Cut tobacco dryer steady-state model predictive control method based on Kalman filtering time delay correction

Abstract

The invention relates to the technical field of intelligent control, in particular to a cut-tobacco dryer steady-state model predictive control method based on Kalman filtering time delay correction, which comprises the following steps of: utilizing second-level historical production data and a system identification technology to process a cut-tobacco drying steady-state production process; according to the method, a dynamic transfer function prediction model and a state-space equation model from the moisture removal air door opening degree and the cylinder wall temperature to the outlet moisture are established, an appropriate Kalman filter (KF) is selected to carry out online correction on a cut-tobacco dryer prediction model with time delay, and the control of the process parameters in the cut-tobacco drying steady-state production stage is realized by using a model predictive controller (MPC) algorithm. Therefore, ideal outlet material moisture is achieved, and the problems that in the cut-tobacco drying process of an existing cut-tobacco dryer, dynamic characteristics of a system are ignored in a control method applied to the cut-tobacco drying process of the cut-tobacco dryer, and the control effect of the cut-tobacco drying process of the cut-tobacco dryer is poor due to the fact that the system with large inertia for controlling the cut-tobacco drying process of the cut-tobacco dryer is poor in prediction effect are solved.

Description

Technical Field

[0001] This invention relates to the field of intelligent control, and in particular to a steady-state model predictive control method for a wire drying machine based on Kalman filter delay correction. Background Technology

[0002] During the drying process, the moisture content and temperature of the material entering the drying drum are affected not only by various factors in the previous production process, but also by various disturbances during storage and transportation. In order to ensure the full preservation and development of the flavor of the material itself, the processing intensity of the drying machine must be reasonable. Therefore, the process parameters used in the drying process are limited to a certain range. However, the control target of the drying steady-state stage is within the adjustment range allowed by the process parameters. By adjusting the process parameters to minimize the fluctuation of the relative standard value, the minimum standard deviation of the moisture content of the outlet material can be achieved, and the stability of the dehydration during the drying process can be maintained.

[0003] However, the wire drying machine is an inertial system with delay and a nonlinear system with multiple input and output variables. Currently, there are many control methods applied to the wire drying process of the wire drying machine, but these control methods ignore the dynamic characteristics of the system. For such a system with large inertia that is controlled in the wire drying process, the prediction effect is poor, resulting in a poor control effect of the wire drying process.

[0004] Therefore, it is necessary to design a steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction, in order to solve the problem that existing control methods applied to the wire drying process ignore the dynamic characteristics of the system, resulting in poor prediction performance for such a system with large inertia, leading to poor control of the wire drying process. Summary of the Invention

[0005] The purpose of this invention is to propose a steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction, in order to solve the problem that existing control methods applied to the wire drying process of a wire drying machine ignore the dynamic characteristics of the system, resulting in poor prediction performance for such a system with large inertia, leading to poor control of the wire drying process.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction includes the following steps:

[0008] (1) Obtain relevant production data of each variable in the thin plate drying process, select controllable variable production data in the thin plate drying process from the relevant production data of each variable, and construct a prediction equation for the thin plate drying process based on the controllable variable production data in the thin plate drying process.

[0009] (2) Based on the prediction equation in the thin plate wire drying process, the state space equation in the steady-state production process of the thin plate wire drying machine is constructed. The state space equation is estimated by using a Karman filter, and the model state and error term before the system delay are corrected to obtain the model state before the system delay.

[0010] (3) Update the model state before the system delay to the current model state, and then synchronously iterate and update the Kalman gain in the current model state.

[0011] (4) Calculate the model prediction value using the current model state, and input the current model state into the MPC controller to calculate the control variables. During the calculation process of the MPC controller, the process standard is used to limit the controllable variables, and the controllable variables in the MPC loss function are evaluated and set.

[0012] Prior to this, step (1), obtaining relevant production data of each variable during the thin plate wire drying process, selecting controllable variable production data from the relevant production data of each variable, and constructing a prediction equation for the thin plate wire drying process based on the controllable variable production data, includes the following steps:

[0013] (1.1) Obtain relevant production data such as grade information, batch information, process standards, inlet material flow rate, inlet moisture, dehumidification damper opening, thin plate temperature, hot air fan frequency, hot air temperature, drum speed and outlet moisture during the plate drying process;

[0014] (1.2) Select controllable production data such as the opening of the dehumidification damper, the cylinder wall temperature and the moisture content at the drying outlet from the brand information, batch information, process standards, inlet material flow rate, inlet moisture, dehumidification damper opening, thin plate temperature, hot air fan frequency, hot air temperature, drum speed and outlet moisture.

