Piezoelectric precision positioning control method

Abstract

The application discloses a piezoelectric precision positioning control method and relates to the technical field of precision positioning control. The method introduces a generalized first-order reset element on the basis of a traditional PI controller. The introduced generalized first-order reset element is different from a standard GFORE pure low-pass form. A first-order linear term is introduced in a GFORE transfer function molecule, a zero point is added to the GFORE, and a reset operation is implemented on the internal state of the GFORE in combination with an error peak value triggering reset mechanism, so that the overshoot and oscillation amplitude of the system are effectively reduced, and the dynamic response performance and closed-loop stability of the system are improved.

Description

Technical Field

[0001] This invention relates to the field of precision positioning control technology, specifically to a piezoelectric precision positioning control method based on a generalized first-order-reset-element (GFORE), and more particularly to a reset control method suitable for oscillation suppression and dynamic performance improvement of piezoelectric flexible positioning platforms. Background Technology

[0002] Piezoelectric-driven precision positioning platforms are widely used in high-precision control scenarios such as semiconductor manufacturing, micro / nano manipulation, precision machining, and optical adjustment due to their advantages of high resolution, fast response speed, and compact structure. Because piezoelectric platforms typically have flexible structures, their dynamic models often exhibit significant second-order oscillation characteristics. In existing technologies, traditional proportional-integral (PI) controllers are used for piezoelectric-driven precision positioning, but these systems are prone to significant oscillations with large overshoot, long oscillation durations, and slow steady-state convergence. Furthermore, increasing the PI controller gain to improve system response speed may exacerbate oscillations or even decrease stability. As a typical linear controller, the PI controller is also subject to Bode gain-phase constraints, making it difficult to balance stability margin and dynamic response performance while increasing system bandwidth.

[0003] Reset control, as a nonlinear technique, is not limited by the Bode gain-phase constraint of linear systems. By resetting the internal state of the controller under specific conditions, it can provide additional phase lead while maintaining high gain characteristics, thereby improving the dynamic performance of the system. Among them, the generalized first-order reset element (GFORE) is a typical reset control structure, which has the advantages of effectively reducing system oscillations and improving closed-loop response speed. However, standard GFOREs usually adopt a pure low-pass form, and their reset operation can only reduce the overall control signal, resulting in a sluggish system response. Moreover, in engineering practice, the zero-crossing triggering method commonly used in GFOREs is at risk of trigger failure when the system damping is strong and the position tracking error does not cross the zero point.

[0004] Therefore, it is necessary to propose a piezoelectric precision positioning control method that can effectively reduce oscillation amplitude and frequency, reduce overshoot, reduce oscillation duration, and improve dynamic response performance while ensuring system stability. Summary of the Invention

[0005] In view of at least one of the above-mentioned technical problems, this application provides a piezoelectric precision positioning control method. This method introduces a generalized-first-order-reset-element (GFORE) on the basis of a traditional PI controller. The generalized-first-order-reset-element introduced in this invention differs from the standard GFORE pure low-pass form. By introducing a first-order linear term into the numerator of the GFORE transfer function, a zero is added to the GFORE. Combined with an error peak trigger reset mechanism, the internal state of the GFORE is reset, thereby effectively reducing system overshoot and oscillation amplitude, improving system dynamic response performance and closed-loop stability. This solves the problems of large overshoot, large and fast oscillation amplitude and frequency, long oscillation duration, and insufficient dynamic response performance in existing piezoelectric precision positioning platforms under traditional PI control.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A piezoelectric precision positioning control method, the method comprising:

[0008] Step 1: Establish a dynamic model of the piezoelectric flexible positioning platform and define the system position tracking error. ;

[0009] Step 2: with As input, a PI control signal is output through the PI controller. ;

[0010] Step 3: Connect a generalized first-order reset element GFORE in series with the output of the PI controller to construct a GFORE control structure. Input GFORE control structure, output GFORE control signal ;

[0011] Step 4: Based on Construct an error peak trigger reset mechanism to... Perform a partial reset of the GFORE internal state to obtain the reset GFORE output signal. ;

