Error compensation optimization method for piezoelectric displacement stage

Abstract

This invention relates to the fine control of a piezoelectric displacement stage, specifically to an error compensation optimization method for the piezoelectric displacement stage. The method involves collecting actual and theoretical displacement data throughout the entire stroke of the piezoelectric displacement stage, performing data preprocessing, and constructing an error compensation model for the stage. With the objective of minimizing the average positioning error throughout the entire stroke after error compensation, and considering constraints, an error compensation optimization model is constructed. An improved mantis shrimp optimization algorithm is used to solve the error compensation optimization model, obtaining the optimal error compensation model parameter set. The updated error compensation model is then used to compensate for the error in the piezoelectric displacement stage, and adaptive corrections are made based on the error compensation effect. The technical solution provided by this invention effectively overcomes the shortcomings of existing technologies, such as the difficulty in constructing a more accurate error compensation model and the poor error compensation effect of the piezoelectric displacement stage.

Description

Technical Field

[0001] This invention relates to the fine control of a piezoelectric displacement stage, specifically to an error compensation optimization method for a piezoelectric displacement stage. Background Technology

[0002] Piezoelectric displacement stages, as high-precision displacement control devices, are widely used in many fields such as precision machining, micro-nano manipulation, and optical adjustment. Their displacement accuracy directly affects the performance and quality of related systems. However, in practical applications, piezoelectric displacement stages inevitably suffer from various error factors, such as the hysteresis, creep, and nonlinear characteristics of piezoelectric ceramics, as well as imperfections in the mechanical structure. These factors lead to a certain degree of deviation between the actual displacement and the theoretical displacement, severely restricting further improvements in the positioning accuracy of piezoelectric displacement stages.

[0003] Traditional error compensation methods are mostly based on simple mathematical models or empirical formulas, which are difficult to comprehensively and accurately describe the complex error characteristics of piezoelectric displacement stages, resulting in limited compensation effects. Moreover, existing optimization algorithms suffer from drawbacks such as getting trapped in local optima and insufficient search accuracy when solving the error compensation optimization problem of piezoelectric displacement stages. They are unable to effectively find the optimal error compensation model parameters, making it difficult to meet the usage requirements of high-precision application scenarios.

[0004] Therefore, how to construct a more accurate and effective error compensation model for piezoelectric displacement stage, and how to use a high-performance optimization algorithm to solve for the optimal error compensation model parameters in order to achieve high-precision compensation for the error of piezoelectric displacement stage and improve its positioning accuracy throughout its entire stroke, has become a key problem that urgently needs to be solved in this field. This is of great significance for promoting the development of related high-precision technologies. Summary of the Invention

[0005] (a) Technical problems to be solved In view of the above-mentioned shortcomings of the existing technology, the present invention provides an error compensation optimization method for piezoelectric displacement stage, which can effectively overcome the shortcomings of the existing technology, such as the difficulty in constructing a more accurate error compensation model and the poor error compensation effect of piezoelectric displacement stage.

[0006] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: The error compensation optimization method for piezoelectric displacement stages includes the following steps: S1. Collect actual and theoretical displacement data of the piezoelectric displacement stage throughout its entire stroke, perform data preprocessing, and construct an error compensation model for the piezoelectric displacement stage. S2. With the goal of minimizing the average positioning error of the entire stroke after piezoelectric displacement stage error compensation, an error compensation optimization model is constructed in combination with constraints. S3. The improved mantis shrimp optimization algorithm is used to solve the error compensation optimization model to obtain the optimal error compensation model parameter set; S4. Use the updated error compensation model to perform error compensation on the piezoelectric displacement stage, and make adaptive corrections based on the error compensation effect. Among them, the improved mantis shrimp optimization algorithm includes: During the global exploration phase, the behavior of mantis shrimp’s asynchronous scanning with both eyes and dynamic polarization focusing with compound eyes was simulated to expand the search range and guide the population toward potential optimal areas, thus avoiding getting trapped in local optima. During the local development phase, the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs, characterized by "charging up, bursting out, and fine-tuning," is simulated. Within the potential optimal area found through global exploration, fine optimization is performed to improve the accuracy of the solution.

