Multi-axis nanometer ultrafast system-based waviness error compensation device and control method

Abstract

The invention provides a waviness error compensation device based on a multi-axis nanometer ultrafast system.The compensation device comprises four driving units of the same model, a flexible hinge, a vacuum adsorption platform, a connecting flange and a fixed base, and each driving unit comprises a piezoelectric ceramic driver and a displacement sensor; the piezoelectric ceramic drivers are located at the bottoms of the flexible hinges, the vacuum adsorption platform is connected with the flexible hinges, the lower ends of the piezoelectric ceramic drivers are connected with the fixed base for supporting, the four sets of flexible hinges are symmetrically distributed on the connecting flange in parallel, the connecting flange is located on the fixed base, and the waviness error compensation device has three degrees of freedom. Voltage is applied to drive the piezoelectric ceramic driver to adjust the posture of the vacuum adsorption platform. By means of the scheme, relative vibration between the tool nose and the workpiece can be compensated in real time, the fly-cutter cutting arc waviness error is restrained, and therefore the quality and precision of the machined surface are remarkably improved.

Description

Technical Field

[0001] The invention belongs to the technical field of precision machining, and in particular relates to a waviness error compensation device and a control method based on a multi-axis nano-ultrafast system. Background Art

[0002] In the field of mechanical processing, especially in the fields of precision engineering and micro-nanotechnology, the requirements for the quality of machined surfaces are getting higher and higher, among which waviness is one of the important quality indicators of machined surfaces. In the processing of single-point diamond flycutting machines, the relative vibration between the tool tip and the workpiece is the main reason for the arc-shaped waviness error on the machined surface. This error will seriously affect the accuracy of the workpiece surface shape and limit the improvement of processing quality. In the actual cutting process, factors such as the dynamic characteristics of the machine tool and the spindle, the vibration caused by cutting, and external disturbances may cause relative vibration between the tool tip and the workpiece. Summary of the invention

[0003] In order to solve the above problems, the present invention proposes a corrugation error compensation device and control method based on a multi-axis nano-ultrafast system. Through a control algorithm composed of hysteresis compensation feedforward, self-disturbance rejection control and zero-phase feedforward, the relative vibration between the tool tip and the workpiece can be compensated in real time, thereby significantly improving the quality and accuracy of the machined surface.

[0004] On the one hand, the present invention proposes a corrugation error compensation device based on a multi-axis nano-ultrafast system, the device comprising four drive units of the same model, four groups of flexible hinges, a vacuum adsorption platform, four connecting flanges and a fixed base, each drive unit comprising a piezoelectric ceramic driver and a displacement sensor, the piezoelectric ceramic driver being located at the bottom of the flexible hinge, the vacuum adsorption platform being connected to the flexible hinge, the vacuum adsorption platform being supported by four piezoelectric ceramic drivers as legs through the flexible hinge, the lower end of the piezoelectric ceramic driver being connected to the fixed base for support, the four groups of flexible hinges being symmetrically distributed in parallel on the connecting flange, the connecting flange being located on the fixed base; the four displacement sensors and the piezoelectric ceramic driver being arranged at four points on the edge of the vacuum adsorption platform in a cross distribution, and being used to measure the posture heights of the corresponding positions, so that the corrugation error compensation device has three degrees of freedom, the three degrees of freedom being the rotational degrees of freedom RX and RY in two horizontal directions of the platform plane of the vacuum adsorption platform and the movement degree of freedom Z in the vertical direction, the piezoelectric ceramic driver being driven by applying voltage to adjust the posture of the vacuum adsorption platform.

[0005] Preferably, the piezoelectric ceramic driver has a stiffness of 50 N / μm, a driving voltage of 100 V, a stroke of 32 μm and a natural frequency of 40 kHz.

[0006] Preferably, the displacement sensor selected in the present invention is a capacitive sensor, and there is a direct linear relationship between its output voltage and displacement.

[0007] Preferably, each of the flexible hinges is composed of two circular flexible hinges, and the flexible hinges are made of aluminum alloy.