[0012] Step 5: As the system control input of the dynamic model of the piezoelectric flexible positioning platform The current output displacement of the piezoelectric platform is obtained. ;

[0013] Step 6: Based on Update the system position tracking error at the current moment. ;

[0014] Step 7: Repeat steps 2 to 6. In each iteration, update the tracking error obtained in the current iteration. As the input to the PI controller in step 2 of the next cycle; the cycle repeats until the current time reaches the preset control termination time or an external stop control command is received, at which point the cycle exits, thereby ending the piezoelectric precision positioning control.

[0015] Furthermore, according to the aforementioned piezoelectric precision positioning control method, the dynamic model of the piezoelectric flexible positioning platform is established as follows:

[0016] ;

[0017] in, These are the coefficients of the second-order equivalent model; Let be the acceleration of the platform's output displacement at time t; The system damping coefficient; The velocity of the platform's output displacement at time t; The platform's equivalent stiffness; The platform output displacement at time t; For driving gain; This represents the system control input at time t; Let t be the external disturbance at time t.

[0018] Furthermore, according to the aforementioned piezoelectric precision positioning control method, the system position tracking error is defined. ,include:

[0019] Preset position command signal Define the system position tracking error as follows:

[0020] ;

[0021] in, Let be the system position tracking error at time t; The position command signal at time t; Let t be the actual output displacement signal of the system at time t.

[0022] Furthermore, according to the aforementioned piezoelectric precision positioning control method, the... As input, a PI control signal is output through the PI controller. The details are as follows:

[0023] ;

[0024] in, The PI control signal output by the PI controller at time t; For proportional gain; This is the integral gain.

[0025] Furthermore, according to the aforementioned piezoelectric precision positioning control method, the... The GFORE control signal is output through the GFORE control structure as input. ,include:

[0026] Define the linear form transfer function of the GFORE control structure. as follows:

[0027] ;

[0028] in, For Laplace complex frequency variables; This is the frequency of the reset filter poles; Zero frequency, This is the filtering ratio coefficient;

[0029] right Performing a Laplace transform yields ,right Performing a Laplace transform yields ,Depend on Push and The relation is as follows:

[0030] ;

[0031] based on Define GFORE internal state variables The details are as follows:

[0032] ;

[0033] Substituting the above equation into... and The relational expression, after substitution and The GFORE output signal is obtained by performing an inverse Laplace transform on the relation. The specific formula is as follows:

[0034] ;

[0035] in, For GFORE internal state variables The inverse Laplace transform form.

[0036] Furthermore, according to the aforementioned piezoelectric precision positioning control method, the method based on... Construct an error peak trigger reset mechanism to... The GFORE output signal is obtained by performing a partial reset of the GFORE internal state. ,include:

[0037] set up: , , They are respectively exist , , The error values ​​at these three consecutive sampling times;

[0038] When the following local peak triggering conditions are met, the system error is considered to have a local peak, and the GFORE partial reset operation is triggered.

[0039] ;

[0040] Regarding the internal state of GFORE A partial reset was performed, and the internal state of GFORE after the partial reset was performed. Represented as:

[0041] ;

[0042] in, Let be the reset coefficient, satisfying ;

[0043] After performing the GFORE internal state reset, Change to GFORE output signal after reset The details are as follows:

[0044] .

[0045] Furthermore, according to the piezoelectric precision positioning control method described above, the method further includes: setting a minimum reset time interval. When the time between two consecutive resets is less than At that time, no new reset operation will be performed.

[0046] The beneficial effects of adopting the above technical solution are as follows:

[0047] 1. To address the issues of large overshoot, significant oscillation, and slow convergence in PI control of piezoelectric positioning platforms, this invention introduces a PI series circuit into the zero-point GFORE and combines it with peak trigger reset, thereby reducing system overshoot, shortening the settling time, reducing the number of oscillation peaks, and achieving rise time and steady-state accuracy comparable to PI control, thus avoiding the problem of increased oscillation caused by increasing PI gain.

