs to the "light amplitude extension" subset, the fuzzy inference method will calculate the corresponding adjustment factor α according to the preset rules. e , β, α ec . The advantage of the fuzzy inference method is that it can handle uncertainties and non-linear problems, making the domain adjustment more in line with the actual control requirements. Among them, the fuzzy rules are obtained through the experience of experts and technicians and a large number of experimental tests. In this embodiment, the adjustment factors α e , β, α ec used in the atomic force microscope control can be shown in Table 1, Table 2, and Table 3 respectively as follows.

[0044] Table 1 Fuzzy rules of α e

[0045] Table 2 Fuzzy rules of β

[0046] Table 3 Fuzzy rules of α ec

[0047] Finally, the centroid method is used for defuzzification to obtain the final adjustment factors α e , β, α ec . The centroid method calculates the centroid of the area enclosed by the membership function curve and the horizontal axis of the coordinate in the fuzzy control process as the output value of each variable after defuzzification. Its formula is expressed as: , where is the output value of each variable after defuzzification, is the th element in the fuzzy set N, represents the membership function value of the element in the fuzzy set N; the membership function adopts at least one of triangle, trapezoid, and Gaussian. For example, when the fuzzy logic inference obtains multiple possible adjustment factor values, the centroid method will comprehensively consider the weights of these values and finally output a most reasonable value. This method can effectively reduce the uncertainty in the fuzzification process and ensure the accuracy and reliability of the adjustment factors.

[0048] Through the above steps, the domain regulator can dynamically adjust the domain range according to the error signal and error change rate signal, thereby improving the performance and stability of the control system.​​

[0049] In another alternative embodiment, in the fuzzy control step, the fuzzy controller outputs the changes ΔK p , ΔK i , ΔK d of the control parameters of the PID controller through the processes of fuzzification, fuzzy logic inference, and defuzzification. The specific steps are as follows: First, the fuzzy controller performs fuzzification processing on the error signal e and the error change rate signal ec by using the membership functions defined by combining trimf and gaussmf to obtain the fuzzified error signal e and error change rate signal ec. Among them, the fuzzy rules are obtained through the experience of experts and technicians and a large number of experimental tests. In this embodiment, the changes ΔK p , ΔK i , ΔK d of the control parameters adopted in the atomic force microscope control can be shown in Table 4, Table 5, and Table 6 respectively as follows.

[0050] Table 4 Fuzzy rules of ΔK p

[0051] Table 5 Fuzzy rules of ΔK i

[0052] Table 6 Fuzzy rules of ΔK d

[0053] Secondly, define the fuzzy subsets of the fuzzy controller, and perform fuzzy logic inference on the fuzzified error signal e and error change rate signal ec according to the fuzzy inference method. In this embodiment, it is preferably set that the fuzzy subsets of the defined fuzzy controller are {NB, NM, NS, ZO, PS, PM, PB}, which respectively represent {extremely small, small and medium, slightly small, medium, slightly large, medium and large, extremely large}. These levels can comprehensively cover the possible value ranges of the error signal and the error change rate signal. The core of the fuzzy inference method is to match the fuzzy values of the input signal with the fuzzy values of the output signal through the rules in the fuzzy rules, and finally obtain a fuzzy logic inference result. In this embodiment, the Mamdani fuzzy inference method is preferably adopted.

[0054] Finally, use the centroid method to defuzzify the inference result to obtain the changes ΔK p , ΔK i , ΔK d ​​​In this embodiment, the centroid method uses the centroid of the area enclosed by the membership function curve selected during the fuzzy control process and the horizontal coordinate axis as the output value of each variable after defuzzification. Its formula is expressed as: , where, is the output value of each variable after defuzzification, is the th element in the fuzzy set N, represents the membership function value of the element in the fuzzy set N; the membership function adopts at least one of triangular, trapezoidal, and Gaussian shapes. The advantage of using the centroid method is that it can comprehensively consider the overall distribution of the fuzzy inference results, thereby obtaining more stable and reliable control parameters.

[0055] Through the above steps, the fuzzy controller can dynamically adjust the parameters of the PID controller according to the changes in the error signal e and the error change rate signal ec, enabling the control system to better adapt to the changes in the external environment and improving the control accuracy and stability. This PID parameter adjustment method based on fuzzy control can not only effectively reduce the steady-state error of the system but also improve the dynamic response speed of the system, thereby significantly enhancing the overall performance of the control system.

