A predictive functional control method for time-delay integral processes based on Smith predictor correction

Abstract

The present invention belongs to the field of industrial automation, and discloses a predictive function control method for a time-delay integral process based on Smith prediction correction. First, a model is built based on the step response data collected in real time to find out the basic characteristics of the object, and then a new error correction compensation is performed on the predictive function control based on Smith prediction correction, and finally the obtained optimal control law is implemented on the controlled integral process. The present invention proposes a corresponding new error correction compensation method for the traditional error correction method that cannot effectively solve the impact of continuous interference on the time-delay integral process under the predictive function control. Finally, based on this error correction method, the predictive function control can effectively solve various types of continuous uncertain interference, improve the stability of the control system, and further promote the application of advanced control algorithms in industry.

Description

Technical Field

[0001] The invention belongs to the field of industrial automation, and in particular relates to a time-delay integral process prediction function control method based on Smith prediction correction. Background Art

[0002] For the integral objects in industry, the common prediction function control method cannot effectively resist various continuous disturbances. Under these disturbances, the integral process will eventually deviate from the set value and fail to achieve the expected control effect. At the same time, large time-delay processes are very common in industry. Smith predictive correction is introduced into the prediction function control to compensate for the time lag. If the corresponding integral process error correction method can be given, it will further promote the application of the prediction function control method based on Smith predictive correction, thereby further promoting the development of intelligent control algorithms. Summary of the invention

[0003] The purpose of the present invention is to provide a predictive function control method for a time-delay integral process based on Smith prediction correction, so as to solve the technical problem that the traditional error correction method cannot effectively solve the influence of continuous interference on the time-delay integral process under predictive function control.

[0004] In order to solve the above technical problems, the specific technical solution of the time-delay integral process prediction function control method based on Smith prediction correction of the present invention is as follows:

[0005] A predictive function control method for a time-delay integral process based on Smith prediction correction comprises the following steps:

[0006] Step 1: Collect the step response data of the integration process and calculate the corresponding object model; build a model based on the step response data collected in real time to find out the basic characteristics of the object;

[0007] Step 2: Perform new error correction compensation on the prediction function control based on Smith prediction correction;

[0008] Establish the transfer function model of the integral process object;

[0009] Step 3: The obtained optimal control law is implemented on the controlled integral process; a prediction function control method based on Smith predictor correction is designed for the integral process.

[0010] Furthermore, the step 1 includes the following specific steps:

[0011] Step 1.1: Add a step signal to the input of the integration process and start recording the step response signal of the integration process;

[0012] Step 1.2: Filter the obtained step response signal, and then fit the part of the smooth curve after filtering that is close to the straight line into a straight line. Then record the corresponding step response data value on the smooth curve at each sampling time. The sampling interval is set to T s The recorded values ​​are based on the increase in the steady-state part, which are b1, b2, …, b d ,b d+1 ,b d+2 ,…, where b1,…,b d is the time lag part, that is, the data value in this interval has basically not changed, b d+1 ,b d+2 ,…is the part where the sampling data value begins to change. The difference between the data sampling values ​​in this interval can be regarded as a constant.

[0013] Furthermore, the step 2 includes the following specific steps:

[0014] Step 2.1: According to the step sampling data, the lag time of the integral process object is τ = d*T s ;

[0015] Step 2.2: The gain of the integrating process object is K = (b d+2 -b d+1 ) / T s ;

[0016] Finally, the integral process transfer function model is obtained as follows:

[0017]

[0018] Where s is the Laplace operator.

[0019] Furthermore, the step 3 includes the following specific steps:

[0020] Step 3.1: For the established transfer function model at sampling time T s1 Discretize it and get the discrete equation model:

[0021] Step 3.2: Remove pure lag from the discrete equation model in step 3.1 to obtain the equation without pure lag;

[0022] Step 3.3: Calculate the predicted value of the integral process model based on the model in step 3.2;

[0023] Step 3.4: Select the Smith predictor-corrected prediction function control objective function of the integral process object;

[0024] Step 3.5: Implement the prediction function optimal control law based on Smith predictor correction obtained in step 3.4 on the integral process object.

[0025] Furthermore, the discrete equation model obtained in step 3.1 is as follows:

[0026] y m (k) = y m (k-1)+K*T s1 *u(k-1-τ / T s1 )

[0027] Among them, y m u(k) and u(k) are the model output and input values ​​of the integral process object at time k respectively.