[0007] Preferably, the error compensation model for constructing the piezoelectric displacement stage in S1 includes: Based on the preprocessed error data, an error compensation model is constructed that conforms to the actual error characteristics of the piezoelectric displacement stage, including hysteresis, creep, and nonlinearity. The parameters of the error compensation model to be optimized are also defined, specifically including: S11. An error compensation model is constructed by adopting a piecewise nonlinear compensation model and combining it with the actual error characteristics of the piezoelectric displacement stage: ; in, Input the displacement after error compensation for the k-th test point. The theoretical input displacement for the k-th test point. This is the hysteresis error compensation function. The scaling factor is the hysteresis characteristic. This is the creep error compensation function. The creep response scaling factor. This is a nonlinear error compensation function. This is the reference scale coefficient for nonlinear stroke. , , All are weighting coefficients; S12. Adjust the weighting coefficients in the error compensation model. , , and hysteresis characteristic scaling coefficient creep response scaling factor Stroke nonlinearity reference scale coefficient The parameters of the error compensation model to be optimized constitute the solution vector. .

[0008] Preferably, in S2, the objective is to minimize the average positioning error over the entire stroke after piezoelectric displacement stage error compensation. Based on the constraints, an error compensation optimization model is constructed, including: S21. Determine the objective function for error compensation optimization, with the goal of minimizing the average positioning error of the entire stroke after piezoelectric displacement stage error compensation. S22. Determine the constraints for error compensation optimization; S23. Combining the objective function and constraints of error compensation optimization, construct an error compensation optimization model.

[0009] Preferably, in S21, the objective function for error compensation optimization is determined with the goal of minimizing the average positioning error over the entire stroke after piezoelectric displacement stage error compensation, including: ; in, X represents the actual output displacement of the k-th test point, where K is the number of test points. j Let X be the j-th error compensation model parameter to be optimized in the solution vector X. The initial average value of the parameters of the j-th error compensation model to be optimized in the solution vector X is set based on empirical values. This is the regularization coefficient, used to constrain parameter fluctuations and avoid overfitting; S22. Determine the constraints for error compensation optimization, including: 1) Weighting coefficient constraints: ,and ; 2) Scale coefficient constraint: .

[0010] Preferably, in S3, an improved mantis shrimp optimization algorithm is used to solve the error compensation optimization model to obtain the optimal error compensation model parameter set, including: S31. Randomly generate an initial population in the search space. The position of each mantis shrimp in the population corresponds to a solution vector, and initialize the algorithm parameters. S32. Implement a dynamic switching mechanism to automatically switch to the global exploration phase / local development phase based on the number of iterations. S33. In the global exploration phase, simulate the asynchronous scanning behavior of the mantis shrimp's eyes and the dynamic polarization focusing behavior of its compound eyes to expand the search range, guide the population to move closer to the potential optimal area, avoid getting trapped in local optima, and enter S35. S34. In the local development stage, simulate the high-speed attack behavior of the mantis shrimp's hammer-shaped rappelling limbs in the process of "charging up - bursting - fine-tuning". Within the potential optimal area found in the global exploration, perform fine optimization to improve the accuracy of the solution, and then proceed to S35. S35. Use the objective function optimized by error compensation to evaluate all mantis shrimp in the current population, calculate the corresponding fitness value, and record and update the historical best solution; S36. Determine whether the iteration termination condition is met. If the iteration termination condition is not met, return to S32. Otherwise, use the historical optimal solution as the parameter set of the optimal error compensation model.

[0011] Preferably, in S33, during the global exploration phase, the behavior of asynchronous binocular scanning and dynamic polarization focusing of compound eyes in mantis shrimp is simulated to expand the search range, guide the population towards the potential optimal region, and avoid getting trapped in local optima, including: S331, Calculation of binocular asynchronous saccade angle, simulating wide-angle inspection by the left eye and directional exploration by the right eye: ; in, , Let be the left and right eye saccade angles of the i-th mantis shrimp at the t-th iteration. , These represent the minimum and maximum scanning angles, respectively, where T is the maximum number of iterations, and r is the maximum number of iterations. i represents the individual random coefficient, with a value range of [0,1]. S332, Ambient polarized light intensity sensing: ; in, Let be the intensity of the ambient polarized light sensed by the i-th mantis shrimp in the t-th iteration. Let be the polarization coefficient of the nth mantis shrimp. This represents calculating the position of the i-th mantis shrimp at the t-th iteration. The position of the nth mantis shrimp at the tth iteration The Euclidean distance between them, UB and LB are the upper and lower bounds of the search space, respectively, and N is the current population size;

[0012] S333, Calculate the polarization focusing coefficient: ; in, Let be the polarization focusing coefficient of the i-th mantis shrimp at the t-th iteration; S334, Dual-view cooperative exploration location update: ; in, Let i be the position of the i-th mantis shrimp in the (t+1)-th iteration. This is the globally optimal solution at the t-th iteration. Let be the position of a random individual at the t-th iteration.