[0056] To effectively illustrate the effects of the above embodiment, this embodiment also compares the tracking effects of different control methods of the atomic force microscope under the same conditions with triangular waves and sine waves as inputs based on the topographical changes during the AFM imaging process. Different control methods include PID, FOPID (Fractional Order PID Control), FFOPID (Fuzzy Fractional Order PID), VD-FFOPID (Variable Domain-Fuzzy Fractional Order PID), and VD-FPFOPID (Variable Domain-Fuzzy Predictive Fractional Order PID, that is, the control method of the embodiment of the present invention). The tracking comparison diagrams, local comparison enlarged diagrams, and error comparison diagrams of triangular waves under different control methods are specifically shown in Figure 5 , Figure 6 , Figure 7 . The tracking RMSE and two-norm errors of triangular waves under different control methods are shown in Table 7; the tracking comparison diagrams, local comparison enlarged diagrams, and error comparison diagrams of sine waves under different control methods are specifically shown in Figure 5 , Figure 6 , Figure 7As shown, the tracking RMSE and two-norm error of the sine wave under different control methods are shown in Table 8.

[0057] Table 7 Triangular wave tracking RMSE and two-norm error

[0058] Table 8 Sine wave tracking RMSE and two-norm error

[0059] As Figures 5 - 10 shown in Table 7 and Table 8, it can be seen that the VD-FPFOPID control method provided by the present invention has the best tracking effect. According to the traditional PID control, the RMSE can only reach 0.19041667 and 0.28335627 respectively, while the VD-FPFOPID control method of AFM proposed by the present invention can reach 0.00011433 and 0.00009003 respectively, which is 99.94% and 99.97% higher than the PID control RMSE, significantly superior to the traditional PID.

[0060] During the actual application, during the high-speed sampling process of the control signal of the piezoelectric ceramic displacement stage of the AFM, due to hardware or software limitations, data loss or discontinuous sampling may occur at some time points, resulting in scanning jitter. This discontinuity will directly affect the output of the PI λ D µ controller, and then cause deviation in the response of the piezoelectric ceramic, ultimately affecting the accuracy and stability of AFM scanning.

[0061] To solve the above problems, this embodiment can use the sampling signal filling step and / or the control quantity filling step to dynamically adjust the data at the current moment and its adjacent time points before and after, so as to effectively eliminate the scanning jitter phenomenon caused by data discontinuity, and then improve the scanning performance and stability of the AFM.

[0062] Specifically, the sampling signal filling step specifically includes: (1) Obtain the sampling signal of the atomic force microscope control, and extract the missing time points of the sampling signal in the time series. Among them, the sampling signal can be collected by a corresponding detection mechanism for the signal output by the executing component in the atomic force microscope, and then the missing time points are marked and extracted by using the time series analysis method for the time series of the sampling signal. On this basis, the characteristics of the actual sampling signal can also be analyzed, not only marking the missing time points, but also marking and extracting the abnormal time points, which can also be applied to the filling in the subsequent steps. For example, the abnormal time points can be marked and extracted by analyzing whether the sampling signal value exceeds the preset threshold.

[0063] Of course, if necessary, after obtaining the sampling signal, the sampling signal can also be filtered, denoised, enhanced, etc. first, and then the missing time points can be extracted to further improve the stability and accuracy of the sampling signal.

[0064] (2) According to the sampling signal, an interpolation algorithm is used to fill in the missing and / or abnormal time points to obtain an interpolated sampling signal; specifically, the current missing time point can be filled in according to the sampling signal values of the previous and subsequent time points. The interpolation algorithm may include but is not limited to linear interpolation, polynomial interpolation, spline interpolation, or Lagrange interpolation. Specifically, a suitable interpolation algorithm can be selected according to the characteristics of the sampling signal and the distribution of the missing points, which is not limited in this embodiment.

