CN115047758A - Smith prediction correction-based time lag integral process prediction function control method - Google Patents

Abstract

The invention belongs to the field of industrial automation, and discloses a time-delay integral process prediction function control method based on Smith prediction and correction. The prediction function control of Smith's prediction correction performs new error correction and compensation, and finally the obtained optimal control law is implemented in the controlled integration process. Aiming at the fact that the traditional error correction method cannot effectively solve the influence of continuous interference in the time-delay integration process under the control of the prediction function, the invention proposes a corresponding new error correction and compensation method, and finally based on the error correction method, the prediction function control can be effectively controlled Solving all kinds of persistent uncertain disturbances improves the stability of the control system and further promotes the application of advanced control algorithms in the industry.

Description

A Predictive Function Control Method for Time-Delay Integral Processes Based on Smith Prediction Correction

technical field

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 and correction.

Background technique

For the integration object in the industry, the ordinary predictive function control method cannot effectively resist various continuous disturbances. Under these disturbances, the integration process will eventually deviate from the set value, and the expected control effect cannot be achieved. At the same time, large time-delay processes are very common in the industry. Smith prediction correction is introduced into the prediction function control to compensate for the time delay. It is a common method. If the corresponding integral process error correction method can be given , which will further promote the application of the predictive function control method based on Smith prediction correction, thereby further promoting the development of intelligent control algorithms.

SUMMARY OF THE INVENTION

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

In order to solve the above-mentioned technical problems, a specific technical scheme of a time-delay integral process prediction function control method based on Smith's prediction and correction of the present invention is as follows:

A time-delay integral process prediction function control method based on Smith prediction correction, comprising the following steps:

Step 1: collect the step response data of the integration process, and calculate the corresponding object model; carry out modeling according to the step response data collected in real time, and find out the basic characteristics of the object;

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

Establish the transfer function model of the integral process object;

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

Further, the step 1 includes the following specific steps:

Step 1.1: Add a step signal to the input end of the integration process, and start recording the step response signal of the integration process;

Step 1.2: Filter the obtained step response signal, then fit the part close to the straight line behind the filtered smooth curve into a straight line, and then record the corresponding step response data value on the smooth curve at each sampling time, and sample The interval is set to T _s , and the recorded values are incremented based on the steady state portion, b ₁ ,b ₂ ,…,b _d ,b _d+1 ,b _d+2 ,…, where b ₁ ,…,b _d is the time delay part, that is, the data value in this interval has not changed basically, b _d+1 , b _d+2 ,… are the part where the sampled data value begins to change, and the difference between the data sampled values in this interval can be regarded as a fixed value. value.

Further, the step 2 includes the following specific steps:

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 integral process object is K=(b _d+2 -b _d+1 )/T _s ;

Finally, the obtained integral process transfer function model is

Among them, s is the Laplacian operator.

Further, the step 3 includes the following specific steps:

Step 3.1: Discrete the established transfer function model at the sampling time T _s1 to obtain a discrete equation model:

Step 3.2: Remove the pure lag from the discrete equation model in Step 3.1, and get the equation with the pure lag removed;

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

Step 3.4: Select the prediction function control objective function based on Smith prediction and correction of the integral process object;

Step 3.5: Implement the optimal control law of the prediction function based on Smith prediction correction obtained in step 3.4 to the integration process object.

Further, 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 value of the integration process object at time k, respectively.

Further, the step 3.2 includes the following specific steps:

Removing the pure lag from the discrete equation model in step 3.1 yields 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 with the lag removed at time k;

Based on the Smith prediction correction, the actual correction output of the integration 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's prediction and correction and the actual output of the process, respectively.

Further, the step 3.3 includes the following specific steps:

Based on the model in step 3.2, the predicted value of the integral process model is calculated, and the basis function is a step function, and the predicted value of the integral process model can be obtained:

y _mav (k+H)=y _mav (k)+H*K*T _s1 *u(k)

Among them, H is the prediction time domain;

In the case of correction based on Smith's prediction, the model error e(k) is calculated as follows:

e(k)=y _pav (k)-y _mav (k)

For the introduced prediction function control, the following error correction formula is used:

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, and λ is the error correction coefficient, which ranges from 0 to 1;

Considering the characteristics of the integration process, the final model prediction output corrected by error compensation is y _{mav_c} (k+H)=y _mav (k+H)+err_sum(k)+(H+τ/T _s1 *λ)*err (k)

Among them, the former part of the error compensation correction is the conventional compensation correction, and the latter 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.