[0013] Preferably, in S34, during the local development phase, the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs—"charging-burst-fine-tuning"—is simulated. Within the potential optimal region found through global exploration, fine optimization is performed to improve the accuracy of the solution, including: S341, Energy Storage: ; ; in, , Let be the acceleration and velocity of the i-th mantis shrimp at the t-th iteration, respectively. For maximum stored acceleration, The energy storage attenuation coefficient is... Let be the energy storage speed of the i-th mantis shrimp in the (t-1)-th iteration. For one iteration step, In each iteration step, all velocities represent the change in position within a single iteration step, and all accelerations represent the change in velocity within a single iteration step. S342, Instantaneous Burst Strike: ; ; in, Let be the burst attack speed of the i-th mantis shrimp in the t-th iteration. To achieve maximum burst strike speed, Let be the position of the i-th mantis shrimp after its attack in the t-th iteration. Let be the unit direction vector pointing from the i-th mantis shrimp to the global optimal solution at the t-th iteration, simulating the burst attack direction. , This represents calculating the position of the i-th mantis shrimp at the t-th iteration. The global optimal solution at the t-th iteration The Euclidean distance between them; S343, Click Point Fine-tuning: ; ; ; in, The rotation angle is finely adjusted for the click point of the i-th mantis shrimp in the t-th iteration, where r1 is a random number uniformly distributed in the range [0,1]. Let be the fine-tuning rotation unit direction vector of the i-th mantis shrimp at the t-th iteration. Unit direction vector The vertical direction vector, This is the fine-tuning coefficient.

[0014] Preferably, in step S4, the piezoelectric displacement stage is error-compensated using the updated parameter error compensation model, and adaptive correction is performed based on the error compensation effect, including: S41. Error Compensation Implementation: The obtained optimal error compensation model parameter set... Substitute the error compensation model, calculate the error compensation for each test point, input the displacement, and input it into the piezoelectric displacement stage to collect the actual output displacement of each test point. S42. Error compensation effect detection: Calculate the error sequence and average error after compensation based on the input displacement and actual output displacement after error compensation at each test point. S43. Adaptive Correction: If the average error is less than the preset error threshold, it indicates that the error compensation effect meets the requirements, and the error compensation optimization ends. Otherwise, it indicates that the error compensation model parameters still need to be optimized. Adjust the maximum number of iterations T, and re-execute S1~S3 for adaptive correction until the accuracy of the solution meets the requirements.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-described error compensation optimization method for a piezoelectric displacement stage.

[0016] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the various steps of the above-described error compensation optimization method for a piezoelectric displacement stage.

[0017] (III) Beneficial Effects Compared with the prior art, the error compensation optimization method for the piezoelectric displacement stage provided by the present invention has the following beneficial effects: 1) Accurately construct the error compensation model to improve the accuracy of error compensation. Based on the preprocessed error data, a piecewise nonlinear compensation model is adopted to fully consider the actual error characteristics of the piezoelectric displacement stage, such as hysteresis, creep, and nonlinearity, and to construct an error compensation model that fits the error characteristics. At the same time, the error compensation model parameters to be optimized are identified. By optimizing these parameters, the error of the piezoelectric displacement stage can be compensated more accurately, effectively reducing the average positioning error of the entire stroke after error compensation, improving the positioning accuracy of the piezoelectric displacement stage, and meeting the usage requirements of high-precision application scenarios. 2) Introduce an improved mantis shrimp optimization algorithm to enhance its optimization efficiency. When solving the error compensation optimization model, an improved mantis shrimp optimization algorithm is adopted. In the global exploration phase, the algorithm simulates the asynchronous scanning behavior of the mantis shrimp's eyes and the dynamic polarization focusing behavior of its compound eyes to expand the search range and guide the population to move closer to the potential optimal area, avoiding getting trapped in local optima. In the local development phase, the algorithm simulates the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs in the "charge-burst-fine-adjust" process, and performs fine optimization within the potential optimal area to improve the accuracy of the solution. Through this optimization method that combines global and local approaches, the optimal error compensation model parameter set can be found more quickly, improving the optimization efficiency of the algorithm. 3) It has an adaptive correction mechanism to enhance the system's adaptive capability. After using the updated error compensation model to compensate for the piezoelectric displacement stage, adaptive correction is performed based on the error compensation effect. If the average error is less than the preset error threshold, the error compensation optimization ends; otherwise, the maximum number of iterations is adjusted, and the relevant steps are re-executed for adaptive correction until the accuracy of the solution meets the requirements. This adaptive correction mechanism can dynamically adjust the optimization process according to the actual error compensation effect, enabling the error compensation model to better adapt to the actual working conditions of the piezoelectric displacement stage, enhancing the system's adaptability, and ensuring the stability and reliability of the error compensation effect. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0019] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of the process of solving the error compensation optimization model using the improved mantis shrimp optimization algorithm in this invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0021] The core of this invention lies in addressing the issue that piezoelectric displacement stage error compensation needs to consider actual error characteristics such as hysteresis, creep, and nonlinearity, and that traditional optimization methods are prone to getting trapped in local optima and have insufficient solution accuracy. Therefore, a piezoelectric displacement stage error compensation optimization method based on an improved mantis shrimp optimization algorithm is proposed. This method constructs a piecewise nonlinear compensation model that closely matches the actual error characteristics, clearly defining the error compensation model parameters to be optimized. It employs the improved mantis shrimp optimization algorithm to expand the search range during the global exploration phase by simulating the asynchronous scanning of the mantis shrimp's eyes and the dynamic polarization focusing behavior of its compound eyes. During the local development phase, it simulates the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs in a "charge-burst-fine-adjust" manner for precise optimization, thereby obtaining the optimal set of error compensation model parameters. Finally, it performs adaptive correction based on the error compensation effect, ultimately achieving high-precision error compensation for the piezoelectric displacement stage.

