Piezoelectric ceramic driving flow control method and device for coping with any data loss and storage medium

Abstract

The invention relates to a piezoelectric ceramic driving flow control method and device for coping with any data loss and a storage medium, and the method comprises the following steps: building a piezoelectric ceramic ARX model based on the operation process of a piezoelectric ceramic driving flow control system and considering the condition of any data loss; solving the piezoelectric ceramic ARX model, and outputting to obtain optimal flow control parameters; and according to the optimal flow control parameter, the working state of the piezoelectric ceramic driving flow control system is correspondingly controlled. Compared with the prior art, accurate parameter estimation can be carried out on the piezoelectric ceramic driving flow control system under the condition of any data loss, so that the accuracy of flow control is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of piezoelectric ceramic driven flow control, and in particular to a piezoelectric ceramic driven flow control method, device and storage medium for coping with arbitrary data loss. Background Art

[0002] With the development of high-tech industries such as aerospace, micro-nano manufacturing and semiconductors, the requirements for positioning accuracy in precision machining and control fields have become more stringent. Piezoelectric ceramics are widely used in the field of micro-nano drive control due to their advantages such as fast response speed, high positioning accuracy and small size. The fast response speed of piezoelectric ceramics makes them suitable for applications that require high-frequency operation, and because of their high-precision positioning capabilities, piezoelectric ceramics have become ideal drive and control elements in micro-nano scale systems. In addition, the relatively small size of piezoelectric ceramics is beneficial to its integration in micro- and nano-level systems, meeting the needs of micro-nano devices with strict requirements on size and weight. These characteristics have made piezoelectric ceramics an important technology in the field of micro-nano drive control, and provide a reliable solution for realizing efficient, high-precision and miniaturized control systems.

[0003] However, for piezoelectric ceramic driven flow control systems, if there is a random loss of output data during the sampling process of actual working conditions, it may affect the performance and stability of the system. For example, sensor failure, communication problems, control algorithm adjustment, instrument failure, power supply problems, and environmental interference may all lead to output data loss, causing the control system to lose accuracy and affect the precise regulation of the system flow. Therefore, considering the case of arbitrary data loss, studying the modeling and parameter estimation methods of the piezoelectric ceramic driven flow control system operation process is of great practical significance for ensuring the accuracy of piezoelectric ceramic driven flow control. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a piezoelectric ceramic driven flow control method, device and storage medium that can cope with any data loss, which can accurately estimate the parameters of the piezoelectric ceramic driven flow control system in the event of any data loss, thereby ensuring the accuracy of flow control.

[0005] The object of the present invention can be achieved by the following technical solution: A piezoelectric ceramic driven flow control method for coping with arbitrary data loss comprises the following steps:

[0006] S1. Based on the operation process of the piezoelectric ceramic driven flow control system and considering the possibility of any data loss, a piezoelectric ceramic ARX (Auto-Regressive with Extra Inputs) model is established;

[0007] S2, solving the piezoelectric ceramic ARX model and outputting the optimal flow control parameters;

[0008] S3. According to the optimal flow control parameters, the working state of the piezoelectric ceramic driven flow control system is controlled accordingly.

[0009] Furthermore, the step S1 specifically includes the following steps:

[0010] S11. Based on the operation process of the piezoelectric ceramic driven flow control system, a discrete time linear system equation is established, and a regression equation is determined;

[0011] S12. Considering the possibility of any data loss, the regression equation is analyzed and summarized to establish the piezoelectric ceramic ARX model.

[0012] Furthermore, the discrete time linear system equation in step S11 is specifically:

[0013] y t =a n y t-1 +a n-1 y t-2 +…+a1y t-n +b m u t-n+m-1 +…+b1u t-n

[0014] Among them, y t is the actual output voltage value of the piezoelectric ceramic driver at time t=n, n+1,…,N, u t is the input gas flow value of the piezoelectric ceramic driven flow control system, a1, a2, …, a n ,b1,b2,…,b m are the piezoelectric ceramic driven flow control system parameters, y0, y1, …, y n-1 is the initial condition of the piezoelectric ceramic driven flow control system.

[0015] Furthermore, the regression equation in step S11 is specifically:

[0016]

[0017] Among them, the information vector Parameter vector θ = [a n ,a n-1 ,…,a1,b m ,…,b1] T ∈R n+m , noise e t =ε t -an ε t-1 -a n-1 ε t-2 -…-a1ε t-n , ε t is the measurement noise with zero mean, Measure the output of the sensor.