[0028] Furthermore, the step 3.2 includes the following specific steps:

[0029] Removing pure lag from the discrete equation model in step 3.1, we get the following equation:

[0030] y mav (k) = y mav (k-1)+K*T s1 *u(k-1)

[0031] Among them, y mav (k) is the model output without lag at time k;

[0032] Based on the Smith predictive correction, the actual correction output of the integral process object is

[0033] y pav (k) = y p (k)+y mav (k)-y mav (k-τ / T s1 )

[0034] Among them, y pav (k),y p (k) are the output of the integral process after Smith estimation correction and the actual output of the process.

[0035] Furthermore, the step 3.3 includes the following specific steps:

[0036] Based on the model in step 3.2, the predicted value of the integral process model is calculated. The basis function takes the step function, and the predicted value of the integral process model is:

[0037] y mav (k+H)=y mav (k)+H*K*T s1 *u(k)

[0038] Among them, H is the prediction time domain;

[0039] Based on the Smith estimate correction, the model error e(k) is calculated as follows:

[0040] e(k)=y pav (k)-y mav (k)

[0041] For the introduced predictive function control, the following error correction formula is adopted:

[0042] err(k)=e(k)-err_sum(k-1)

[0043] err_sum(k)=err_sum(k-1)+λ*err(k)

[0044] Among them, the initial value of err_sum(k) is 0, λ is the error correction coefficient, and its value ranges from 0 to 1;

[0045] Considering the characteristics of the integration process, the final model prediction output after error compensation correction is y mav_c (k+H)=y mav (k+H)+err_sum(k)+(H+τ / T s1 *λ)*err(k)

[0046] The first part of the error compensation correction is conventional compensation correction, and the second part is compensation correction for the time-delay integral characteristic. The strength of the error compensation is adjusted by adjusting the error correction coefficient.

[0047] Furthermore, the step 3.4 includes the following specific steps:

[0048] The prediction function control objective function based on Smith predictor correction for selecting the integral process object is as follows:

[0049]

[0050] Among them, y r (k) is the reference trajectory point of the integral process object at time k, and the following calculation formula is used: r (k+H)=η H y(k)+(1-η H )c(k)

[0051] η is the softening coefficient of the reference trajectory, c(k) is the set value of the integral process object at time k, and Q is the weighting coefficient of the tracking error;

[0052] By deriving the above objective function, we can obtain the prediction function control law based on Smith prediction correction:

[0053] Furthermore, the step 3.5 includes the following specific steps:

[0054] In the next sampling period, the latest prediction function optimal control law is solved according to the steps in step 3.2 to step 3.4 and acts on the controlled integral process, and the cycle is repeated.

[0055] The predictive function control method for a time-delay integral process based on Smith prediction correction of the present invention has the following advantages: the present invention proposes a corresponding new error correction and compensation method for the problem that traditional error correction methods cannot effectively solve the impact of continuous interference on the time-delay integral process under predictive function control. Finally, based on this error correction method, predictive function control can effectively solve various types of continuous uncertain interference, improve the stability of the control system, and further promote the application of advanced control algorithms in industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] none. DETAILED DESCRIPTION

[0057] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a time-delay integral process prediction function control method based on Smith prediction correction of the present invention in conjunction with the accompanying drawings.

[0058] The method of the present invention firstly builds a model based on the step response data collected in real time to find out the basic characteristics of the object, then performs new error correction compensation on the prediction function control based on Smith prediction correction, and finally implements the obtained optimal control law on the controlled integral process.

[0059] The technical solution of the present invention is to establish a prediction function integration process control method based on Smith prediction correction through process data collection, process model establishment, Smith prediction correction, error compensation correction, objective function solution and other means to solve the influence of various interferences on the integration process and ultimately improve the stability of the overall system.

[0060] The steps of the present invention include:

[0061] Step 1: Collect the step response data of the integration process and calculate the corresponding object model. The specific steps are as follows:

[0062] Step 1.1: Add a step signal to the input of the integration process and start recording the step response signal of the integration process.

[0063] Step 1.2: Filter the obtained step response signal, and then fit the part of the smooth curve after filtering that is close to the straight line into a straight line, and then record each sampling moment (the sampling interval is set to T s) The corresponding step response data values ​​on the smooth curve (the recorded values ​​are based on the values ​​increased in the steady-state part) are b1, b2, …, b d ,b d+1 ,b d+2 ,…. Among them b1,…,b d is the time lag part, that is, the data value in this interval has basically not changed. d+1 ,b d+2 ,…is the part where the sampling data value starts to change (due to the integral characteristics of the process system, the difference between the data sampling values ​​in this interval can be regarded as a constant).