[0022] The core improvements to the mantis shrimp optimization algorithm in this invention include: During the global exploration phase, the behavior of mantis shrimp’s asynchronous scanning with both eyes and dynamic polarization focusing with compound eyes was simulated to expand the search range and guide the population toward potential optimal areas, thus avoiding getting trapped in local optima. During the local development phase, the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs, characterized by "charging up, bursting out, and fine-tuning," is simulated. Within the potential optimal area found through global exploration, fine optimization is performed to improve the accuracy of the solution.

[0023] The following describes the specific process of the error compensation optimization method for the piezoelectric displacement stage provided by this invention, using a concrete example (e.g.) Figure 1 (as shown) and technical effects.

[0024] S1. Collect actual and theoretical displacement data of the piezoelectric displacement stage throughout its entire stroke, perform data preprocessing, and construct an error compensation model for the piezoelectric displacement stage.

[0025] Specifically, the error compensation model for the piezoelectric displacement stage is constructed in S1, including: Based on the preprocessed error data, an error compensation model is constructed that conforms to the actual error characteristics of the piezoelectric displacement stage, including hysteresis, creep, and nonlinearity. The parameters of the error compensation model to be optimized are also defined, specifically including: S11. An error compensation model is constructed by adopting a piecewise nonlinear compensation model and combining it with the actual error characteristics of the piezoelectric displacement stage: ; in, Input the displacement after error compensation for the k-th test point. The theoretical input displacement for the k-th test point. This is the hysteresis error compensation function. The scaling factor is the hysteresis characteristic. This is the creep error compensation function. The creep response scaling factor. This is a nonlinear error compensation function. This is the reference scale coefficient for nonlinear stroke. , , All are weighting coefficients; S12. Adjust the weighting coefficients in the error compensation model. , , and hysteresis characteristic scaling coefficient creep response scaling factor Stroke nonlinearity reference scale coefficient The parameters of the error compensation model to be optimized constitute the solution vector. .

[0026] The above technical solution, based on preprocessed error data, adopts a piecewise nonlinear compensation model to fully consider the actual error characteristics of the piezoelectric displacement stage, such as hysteresis, creep, and nonlinearity, and constructs an error compensation model that fits the error characteristics. At the same time, it clarifies the error compensation model parameters to be optimized. By optimizing these parameters, the error of the piezoelectric displacement stage can be compensated more accurately, effectively reducing the average positioning error of the entire stroke after error compensation, improving the positioning accuracy of the piezoelectric displacement stage, and meeting the usage requirements of high-precision application scenarios.