[0048] 2. To address the issue that the reset operation in the standard GFORE pure low-pass mode can only reduce the overall control signal, resulting in a sluggish system response, this invention introduces a first-order term into the numerator of the GFORE transfer function to add a zero, making the output divided into two terms. The reset only compresses the term containing the internal state, achieving directional suppression at the oscillation peak and avoiding the problem of sluggish response caused by the reset.

[0049] 3. To address the issue that existing reset control zero-crossing triggering methods may fail when the system damping is strong and the error does not cross the zero point, this invention improves the zero-crossing triggering to error local peak triggering. By comparing the absolute values ​​of the error at three consecutive sampling times, it determines whether a local peak has occurred. Reset intervention is applied at the moment of maximum oscillation energy, which improves the oscillation suppression efficiency and can still effectively trigger the reset when the error does not cross the zero point. Attached Figure Description

[0050] Figure 1 This is a flowchart of the piezoelectric precision positioning control method proposed in an embodiment of the present invention;

[0051] Figure 2 A comparison diagram of the position tracking response between ordinary PI control and PI control using GFORE proposed in this embodiment of the invention;

[0052] Figure 3 The graphs show the tracking error variations of ordinary PI control and PI control using GFORE as proposed in the embodiments of the present invention.

[0053] Figure 4 This is a graph showing the change in the reset trigger time of the PI control using GFORE proposed in an embodiment of the present invention;

[0054] Figure 5 The control input variation curves for ordinary PI control and PI control using GFORE are shown in the embodiments of the present invention.

[0055] Figure 6 This is a comparison chart of the position response of ordinary PI control and PI control using GFORE under representative combined non-ideal operating conditions, as proposed in the embodiments of the present invention. Detailed Implementation

[0056] To describe the present invention in more detail, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] The piezoelectric precision positioning control method of this embodiment, such as Figure 1 As shown, it includes the following steps:

[0058] Step 1: Establish a dynamic model of the piezoelectric flexible positioning platform and define the system position tracking error;

[0059] Step 1.1: Establish the dynamic model of the piezoelectric flexible positioning platform:

[0060]

[0061] in, These are the coefficients of the second-order equivalent model; Let be the acceleration of the platform's output displacement at time t; The system damping coefficient; The velocity of the platform's output displacement at time t; The platform's equivalent stiffness; The platform output displacement at time t; For driving gain; This represents the system control input at time t; Let be the external disturbance at time t. Furthermore, in Figures 2 to 5 In the corresponding nominal operating condition simulation, the external disturbance is temporarily set aside. Ignoring model mismatch due to parameter perturbation and measurement noise, and substituting the parameter values ​​of this embodiment into formula (1), the following dynamic model is obtained:

[0062]

[0063] The parameter values ​​in this embodiment are as follows: Second-order equivalent model coefficients System damping coefficient Platform equivalent stiffness Driven gain .

[0064] This embodiment focuses on an equivalent model of a piezoelectric positioning platform guided by a single-degree-of-freedom flexible hinge. Its components include a piezoelectric stacked actuator, a flexible hinge guiding mechanism, a moving worktable, and a load. It does not involve any specific commercial product model. The second-order identification transfer function derived from the publicly available precision motion platform is used in this embodiment as the coefficient of the second-order term in the denominator of the normalized equivalent model, and is not the actual weighing mass of the moving worktable and load. , and These are the corresponding coefficients of the identification model and are not interpreted as actual physical parameters.

[0065] Step 1.2: Define the system position tracking error;

[0066] First, the reference input module generates the system position command signal. The system outputs a position signal as follows: According to the reference input Compared with actual output Construction system position tracking error The specific calculation formula is as follows:

[0067]

[0068] in, Let be the system position tracking error at time t; The reference input signal at time t is the system position command signal. Let t be the actual output displacement signal of the system at time t.

[0069] Step 2: Use a PI controller as the basic control structure of the system to obtain the system position tracking error. For input,

[0070] Output PI control signal through a standard PI controller This can be achieved through the following formula:

[0071]

[0072] in, The PI control signal output by the PI controller at time t; For proportional gain; This is the integral gain.