[0065] (3) The interpolated sampling signal is iteratively optimized by a rolling horizon algorithm, and the iteratively optimized interpolated signal is combined with the sampling signal to form the output signal to be obtained in the signal acquisition step. Specifically, the window size and the number of iterations of the rolling horizon can be set first, and then the rolling horizon algorithm is applied to the interpolated sampling signal to iteratively optimize the data within the window. In each iteration, the data within the window is adjusted according to a preset optimization criterion (such as minimizing the sum of squared errors) to gradually approximate the true signal characteristics. Finally, the iteratively optimized interpolated signal is combined with the non-missing part of the original sampling signal to form the final output signal, and the output signal is applied to the subsequent signal acquisition step.

[0066] The control quantity filling step specifically includes: (1) Obtain the optimized control quantity, and extract the missing and / or abnormal time points of the optimized control quantity in the time series. Among them, the optimized control quantity is obtained from the optimization output step, and then the optimized control quantity is subjected to time series analysis to identify and extract the missing and / or abnormal time points.

[0067] (2) According to the optimized control quantity, an interpolation algorithm is used to fill in the missing and / or abnormal time points to obtain an interpolated control signal; the interpolation algorithm can be but is not limited to linear interpolation, polynomial interpolation, spline interpolation, or Lagrange interpolation. Specifically, it can be selected according to the smoothness of the control quantity and the density of the missing points, which is not limited in this embodiment. The selected interpolation algorithm is used to fill in the extracted missing and / or abnormal time points, and the interpolation data of the missing and / or abnormal time points is generated by calculating the values of the adjacent known control quantities before and after, so as to form an interpolated control signal.

[0068] (3) Iteratively optimize the interpolation control signal through a receding horizon algorithm, combine the iteratively optimized interpolation control signal with the optimized control quantity to form an actual control signal, and apply the actual control signal to the atomic force microscope. Apply the receding horizon algorithm to the interpolation control signal for iterative optimization. In each iteration, adjust the control input according to a preset optimization objective (such as minimizing the tracking error, maximizing the system stability, etc.) and predict the future state of the system. Input the synthesized actual control signal into the control system of the AFM to achieve precise control of the AFM.

[0069] Among them, the actual control signal is used to control the piezoelectric ceramic displacement stage of the atomic force microscope for precise scanning. To further eliminate the adverse effects brought by the hysteresis characteristics, creep characteristics, and vibration characteristics of the piezoelectric ceramic displacement stage, and further improve the control accuracy of AFM scanning.

[0070] Embodiment 2 Embodiment 2 of the present invention also provides a control system for an atomic force microscope, including at least: A signal acquisition module; acquire the reference signal and output signal for atomic force microscope control; calculate the error signal e and the error change rate ec according to the reference signal and output signal; A universe adjustment module; input the error signal e and the error change rate ec into the universe regulator for variable universe, and the universe regulator obtains the adjustment factors α e , β, α ec ; A fuzzy control module; input the error signal e, the error change rate ec, and the adjustment factors α e , β, α ec into the fuzzy controller respectively. The fuzzy controller outputs the control parameter variations ΔK p , ΔK i , ΔK d of the PID controller through the processes of fuzzification, fuzzy logic inference, and defuzzification respectively, and obtain the control parameters K p , ΔK i , ΔK d of the PID controller through the control parameter variations ΔK p , K i , K d ; An optimization output module; obtain the PI λ D µ controller by taking the fractional order of the integral term and the differential term of the PID controller respectively; and perform iterative optimization on the control parameters K λ D µ of the PI p, K i , K d Perform optimization control to obtain an optimized control quantity, and apply the optimized control quantity to the atomic force microscope.

[0071] This system can effectively avoid problems existing in traditional fuzzy control, such as it is difficult to select the domain of the controller when the input error change range is large, and too many rules lead to a decrease in decision-making speed. The specific ways for each module in the second embodiment above to perform operations have been described in detail in the first embodiment of the method, and will not be elaborated here.

[0072] Embodiment 3 The embodiment of the present invention further provides a storage medium, which is a non-volatile storage medium or a non-transient storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the control method of the atomic force microscope described in any one of the above embodiments.

[0073] Specifically, the storage medium is a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory, a hard disk drive (HDD), or a solid-state drive (SSD), etc.; the storage medium can also include a combination of the above types of memories.