[0008] On the other hand, the present invention also proposes a control method for a waviness error compensation device based on a multi-axis nano-ultrafast system, wherein the vacuum adsorption platform is regarded as a rigid body, a displacement sensor detects the position height of the vacuum adsorption platform, and the actual position and posture of the vacuum adsorption platform is obtained by a plane fitting calculation method, which specifically includes the following steps:

[0009] Step S1, the height of the corresponding measuring point is input into each drive unit. At this time, the displacement influence of the three piezoelectric ceramic drivers outside the drive unit on the drive unit is regarded as disturbance, and the piezoelectric ceramic driver in the drive unit performs compensation control to achieve target decoupling, so as to more conveniently control a single drive unit;

[0010] Step S2, converting the position information into an actual voltage input signal through a driving power supply, driving the piezoelectric ceramic driver to push the flexible hinge to move upward, thereby achieving posture adjustment of the vacuum adsorption platform.

[0011] Preferably, the control method of a single driving unit in step S1 comprises the following steps:

[0012] Step S11, modeling the piezoelectric drive unit system, the piezoelectric drive unit system includes the strong hysteresis nonlinear characteristics of the piezoelectric ceramic driver and the linear characteristics of the flexible hinge mechanism, the two characteristics are modeled separately and integrated into the dynamic characteristics of the overall system, and a complete piezoelectric drive unit system dynamic characteristics description model is obtained, so as to design the control method later;

[0013] Step S12, building a hysteresis inverse model according to the description model established in step S11, so as to calculate the corresponding input control voltage according to the target hysteresis intermediate amount, eliminate the influence of hysteresis characteristics, and linearize the piezoelectric drive unit system;

[0014] Step S13, compensating the error caused by linearization by using an anti-disturbance control algorithm, which observes the disturbance of the system by using a linear form of a Lomberg state observer, and compensates the disturbance to the input end, thereby achieving the purpose of eliminating internal and external disturbances of the system;

[0015] Step S14: Under the condition of extended state observation compensation, the system characteristics approach the linear system model. In order to make the observer tracking more accurate, the system characteristics need to be reduced to a second-order system:

[0016] ;

[0017] Where s is the complex variable of the transfer function of the multi-axis nano-ultrafast system, , , It is a constant of the second-order system, obtained by simulation or experimental calibration. Based on the reduced-order second-order system characteristics, the original system is subjected to second-order state feedback control. In order to make the system response characteristics close to a completely identical linear relationship in a wider frequency range, that is, the amplitude response and phase lag both tend to 0, according to the response characteristics of the second-order system, the natural frequency of the closed-loop system needs to be increased, and the damping ratio needs to be reduced to near the critical damping;

[0018] Step S15, after closed-loop feedback adjustment, the phase response of the system still has a lag, so a zero-phase tracking feedforward compensation term is added before the closed-loop system to ensure that the system output has no phase lag in theory, thereby improving the dynamic tracking performance and control accuracy of the system as a whole.

[0019] Preferably, the two characteristics in step S11 are modeled as MPI model and ARX model respectively, wherein the MPI model, i.e. magnetic particle imaging model, can better characterize the strong hysteresis nonlinear characteristics, and the ARX model, i.e. organic derivative regression model, can summarize the linear part characteristics of the system.

[0020] The beneficial technical effects of the present invention are:

[0021] The present invention provides a corrugation error compensation device and control method based on a multi-axis nano-ultrafast system. In addition to improving the characteristics of the machine tool itself, the multi-axis nano-ultrafast system driven by piezoelectric ceramics and flexible hinges is precisely controlled by a piezoelectric ceramic driver and can be used as a micro-feed and micro-adjustment device for the workpiece being processed. The control algorithm composed of hysteresis compensation feedforward, auto-disturbance rejection control and zero-phase feedforward can compensate for the relative vibration between the tool tip and the workpiece in real time, suppress the arc-shaped corrugation error of the flying cutter, and thus significantly improve the quality and accuracy of the processed surface. Compared with other technical means, the present invention reduces the requirements for the configuration of machine tool components and the operating cost. At the same time, the feedforward linearization control method based on the hysteresis nonlinear model and the auto-disturbance rejection control algorithm with zero-phase feedforward proposed by the present invention realize closed-loop control, which can greatly improve the tracking control accuracy of the system and effectively suppress the PV value, i.e., the peak-to-valley value, of the processed arc-shaped surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0023] Figure 1 is a structural schematic diagram of a waviness error compensation device based on a multi-axis nano-ultrafast system provided by an embodiment of the present invention;