[0073] In this embodiment, the PI controller parameters are set as follows: =0.018; =0.6.

[0074] A standard PI controller can ensure basic closed-loop stability of the system, but due to the existence of flexible oscillation modes in the system, significant overshoot and continuous oscillation will still occur.

[0075] Step 3: Connect a generalized first-order reset element GFORE in series at the output of the PI controller to construct a GFORE control structure, thereby converting the PI control signal... Input GFORE control structure, output GFORE control signal .

[0076] The purpose of constructing the GFORE control structure is to improve the dynamic performance of ordinary PI controllers. The GFORE control structure is used to dynamically filter the PI control signal, preparing for subsequent GFORE reset control.

[0077] Linear transfer function of GFORE control structure Represented as:

[0078]

[0079] in, For Laplace complex frequency variables; The reset filter pole frequency can be selected based on the system bandwidth and oscillation frequency to balance the system's dynamic response speed and stability. The introduced zero frequency, This is the filtering scaling factor. In this embodiment: ; ; The GFORE control structure of this invention differs from the standard GFORE form. To address the problem that the reset operation in the standard GFORE pure low-pass form can only reduce the overall control signal, leading to a sluggish system response, this embodiment introduces a first-order linear term into the transfer function numerator, adding a zero-point frequency to the standard GFORE. .

[0080] Reset filter pole frequency The specific selection process is as follows: First, obtain the frequency response of the closed-loop system under PI control, and determine the closed-loop bandwidth and the main oscillation angular frequency of the flexible mode based on this frequency response; under the constraint of not reducing the closed-loop stability margin and GFORE providing phase lead near the main oscillation angular frequency, select candidates within the range of 1 to 10 times the bandwidth. Perform parameter scanning; calculate overshoot, settling time, and absolute error integral for each candidate value, and eliminate candidate values ​​with divergent response or control input exceeding the actuator's allowable range; normalize the overshoot, settling time, and absolute error integral corresponding to the remaining candidate values, assign preset weights to each performance index, and obtain a weighted summation to obtain a comprehensive evaluation function, from which the value with the smallest comprehensive evaluation function is selected. .Sure Afterwards, according to Determine the zero frequency This embodiment uses the above-described scanning method to obtain... , .

[0081] Define the output of the PI controller The functional form used for the Laplace transform is GFORE control signal Functional form for Laplace transform The transfer function is derived from formula (5). and The relation is as follows:

[0082]

[0083] To obtain the dynamic characteristics of the GFORE filter state, based on Define GFORE internal state variables for

[0084]

[0085] Substituting equation (7) into equation (6) and performing an inverse Laplace transform yields the GFORE output signal. The specific formula is as follows:

[0086]

[0087] in: For GFORE internal state variables The inverse Laplace transform form.

[0088] Step 4: Based on the local peak value of the tracking error, adjust the GFORE control signal. Perform a partial reset of the GFORE internal state to obtain the reset GFORE output signal. ;

[0089] To further reduce system oscillations and improve dynamic performance, this embodiment introduces an error peak trigger reset mechanism based on GFORE. The core difference between this mechanism and the standard GFORE reset mechanism is that the standard GFORE adopts a traditional zero-crossing trigger strategy, which performs a partial reset operation on the internal state of GFORE when the system position tracking error is 0, while this embodiment performs a partial reset operation on the internal state of GFORE when the system position tracking error meets the local peak condition.

[0090] When the system error meets the local peak condition, the GFORE partial reset operation is triggered.

[0091] A peak error trigger reset mechanism is constructed to monitor changes in system error in real time.

[0092] set up: ; ; They are respectively exist , , Error values ​​at these three consecutive sampling times.

[0093] When the following local peak trigger condition is met:

[0094]

[0095] If a local peak is observed in the system error, a partial reset operation of GFORE is triggered.