[0027] S2. Taking the minimum average positioning error of the entire stroke after piezoelectric displacement stage error compensation as the objective, and combining the constraints, an error compensation optimization model is constructed, including: S21. Taking the minimum average positioning error of the entire stroke after piezoelectric displacement stage error compensation as the objective, determine the objective function for error compensation optimization, including: ; in, X represents the actual output displacement of the k-th test point, where K is the number of test points. j Let X be the j-th error compensation model parameter to be optimized in the solution vector X. The initial average value of the parameters of the j-th error compensation model to be optimized in the solution vector X is set based on empirical values. This is the regularization coefficient, used to constrain parameter fluctuations and avoid overfitting; S22. Determine the constraints for error compensation optimization, including: 1) Weighting coefficient constraints: ,and ; 2) Scale coefficient constraint: ; S23. Combining the objective function and constraints of error compensation optimization, construct an error compensation optimization model.

[0028] S3. The improved mantis shrimp optimization algorithm is used to solve the error compensation optimization model to obtain the optimal error compensation model parameter set, such as... Figure 2 As shown, it includes: S31. Randomly generate an initial population in the search space. The position of each mantis shrimp in the population corresponds to a solution vector, and initialize the algorithm parameters. S32. Implement a dynamic switching mechanism to automatically switch to the global exploration phase / local development phase based on the number of iterations. S33. In the global exploration phase, simulate the asynchronous scanning behavior of the mantis shrimp's eyes and the dynamic polarization focusing behavior of its compound eyes to expand the search range, guide the population to move closer to the potential optimal area, avoid getting trapped in local optima, and enter S35. S34. In the local development stage, simulate the high-speed attack behavior of the mantis shrimp's hammer-shaped rappelling limbs in the process of "charging up - bursting - fine-tuning". Within the potential optimal area found in the global exploration, perform fine optimization to improve the accuracy of the solution, and then proceed to S35. S35. Use the objective function optimized by error compensation to evaluate all mantis shrimp in the current population, calculate the corresponding fitness value, and record and update the historical best solution; S36. Determine whether the iteration termination condition is met. If the iteration termination condition is not met, return to S32. Otherwise, use the historical optimal solution as the parameter set of the optimal error compensation model.

[0029] Specifically, in S33, during the global exploration phase, the asynchronous scanning behavior of the mantis shrimp's two eyes and the dynamic polarization focusing behavior of its compound eyes are simulated to expand the search range and guide the population towards the potential optimal region, avoiding getting trapped in local optima. This includes: S331, Calculation of binocular asynchronous saccade angle, simulating wide-angle inspection by the left eye and directional exploration by the right eye: ; in, , Let be the left and right eye saccade angles of the i-th mantis shrimp at the t-th iteration. , These represent the minimum and maximum scanning angles, respectively, where T is the maximum number of iterations, and r is the maximum number of iterations. i represents the individual random coefficient, with a value range of [0,1]. S332, Ambient polarized light intensity sensing: ; in, Let be the intensity of the ambient polarized light sensed by the i-th mantis shrimp in the t-th iteration. Let be the polarization coefficient of the nth mantis shrimp. This represents calculating the position of the i-th mantis shrimp at the t-th iteration. The position of the nth mantis shrimp at the tth iteration The Euclidean distance between them, UB and LB are the upper and lower bounds of the search space, respectively, and N is the current population size; S333, Calculate the polarization focusing coefficient: ; in, Let be the polarization focusing coefficient of the i-th mantis shrimp at the t-th iteration; S334, Dual-view cooperative exploration location update: ; in, Let i be the position of the i-th mantis shrimp in the (t+1)-th iteration. This is the globally optimal solution at the t-th iteration. Let be the position of a random individual at the t-th iteration.

[0030] The above technical solution fully simulates the real biological behavior of mantis shrimp, which involves asynchronous scanning of both eyes and dynamic polarization focusing of compound eyes. The left eye conducts a wide-angle survey to explore a large area corresponding to the parameters, while the right eye conducts a directional search for the corresponding parameters. The mantis shrimp senses the intensity of polarized light in the environment and locks in the potential optimal area through polarization signals. The dual-view collaborative exploration and position update achieve "large-area coverage + directional guidance" to avoid getting trapped in local optima.