[0064] Step 2: Establish the transfer function model of the integral process object, as follows:

[0065] Step 2.1: According to the step sampling data, the lag time of the integral process object is τ = d*T s .

[0066] Step 2.2: The gain of the integrating process object is K = (b d+2 -b d+1 ) / T s .

[0067] Finally, the integral process transfer function model is obtained as follows:

[0068]

[0069] Where s is the Laplace operator.

[0070] Step 3: Design a predictive function control method based on Smith predictor correction for the integral process.

[0071] Step 3.1: For the established transfer function model at sampling time T s1 Discretize it and get the following discrete equation model:

[0072] y m (k) = y m (k-1)+K*T s1 *u(k-1-τ / T s1 )

[0073] Among them, y m u(k) and u(k) are the model output and input values ​​of the integral process object at time k respectively.

[0074] Step 3.2: Remove the pure lag from the discrete equation model in step 3.1, and we get the following equation:

[0075] y mav (k) = y mav (k-1)+K*T s1*u(k-1)

[0076] Among them, y mav (k) is the model output without lag at time k.

[0077] Based on the Smith predictive correction, the actual correction output of the integral process object is

[0078] y pav (k) = y p (k)+y mav (k)-y mav (k-τ / T s1 )

[0079] Among them, y pav (k),y p (k) are the output of the integral process after Smith estimation correction and the actual output of the process.

[0080] Step 3.3: Calculate the predicted value of the integral process model based on the model in step 3.2. For the convenience of calculation, the basis function is a step function. The predicted value of the integral process model is

[0081] y mav (k+H)=y mav (k)+H*K*T s1 *u(k)

[0082] Among them, H is the prediction time domain.

[0083] Based on the Smith estimate correction, the model error e(k) is calculated as follows:

[0084] e(k)=y pav (k)-y mav (k)

[0085] For the introduced predictive function control, the following error correction formula is used here:

[0086] err(k)=e(k)-err_sum(k-1)

[0087] err_sum(k)=err_sum(k-1)+λ*err(k)

[0088] The initial value of err_sum(k) is 0, and λ is the error correction coefficient, which ranges from 0 to 1.

[0089] Taking into account the characteristics of the integration process, the final model prediction output after error compensation correction is

[0090] y mav_c (k+H)=y mav(k+H)+err_sum(k)+(H+τ / T s1 *λ)*err(k)

[0091] The first part of the error compensation correction is the conventional compensation correction, and the second part is the compensation correction for the time-delay integral characteristic. By adjusting the error correction coefficient, the strength of the error compensation can be adjusted.

[0092] Step 3.4: Select the Smith predictor-corrected prediction function control objective function of the integral process object as follows:

[0093]

[0094] Among them, y r (k) is the reference trajectory point of the integral process object at time k, which can be calculated as follows: r (k+H)=η H y(k)+(1-η H )c(k)

[0095] η is the softening coefficient of the reference trajectory, c(k) is the set value of the integral process object at time k, and Q is the weighting coefficient of the tracking error.

[0096] By deriving the above objective function, we can obtain the prediction function control law based on Smith prediction correction:

[0097]

[0098] Step 3.5: Apply the prediction function optimal control law based on Smith prediction correction obtained in step 3.4 to the integral process object. In the next sampling period, solve the latest prediction function optimal control law according to the steps in steps 3.2 to 3.4 and apply it to the controlled integral process, and repeat the cycle.

[0099] Example:

[0100] The specific implementation takes the control of boiler drum water level process as an example:

[0101] The boiler drum water level is a typical integral process, in which the feed water volume is the means of regulation.

[0102] Step 1: Collect the step response data of the boiler drum water level process and calculate the object model of the boiler drum water level process. The specific steps are as follows:

[0103] Step 1.1: Add a step signal to the water feed rate of the boiler drum water level process, and start recording the step response signal of the boiler drum water level process.