[0018] Furthermore, the specific process of step S12 is as follows:

[0019] Consider the case where the sampled output data is lost, let N = {0, 1, ..., N}, and the lost output data The time is denoted as k j ,j=1,2,…,N s , the moment of losing output data can be summarized as N c N s The complement of N, if t∈N c , then the output Measurable;

[0020] Let t∈N c The moments are divided into two categories:

[0021] The first type is t∈N c and There is no data loss in All can be measured, the regression equation is not affected by missing data, and the least squares algorithm is used to calculate the moments that meet the conditions.

[0022]

[0023] The second type is t∈N c and There is data loss in Measurable, but There is data loss in the

[0024] In order to improve the utilization of data information and the performance of parameter estimation, the missing output data is predicted from the most recent known output data, and the predicted results are used to replace the missing output data to form a predicted output When the regression equation Measurable, summarize the moments that meet the conditions as N a :

[0025]

[0026] For a general n-order system, let t = h l ∈N a , l=1,2,…,I;

[0027] For t = h l Regression equation at time +1 The information vector in Get the predicted value

[0028] For t = h l Regression equation at time +2 Classify and discuss based on whether the output of the previous moment is lost: If h l +1∈N c , the information vector in the regression equation If h l +1∈N s , information vector And the noise is

[0029] In order to unify the formula, define:

[0030]

[0031] Therefore, we get t = h l +2 predicted value

[0032] For t = h l The regression equation at time +3 is similarly derived to obtain the predicted value

[0033] Based on the above prediction method, the output formula for a general n-order system can be expressed as:

[0034]

[0035] Among them, the information vector

[0036] Furthermore, the step S2 specifically adopts a gradient descent algorithm or a Newton-Raphson algorithm to solve the piezoelectric ceramic ARX model.

[0037] Furthermore, when the step S2 uses the gradient descent algorithm to solve the piezoelectric ceramic ARX model, it includes the following process:

[0038] Construct the criteria function:

[0039]

[0040] The general form of the gradient descent algorithm is:

[0041]

[0042] Take the partial derivative of the output formula of the general n-order system with respect to θ:

[0043]

[0044] Depend on The definition of can be obtained:

[0045]

[0046] According to the gradient descent algorithm, the optimal parameter estimation is performed along the direction of gradient descent:

[0047]

[0048] Among them, γ is the step size, To predict the output, is the estimated value of the parameter vector corresponding to the iteration number k+1, is the estimated value of the parameter vector corresponding to the iteration number k.

[0049] Furthermore, when the Newton-Raphson algorithm is used to solve the piezoelectric ceramic ARX model in step S2, the following process is included:

[0050] Assume that the function f(θ) is the partial derivative of the least squares with respect to θ, and the local minimum of the least squares can be achieved at the point where f(θ) = 0. Use the Newton-Raphson algorithm to solve f(θ) = 0;

[0051] According to the general form of the Newton-Raphson algorithm, we need to take f(θ) versus θ T The partial derivative of The second partial derivative of is:

[0052]

[0053]

[0054] Depend on The definition of can be obtained:

[0055]

[0056] It follows from this The expression is:

[0057]

[0058] Optimal parameter estimation using the Newton-Raphson algorithm:

[0059]

[0060] in, To predict the output, is the estimated value of the parameter vector corresponding to the iteration number k+1, is the estimated value of the parameter vector corresponding to the iteration number k.

[0061] A piezoelectric ceramic driven flow control device for coping with arbitrary data loss includes a processor, the processor is communicatively connected to a memory, the memory stores a computer-readable program, and the processor implements the above-mentioned piezoelectric ceramic driven flow control method for coping with arbitrary data loss when executing the computer-readable program.

[0062] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the piezoelectric ceramic driven flow control method for coping with arbitrary data loss.

[0063] Compared with the prior art, the present invention has the following advantages:

[0064] 1. Based on the operation process of the piezoelectric ceramic driven flow control system, the present invention establishes a piezoelectric ceramic ARX model under the consideration of arbitrary data loss, which can accurately map the relationship between the input and output data of the discrete dynamic system. In addition, for given input and output data, a parameter identification scheme with arbitrary data loss is proposed, and the output prediction is recursively and multi-step constructed for the most recent available output value, thereby making full use of batch input and output data to identify the parameters of the system in the parameter identification process, so that accurate calculations can be performed and the accuracy of parameter estimation can be improved. It is suitable for modeling and control of complex industrial processes and is conducive to improving the accuracy of flow control.