[0015] (1.3) Based on controllable variable data such as the opening degree of the exhaust damper, the cylinder wall temperature, and the moisture content at the outlet of the drying wire, prediction equations for the opening degree of the exhaust damper, the cylinder wall temperature, and the outlet moisture content are constructed using transfer functions, and their expressions are as follows:

[0016] x1(k+1))=u1(k)

[0017]

[0018] y2(k)=x1(k)+d2(k)

[0019] y3(k) = x2(k) + d3(k)

[0020] Among them, u1 ( k) represents the setpoint of the exhaust damper opening at time k; u2(k) represents the setpoint of the exhaust damper opening at time k; w(k) represents the inlet moisture at time k; x1(k) represents the actual value of the exhaust damper opening; x2(k) represents the actual measured value of the cylinder wall temperature; x3(k) represents the contribution of the exhaust damper opening; x4(k) represents the contribution of the cylinder wall temperature; x5(k) represents the contribution of the inlet moisture; d(k) is the model error (constant); T s w(kk) represents the sampling period of the discrete system. w (k) represents the time delay (k) from inlet water to the cylinder wall temperature. w The inlet moisture at each moment; y1(k+k p |k) represents the measured values ​​of the cylinder wall temperature and the exhaust damper opening at a given time k, where k+k p The predicted outlet moisture content at time k, y2(k) and y3(k) represent the predicted actual opening of the exhaust damper at time k and the predicted actual cylinder wall temperature at time k, respectively; τ is the first-order low-pass filter coefficient for inlet moisture content, and 1 / τ is the cutoff frequency of the low-pass filter; K Pi T is the gain coefficient. Pi Let i be the time constant, i = 1, 2, 3.

[0021] Prior to this, (2) constructing the state-space equation for the steady-state production process of the thin plate wire drying machine based on the prediction equation in the thin plate wire drying process, using a Karman filter to estimate the state of the state-space equation, and correcting the model state and error terms before the system delay to obtain the model state before the system delay, includes the following steps:

[0022] (2.1) Based on the prediction equations for the opening of the dehumidification damper, the cylinder wall temperature, and the outlet moisture content during the thin plate drying process, the state-space equation for the steady-state production process of the thin plate drying machine is constructed, and its expression is as follows:

[0023] x(k+1)=Ax(k)+Bu(k)+B w (kk w )

[0024] d(k+1)=d(k)

[0025] y(k)=Cx(k)+d(k)

[0026] Here, x has a total of 5 dimensions, which serve as an intermediate variable. The model output is d, where d is the model error (a constant), or it can be considered as a model state. A is the state matrix, B, B w Let C be the input matrix and C be the output matrix. The mathematical expression is:

[0027]

[0028]

[0029] (2.2) Define the variables of the Kalman filter as follows:

[0030]

[0031] Where k|k-1 represents the prediction for time k given information at time k-1; k+k p |k represents the information given at time k, for k+k p Prediction of time; predictions obtained purely from the model without Kalman filtering correction. Recorded as That is, the prior state; after Kalman filtering correction. Recorded as That is, the posterior state.

[0032] (2.3) Using the defined Mann filter, the state space equation is estimated, and the model state and error terms before the system delay are corrected to obtain the model state before the system delay, which is expressed as follows:

[0033] Because the system has a time delay k p At time k, the Kalman filter corrects for kk. p The state x and error d at time x,

[0034]

[0035] in, y(k) represents the Kalman gain; y(k) represents the actual measured value. Given information at time kp, the model prediction output at time k without Kalman filtering correction.

[0036] Prior to this, step (3) recursively updates the model state before the system delay to the current model state, and then synchronously iteratively updates the Kalman gain in the current model state, as follows:

[0037] (3.1) The past kk p The model state x and error d at time k are updated to the current state to obtain the current state estimate at time k. Error estimation and model prior prediction output The mathematical expression for the update process is:

[0038]

[0039] in, k is the state matrix A p Power of 1 k is the state matrix A p -1 to the power of j, B, B w Let u(kk) be the input matrix of the state-space equation. p +j) is k p The actual setpoint before time -j, w(kk) w -k p +j) is k p The actual inlet moisture value before time -j.