Further, the step 3.4 includes the following specific steps:

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

Among them, y _r (k) is the reference trajectory point of the integration process object at time k, and the following calculation formula is taken: y _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;

The derivation of the above objective function can be obtained, and the control law of the prediction function based on Smith prediction correction is:

Further, the step 3.5 includes the following specific steps:

In the next sampling period, follow the steps in steps 3.2 to 3.4 to obtain the latest optimal control law of the prediction function to act on the controlled integration process, and the cycle follows.

A time-delay integral process prediction function control method based on Smith's prediction and correction of the present invention has the following advantages: the present invention cannot effectively solve the influence of continuous interference encountered in the time-delay integral process under the prediction function control due to the traditional error correction method, A corresponding new error correction compensation method is proposed. Finally, based on this error correction method, predictive function control can effectively solve all kinds of continuous uncertain disturbances, improve the stability of the control system, and further promote the application of advanced control algorithms in the industry. Applications.

Description of drawings

none.

Detailed ways

In order to better understand the purpose, structure and function of the present invention, a method for controlling the prediction function of a time-delay integral process based on Smith prediction and correction of the present invention will be described in further detail below with reference to the accompanying drawings.

The method of the invention first conducts modeling according to the step response data collected in real time, finds out the basic characteristics of the object, then performs new error correction and compensation for the prediction function control based on Smith's prediction and correction, and finally calculates the obtained optimal control law Implemented in the controlled integration process.

The technical scheme of the present invention is to establish a process control method of prediction function integration based on Smith's prediction and correction by means of process data acquisition, process model establishment, Smith prediction correction, error compensation correction, objective function solution, etc., so as to solve various disturbances. The impact on the integration process will ultimately improve the stability of the overall system.

The steps of the present invention include:

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

Step 1.1: Add a step signal to the input end of the integration process, and start recording the step response signal of the integration process.

Step 1.2: Filter the obtained step response signal, 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 ) corresponding to the smooth curve. The step response data values of (recorded values are based on the increase in the steady state part), respectively b ₁ , b ₂ ,…, b _d , b _d+1 , b _d+2 ,…. Among them, b ₁ ,...,b _d is the time-delay part, that is, the data value in this interval has basically not changed. b _d+1 , b _d+2 ,…are the parts where the sampled data values begin to change (due to the integral characteristics of the process system, the difference between the data sampled values in this interval can be regarded as a fixed value).

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

Step 2.1: According to the step sampling data, the lag time of the integration process object is τ=d*T _s .

Step 2.2: The gain of the integral process object is K=(b _d+2 - b _d+1 )/T _s .

Finally, the obtained integral process transfer function model is

Among them, s is the Laplacian operator.

Step 3: Design a prediction function control method based on Smith prediction correction for the integration process.

Step 3.1: Discrete the established transfer function model at the sampling time T _s1 to obtain the following discrete equation model:

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 value of the integration process object at time k, respectively.

Step 3.2: Remove the pure lag from the discrete equation model in Step 3.1 to 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 with the lag removed at time k.

Based on the Smith prediction correction, the actual correction output of the integration 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's prediction and correction and the actual output of the process, respectively.

Step 3.3: Calculate the predicted value of the integral process model based on the model in step 3.2. Here, for the convenience of calculation, the basis function is a step function, and the predicted value of the integral process model can be obtained as

y _mav (k+H)=y _mav (k)+H*K*T _s1 *u(k)

Among them, H is the prediction time domain.

In the case of correction based on Smith's prediction, the model error e(k) is calculated as follows:

e(k)=y _pav (k)-y _mav (k)

For the introduced prediction function control, the following error correction formula is used here:

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, and λ is the error correction coefficient, which ranges from 0 to 1.

Considering the characteristics of the integration process, the final model prediction output corrected by error compensation is

y _{mav_c} (k+H)=y _mav (k+H)+err_sum(k)+(H+τ/T _s1 *λ)*err(k)

Among them, the former part of the error compensation correction is the conventional compensation correction, and the latter 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.