[0024] Figure 2 is a structural block diagram of an inverse hysteresis feedforward linearization method provided by an embodiment of the present invention;

[0025] Figure 3 is an equivalent system block diagram after inverse hysteresis feedforward linearization provided by an embodiment of the present invention, wherein (a) represents an equivalent system block diagram including various error components, and (b) represents an equivalent system block diagram including a lumped error;

[0026] Figure 4 It is a control block diagram of introducing an extended state observer to perform disturbance observation compensation provided by an embodiment of the present invention;

[0027] Figure 5 It is a system control block diagram of state feedback regulation provided by an embodiment of the present invention.

[0028] Explanation of the accompanying drawings: 1. driving unit; 2. flexible hinge; 3. vacuum adsorption platform; 4. connecting flange; 5. fixed base; 1-1. piezoelectric ceramic driver; 1-2. displacement sensor. DETAILED DESCRIPTION

[0029] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0030] like Figure 1As shown, the present invention provides a corrugation error compensation device based on a multi-axis nano-ultrafast system, comprising four drive units 1 of the same model, four sets of flexible hinges 2, a vacuum adsorption platform 3, four connecting flanges 4 and a fixed base 5, each drive unit 1 comprises a piezoelectric ceramic driver 1-1 and a displacement sensor 1-2, the piezoelectric ceramic driver 1-1 is located at the bottom of the flexible hinge 2, the vacuum adsorption platform 3 is connected to the flexible hinge 2, the vacuum adsorption platform 3 is supported by the four piezoelectric ceramic drivers 1-1 through the flexible hinge 2, and the lower end of the piezoelectric ceramic driver 1-1 is connected to the fixed base 5. The four groups of flexible hinges 2 are symmetrically distributed in parallel on the connecting flange 4, and the connecting flange 4 is located on the fixed base 5. The four displacement sensors 1-2 and the piezoelectric ceramic driver 1-1 are arranged at four points on the edge of the vacuum adsorption platform 3 in a cross distribution, which are used to measure the posture height of the corresponding position, so that the corrugation error compensation device has three degrees of freedom, namely the rotational freedom RX and RY in the two horizontal directions of the platform plane of the vacuum adsorption platform 3 and the movement freedom Z in the vertical direction. The piezoelectric ceramic driver 1-1 is driven by applying voltage to adjust the posture of the vacuum adsorption platform 3.

[0031] The piezoelectric ceramic actuator 1 - 1 has a stiffness of 50 N / μm, a driving voltage of 100 V, a stroke of 32 μm and a natural frequency of 40 kHz.

[0032] Displacement sensor 1-2 uses a capacitive sensor, and the specific probe model is C8-2.0-2.0. The appropriate distance range between the probe of this sensor and the measurement target is 75-125μm, and there is a direct linear relationship between its output voltage and the displacement: when the output voltage is 10V, it means that the measurement object is 75μm away from the probe; when the output voltage is -10V, it corresponds to a distance of 125μm. The measurement range of this sensor is 50μm, and it has a measurement accuracy of up to 0.003% of the full scale.

[0033] Each flexible hinge 2 is connected by two circular flexible hinges. The flexible hinge 2 is made of aluminum alloy 7075-T6. Four groups of flexible hinges are arranged in parallel and symmetrically. Each motion branch chain adopts a flexible moving pair.

[0034] The present invention also provides a method for controlling the above-mentioned corrugation error compensation device based on the multi-axis nano-ultrafast system, wherein the vacuum adsorption platform 3 is regarded as a rigid body, the displacement sensor 1-2 detects the position height of the vacuum adsorption platform, and the actual position and posture of the vacuum adsorption platform is obtained by plane fitting calculation, which specifically includes the following steps:

[0035] In step S1, the height of the corresponding measuring point is input into each drive unit 1. At this time, the displacement influence of the three piezoelectric ceramic drivers 1-1 outside the drive unit 1 on the drive unit 1 is regarded as a disturbance, and the piezoelectric ceramic driver 1-1 in the drive unit 1 performs compensation control to achieve target decoupling, so as to more conveniently control a single drive unit 1.