[0040] (3.2) During the state estimation process using Kalman filtering, the Kalman gain needs to be iteratively updated simultaneously. The update calculation expression is as follows:

[0041]

[0042] Among them, R est Let Q be the variance corresponding to y, which is the measurement noise. est The variance corresponding to x, i.e. the model uncertainty, is determined from historical data and filtering requirements. P 0|-1 =P0=cov{x0} serves as the starting point for iterative calculations, both of which are derived from historical data.

[0043] Priority, step (4) involves calculating the model prediction value using the current model state and simultaneously inputting the current model state into the MPC controller for calculating the control variables. During the calculation process of the MPC controller, process standards are used to limit the controllable variables, and the controllable variables in the MPC loss function are evaluated and set, including the following steps:

[0044] (4.1) Using the current model state in (3.1) The model's predicted values ​​are calculated and expressed as follows:

[0045]

[0046] in, For k+k p Predicted moisture content at the outlet of the drying wire; Let k be the predicted actual opening of the exhaust damper at time k. The actual predicted value of the cylinder wall temperature at that moment;

[0047] (4.2) Change the current model state in (3.1) The MPC controller calculates the control variables, and the expression is as follows:

[0048]

[0049] Among them, J k；N Let N be the value function at time k, and N be the prediction horizon. The optimal control variables at time k obtained by solving the above optimization problem for MPC are, in other words, the optimal control variables at time k that make the value function J equal to the optimal control variables obtained by MPC. k；N Minimum current control variable In the value function, ε(j) represents the model's predicted output value compared to the target setpoint y. SP The deviation is expressed as follows:

[0050] ε(y)=y(j+k d |j)-y SP =Cx(j)-y SP #

[0051] δu(j) represents the change in the control variable u(j) at the current time compared to the control variable u(j-1) at the previous time, and its expression is as follows: δu(j)=u(j)-u(j-1)#

[0052] (4.3) During the calculation of the MPC controller, the controllable variables are limited by the process standard, and the controllable variables in the MPC loss function are evaluated and set.

[0053] Prioritize, (4.3) during the MPC controller calculation process, use process standards to limit the controllable variables and evaluate and set the controllable variables in the MPC loss function, including the following steps:

[0054] (4.3.1) During the calculation process of the MPC controller, the controllable variables are limited using process standards, and the expression is as follows:

[0055] x min ≤x(j)≤x max j = k+1, ..., k+N

[0056] u min ≤u(j)≤u max j = k,...,k+N-1

[0057] Where, x min u min For the minimum amplitude of state and control variables; x max u max Maximum amplitude;

[0058] (4.3.2) The controllable variables in the MPC loss function are evaluated and defined, and their expressions are as follows:

[0059]

[0060] Wherein, the diagonal matrices Q, R, R d The three weight matrices of the controller determine the effects of the predicted value deviation, the control input value, and the change in the control input value compared to the previous time step on J, respectively. k；N How much weight did it contribute; n y The number of system output variables; n u The number of control variables in the demand solution; r1, r2, correspond to the value weights of cylinder wall temperature and exhaust damper opening, respectively.

[0061] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0062] This invention presents a steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction. It utilizes second-level historical production data and system identification technology to establish a dynamic transfer function prediction model and state-space equation model for the steady-state production process of the wire drying machine, relating the opening of the exhaust damper to the cylinder wall temperature and the outlet moisture content. A suitable Kalman filter (KF) is selected to correct the time-delayed prediction model online. By using a Model Predictive Control (MPC) algorithm, the process parameters during the steady-state production stage of the wire drying machine are controlled, achieving the ideal outlet material moisture content. This method addresses the problem that existing control methods applied to the wire drying process ignore the dynamic characteristics of the system, resulting in poor prediction performance for systems with significant inertia, such as those used in wire drying machines, leading to ineffective control of the wire drying process. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the steady-state model predictive control method for a wire drying machine based on Kalman filter delay correction, as described in this invention.

[0064] Figure 2 This is a schematic diagram illustrating the working principle of Model Predictive Control (MPC) in this invention.

[0065] Figure 3 This is a diagram illustrating the effect of using a transfer function model to predict the actual temperature of the cylinder wall in the absence of state estimation in this invention.