[0031] Specifically, in the local development phase of S34, the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs, characterized by "charging-burst-fine-tuning," is simulated. Within the potential optimal region found through global exploration, fine-tuning is performed to improve the accuracy of the solution, including: S341, Energy Storage: ; ; in, , Let be the acceleration and velocity of the i-th mantis shrimp at the t-th iteration, respectively. For maximum stored acceleration, The energy storage attenuation coefficient is... Let be the energy storage speed of the i-th mantis shrimp in the (t-1)-th iteration. For one iteration step, In each iteration step, all velocities represent the change in position within a single iteration step, and all accelerations represent the change in velocity within a single iteration step. S342, Instantaneous Burst Strike: ; ; in, Let be the burst attack speed of the i-th mantis shrimp in the t-th iteration. To achieve maximum burst strike speed, Let be the position of the i-th mantis shrimp after its attack in the t-th iteration. Let be the unit direction vector pointing from the i-th mantis shrimp to the global optimal solution at the t-th iteration, simulating the burst attack direction. , This represents calculating the position of the i-th mantis shrimp at the t-th iteration. The global optimal solution at the t-th iteration The Euclidean distance between them; S343, Click Point Fine-tuning: ; ; ; in, The rotation angle is finely adjusted for the click point of the i-th mantis shrimp in the t-th iteration, where r1 is a random number uniformly distributed in the range [0,1]. Let be the fine-tuning rotation unit direction vector of the i-th mantis shrimp at the t-th iteration. Unit direction vector The vertical direction vector, This is the fine-tuning coefficient.

[0032] The above technical solution fully simulates the complete predation behavior of the mantis shrimp's hammer-shaped rappelling limbs. The energy storage corresponds to the mantis shrimp's muscle power storage after locking onto its prey, the instantaneous burst strike corresponds to the high-speed impact on the prey (approaching the error compensation model parameter group), and the fine-tuning of the strike point corresponds to the accuracy correction after the strike, ensuring the accuracy of parameter optimization and achieving "rapid convergence + precise refinement".

[0033] When solving the error compensation optimization model, an improved mantis shrimp optimization algorithm is adopted. In the global exploration phase, the algorithm simulates the asynchronous scanning behavior of the mantis shrimp's eyes and the dynamic polarization focusing behavior of its compound eyes to expand the search range and guide the population to move closer to the potential optimal area, avoiding getting trapped in local optima. In the local development phase, the algorithm simulates the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs in the "charge-burst-fine-adjust" process, and performs fine optimization within the potential optimal area to improve the accuracy of the solution. Through this optimization method that combines global and local approaches, the optimal error compensation model parameter set can be found more quickly, improving the optimization efficiency of the algorithm.

[0034] S4. Perform error compensation on the piezoelectric displacement stage using the updated parameter error compensation model, and make adaptive corrections based on the error compensation effect, including: S41. Error Compensation Implementation: The obtained optimal error compensation model parameter set... Substitute the error compensation model, calculate the error compensation for each test point, input the displacement, and input it into the piezoelectric displacement stage to collect the actual output displacement of each test point. S42. Error compensation effect detection: Calculate the error sequence and average error after compensation based on the input displacement and actual output displacement after error compensation at each test point. S43. Adaptive Correction: If the average error is less than the preset error threshold, it indicates that the error compensation effect meets the requirements, and the error compensation optimization ends. Otherwise, it indicates that the error compensation model parameters still need to be optimized. Adjust the maximum number of iterations T, and re-execute S1~S3 for adaptive correction until the accuracy of the solution meets the requirements.

[0035] The above technical solution uses an updated error compensation model to compensate for the error of the piezoelectric displacement stage. Then, it performs adaptive correction based on the error compensation effect. If the average error is less than a preset error threshold, the error compensation optimization ends; otherwise, the maximum number of iterations is adjusted, and the relevant steps are re-executed for adaptive correction until the accuracy of the solution meets the requirements. This adaptive correction mechanism can dynamically adjust the optimization process according to the actual error compensation effect, enabling the error compensation model to better adapt to the actual working conditions of the piezoelectric displacement stage, enhancing the system's adaptability, and ensuring the stability and reliability of the error compensation effect.

[0036] Based on the above-disclosed error compensation optimization method for piezoelectric displacement stages, this invention also discloses a computer device and a computer-readable storage medium.

[0037] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned error compensation optimization method for the piezoelectric displacement stage.

[0038] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the various steps of the above-described error compensation optimization method for a piezoelectric displacement stage.