[0036] In order to convert the precise control of the end posture of the positioning platform into high-precision anti-disturbance control of a single drive unit 1, this embodiment needs to construct a redundant degree of freedom decoupling control framework for the multi-axis nano-ultrafast system. This framework requires a feedforward linearization control method based on a hysteresis nonlinear model and an anti-disturbance control algorithm with zero-phase feedforward, so as to realize high dynamic decoupling closed-loop control of the motion compensation system.

[0037] The control method of the single drive unit 1 in step S1 comprises the following steps:

[0038] Step S11, firstly, the piezoelectric drive unit system is modeled. The piezoelectric drive unit system includes the strong hysteresis nonlinear characteristics of the piezoelectric ceramic driver 1-1 and the linear characteristics of the flexible hinge mechanism. Therefore, it is necessary to model the two characteristics separately and integrate them into the dynamic characteristics of the overall system to obtain a complete piezoelectric drive unit system dynamic characteristics description model, so as to design the control method later;

[0039] In step S11, the two characteristics are modeled as MPI model and ARX model respectively, wherein the MPI model, namely the magnetic particle imaging model, can better characterize the strong hysteresis nonlinear characteristics, and the ARX model, namely the organic self-regression model, can summarize the linear part characteristics of the system.

[0040] Step S12, building a hysteresis inverse model according to the description model established in step S11, so as to calculate the corresponding input control voltage according to the target hysteresis intermediate amount, eliminate the influence of hysteresis characteristics, and linearize the piezoelectric drive unit system;

[0041] like Figure 2 The figure shows the process of modeling the hysteresis inverse model. represents the ideal input of the system, represents the voltage input of the piezoelectric drive unit; Indicates the intermediate value of hysteresis output, H [ u ] represents the hysteresis characteristic of the system, H n − 1 [ u ] Then it represents the inverse model of hysteresis characteristics, Represents the linear characteristics of the system. According to the established description model, the hysteresis inverse model is modeled to calculate the corresponding input control voltage according to the target hysteresis intermediate quantity, eliminate the influence of hysteresis characteristics, and linearize the piezoelectric drive unit system. Since the feedforward linearized system still has some nonlinear errors due to the difference between the theoretical model and the actual system, and since the control input is discrete, it will cause integral errors. These two errors are equivalent to the nonlinear errors of the inverse hysteresis compensation, recorded as , considering the modeling error, the system can be equivalent to Figure 3 As shown in (a), there must be some errors in the modeling and identification of the hysteresis model. ,in is a bounded system uncertainty. After equating the errors of each part, we have Δ w = Δ ⋅ w f + ( 1 + Δ ) ⋅ e [ w f ] ,in, e [ w f ] Represents the nonlinear modeling error, which is equivalent to Figure 3 As shown in (b), Figure 3 (a) shows the equivalent system block diagram including various error components, and (b) shows the equivalent system block diagram including the lumped error.

[0042] Step S13, through the anti-disturbance control algorithm, the error caused by linearization can be better compensated. The algorithm observes the disturbance of the system by using a linear form of the Lomberg state observer, compensates the disturbance to the input end, and achieves the purpose of eliminating the internal and external disturbances of the system.

[0043] For internal disturbance The above has been obtained, but in actual working conditions, external disturbances will also be encountered. Represents external disturbances related to system characteristics, such as input voltage fluctuations, machine tool vibrations, etc., which can be equivalent to the input end. Represents external disturbances that come directly from the outside world and are unrelated to system characteristics, such as coupled axis motion, cutting force excitation, etc., which can be equivalent to the output end. Under the total disturbance assumption of the self-disturbance rejection algorithm, there is a total disturbance observation value ,in is the linear characteristic obtained for the model The control framework diagram of the extended state observer for disturbance observation compensation is shown in the inverse of Figure 4 As shown, due to the influence of disturbance, is the ideal input of the system after observer compensation, is the output of the linearized system, is the system displacement output after disturbance.