[0066] Figure 4 This demonstrates the prediction effect of the state-space equation based on Kalman filter delay correction on the moisture content at the wire drying outlet in this invention.

[0067] Figure 5 The image shows the steady-state model predictive control method for the wire drying machine based on Kalman filter delay correction before and after application in this invention. Detailed Implementation

[0068] like Figure 1-5 As shown, to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the scope of the present invention.

[0069] Example

[0070] The wire drying machine is an inertial system with delay and a nonlinear system with multiple input and output variables. Currently, there are many control methods applied to the wire drying process of the wire drying machine. However, these control methods ignore the dynamic characteristics of the system. For such a system with large inertia that is controlled in the wire drying process, the prediction effect is not good, resulting in poor control effect of the wire drying process.

[0071] Therefore, it is necessary to design a steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction, in order to solve the problem that existing control methods applied to the wire drying process ignore the dynamic characteristics of the system, resulting in poor prediction performance for such a system with large inertia, leading to poor control of the wire drying process.

[0072] For details, please refer to Figure 1 A steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction includes...

[0073] The first step is to obtain relevant production data for each variable during the thin-plate wire drying process, and then select the controllable variable production data from this data. Based on this controllable variable production data, a prediction equation for the thin-plate wire drying process is constructed, as follows:

[0074] Acquire relevant production data during the sheet drying process, including grade information, batch information, process standards, inlet material flow rate, inlet moisture content, exhaust damper opening, sheet temperature, hot air fan frequency, hot air temperature, drum speed, and outlet moisture content.

[0075] Controllable production data such as the opening of the dehumidifier, the cylinder wall temperature, and the moisture content at the yarn drying outlet are selected from the brand information, batch information, process standards, inlet material flow rate, inlet moisture, dehumidifier opening, sheet temperature, hot air fan frequency, hot air temperature, drum speed, and outlet moisture.

[0076] Based on controllable variable data such as exhaust damper opening, cylinder wall temperature, and outlet moisture content, discrete prediction equations for exhaust damper opening, cylinder wall temperature, and outlet moisture content are constructed using transfer functions, as shown in the following expressions:

[0077] x1(k+1) = u1(k)

[0078]

[0079] y2(k)=x1(k)+d2(k)

[0080] y3(k) = x2(k) + d3(k)

[0081] Where u1(k) represents the set value of the exhaust damper opening at time k; u2(k) represents the set value of the exhaust damper opening at time k; w(k) represents the inlet moisture at time k; x1(k) represents the actual value of the exhaust damper opening; x2(k) represents the actual measured value of the cylinder wall temperature; x3(k) represents the contribution of the exhaust damper opening; x4(k) represents the contribution of the cylinder wall temperature; x5(k) represents the contribution of the inlet moisture; d(k) is the model error (constant); T s w(kk) represents the sampling period of the discrete system. w (k) represents the time delay (k) from inlet water to the cylinder wall temperature. w The inlet moisture at each moment; y1(k+k p |k) represents the measured values ​​of the cylinder wall temperature and the exhaust damper opening at a given time k, where k+k p The predicted outlet moisture content at time k, y2(k) and y3(k) represent the predicted actual opening of the exhaust damper at time k and the predicted actual cylinder wall temperature at time k, respectively.

[0082] K Pi T is the gain coefficient. Pi Let i be a time constant, i = 1, 2, 3. After establishing the above transfer function expression, use common system identification tools to analyze K. Pi T Pi Identification is performed; τ is the first-order low-pass filter coefficient of the inlet water, and 1 / τ is the cutoff frequency of the low-pass filter; signals exceeding this frequency will have their amplitude drastically attenuated after passing through the low-pass filter.

[0083] In this embodiment, by using production and testing data and continuously adjusting the value of τ, an inlet material moisture filter with a reasonable signal-to-noise ratio was finally obtained.

[0084] In this embodiment, the discrete sampling period T s =5 seconds. The Matlab System Identification Toolbox was used to perform system identification on the parameters in the transfer function. The identification results are shown in the table below. Figure 4As shown, this embodiment uses the method in the absence of state estimation. The prediction of the cylinder wall temperature is obtained by using y3(k)=x2(k), and the results are shown in Table 1.