[0065] Second, the present invention fully considers that in actual operation, the system may lose accuracy due to sensor failure, communication problems, control algorithm adjustment, instrument failure, power supply problems, environmental interference, etc., which may cause the output data to fail to reach the server and the system sampling data to be lost. The design is based on real and measurable data to predict and replace the lost data of the system, making the predicted value of the lost data more accurate, improving the utilization of data information and the performance of parameter estimation.

[0066] 3. The present invention utilizes a system identification solution based on data modeling, and utilizes the measurable input and output data during the operation of the piezoelectric ceramic driven flow control system. Through linear transformation technology, the ARX model is converted into a system identification model in the form of least squares. After predicting the lost data of the system, the output data is approximated by the initial parameters of the identification model and the constructed information vector. The unknown parameters and information vectors in the model are replaced by their estimated values. Combined with the assumed initial state of the system and the measurable input and output data of the system, the parameters output at the current moment can be quickly and accurately identified.

[0067] Fourth, the present invention proposes the model establishment and parameter estimation of a discrete linear piezoelectric ceramic driven flow control system with arbitrary data loss. Numerical examples show that the parameter estimation converges to its true value, and the model estimated output curve of the system matches the measured output curve. The model establishment and parameter estimation of the piezoelectric ceramic driven flow control system considering arbitrary data loss proposed in the present invention can be combined with other estimation algorithms to study the parameter identification of linear and nonlinear random systems with colored noise, and can be applied to other fields, such as information processing and transportation communication systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0069] Figure 2 is the iterative estimation error of the four algorithms in the embodiment;

[0070] Figure 3a~3d is the estimation error with data loss of the two gradient descent algorithms in the embodiment;

[0071] Figure 4 is the estimated error of the two Newton iteration algorithms in the embodiment;

[0072] Figure 5a-5b Output the comparison between the predicted value and the measured value in the embodiment;

[0073] Figure 6 are the estimated output and the measured output in the embodiment. DETAILED DESCRIPTION

[0074] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0075] Example

[0076] like Figure 1 As shown, a piezoelectric ceramic driven flow control method for coping with arbitrary data loss includes the following steps:

[0077] S1. Based on the operation process of the piezoelectric ceramic driven flow control system and considering the situation of arbitrary data loss, the piezoelectric ceramic ARX model is established;

[0078] S2, solving the piezoelectric ceramic ARX model and outputting the optimal flow control parameters;

[0079] S3. According to the optimal flow control parameters, the working state of the piezoelectric ceramic driven flow control system is controlled accordingly.

[0080] This embodiment applies the above technical solution, and the main contents are:

[0081] (1) The piezoelectric ceramic driven flow control system measures the response of the piezoelectric ceramic driver by converting the gas flow into a voltage signal. Based on the operation process of the piezoelectric ceramic driven flow control system, a discrete time linear system equation is established.

[0082] y t =a n y t-1 +a n-1 y t-2 +…+a1y t-n +b m u t-n+m-1 +…+b1u t-n

[0083] y t is the real (or clean) output voltage value of the piezoelectric ceramic driver at time t=n, n+1,…,N, u t is the input gas flow value of the piezoelectric ceramic driven flow control system, a1, a2, …, a n ,b1,b2,…,b m are the piezoelectric ceramic driven flow control system parameters, y0, y1, …, y n-1 is the initial condition of the piezoelectric ceramic driven flow control system.

[0084] The true output is not available, the output measured by the sensor There is noise ε t , we can get the regression equation:

[0085]

[0086] Among them, the information vector Parameter vector θ = [a n ,a n-1 ,…,a1,b m ,…,b1] T ∈R n+1m , noise e t =ε t -a nε t-1 -a n-1 ε t-2 -…-a1ε t-n , ε t is the measurement noise with zero mean, For measurement output.

[0087] In actual systems, due to sensor or network transmission failures and other reasons, the output data may not be able to reach the server, resulting in the loss of system sampling data.

[0088] Let N = {0, 1, ..., N}, and lose output data The time is denoted as k j ,j=1,2,…,N s , the moment of losing output data can be summarized as N c N s The complement of N, if t∈N c , output Measurable.

[0089] Let t∈N c The moments are divided into two categories:

[0090] The first type is t∈N c and There is no data loss in The regression equation is not affected by missing data and is calculated using the least squares algorithm. The moments that meet the conditions are summarized as

[0091]

[0092] The second type is t∈N c and There is data loss in Measurable, but There is data loss in .

[0093] In order to improve the utilization of data information and the performance of parameter estimation, the missing output data is predicted from the most recent known output data, and the predicted results are used to replace the missing output data to form a predicted output When the regression equation Measurable, summarize the moments that meet the conditions as N a :

[0094]

[0095] For a general n-order system, let t = h l ∈N a , l=1,2,…,I.