Step 3.4: Select the prediction function based on Smith prediction correction of the integral process object The control objective function is as follows:

Among them, y _r (k) is the reference trajectory point of the integration process object at time k, and the following calculation formula can be taken: y _r (k+H)=η ^H y(k)+(1-η ^H )c(k)

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

The derivation of the above objective function can be obtained, and the control law of the prediction function based on Smith prediction correction is:

Step 3.5: Implement the optimal control law of the prediction function based on Smith prediction correction obtained in step 3.4 to the integration process object. In the next sampling period, follow the steps in steps 3.2 to 3.4 to obtain the latest optimal control law of the prediction function to act on the controlled integration process, and the cycle follows.

Example:

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

The boiler drum water level is a typical integral process, and the water supply is the adjustment method.

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:

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

Step 1.2: Filter the obtained step response signal of the boiler drum water level process, 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 value of the boiler drum water level process corresponding to the smooth curve (the recorded value is based on the increased value of the steady-state part), respectively denoted as b ₁ , b ₂ ,…, b _d , b _d+1 , b _d+2 ,…. Among them, b ₁ ,...,b _d is the time delay part of the boiler drum water level process, that is, the data value of the boiler steam drum water level in this interval has basically not changed. b _d+1 , b _d+2 ,…are the part where the sampling data values of the boiler drum water level process begin to change (due to the integral characteristic of the boiler drum water level process, the difference between the data sampling values of the boiler drum water level in this interval value can be regarded as a fixed value).

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

Step 2.1: According to the step sampling data of the boiler drum water level process, it can be known that the lag time of the boiler drum water level process object is τ=d*T _s .

Step 2.2: The gain of the boiler drum water level process object is K=(b _d+2 - b _d+1 )/T _s .

Finally, the transfer function model of the boiler drum water level process is obtained as

Among them, s is the Laplacian operator.

Step 3: Design a prediction function control method based on Smith prediction correction for the boiler drum water level process.

Step 3.1: Discrete the established transfer function model of the boiler drum water level process at the sampling time T _s1 , and obtain the following discrete equation model of the boiler drum water level process:

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 boiler drum water level process at time k, respectively.

Step 3.2: Remove the pure lag from the discrete equation model in Step 3.1 to 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 of the boiler drum water level process with the lag removed at time k.

Based on Smith's prediction correction, the actual correction output of the boiler drum water level process 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 boiler drum water level process after Smith's prediction and correction and the actual output of the process, respectively.

Step 3.3: Calculate the corresponding predicted value of the boiler drum water level based on the boiler drum water level process model in step 3.2. Here, for the convenience of calculation, the basis function is a step function, and the predicted value of the boiler drum water level 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 Smith's prediction and correction, the model error e(k) of the boiler drum water level process is calculated as follows:

e(k)=y _pav (k)-y _mav (k)

For the introduced prediction function control, the following error correction formula is used here:

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, and λ is the error correction coefficient, which ranges from 0 to 1.

Considering the integral characteristics of the boiler drum water level process, the final model prediction output of the boiler drum water level process corrected by error compensation is:

y _{mav_c} (k+H)=y _mav (k+H)+err_sum(k)+(H+τ/T _s1 *λ)*err(k)

Among them, the former part of the error compensation correction is the conventional compensation correction, and the latter 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.

Step 3.4: Select the prediction function based on Smith prediction correction for the boiler drum water level process The control objective function is as follows:

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:

y _r (k+H)=η ^H y(k)+(1-η ^H )c(k)

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

The derivation of the objective function of the above boiler drum water level process can be obtained, and the control law of the prediction function based on Smith's prediction correction is:

Step 3.5: Implement the optimal feed water amount of the prediction function based on Smith's prediction correction obtained in Step 3.2 into the boiler drum water level process. In the next sampling period, follow the steps in step 3.2 to step 3.3 to find out the process of the latest optimal feed water amount acting on the water level of the controlled boiler drum, and then follow this cycle.

It can be understood that the present invention is described by some embodiments, and those skilled in the art know that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, in the teachings of this invention, these features and embodiments may be modified to adapt a particular situation and material without departing from the spirit and scope of the 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 the present application fall within the protection scope of the present invention.