[0085] Table 1 Predicted Cylinder Wall Temperature

[0086]

[0087] The second step involves constructing the state-space equations for the steady-state production process of the thin-plate wire drying machine based on the prediction equations during the thin-plate wire drying process. A Karman filter is then used to estimate the state of the state-space equations, and the model states and error terms before the system delay are corrected to obtain the model states before the system delay, as detailed below:

[0088] Based on the prediction equations for the dehumidification damper opening, cylinder wall temperature, and outlet moisture content during the thin plate drying process, a state-space equation for the steady-state production process of the thin plate drying machine is constructed, and its expression is as follows:

[0089] x(k+1)=Ax(k)+Bu(k)+B w w(kk w )

[0090] d(k+1)=d(k)

[0091] y(k)=Cx(k)+d(k)

[0092] Here, x has a total of 5 dimensions, which serve as an intermediate variable. The model output is d, where d is the model error (a constant), or it can be considered as a model state. A is the state matrix, B, B w Let C be the input matrix and C be the output matrix. The mathematical expression is:

[0093]

[0094] (2.2) Define the variables of the Kalman filter as follows:

[0095]

[0096]

[0097] Where k|k-1 represents the prediction for time k given information at time k-1; k+k p |k represents the information given at time k, for k+k p Prediction of time; predictions obtained purely from the model without Kalman filtering correction. Recorded as That is, the prior state; after Kalman filtering correction. Recorded as That is, the posterior state.

[0098] The state space equations are estimated using a Mann filter with defined variables, and the model state and error terms before the system delay are corrected to obtain the model state before the system delay, which is expressed as follows:

[0099] Because the system has a time delay k p At time k, the Kalman filter corrects for kk. p The state x and error d at time x,

[0100]

[0101] in, y(k) represents the Kalman gain; y(k) represents the actual measured value. Given information at time kp, the model prediction output at time k without Kalman filtering correction.

[0102] Step 3: Recursively update the model state before the system delay to the current model state, and then synchronously iteratively update the Kalman gain in the current model state, as follows:

[0103] The past kk p The model state x and error d at time k are updated to the current state to obtain the current state estimate at time k. Error estimation and model prior prediction output The mathematical expression for the update process is:

[0104]

[0105] in, k is the state matrix A p Power of 1 k is the state matrix A p -1 to the power of j, B, B w Let u(kk) be the input matrix of the state-space equation. p +j) is k p The actual setpoint before time -j, w(kk) w -k p +j) is k p The actual inlet moisture value before time -j.

[0106] When using Kalman filtering for state estimation, the Kalman gain needs to be iteratively updated simultaneously. The update calculation expression is as follows:

[0107]

[0108] Among them, R est Let Q be the variance corresponding to y, which is the measurement noise. est The variance corresponding to x, i.e. the model uncertainty, is determined from historical data and filtering requirements. P 0|-1 =P0=cov{x0} serves as the starting point for iterative calculations, both of which are derived from historical data.

[0109] In this embodiment, P0 is obtained by calculating the covariance of x(k) for the first period of each batch, and R... est The following method is used: First, calculate the covariance of y1, y2, and y3 for each batch during the stable data period; then calculate the mean of the covariance matrix for each batch. Calculate Q. est At that time, firstly, similar to R est Calculate the covariance matrix Q of u1 and u2 for each batch during the stable data period. u The variance Q of w1 w and each batch of Q u Q w mean, then The specific parameters are as follows:

[0110]

[0111] Step 4: Calculate the model prediction value using the current model state, and simultaneously input the current model state into the MPC controller for calculating the control variables. During the MPC controller calculation process, process standards are used to limit the controllable variables, and the controllable variables in the MPC loss function are evaluated and set, including the following steps.

[0112] Using the current model state The model's predicted values ​​are calculated and expressed as follows:

[0113]

[0114] in, For k+k p Predicted moisture content at the outlet of the drying wire; Let k be the predicted actual opening of the exhaust damper at time k. The actual predicted value of the cylinder wall temperature at that moment;

[0115] Current model state The MPC controller calculates the control variables, and the expression is as follows:

[0116]

[0117] Among them, J k；NLet N be the value function at time k, and N be the prediction horizon. The optimal control variables at time k obtained by solving the above optimization problem for MPC are, in other words, the optimal control variables at time k that make the value function J equal to the optimal control variables obtained by MPC. k；N Minimum current control variable In the value function, ε(j) represents the model's predicted output value compared to the target setpoint y. SP The deviation is expressed as follows:

[0118] ε(j)=y(j+k d |j)-y SP =Cx(j)-y SP #

[0119] δu(j) represents the change in the control variable u(j) at the current time compared to the control variable u(j-1) at the previous time, and its expression is as follows:

[0120] δu(j)=u(j)-u(j-1)#

[0121] During the MPC controller calculation process, process standards are used to limit the controllable variables, and the controllable variables in the MPC loss function are evaluated and set, including the following steps:

[0122] During the calculation process of the MPC controller, process standards are used to limit the controllable variables, and the expression is as follows:

[0123] x min ≤x(j)≤ xma x, j = k+1, ..., k+N

[0124] u min ≤u(j)≤u max j = k, ..., k + N - 1

[0125] Where, x min u min For the minimum amplitude of state and control variables; x max u max Maximum amplitude;

[0126] The controllable variables in the MPC loss function are evaluated and defined, and their expressions are as follows:

[0127]

[0128] Wherein, the diagonal matrices Q, R, R d The three weight matrices of the controller determine the effects of the predicted value deviation, the control input value, and the change in the control input value compared to the previous time step on J, respectively. k；N How much weight did it contribute; ny The number of system output variables; n u The number of control variables in the demand solution; r1, r2, correspond to the value weights of cylinder wall temperature and exhaust damper opening, respectively.

[0129] In this embodiment, since the cylinder wall temperature has a greater impact on the processing intensity of the drying machine than the dehumidification damper opening, the value of r2 is greater than r1. Because the outlet moisture content is often unstable in the initial stage of the material, the adjustment of the dehumidification damper opening may be more drastic and frequent than in the stable stage, thus affecting the deflection of the dehumidification damper opening. Therefore, a piecewise varying R matrix is ​​designed to suppress excessive adjustment in the initial stage of the material. The value of N takes into account k in the state-space equation. w The maximum value is chosen to ensure that the controller can fully utilize as much inlet moisture data as possible when solving the MPC value function. Long-term online operation of the controller has proven that N=40 does not significantly impact server performance. Specific parameters are as follows:

[0130] Q=diag([q 0 0])=diag([1000 0 0])

[0131] R d =diag([r d1 r d2 ])=diag([0.3 0.3])

[0132]

[0133] N = 40

[0134] Where r1 and r2 correspond to the value weights of the cylinder wall temperature and the opening of the exhaust damper, respectively. diag represents a diagonal matrix formed by the vectors within the parentheses.

[0135] According to statistical results, the prediction accuracy (MSE) for most batches is within 0.1; such as Figure 4 The figure shows the prediction effect of the state-space equation based on Kalman filter time delay correction in this embodiment. The MSE is 0.078, and the predicted value is very close to the actual value, indicating a good prediction effect. It can be seen that the moisture prediction model for the drying material outlet established using this invention has a good prediction effect for most production batches. Figure 5 As shown, after applying the method of the present invention, the standard deviation of moisture content at the drying outlet decreased from 0.096 to 0.078. It can be seen that the method of the present invention has a very good control effect on the moisture content at the drying outlet, and has greatly improved the process control of the yarn making and drying process, realizing the transformation from traditional PID control to model predictive control.

[0136] This application presents a steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction. It utilizes second-level historical production data and system identification technology to establish a dynamic transfer function prediction model and state-space equation model for the steady-state production process of the wire drying machine, relating the opening of the exhaust damper to the cylinder wall temperature and the outlet moisture content. A suitable Kalman filter (KF) is selected to correct the time-delayed prediction model online. Furthermore, a Model Predictive Control (MPC) algorithm (combining the current model state with the MPC controller) is used to control the process parameters during the steady-state production stage of the wire drying machine, thereby achieving the ideal outlet material moisture content. This method addresses the problem that existing control methods applied to the wire drying process neglect the dynamic characteristics of the system, resulting in poor prediction performance for systems with significant inertia, such as the wire drying machine, leading to poor control of the wire drying process.

[0137] Although the invention has been described herein with reference to several illustrative embodiments, it should be understood that many other modifications and implementations can be devised by those skilled in the art, which will fall within the scope and spirit of the principles disclosed herein. More specifically, various variations and modifications can be made to the components and / or layout of the subject matter arrangement within the scope of the disclosure, drawings, and claims. Besides variations and modifications to the components and / or layout, other uses will be apparent to those skilled in the art.