[0039] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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 of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An error compensation optimization method for a piezoelectric displacement stage, characterized in that: Includes the following steps: S1. Collect actual and theoretical displacement data of the piezoelectric displacement stage throughout its entire stroke, perform data preprocessing, and construct an error compensation model for the piezoelectric displacement stage. S2. With the goal of minimizing the average positioning error of the entire stroke after piezoelectric displacement stage error compensation, an error compensation optimization model is constructed in combination with constraints. S3. The improved mantis shrimp optimization algorithm is used to solve the error compensation optimization model to obtain the optimal error compensation model parameter set; S4. Use the updated error compensation model to perform error compensation on the piezoelectric displacement stage, and make adaptive corrections based on the error compensation effect. Among them, the improved mantis shrimp optimization algorithm includes: During the global exploration phase, the behavior of mantis shrimp’s asynchronous scanning with both eyes and dynamic polarization focusing with compound eyes was simulated to expand the search range and guide the population toward potential optimal areas, thus avoiding getting trapped in local optima. During the local development phase, the high-speed attack behavior of the mantis shrimp, characterized by "charging-bursting-fine-tuning" with its hammer-like rappelling limbs, is simulated. Within the potential optimal area found through global exploration, fine optimization is performed to improve the accuracy of the solution.

2. The error compensation optimization method for the piezoelectric displacement stage according to claim 1, characterized in that: The error compensation model for the piezoelectric displacement stage is constructed in S1, including: Based on the preprocessed error data, an error compensation model is constructed that conforms to the actual error characteristics of the piezoelectric displacement stage, including hysteresis, creep, and nonlinearity. The parameters of the error compensation model to be optimized are also defined, specifically including: S11. An error compensation model is constructed by adopting a piecewise nonlinear compensation model and combining it with the actual error characteristics of the piezoelectric displacement stage: ； in, Input the displacement after error compensation for the k-th test point. The theoretical input displacement for the k-th test point. This is the hysteresis error compensation function. The scaling factor is the hysteresis characteristic. This is the creep error compensation function. The creep response scaling factor. This is a nonlinear error compensation function. This is the reference scale coefficient for nonlinear stroke. , , All are weighting coefficients; S12. Adjust the weighting coefficients in the error compensation model. , , and hysteresis characteristic scaling coefficient creep response scaling factor Stroke nonlinearity reference scale coefficient The parameters of the error compensation model to be optimized constitute the solution vector. .

3. The error compensation optimization method for the piezoelectric displacement stage according to claim 1, characterized in that: In S2, the objective is to minimize the average positioning error over the entire stroke after piezoelectric displacement stage error compensation. Based on the constraints, an error compensation optimization model is constructed, including: S21. Determine the objective function for error compensation optimization, with the goal of minimizing the average positioning error of the entire stroke after piezoelectric displacement stage error compensation. S22. Determine the constraints for error compensation optimization; S23. Combining the objective function and constraints of error compensation optimization, construct an error compensation optimization model.

4. The error compensation optimization method for the piezoelectric displacement stage according to claim 3, characterized in that: In S21, the objective function for error compensation optimization is determined with the goal of minimizing the average positioning error over the entire stroke after piezoelectric displacement stage error compensation. This function includes: ； in, X represents the actual output displacement of the k-th test point, where K is the number of test points. j Let X be the j-th error compensation model parameter to be optimized in the solution vector X. The initial average value of the parameters of the j-th error compensation model to be optimized in the solution vector X is set based on empirical values. This is the regularization coefficient, used to constrain parameter fluctuations and avoid overfitting; S22. Determine the constraints for error compensation optimization, including: 1) Weighting coefficient constraints: ,and ; 2) Scale coefficient constraint: .

5. The error compensation optimization method for the piezoelectric displacement stage according to claim 1, characterized in that: In S3, an improved mantis shrimp optimization algorithm is used to solve the error compensation optimization model, obtaining the optimal error compensation model parameter set, including: S31. Randomly generate an initial population in the search space. The position of each mantis shrimp in the population corresponds to a solution vector, and initialize the algorithm parameters. S32. Implement a dynamic switching mechanism to automatically switch to the global exploration phase / local development phase based on the number of iterations. S33. In the global exploration phase, simulate the asynchronous scanning behavior of the mantis shrimp's eyes and the dynamic polarization focusing behavior of its compound eyes to expand the search range, guide the population to move closer to the potential optimal area, avoid getting trapped in local optima, and enter S35. S34. In the local development stage, simulate the high-speed attack behavior of the mantis shrimp's hammer-shaped rappelling limbs in the process of "charging up - bursting - fine-tuning". Within the potential optimal area found in the global exploration, perform fine optimization to improve the accuracy of the solution, and then proceed to S35. S35. Use the objective function optimized by error compensation to evaluate all mantis shrimp in the current population, calculate the corresponding fitness value, and record and update the historical best solution; S36. Determine whether the iteration termination condition is met. If the iteration termination condition is not met, return to S32. Otherwise, use the historical optimal solution as the parameter set of the optimal error compensation model.