[0096] For t = h l Regression equation at time +1 The information vector in Get the predicted value

[0097] For t = h l Regression equation at time +2 Classify and discuss based on whether the output of the previous moment is lost: If h l +1∈N c , the information vector in the regression equation If h l +1∈N s , information vector And the noise is

[0098] In order to unify the formula, define:

[0099]

[0100] Therefore, we get t = h l +2 predicted value

[0101] For t = h l The regression equation at time +3 is similarly derived to obtain the predicted value

[0102] Based on the above prediction method, the output formula for a general n-order system can be expressed as:

[0103]

[0104] Among them, the information vector

[0105] (2) Construct a criterion function based on the obtained output prediction:

[0106]

[0107] The general form of the gradient descent algorithm is:

[0108]

[0109] Take the partial derivative of the output formula of the general n-order system with respect to θ:

[0110]

[0111] Depend on The definition of can be obtained:

[0112]

[0113] According to the gradient descent algorithm, the optimal parameter estimation is performed along the direction of gradient descent:

[0114]

[0115] Among them, γ is the step size, To predict the output, is the estimated value of the parameter vector corresponding to the iteration number k+1, is the estimated value of the parameter vector corresponding to the iteration number k.

[0116] (3) This embodiment takes into account that the gradient descent algorithm needs to select γ, and the simulation results show that the convergence speed of the algorithm is relatively slow. Therefore, this embodiment adopts another fast algorithm - assuming that the function f(θ) is the partial derivative of the least squares with respect to θ, the local minimum of the least squares can be achieved at the point where f(θ) = 0, and the Newton-Raphson algorithm is used to solve f(θ) = 0.

[0117] According to the general form of the Newton-Raphson algorithm, we need to take f(θ) versus θ T The partial derivative of The second partial derivative of is:

[0118]

[0119] Depend on The definition of can be obtained:

[0120]

[0121] It follows from this The expression is:

[0122]

[0123] Optimal parameter estimation using the Newton-Raphson algorithm:

[0124]

[0125] in, To predict the output, is the estimated value of the parameter vector corresponding to the iteration number k+1, is the estimated value of the parameter vector corresponding to the iteration number k.

[0126] (4) Continue the calculation until the preset number of iterations is reached and the solution process ends.

[0127] With reference to the attached drawings Figure 2-Figure 6 Some conclusions can be drawn: Figure 2 The horizontal axis K is the number of iterations, and the vertical axis δ is the error. Figure 2 The results show that the Newton-Raphson algorithm converges faster than the gradient descent algorithm;

[0128] Figure 3a~3d The horizontal coordinate K is the number of iterations, and the vertical coordinates a1, a2, b1, and b2 are system parameters. It can be seen that the algorithm proposed in the present invention has higher accuracy;

[0129] Figure 4 The horizontal axis K is the number of iterations, and the vertical axis δ is the error, which shows that under the Newton-Raphson algorithm, the method proposed in the present invention has a faster convergence speed and higher accuracy than the auxiliary model;

[0130] Figure 5a-5b The horizontal axis is time and the vertical axis is system output, which shows the effectiveness of the algorithm proposed in this scheme;

[0131] Figure 6 The horizontal axis is time and the vertical axis is system output. It can be seen that the model prediction output of this scheme can track the measured output well.

[0132] The above response results fully verify the performance and design efficiency of this technical solution.

[0133] In summary, this scheme establishes a piezoelectric ceramic ARX model while taking into account arbitrary data loss, which can accurately map the relationship between the input and output data of the discrete dynamic system. Based on the given piezoelectric ceramic input and output data, the model is solved by using an estimation algorithm (such as gradient descent algorithm and Newton-Raphson algorithm), which can accurately estimate the parameters of the piezoelectric ceramic driven flow control system, thereby ensuring the accuracy of flow control.

Claims

1. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss, characterized in that: The following steps are involved: S1. Based on the operation process of the piezoelectric ceramic driven flow control system and considering the possibility of arbitrary data loss, a piezoelectric ceramic ARX model is established; S2, solving the piezoelectric ceramic ARX model and outputting the optimal flow control parameters; S3. According to the optimal flow control parameters, the working state of the piezoelectric ceramic driven flow control system is controlled accordingly.

2. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss according to claim 1, characterized in that: The step S1 specifically includes the following steps: S11. Based on the operation process of the piezoelectric ceramic driven flow control system, a discrete time linear system equation is established, and a regression equation is determined; S12. Considering the possibility of any data loss, the regression equation is analyzed and summarized to establish the piezoelectric ceramic ARX model.

3. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss according to claim 2, characterized in that: The discrete time linear system equation in step S11 is specifically: and t =a n and t-1 +a n-1 and t-2 +…+a1y t-n +b m or t-n+m-1 +…+b1u t-n Among them, y t is the actual output voltage value of the piezoelectric ceramic driver at time t=n, n+1,…,N, u t is the input gas flow value of the piezoelectric ceramic driven flow control system, a 10 ,a2,…,a n ,b1,b2,…,b m are the piezoelectric ceramic driven flow control system parameters, y0, y1, …, y n-1 is the initial condition of the piezoelectric ceramic driven flow control system.

4. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss according to claim 3, characterized in that: The regression equation in step S11 is specifically: Among them, the information vector Parameter vector θ = [a n ,a n-1 ,…,a1,b m ,…,b1] T ∈R n+m , noise e t =ε t -a n ε t-1 -a n-1 ε t-2 -…-a1ε t-n , ε t is the measurement noise with zero mean, Measure the output of the sensor.

5. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss according to claim 4, characterized in that: The specific process of step S12 is as follows: Consider the case where the sampled output data is lost, let N = {0, 1, ..., N}, and the lost output data The time is denoted as k j ,j=1,2,…,N s , the moment of losing output data can be summarized as N c N s The complement of N, if t∈N c , then the output Measurable; Let t∈N c The moments are divided into two categories: The first type is t∈N c and There is no data loss in All can be measured, the regression equation is not affected by missing data, and the least squares algorithm is used to calculate the moments that meet the conditions. The second type is t∈N c and There is data loss in Measurable, but There is data loss in the In order to improve the utilization of data information and the performance of parameter estimation, the missing output data is predicted from the most recent known output data, and the predicted results are used to replace the missing output data to form a predicted output When the regression equation Measurable, summarize the moments that meet the conditions as N a : For a general n-order system, let t = h l ∈N a , l=1,2,…,I; For t = h l Regression equation at time +1 The information vector in Get the predicted value For t = h l Regression equation at time +2 Classify and discuss based on whether the output of the previous moment is lost: If h l +1∈N c , the information vector in the regression equation If h l +1∈N s , information vector And the noise is In order to unify the formula, define: Therefore, we get t = h l +2 predicted value For t = h l The regression equation at time +3 is similarly derived to obtain the predicted value Based on the above prediction method, the output formula for a general n-order system can be expressed as: Among them, the information vector 6. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss according to claim 5, characterized in that: The step S2 specifically adopts a gradient descent algorithm or a Newton-Raphson algorithm to solve the piezoelectric ceramic ARX model.

7. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss according to claim 6, characterized in that: When the step S2 uses the gradient descent algorithm to solve the piezoelectric ceramic ARX model, it includes the following process: Construct the criteria function: The general form of the gradient descent algorithm is: Take the partial derivative of the output formula of the general n-order system with respect to θ: Depend on The definition of can be obtained: According to the gradient descent algorithm, the optimal parameter estimation is performed along the direction of gradient descent: Among them, γ is the step size, To predict the output, is the estimated value of the parameter vector corresponding to the iteration number k+1, is the estimated value of the parameter vector corresponding to the iteration number k.

8. A piezoelectric ceramic driven flow control method for coping with arbitrary data loss according to claim 6, characterized in that: When the step S2 uses the Newton-Raphson algorithm to solve the piezoelectric ceramic ARX model, it includes the following process: Assume that the function f(θ) is the partial derivative of the least squares with respect to θ, and the local minimum of the least squares can be achieved at the point where f(θ) = 0. Use the Newton-Raphson algorithm to solve f(θ) = 0; According to the general form of the Newton-Raphson algorithm, we need to take f(θ) versus θ T The partial derivative of The second partial derivative of is: Depend on The definition of can be obtained: It follows from this The expression is: Optimal parameter estimation using the Newton-Raphson algorithm: in, To predict the output, is the estimated value of the parameter vector corresponding to the iteration number k+1, is the estimated value of the parameter vector corresponding to the iteration number k.

9. A piezoelectric ceramic driven flow control device for coping with arbitrary data loss, comprising a processor, the processor being communicatively connected to a memory, the memory storing a computer readable program, characterized in that: When the processor executes the computer-readable program, the piezoelectric ceramic driven flow control method for coping with arbitrary data loss as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the piezoelectric ceramic driven flow control method for coping with arbitrary data loss as claimed in any one of claims 1 to 8 are implemented.

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