[0096] Compared to the traditional zero-crossing error triggering method, this peak triggering method can more accurately correspond to the peak position of system oscillation, thereby improving the system oscillation suppression effect.

[0097] After triggering a partial reset operation of GFORE, the internal state of GFORE is... A partial reset was performed, and the internal state of GFORE after the partial reset was performed. Represented as:

[0098]

[0099] in: This is the GFORE state after reset; The reset coefficient; satisfy .

[0100] After the GFORE internal state is reset, the original GFORE output signal Change to GFORE output signal after reset :

[0101]

[0102] when This indicates that the GFORE state has been completely reset, i.e., a reset has been performed. The state will be completely reset to 0; when This indicates that the GFORE state is partially reset, i.e., a reset is performed. Preserve the state as ;when When this happens, the GFORE structure degenerates into a linear structure and no longer performs state reset. The smaller the value, the stronger the reset effect, and the more effectively the system overshoot and oscillation amplitude can be reduced; when As the value gradually increases, the system reset effect weakens, and the control structure gradually approaches a linear structure. In practical applications, the control structure can be adjusted according to the system oscillation degree, overshoot, and dynamic response requirements. Adjustments will be made.

[0103] Reset coefficient The specific adjustment process is as follows: in the interval Within, with a step size of 0.05, During the scan, adjustments are made dynamically based on the system response: if the overshoot, number of oscillation peaks, or settling time exceed the design specifications, the settings are reduced. To enhance the reset function; if the peak value of the control input exceeds the actuator limit, or the system response speed decreases significantly, then increase the [unclear - possibly a specific setting or function]. To weaken the reset effect, from all candidate values ​​that satisfy closed-loop stability, actuator input constraints, and steady-state error constraints, the value that minimizes the comprehensive index of overshoot, settling time, and error absolute value integral is selected. This embodiment selects according to the above process. .

[0104] Since high-frequency continuous peaks may occur during system oscillation, this embodiment sets a minimum reset time interval to avoid excessively frequent reset actions. Used to limit frequent resets of the GFORE structure When the time between two consecutive resets is less than In this case, no new reset operation is performed. This method can effectively avoid high-frequency repeated system resets and improve the stability of engineering implementation.

[0105] In this embodiment:

[0106] ,satisfy: This indicates that the GFORE state is partially reset, i.e., a reset is performed. Preserve the state as .

[0107] Step 5: Output the reset GFORE signal The dynamic model of the piezoelectric flexible positioning platform is applied, based on... Calculate the output position of the piezoelectric positioning platform ;

[0108] The GFORE output signal after reset As the system control input in the positioning platform dynamics model established in step 1 Thus, the output displacement of the piezoelectric platform at the current moment is obtained. .

[0109] Step 6: Use reference input The piezoelectric platform output displacement at the current moment Difference, update the system position tracking error at the current moment. .

[0110] Step 7: Repeat steps 2 to 6. In each iteration, update the tracking error obtained in the current iteration. As the input to the PI controller in step 2 of the next cycle; the cycle repeats until the current time reaches the preset control termination time or an external stop control command is received, at which point the cycle exits, thereby ending the piezoelectric precision positioning control.

[0111] Among them, the preset control termination time Set according to the allowed execution duration of the location task; when the current time reaches... Alternatively, the control system may terminate the control loop when it receives an external stop control command.

[0112] In this embodiment, the updated tracking error In the next cycle, the feedback can be used to two stages: firstly, to the input of the PI controller in step 2, and then to calculate the PI control signal at the next moment according to formula (4). Secondly, the feedback is sent to the local peak detection stage in step 4, and compared with the historical error value. , Together they are used to determine whether the local peak triggering condition is met.

[0113] This embodiment uses MATLAB for system simulation verification. The system simulation parameters are set as follows: simulation step size. Total simulation time Reference input signal A unit step signal is used. The following two control methods are compared: ordinary PI control; and PI control using GFORE.