6. The error compensation optimization method for the piezoelectric displacement stage according to claim 5, characterized in that: In S33, during the global exploration phase, the behavior of mantis shrimp—asynchronous binocular scanning and dynamic polarization focusing of compound eyes—is simulated to expand the search range and guide the population towards potential optimal regions, avoiding getting trapped in local optima. This includes: S331, Calculation of binocular asynchronous saccade angle, simulating wide-angle inspection by the left eye and directional exploration by the right eye: ； in, , Let be the left and right eye saccade angles of the i-th mantis shrimp at the t-th iteration. , These represent the minimum and maximum scanning angles, respectively, where T is the maximum number of iterations, and r is the maximum number of iterations. i represents the individual random coefficient, with a value range of [0,1]. S332, Ambient polarized light intensity sensing: ； in, Let be the intensity of the ambient polarized light sensed by the i-th mantis shrimp in the t-th iteration. Let be the polarization coefficient of the nth mantis shrimp. This represents calculating the position of the i-th mantis shrimp at the t-th iteration. The position of the nth mantis shrimp at the tth iteration The Euclidean distance between them, UB and LB are the upper and lower bounds of the search space, respectively, and N is the current population size; S333, Calculate the polarization focusing coefficient: ； in, Let be the polarization focusing coefficient of the i-th mantis shrimp at the t-th iteration; S334, Dual-view cooperative exploration location update: ； in, Let i be the position of the i-th mantis shrimp in the (t+1)-th iteration. This is the globally optimal solution at the t-th iteration. Let be the position of a random individual at the t-th iteration.

7. The error compensation optimization method for the piezoelectric displacement stage according to claim 6, characterized in that: In S34, during the local development phase, the high-speed attack behavior of the mantis shrimp's hammer-like rappelling limbs—"charging-burst-fine-tuning"—is simulated. Within the potential optimal region found through global exploration, fine-tuning is performed to improve the accuracy of the solution, including: S341, Energy Storage: ； ； in, , Let be the acceleration and velocity of the i-th mantis shrimp at the t-th iteration, respectively. For maximum stored acceleration, The energy storage attenuation coefficient is... Let be the energy storage speed of the i-th mantis shrimp in the (t-1)-th iteration. For one iteration step, In each iteration step, all velocities represent the change in position within a single iteration step, and all accelerations represent the change in velocity within a single iteration step. S342, Instantaneous Burst Strike: ； ； in, Let be the burst attack speed of the i-th mantis shrimp in the t-th iteration. To achieve maximum burst strike speed, Let be the position of the i-th mantis shrimp after its attack in the t-th iteration. Let be the unit direction vector pointing from the i-th mantis shrimp to the global optimal solution at the t-th iteration, simulating the burst attack direction. , This represents calculating the position of the i-th mantis shrimp at the t-th iteration. The global optimal solution at the t-th iteration The Euclidean distance between them; S343, Click Point Fine-tuning: ； ； ； in, To fine-tune the rotation angle of the i-th mantis shrimp at the t-th iteration, r1 is a random number uniformly distributed in the range [0,1]. Let be the fine-tuning rotation unit direction vector of the i-th mantis shrimp at the t-th iteration. Unit direction vector The vertical direction vector, This is the fine-tuning coefficient.

8. The error compensation optimization method for the piezoelectric displacement stage according to claim 1, characterized in that: In S4, the updated error compensation model is used to compensate for the error of the piezoelectric displacement stage, and adaptive correction is performed based on the error compensation effect, including: S41. Error Compensation Implementation: Obtain the optimal error compensation model parameter set. Substitute the error compensation model, calculate the error compensation for each test point, input the displacement, and input it into the piezoelectric displacement stage to collect the actual output displacement of each test point. S42. Error compensation effect detection: Calculate the error sequence and average error after compensation based on the input displacement and actual output displacement after error compensation at each test point. S43. Adaptive Correction: If the average error is less than the preset error threshold, it indicates that the error compensation effect meets the requirements, and the error compensation optimization ends. Otherwise, it indicates that the error compensation model parameters still need to be optimized. Adjust the maximum number of iterations T, and re-execute S1~S3 for adaptive correction until the accuracy of the solution meets the requirements.

9. A computer device, characterized in that: The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the error compensation optimization method for the piezoelectric displacement stage as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: It stores a computer program, which, when executed by a processor, implements the steps of the error compensation optimization method for the piezoelectric displacement stage as described in any one of claims 1 to 8.

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