[0044] Step S14: Under the condition of extended state observation compensation, the system characteristics approach the linear system model. In order to make the observer tracking more accurate, the system characteristics need to be reduced to a second-order system:

[0045] ;

[0046] Where s is the complex variable of the transfer function of the multi-axis nano-ultrafast system, , , is a constant of the second-order system, obtained by simulation or experimental calibration. Based on the characteristics of the reduced-order system, the original system is subjected to second-order state feedback control. In order to make the system response characteristics close to a completely identical linear relationship in a wider frequency range, that is, the amplitude response and phase lag both tend to 0, according to the response characteristics of the second-order system, the natural frequency of the closed-loop system needs to be increased, and the damping ratio needs to be reduced to near the critical damping. Preferably, the natural frequency of the target system can be set to , the damping ratio is critical damping , under the condition that the static amplitude gain of the system remains unchanged, the second-order system is transformed into an ideal closed-loop system:

[0047] .

[0048] in, , , is the constant of the ideal closed-loop system. In order to perform feedback control, it is necessary to Figure 4 Based on the introduction of the system state feedback coefficient and input gain factor , to ensure that the static gain of the system remains unchanged. The system control block diagram after closed-loop state adjustment is shown in Figure 5.

[0049] Step S15: After the closed-loop feedback adjustment, the phase response of the system still has a certain lag, so zero-phase tracking control is added on the basis of the anti-disturbance control algorithm to Adding a zero-phase tracking feedforward compensation term can theoretically ensure that the system output has no phase lag, and generally improve the dynamic tracking performance and control accuracy of the system.

[0050] Step S2, converting the position information into an actual voltage input signal through a driving power supply, driving the piezoelectric ceramic driver 1-1 to push the flexible hinge 2 to move upward, thereby achieving posture adjustment of the vacuum adsorption platform 3.

[0051] The present invention verifies the dynamic characteristics of the multi-axis nano-ultrafast system through simulation modal analysis and experimental modal analysis, ensuring that the system design meets the requirements of high-performance dynamic response, so as to facilitate subsequent research on the control system.

[0052] The control system is required to be sufficiently accurate, capable of reflecting the processing status in real time and making corresponding posture adjustments in a timely and accurate manner, thereby reducing the waviness error. Therefore, the present invention decouples the platform's degrees of freedom, converts the posture control of the positioning platform into a separate compensation control of each drive unit 1 by the piezoelectric ceramic driver 1-1, offsets the coupling effect, and simplifies the control process. The control algorithm proposed is a feedforward linearization control method based on a hysteresis nonlinear model and an anti-disturbance control algorithm with zero-phase feedforward. Considering the strong hysteresis nonlinear characteristics and linear characteristics such as flexible hinges of the piezoelectric ceramic driver 1-1, the nonlinear characteristics are modeled by the MPI+high-order linear system series model and the linear characteristics are modeled by the ARX model, respectively, to obtain a complete description model of the dynamic characteristics of the electromechanical system of the drive unit. Based on the model, the piezoelectric drive unit system is linearized to eliminate the influence of nonlinear characteristics, and then the errors caused by feedforward linearization and external disturbances are further compensated by using the anti-disturbance control algorithm with zero-phase feedforward.

[0053] 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 it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, 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 waviness error compensation device based on a multi-axis nano-ultrafast system, characterized in that: The device comprises four drive units (1) of the same model, four sets of flexible hinges (2), a vacuum adsorption platform (3), four connecting flanges (4) and a fixed base (5), each drive unit (1) comprises a piezoelectric ceramic drive (1-1) and a displacement sensor (1-2), the piezoelectric ceramic drive (1-1) is located at the bottom of the flexible hinge (2), the vacuum adsorption platform (3) is connected to the flexible hinge (2), the vacuum adsorption platform (3) is supported by the four piezoelectric ceramic drives (1-1) as legs through the flexible hinge (2), the lower end of the piezoelectric ceramic drive (1-1) is connected to the fixed base (5) for support, and the four sets of The flexible hinges (2) are symmetrically distributed in parallel on the connecting flange (4), and the connecting flange (4) is located on the fixed base (5); four displacement sensors (1-2) and the piezoelectric ceramic driver (1-1) are arranged at four points on the edge of the vacuum adsorption platform (3) in a cross distribution, and are used to measure the posture height of the corresponding position, so that the corrugation error compensation device has three degrees of freedom, which are the rotational degrees of freedom RX and RY in two horizontal directions of the platform plane of the vacuum adsorption platform (3) and the movement degree of freedom Z in the vertical direction. The piezoelectric ceramic driver (1-1) is driven by applying a voltage to adjust the posture of the vacuum adsorption platform (3).