[0074] Embodiment 4 The embodiment of the present invention further provides a terminal, which includes a memory and a processor. A computer program capable of running on the processor is stored on the memory. When the processor operates the computer program, it executes the control method of the atomic force microscope described in any one of the above embodiments.

[0075] Specifically, the number of processors can be one or more, and the processor can be a central processing unit (CPU). The processor can also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. chips, or a combination of the above types of chips. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc.

[0076] The memory and the processor can be communicatively connected through a bus or other means. The memory stores program instructions executable by at least one processor. The program instructions are executed by at least one processor so that the processor executes the control method of the atomic force microscope described in any of the foregoing embodiments.

[0077] In summary, for the control method, system, medium, and terminal of the atomic force microscope provided by the present invention, an error signal e and an error change rate ec are calculated through the signal acquisition step; adjustment factors α e , β, α ec are obtained through the universe of discourse adjustment step; the control parameters K p , K i , K d of the PID controller are obtained through the fuzzy control step; the control parameters K λ of the PI µ D p , K i , K d controller are optimized through the optimized output step and used to control the atomic force microscope. Through the above steps, the combination of variable universe of discourse fuzzy control and fractional-order PID is achieved, and rolling horizon optimization is added to realize precise control of the scanning process of the atomic force microscope.

[0078] In addition, those skilled in the art should understand that although there are many problems in the prior art, each embodiment or technical solution of the present invention can be improved in only one or several aspects, and it is not necessary to solve all the technical problems listed in the prior art or the background art at the same time. Those skilled in the art should understand that the content not mentioned in a claim should not be used as a limitation to that claim.

[0079] Although terms such as signal acquisition step, universe of discourse adjustment step, fuzzy control step, optimized output step, sampling signal filling step, control quantity filling step, etc. are used more frequently herein, the possibility of using other terms is not excluded. These terms are only used to more conveniently describe and explain the essence of the present invention; interpreting them as any additional limitation is contrary to the spirit of the present invention; the terms "first", "second", etc. (if any) in the specification, claims, and the above-mentioned drawings of the embodiments of the present invention are used to distinguish similar objects and do not have to be used to describe a specific order or sequence.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A control method for an atomic force microscope, characterized in that: The following steps are involved: Signal acquisition steps; Acquire a reference signal and an output signal controlled by the atomic force microscope; calculate an error signal e and an error change rate ec according to the reference signal and the output signal; The domain adjustment step: the error signal e and the error change rate ec are input into the domain regulator to change the domain, and the domain regulator obtains the adjustment factor α through fuzzification, fuzzy logic reasoning and defuzzification process respectively. e , β, α ec ; Fuzzy control steps: Error signal e, error change rate ec and adjustment factor α e , β, α ec The fuzzy controller is input into the fuzzy controller respectively, and the fuzzy controller outputs the control parameter change ΔK of the PID controller through the fuzzification, fuzzy logic reasoning and defuzzification process. p , ΔK i , ΔK d , and through the PID control parameter change ΔK p , ΔK i , ΔK d Get the control parameter K of the PID controller p , K i , K d ; Optimize the output steps; by calculating the fractional order of the integral term and the differential term of the PID controller, we can get PI λ D µ controller; and use the rolling horizon algorithm to λ D µ The control parameter K of the controller p , K i , K d Optimizing control is performed to obtain an optimized control amount, and the optimized control amount is applied to the atomic force microscope.

2. The control method of an atomic force microscope according to claim 1, characterized in that: In the domain adjustment step, the domain adjuster obtains the adjustment factor α through fuzzification, fuzzy logic reasoning and defuzzification process respectively. e , β, α ec The specific steps include: The domain regulator uses trimf and gaussmf combined with the defined membership function to fuzzify the error signal e and the error change rate signal ec; defines a fuzzy subset of the domain regulator, and uses the Mamdani fuzzy reasoning method for fuzzy logic reasoning; uses the centroid method to defuzzify to obtain the regulation factor α e , β, α ec The regulatory factor α e , α ec The input is adjusted by the corresponding quantization factor Ke and quantization factor Kec respectively, and the adjustment factor β adjusts the output by the corresponding scale factor Ku.