Claims

1. A steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction, characterized in that: Includes the following steps: (1) Obtain relevant production data of each variable in the thin plate drying process, select controllable variable production data in the thin plate drying process from the relevant production data of each variable, and construct a prediction equation for the thin plate drying process based on the controllable variable production data in the thin plate drying process. (2) Based on the prediction equation in the thin plate wire drying process, the state space equation in the steady-state production process of the thin plate wire drying machine is constructed. The state space equation is estimated by using a Karman filter, and the model state and error term before the system delay are corrected to obtain the model state before the system delay. (3) Update the model state before the system delay to the current model state, and then synchronously iterate and update the Kalman gain in the current model state. (4) Calculate the model prediction value using the current model state, and input the current model state into the MPC controller to calculate the control variables. During the calculation process of the MPC controller, the process standard is used to limit the controllable variables, and the controllable variables in the MPC loss function are evaluated and set.

2. The steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction according to claim 1, characterized in that: The step (1), obtaining relevant production data of each variable during the thin plate wire drying process, selecting controllable variable production data from the relevant production data of each variable, and constructing a prediction equation for the thin plate wire drying process based on the controllable variable production data, includes the following steps: (1.1) Obtain relevant production data such as grade information, batch information, process standards, inlet material flow rate, inlet moisture, dehumidification damper opening, thin plate temperature, hot air fan frequency, hot air temperature, drum speed and outlet moisture during the plate drying process; (1.2) Select controllable production data such as the opening of the dehumidification damper, the cylinder wall temperature and the moisture content at the drying outlet from the brand information, batch information, process standards, inlet material flow rate, inlet moisture, dehumidification damper opening, thin plate temperature, hot air fan frequency, hot air temperature, drum speed and outlet moisture. (1.3) Based on controllable variable data such as the opening degree of the exhaust damper, the cylinder wall temperature, and the moisture content at the outlet of the drying wire, prediction equations for the opening degree of the exhaust damper, the cylinder wall temperature, and the outlet moisture content are constructed using transfer functions, and their expressions are as follows: x1(k+1) = u1(k) y2(k)=x1(k)+d2(k) y3(k) = x2(k) + d3(k) Where u1(k) represents the set value of the exhaust damper opening at time k; u2(k) represents the set value of the exhaust damper opening at time k; w(k) represents the inlet moisture at time k; x1(k) represents the actual value of the exhaust damper opening; x2(k) represents the actual measured value of the cylinder wall temperature; x3(k) represents the contribution of the exhaust damper opening; x4(k) represents the contribution of the cylinder wall temperature; x5(k) represents the contribution of the inlet moisture; d(k) is the model error (constant); T s w(kk) represents the sampling period of the discrete system. w (k) represents the time delay (k) from inlet water to the cylinder wall temperature. w The inlet moisture at each moment; y1(k+k p |k) represents the measured values ​​of the cylinder wall temperature and the exhaust damper opening at a given time k, where k+k p The predicted outlet moisture content at time k; y2(k) and y3(k) represent the predicted actual opening of the exhaust damper at time k and the predicted actual cylinder wall temperature at time k, respectively; τ is the first-order low-pass filter coefficient for inlet moisture content, and 1 / τ is the cutoff frequency of the low-pass filter; K Pi T is the gain coefficient. Pi Let i be the time constant, i = 1, 2, 3.

3. The steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction as described in claim 1, characterized in that: The steps (2) are as follows: Based on the prediction equation in the thin plate wire drying process, the state space equation in the steady-state production process of the thin plate wire drying machine is constructed. A Karman filter is used to estimate the state of the state space equation, and the model state and error terms before the system delay are corrected to obtain the model state before the system delay. (2.1) Based on the prediction equations for the opening of the dehumidification damper, the cylinder wall temperature, and the outlet moisture content during the thin plate drying process, the state-space equation for the steady-state production process of the thin plate drying machine is constructed, and its expression is as follows: x(k+1)=Ax(k)+Bu(k)+B w w(kk w ) d(k+1)=d(k) y(k)=Cx(k)+d(k) Here, x has a total of 5 dimensions, which serve as an intermediate variable. The model output is d, where d is the model error (a constant), or it can be considered as a model state. A is the state matrix, B, B w Let C be the input matrix and C be the output matrix. The mathematical expression is: (2.2) Define the variables of the Kalman filter as follows: Where k|k-1 represents the prediction for time k given information at time k-1; k+kp|k represents the prediction for time k+k given information at time k. p Prediction of time; predictions obtained purely from the model without Kalman filtering correction. Recorded as That is, the prior state; after Kalman filtering correction. Recorded as That is, the posterior state. (2.3) Using the defined Mann filter, the state space equation is estimated, and the model state and error terms before the system delay are corrected to obtain the model state before the system delay, which is expressed as follows: Because the system has a time delay k p At time k, the value that can be corrected using Kalman filtering is kk. p The mathematical expressions for the state x and error d at time t are: in, y(k) represents the Kalman gain; y(k) represents the actual measured value. Given information at time kp, the model prediction output at time k without Kalman filtering correction.