Claims (9)

1. a time-delay integral process prediction function control method based on Smith's prediction correction, is characterized in that, comprises the steps: Step 1: collect the step response data of the integration process, and calculate the corresponding object model; carry out modeling according to the step response data collected in real time, and find out the basic characteristics of the object; Step 2: Perform new error correction compensation for the prediction function control based on Smith prediction correction; Establish the transfer function model of the integral process object; Step 3: The obtained optimal control law is implemented in the controlled integral process; a predictive function control method based on Smith prediction correction is designed for the integral process. 2. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 1, is characterized in that, described step 1 comprises following concrete steps: Step 1.1: Add a step signal to the input end of the integration process, and start recording the step response signal of the integration process; Step 1.2: Filter the obtained step response signal, then fit the part close to the straight line behind the filtered smooth curve into a straight line, and then record the corresponding step response data value on the smooth curve at each sampling time, and sample The interval is set to T _s , and the recorded values are incremented based on the steady state portion, b ₁ ,b ₂ ,…,b _d ,b _d+1 ,b _d+2 ,…, where b ₁ ,…,b _d is the time delay part, that is, the data value in this interval has not changed basically, b _d+1 , b _d+2 ,… are the part where the sampled data value begins to change, and the difference between the data sampled values in this interval can be regarded as a fixed value. value. 3. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 1, is characterized in that, described step 2 comprises following concrete steps: 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 integral process object is K=(b _d+2 -b _d+1 )/T _s ; Finally, the obtained integral process transfer function model is

Among them, s is the Laplacian operator. 4. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 1, is characterized in that, described step 3 comprises following concrete steps: Step 3.1: Discrete the established transfer function model at the sampling time T _s1 to obtain a discrete equation model: Step 3.2: Remove the pure lag from the discrete equation model in Step 3.1, and get the equation with the pure lag removed; Step 3.3: Calculate the predicted value of the integral process model based on the model in Step 3.2; Step 3.4: Select the prediction function control objective function based on Smith prediction and correction of the integral process object; Step 3.5: Implement the optimal control law of the prediction function based on Smith prediction correction obtained in step 3.4 to the integration process object. 5. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 4, is characterized in that, described step 3.1 obtains discrete equation model 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 value of the integration process object at time k, respectively. 6. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 5, is characterized in that, described step 3.2 comprises following concrete steps: Removing the pure lag from the discrete equation model in step 3.1 yields 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 with the lag removed at time k; Based on the Smith prediction correction, the actual correction output of the integration 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's prediction and correction and the actual output of the process, respectively. 7. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 6, is characterized in that, described step 3.3 comprises following concrete steps: Based on the model in step 3.2, the predicted value of the integral process model is calculated, and the basis function is a step function, and the predicted value of the integral process model can be obtained: y _mav (k+H)=y _mav (k)+H*K*T _s1 *u(k) Among them, H is the prediction time domain; In the case of correction based on Smith's prediction, the model error e(k) is calculated as follows: e(k)=y _pav (k)-y _mav (k) For the introduced prediction function control, the following error correction formula is used: 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, and λ is the error correction coefficient, which ranges from 0 to 1; Considering the characteristics of the integration process, the final model prediction output corrected by error compensation is y _{mav_c} (k+H)=y _mav (k+H)+err_sum(k)+(H+τ/T _s1 *λ)*err(k) Among them, the former part of the error compensation correction is the conventional compensation correction, and the latter 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. 8. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 7, is characterized in that, described step 3.4 comprises following concrete steps: The prediction function control objective function based on Smith prediction correction for selecting the integral process object is as follows:

Among them, y _r (k) is the reference trajectory point of the integration process object at time k, and the following calculation formula is taken: y _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; The derivation of the above objective function can be obtained, and the control law of the prediction function based on Smith prediction correction is:

9. the time-delay integral process prediction function control method based on Smith prediction correction according to claim 8, is characterized in that, described step 3.5 comprises following concrete steps: In the next sampling period, according to the steps in step 3.2 to step 3.4, the latest optimal control law of the prediction function is obtained to act on the controlled integration process, and the cycle follows.