3. The control method of an atomic force microscope according to claim 1, characterized in that: In the fuzzy control step, the fuzzy controller outputs the control parameter change ΔK of the PID controller through fuzzification, fuzzy logic reasoning and defuzzification. p , ΔK i , ΔK d The specific steps include: The fuzzy controller uses the membership function defined by trimf and gaussmf to perform fuzzy processing on the error signal e and the error change rate signal ec to obtain the fuzzy error signal e and the error change rate signal ec; Define the fuzzy subset of the fuzzy controller, and perform fuzzy logic reasoning on the fuzzified error signal e and the error change rate signal ec according to the Mamdani fuzzy reasoning method; The centroid method is used to defuzzify the inference results and obtain the control parameter change ΔK of the PID controller. p , ΔK i , ΔK d .

4. The control method of the atomic force microscope according to claim 2 or 3, characterized in that: The centroid method is based on the centroid of the area enclosed by the membership function curve selected in the fuzzy control process and the horizontal axis of the coordinate as the output value of each variable after defuzzification. Its formula is expressed as follows: , where is the output value of each variable after defuzzification, is the first elements, Represented as an element in the fuzzy set N The membership function value is a triangle, a trapezoid, or a Gaussian shape.

5. The control method of an atomic force microscope according to claim 1, characterized in that: The PI is calculated by the rolling time domain algorithm. λ D µ The control parameter K of the controller p , K i , K d Perform optimization control to obtain the optimized control quantity, specifically including: adjusting the PI according to the dynamic model, current state, expected state and future control quantity λ D µ The controller predicts the output-related parameters Np, Nc and rω; and minimizes the deviation between the predicted output-related parameters Np, Nc and rω and the desired state through a cost function to obtain an optimized control amount.

6. The control method of an atomic force microscope according to claim 1, characterized in that: The method also includes a sampling signal filling step; acquiring a sampling signal controlled by an atomic force microscope, and extracting time points at which the sampling signal is missing and / or abnormal in a time series; using an interpolation algorithm to fill in the missing and / or abnormal time points according to the sampling signal to obtain an interpolated sampling signal; iteratively optimizing the interpolated sampling signal through a rolling time domain algorithm, and combining the iteratively optimized interpolated signal with the sampling signal to form the output signal to be acquired in the signal acquisition step.

7. The control method of an atomic force microscope according to claim 1, characterized in that: The method also includes a control quantity filling step; obtaining the optimized control quantity, and extracting the time points at which the optimized control quantity is missing and / or abnormal in the time series; filling the missing and / or abnormal time points with an interpolation algorithm according to the optimized control quantity to obtain an interpolation control signal; iteratively optimizing the interpolation control signal with a rolling time domain algorithm, combining the iteratively optimized interpolation control signal with the optimized control quantity to form an actual control signal, and applying the actual control signal to the atomic force microscope.

8. A control system for an atomic force microscope, characterized in that: include: Signal acquisition module; Obtain reference signals and output signals for AFM control; Calculate the error signal e and the error change rate ec according to the reference signal and the output signal; The domain adjustment module inputs the error signal e and the error change rate ec into the domain regulator to change the domain, and the domain regulator obtains the adjustment factor α through fuzzification, fuzzy logic reasoning and defuzzification process respectively e , β, α ec ; Fuzzy control module; the error signal e, error change rate ec and adjustment factor α e , β, α ec The fuzzy controller is input into the fuzzy controller respectively, and the fuzzy controller outputs the control parameter change ΔK of the PID controller through the fuzzification, fuzzy logic reasoning and defuzzification process. p , ΔK i , ΔK d , and through the PID control parameter change ΔK p , ΔK i , ΔK d Get the control parameter K of the PID controller p , K i , K d ; Optimize the output module; by calculating the fractional order of the integral term and differential term of the PID controller, we can get PI λ D µ controller; and use the rolling horizon algorithm to λ D µ The control parameter K of the controller p , K i , K d Optimizing control is performed to obtain an optimized control amount, and the optimized control amount is applied to the atomic force microscope.

9. A storage medium, characterized in that: The storage medium is a non-volatile storage medium or a non-transient storage medium, on which a computer program is stored. When the computer program is executed by a processor, the control method of the atomic force microscope according to any one of claims 1 to 7 is executed.

10. A terminal, characterized in that: The invention comprises a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and the processor executes the control method of the atomic force microscope according to any one of claims 1 to 7 when running the computer program.

Images