[0104] Step 1.2: Filter the obtained boiler drum water level process step response signal, and then fit the part close to the straight line behind the filtered smooth curve into a straight line, and then record each sampling time (the sampling interval is set to T s ) The step response data values ​​of the boiler drum water level process corresponding to the smooth curve (the recorded value is the value increased based on the steady-state part), which are recorded as b1, b2, ..., b d ,b d+1 ,b d+2 ,…. Among them b1,…,b d It is the time lag part of the boiler drum water level process, that is, the boiler drum water level data value in this interval has basically not changed. d+1 ,b d+2 ,…is the part where the sampling data value of the boiler drum water level process begins to change (due to the integral characteristics of the boiler drum water level process, the difference between the data sampling values ​​of the boiler drum water level in this interval can be regarded as a constant).

[0105] Step 2: Establish the transfer function model of the boiler drum water level process, as follows:

[0106] Step 2.1: According to the step sampling data of the boiler drum water level process, the lag time of the boiler drum water level process object is τ = d*T s .

[0107] Step 2.2: The gain of the boiler drum water level process object is K = (b d+2 -b d+1 ) / T s .

[0108] Finally, the transfer function model of the boiler drum water level process is obtained as follows:

[0109]

[0110] Where s is the Laplace operator.

[0111] Step 3: Design a predictive function control method for the boiler drum water level process based on Smith predictor correction.

[0112] Step 3.1: Establish the transfer function model of the boiler drum water level process at sampling time T s1 Discretize it under the following conditions and get the discrete equation model of boiler drum water level process:

[0113] y m (k) = y m (k-1)+K*T s1 *u(k-1-τ / T s1 )

[0114] Among them, ym (k),u(k) are the model output and input values ​​of the boiler drum water level process at time k respectively.

[0115] Step 3.2: Remove the pure lag from the discrete equation model in step 3.1, and we get the following equation:

[0116] y mav (k) = y mav (k-1)+K*T s1 *u(k-1)

[0117] Among them, y mav (k) is the model output of the boiler drum water level process without the lag at time k.

[0118] Based on the Smith prediction correction, the actual correction output of the boiler drum water level process is:

[0119] y pav (k) = y p (k)+y mav (k)-y mav (k-τ / T s1 )

[0120] Among them, y pav (k),y p (k) are the output of the boiler drum water level process after Smith estimation correction and the actual output of the process.

[0121] Step 3.3: Calculate the corresponding boiler drum water level prediction value based on the boiler drum water level process model in step 3.2. For the convenience of calculation, the basis function takes the step function, and the prediction value of the boiler drum water level process model is

[0122] y mav (k+H)=y mav (k)+H*K*T s1 *u(k)

[0123] Among them, H is the prediction time domain.

[0124] Based on the Smith predictor correction, the model error e(k) of the boiler drum water level process is calculated as follows:

[0125] e(k)=y pav (k)-y mav (k)

[0126] For the introduced predictive function control, the following error correction formula is used here:

[0127] err(k)=e(k)-err_sum(k-1)

[0128] err_sum(k)=err_sum(k-1)+λ*err(k)

[0129] The initial value of err_sum(k) is 0, and λ is the error correction coefficient, which ranges from 0 to 1.

[0130] Considering the integral characteristics of the boiler drum water level process, the model prediction output of the boiler drum water level process after error compensation correction is:

[0131] y mav_c (k+H)=y mav (k+H)+err_sum(k)+(H+τ / T s1 *λ)*err(k)

[0132] The first part of the error compensation correction is the conventional compensation correction, and the second part is the compensation correction for the time-delay integral characteristic of the boiler drum water level process. By adjusting the error correction coefficient, the strength of the error compensation of the boiler drum water level process can be adjusted.

[0133] Step 3.4: Select the Smith predictor-corrected prediction function control objective function of the boiler drum water level process as follows:

[0134]

[0135] Among them, y r (k) is the reference trajectory point of the boiler drum water level process at time k, which can be calculated as follows:

[0136] y r (k+H)=η H y(k)+(1-η H )c(k)

[0137] η is the softening coefficient of the reference trajectory of the boiler drum water level process, c(k) is the set value of the boiler drum water level at time k, and Q is the weighting coefficient of the boiler drum water level tracking error.

[0138] By derivation of the objective function of the above boiler drum water level process, the prediction function control law based on Smith prediction correction is obtained as follows:

[0139]

[0140] Step 3.5: Apply the optimal feed water quantity of the prediction function based on Smith estimation correction obtained in step 3.2 to the boiler drum water level process. In the next sampling period, the latest optimal feed water quantity is solved according to the steps in step 3.2 to step 3.3 and applied to the controlled boiler drum water level process, and the cycle is repeated later.