[0114] It should be noted that, Figures 2 to 5 Use the normalized unit step instruction: Figure 2 The ordinate represents the normalized system output. , Figure 3 The ordinate represents the normalized tracking error. Both are dimensionless; Figure 4 The vertical axis represents the reset trigger flag, where 1 indicates a reset has occurred and 0 indicates no reset has occurred; it is dimensionless. Figure 5 The vertical axis represents the normalized control input. , dimensionless.

[0115] Figure 2 The system position tracking response results are presented under two different control methods: ordinary PI control and PI control using GFORE. Figure 2 It can be seen that ordinary PI control has obvious overshoot and oscillation phenomena. Using GFORE's PI control can significantly reduce the system overshoot and oscillation duration, reduce the oscillation frequency and improve the system dynamic response speed. Figure 3 The curves showing the variation of system tracking error under different control methods are presented. Figure 3 It can be seen that the system error decay speed is significantly faster under GFORE PI control than that of ordinary PI control, the dynamic response performance is stronger, and the error oscillation amplitude is smaller. Figure 4 The changes in the reset trigger time when using GFORE's PI control are presented. Figure 4 It can be seen that the reset operation mainly occurs near the peak of the system oscillation. By resetting the internal state of GFORE, the subsequent oscillation amplitude of the system is effectively reduced. Figure 5 The control input variation curves under different control methods are presented. Figure 5It can be seen that using GFORE's PI control reduces system oscillations while keeping the control input changes stable, with smaller oscillation amplitudes and no obvious high-frequency abrupt changes.

[0116] To verify the control effect of the described control method under the combined effects of model parameter deviation, external disturbance, and measurement noise, a representative combined non-ideal simulation condition was set in addition to the nominal operating condition. That is, model parameter deviation, external disturbance, and measurement noise were simultaneously added to the simulation to simulate a typical non-ideal operating condition. The ordinary PI control and the PI control using GFORE employed the exact same non-ideal conditions: throughout the simulation... , , 110%, 90%, and 90% of the nominal value were taken respectively to characterize the model mismatch caused by object parameter deviation and other unmodeled factors; an external pulse disturbance with an amplitude of 5% of the nominal static driving force was applied from 0.60s to 0.65s. The output displacement measurement value is superimposed with zero-mean Gaussian measurement noise with a standard deviation of 0.2% of the position command amplitude throughout. To avoid spurious local peaks caused by measurement noise, the reset peak detection branch uses first-order low-pass processing with a time constant of 0.010s, and the reset dead zone is set to 5 times the standard deviation of the measurement noise, i.e., 1% of the position command amplitude; at the same time, the minimum reset time interval is maintained. .

[0117] Simulation results under representative combinations of non-ideal working conditions are as follows: Figure 6 As shown, the main graph displays the position response of ordinary PI control and PI control using GFORE, while the embedded window shows the disturbance recovery error within the range of 0.50s to 0.85s. The maximum output of ordinary PI control is 1.431159, corresponding to an overshoot of 43.12%; the maximum output of PI control using GFORE is 1.122524, corresponding to an overshoot of 12.25%. Within the range of 0.60s to 0.80s, the maximum absolute tracking errors of ordinary PI control and PI control using GFORE are 0.042055 and 0.039524, respectively. After the disturbance is removed at 0.65s, the times required for both to re-enter and remain within the ±2% error band are 0.0768s and 0.0304s, respectively, with the disturbance recovery time of PI control using GFORE being shortened by approximately 60.4%. Under this operating condition, GFORE triggers a reset 21 times, with the minimum time interval between adjacent resets being 0.0031s, which is not less than... .

[0118] Furthermore, this embodiment performs statistical analysis on the system performance indicators under nominal operating conditions and representative combination non-ideal operating conditions.