4. The steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction according to claim 3, characterized in that: (3) The model state before the system delay is recursively updated to the current model state, and then the Kalman gain in the current model state is synchronously iteratively updated, as follows: (3.1) The past kk p The model state x and error d at time k are updated to the current state to obtain the current state estimate at time k. Error estimation and model prior prediction output The mathematical expression for the update process is: in, k is the state matrix A p Power of 1 k is the state matrix A p -1 to the power of j, B, B w Let u(kk) be the input matrix of the state-space equation. p +j) is k p The actual setpoint before time -j, w(kk) w -k p +j) is k p The actual inlet moisture value before time -j. (3.2) During the state estimation process using Kalman filtering, the Kalman gain needs to be iteratively updated simultaneously. The update calculation expression is as follows: Among them, R est Let Q be the variance corresponding to y, which is the measurement noise. est The variance corresponding to x, i.e. the model uncertainty, is determined from historical data and filtering requirements. P 0|-1 =P0=cov{x0} serves as the starting point for iterative calculations, both of which are derived from historical data.

5. The steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction according to claim 1, characterized in that: The step (4) involves calculating the model prediction value using the current model state and simultaneously inputting the current model state into the MPC controller for calculating the control variables. During the calculation process of the MPC controller, process standards are used to limit the controllable variables, and the controllable variables in the MPC loss function are evaluated and set, including the following steps: (4.1) Using the current model state in (3.1) The model's predicted values ​​are calculated and expressed as follows: in, For k+k p Predicted moisture content at the outlet of the drying wire; Let k be the predicted actual opening of the exhaust damper at time k. The actual predicted value of the cylinder wall temperature at time k; (4.2) Change the current model state in (3.1) The MPC controller calculates the control variables, and the expression is as follows: Among them, J k；N Let N be the value function at time k, and N be the prediction horizon. The optimal control variables at time k obtained by solving the above optimization problem for MPC are, in other words, the optimal control variables at time k that make the value function J equal to the optimal control variables obtained by MPC. k；N Minimum current control variable In the value function, ε(j) represents the model's predicted output value compared to the target setpoint y. SP The deviation is expressed as follows: ε(j)=y(j+k d |j)-y SP =Cx(j)-y SP δu(j) represents the change in the control variable u(j) at the current time compared to the control variable u(j-1) at the previous time, and its expression is as follows: δu(j)=u(j)-u(j-1) (4.3) During the calculation of the MPC controller, the controllable variables are limited by the process standard, and the controllable variables in the MPC loss function are evaluated and set.

6. The steady-state model predictive control method for a wire drying machine based on Kalman filter time delay correction according to claim 5, characterized in that: In step (4.3), during the MPC controller calculation process, process standards are used to limit the controllable variables, and the controllable variables in the MPC loss function are evaluated and set, including the following steps: (4.3.1) During the calculation process of the MPC controller, the controllable variables are limited using process standards, and the expression is as follows: x min ≤x(j)≤x max ,j=k+1,...,k+N u min ≤u(j)≤u max ,j=k,...,k+N-1 Where, x min u min For the minimum amplitude of state and control variables; x max u max This is the maximum amplitude limit. (4.3.2) The controllable variables in the MPC loss function are evaluated and defined, and their expressions are as follows: in, Diagonal matrices Q, R, R d The three weight matrices of the controller determine the effects of the predicted value deviation, the control input value, and the change in the control input value compared to the previous time step on J, respectively. k；N How much weight did it contribute; n y n is the number of system output variables. u The number of control variables in the demand solution; r1 and r2 correspond to the value weights of cylinder wall temperature and exhaust damper opening, respectively.

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