[0141] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A predictive function control method for a time-delay integral process based on Smith prediction correction, characterized in that: The steps include: Step 1: Collect the step response data of the integration process and calculate the corresponding object model; build a model based on the step response data collected in real time to find out the basic characteristics of the object; Step 1.1: Add a step signal to the input of the integration process and start recording the step response signal of the integration process; Step 1.2: Filter the obtained step response signal, and then fit the part of the smooth curve after filtering that is close to the straight line into a straight line. Then record the corresponding step response data value on the smooth curve at each sampling time. The sampling interval is set to T s The recorded values ​​are based on the increase in the steady-state part, which are b1, b2, …, b d ,b d+1 ,b d+2 ,…, where b1,…,b d is the time lag part, that is, the data value in this interval has basically not changed, b d+1 ,b d+2 ,… is the part where the sampled data value starts to change, and the difference between the sampled values ​​of the data in this interval can be regarded as a constant; Step 2: Perform new error correction compensation on the prediction function control based on Smith prediction correction; Establish the transfer function model of the integral process object; Step 2.1: According to the step sampling data, the lag time of the integral process object is τ = d*T s ; Step 2.2: The gain of the integrating process object is K = (b d+2 -b d+1 ) / T s ; Finally, the integral process transfer function model is obtained as follows: Where s is the Laplace operator; Step 3: The obtained optimal control law is implemented on the controlled integral process; a prediction function control method based on Smith predictor correction is designed for the integral process; Step 3.1: For the established transfer function model at sampling time T s1 Discretize it and get the discrete equation model: The discrete equation model obtained in step 3.1 is as follows: y m (k)=y m (k-1)+K*T s1 *u(k-1-τ / T s1 ) Among them, y m (k), u(k) are the model output and input values ​​of the integral process object at time k respectively; Step 3.2: Remove pure lag from the discrete equation model in step 3.1 to obtain the equation without pure lag; Removing pure lag from the discrete equation model in step 3.1, we get the following equation: y mav (k)=y mav (k-1)+K*T s1 *u(k-1) Among them, y mav (k) is the model output without lag at time k; Based on the Smith predictor correction, the actual correction output of the integral process object is y pav (k) = y p (k)+y mav (k)-y mav (k-τ / T s1 ) Among them, y pav (k),y p (k) are the output of the integration process after Smith estimation correction and the actual output of the process; Step 3.3: Calculate the predicted value of the integral process model based on the model in step 3.2; Based on the model in step 3.2, the predicted value of the integral process model is calculated. The basis function takes the step function, and the predicted value of the integral process model is: y mav (k+H)=y mav (k)+H*K*T s1 *u(k) Among them, H is the prediction time domain; Based on the Smith estimate correction, the model error e(k) is calculated as follows: e(k)=y pav (k)-y mav (k) For the introduced predictive function control, the following error correction formula is adopted: err(k)=e(k)-err_sum(k-1) err_sum(k)=err_sum(k-1)+λ*err(k) Among them, the initial value of err_sum(k) is 0, λ is the error correction coefficient, and its value ranges from 0 to 1; Considering the characteristics of the integration process, the final model prediction output after error compensation correction is y mav_c (k+H)=y mav (k+H)+err_sum(k)+(H+τ / T s1 *λ)*err(k) Among them, the first part of the error compensation correction is the conventional compensation correction, and the second part is the compensation correction for the time-delay integral characteristic. By adjusting the error correction coefficient, the strength of the error compensation is adjusted; Step 3.4: Select the prediction function control objective function based on Smith estimation correction of the integral process object; The prediction function control objective function based on Smith predictor correction for selecting the integral process object is as follows: Among them, y r (k) is the reference trajectory point of the integral process object at time k, and the following calculation formula is used: r (k+H)=η H y(k)+(1-η H )c(k) η is the softening coefficient of the reference trajectory, c(k) is the set value of the integral process object at time k, and Q is the weighting coefficient of the tracking error; By deriving the above objective function, we can obtain the prediction function control law based on Smith prediction correction: Step 3.5: Implement the prediction function optimal control law based on Smith prediction correction obtained in step 3.4 to the integral process object; In the next sampling period, the latest prediction function optimal control law is solved according to the steps in step 3.2 to step 3.4 and acts on the controlled integral process, and the cycle is repeated.

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