[0119] Experimental results show that:

[0120] Compared to a conventional PI controller, the GFORE PI control structure significantly reduces system overshoot from 34.22% to 2.36%, reduces the number of oscillation peaks from 28 to 22, and shortens system settling time from 0.3452s to 0.2707s. Under representative non-ideal operating conditions, the GFORE PI control structure still reduces overshoot from 43.12% to 12.25%, and shortens the time to re-enter and remain within the ±2% error band after disturbance removal from 0.0768s to 0.0304s, with the minimum time interval between adjacent resets not less than 0.0031s. The above results demonstrate that the piezoelectric precision positioning control method proposed in this invention can reduce system overshoot and oscillation amplitude, shorten oscillation duration, and improve dynamic response performance under nominal operating conditions and the combined effects of external disturbances, model mismatch, and measurement noise.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A piezoelectric precision positioning control method, characterized in that, The method includes: Step 1: Establish a dynamic model of the piezoelectric flexible positioning platform and define the system position tracking error. ; Step 2: with As input, a PI control signal is output through the PI controller. ; Step 3: Connect a generalized first-order reset element GFORE in series with the output of the PI controller to construct a GFORE control structure. Input GFORE control structure, output GFORE control signal ; Step 4: Based on Construct an error peak trigger reset mechanism to... Perform a partial reset of the GFORE internal state to obtain the reset GFORE output signal. ; Step 5: As the system control input of the dynamic model of the piezoelectric flexible positioning platform The current output displacement of the piezoelectric platform is obtained. ; Step 6: Based on Update the system position tracking error at the current moment. ; Step 7: Repeat steps 2 to 6. In each iteration, update the tracking error obtained in the current iteration. As the input to the PI controller in step 2 of the next cycle; the cycle repeats until the current time reaches the preset control termination time or an external stop control command is received, at which point the cycle exits, thereby ending the piezoelectric precision positioning control.

2. The piezoelectric precision positioning control method according to claim 1, characterized in that, The dynamic model of the piezoelectric flexible positioning platform is established as follows: ； in, These are the coefficients of the second-order equivalent model; Let be the acceleration of the platform's output displacement at time t; The system damping coefficient; The velocity of the platform's output displacement at time t; The platform's equivalent stiffness; The platform output displacement at time t; For driving gain; This represents the system control input at time t; Let t be the external disturbance at time t.

3. The piezoelectric precision positioning control method according to claim 1, characterized in that, The definition of system position tracking error ,include: Preset position command signal Define the system position tracking error as follows: ； in, Let be the system position tracking error at time t; The position command signal at time t; Let t be the actual output displacement signal of the system at time t.

4. The piezoelectric precision positioning control method according to claim 3, characterized in that, The As input, a PI control signal is output through the PI controller. The details are as follows: ； in, The PI control signal output by the PI controller at time t; For proportional gain; This is the integral gain.

5. The piezoelectric precision positioning control method according to claim 4, characterized in that, The The GFORE control signal is output through the GFORE control structure as input. ,include: Define the linear form transfer function of the GFORE control structure. as follows: ； in, For Laplace complex frequency variables; This is the frequency of the reset filter poles; Zero frequency, This is the filtering ratio coefficient; right Performing a Laplace transform yields ,right Performing a Laplace transform yields ,Depend on Push and The relation is as follows: ； based on Define GFORE internal state variables The details are as follows: ； Substituting the above equation into... and The relational expression, after substitution and The GFORE output signal is obtained by performing an inverse Laplace transform on the relation. The specific formula is as follows: ； in, For GFORE internal state variables The inverse Laplace transform form.

6. The piezoelectric precision positioning control method according to claim 5, characterized in that, The basis Construct an error peak trigger reset mechanism to... The GFORE output signal is obtained by performing a partial reset of the GFORE internal state. ,include: set up: , , They are respectively exist , , The error values ​​at these three consecutive sampling times; When the following local peak triggering conditions are met, the system error is considered to have a local peak, and the GFORE partial reset operation is triggered. ； Regarding the internal state of GFORE A partial reset was performed, and the internal state of GFORE after the partial reset was performed. Represented as: ； in, Let be the reset coefficient, satisfying ; After performing the GFORE internal state reset, Change to GFORE output signal after reset The details are as follows: 。 7. The piezoelectric precision positioning control method according to claim 6, characterized in that, The method also includes: setting a minimum reset time interval. When the time between two consecutive resets is less than At that time, no new reset operation will be performed.

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