2. The waviness error compensation device based on a multi-axis nano-ultrafast system according to claim 1, characterized in that: The piezoelectric ceramic driver (1-1) has a stiffness of 50 N / μm, a driving voltage of 100 V, a stroke of 32 μm and a natural frequency of 40 kHz.

3. The waviness error compensation device based on a multi-axis nano-ultrafast system according to claim 1 is characterized in that: The displacement sensor (1-2) is a capacitive sensor, and there is a direct linear relationship between its output voltage and displacement.

4. The waviness error compensation device based on a multi-axis nano-ultrafast system according to claim 1, characterized in that: Each flexible hinge (2) is composed of two circular flexible hinges, and the flexible hinge (2) is made of aluminum alloy.

5. A corrugation error compensation control method based on a multi-axis nano-ultrafast system, characterized in that: The method is applied to the corrugation error compensation device based on a multi-axis nano-ultrafast system as described in any one of claims 1 to 4, wherein the vacuum adsorption platform (3) is regarded as a rigid body, the displacement sensor (1-2) detects the position height of the vacuum adsorption platform, and the actual position and posture of the vacuum adsorption platform is obtained by plane fitting calculation, specifically comprising the following steps: Step S1, the height of the corresponding measuring point is input into each drive unit (1), and the displacement influence of the three piezoelectric ceramic drivers outside the drive unit on the drive unit is regarded as disturbance, and the piezoelectric ceramic driver in the drive unit performs compensation control to achieve target decoupling, so as to more conveniently control the single drive unit (1); Step S2, converting the position information into an actual voltage input signal through a driving power supply, driving the piezoelectric ceramic driver (1-1) to push the flexible hinge (2) to move upward, thereby achieving position adjustment of the vacuum adsorption platform (3).

6. The method for compensating the waviness error based on a multi-axis nano-ultrafast system according to claim 5, characterized in that: The control method of the single drive unit (1) in step S1 comprises the following steps: Step S11, modeling a piezoelectric drive unit system, the piezoelectric drive unit system including the strong hysteresis nonlinear characteristics exhibited by the piezoelectric ceramic driver (1-1) and the linear characteristics exhibited by the flexible hinge mechanism, modeling the two characteristics separately and integrating them into the dynamic characteristics of the overall system, thereby obtaining a complete piezoelectric drive unit system dynamic characteristics description model; Step S12, building a hysteresis inverse model according to the description model established in step S11, so as to calculate the corresponding input control voltage according to the target hysteresis intermediate amount, eliminate the influence of hysteresis characteristics, and linearize the piezoelectric drive unit system; Step S13, compensating the error caused by linearization by using an anti-disturbance control algorithm, which observes the disturbance of the system by using a linear form of a Lomberg state observer, and compensates the disturbance to the input end, thereby achieving the purpose of eliminating internal and external disturbances of the system; Step S14: Under the condition of extended state observation compensation, the system characteristics approach the linear system model. In order to make the observer tracking more accurate, the system characteristics need to be reduced to a second-order system: ； Where s is the complex variable of the transfer function of the multi-axis nano-ultrafast system, , , It is a constant of the second-order system, obtained by simulation or experimental calibration. Based on the characteristics of the reduced second-order system, the original system is subjected to second-order state feedback control. In order to make the amplitude response and phase lag of the system approach 0, according to the response characteristics of the second-order system, the natural frequency of the closed-loop system needs to be increased, and the damping ratio needs to be reduced to near the critical damping; Step S15: After the closed-loop feedback adjustment, the phase response of the system still has a lag, so a zero-phase tracking feedforward compensation term is added before the closed-loop system to ensure that the system output has no phase lag in theory.

7. The method for compensating and controlling the waviness error based on a multi-axis nano-ultrafast system according to claim 6, characterized in that: In step S11, the two characteristics are modeled as an MPI model and an ARX model respectively, wherein the MPI model is a magnetic particle imaging model, which can characterize the strong hysteresis nonlinear characteristics, and the ARX model is an organic regression model, which can summarize the linear part characteristics of the system.

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