A model-based metric for evaluating performance of a split-range control system

Abstract

The application discloses a kind of based on model metric index's split-range control system performance evaluation method, belong to control system evaluation field.It includes: acquisition split-range control system output value, split-range control system's controller output value, split-range control system's candidate split-range point value, according to the comparison result of split-range control system's controller output value and candidate split-range point value, the output value of split-range control system obtained in sampling time period is divided into two data sets;Using prediction error algorithm, establish two time series autoregressive model and from discrete domain to continuous domain, with candidate split-range point as boundary, calculate the model metric index value of two continuous domain autoregressive model, the index reflects the split-range control system performance, to determine whether the optimal candidate split-range point is reasonable to judge candidate split-range point selection.The application solves the problem of split-range control system performance evaluation in complex control system, and the split-range control system can maintain good control level by determining the optimal split-range point.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of control system evaluation, and particularly relates to a performance evaluation method for split-range control system based on a gap metric. BACKGROUND

[0002] Automatic control technology has achieved rapid development in theoretical research and industrial application, and application of automatic control technology has brought huge economic benefits to enterprises and society. However, in the practical process, it is gradually found that the performance of the control system does not always remain in a good state. Even in the initial stage of operation, the performance of the control system meets the requirements, but with the passage of time, the performance of the control system will slowly degrade.

[0003] On the basis of a single-loop control system, a control system with additional calculation links, control links or other links is called a complex control system. The split-range control system is one of the complex control systems. The split-range control system refers to a control system in which the output signal of a controller controls two or more split-range valves. In the split-range control system, linear split-range valves are generally used, and the flow characteristics of each split-range valve show linear characteristics in each split-range signal section. However, in the split-range control system in which the split-range valves move in the same direction, when different split-range valves with different characteristics are used in combination, non-linear characteristics are shown at the split-range points; in the control system in which the split-range valves move in opposite directions, the non-linear characteristics at the split-range points are particularly obvious. There is no effective method for evaluating the split-range control system at a certain split-range point in the prior art. SUMMARY

[0004] In order to overcome the deficiencies of the prior art, the application provides a performance evaluation method for a split-range control system based on a model metric index. The system output values of each split-range linear interval are modeled respectively. If the closed-loop system characteristics are consistent, and the model metric index values of the two models in the continuous domain should be in a small range, the performance of the split-range control system at a certain split-range point can be evaluated by the size of the model metric index value.

[0005] The technical scheme specifically adopted by the application is as follows:

[0006] A performance evaluation method for a split-range control system based on a model metric index, comprising the following steps:

[0007] S1: collecting the output value of the split-range control system, the output value of the controller of the split-range control system, and the candidate split-range point value of the split-range control system, and dividing the output value of the split-range control system obtained in the sampling time period into a first data set and a second data set according to the comparison result of the output value of the controller of the split-range control system and the candidate split-range point value;

[0008] S2: adopting a prediction error algorithm, two time series autoregressive models are respectively established according to the first data set and the second data set;

[0009] S3: the two time series autoregressive models are converted from discrete domain to continuous domain, and a continuous domain autoregressive model above the candidate split point and a continuous domain autoregressive model below the candidate split point are respectively obtained;

[0010] S4: taking the candidate split point as a boundary, the model metric index values of the two continuous domain autoregressive models are calculated, the model metric index reflects the performance of the split range control system, so as to determine whether the candidate split point is reasonable and determine the optimal candidate split point.

[0011] Further, in step S1, if the controller output value of the split range control system at a certain time is less than the candidate split point value, the controller output value at the time is divided into the first data set, otherwise, the controller output value at the time is divided into the second data set.

[0012] Further, the step S2 comprises:

[0013] 2.1) pre-processing the first data set and the second data set, respectively obtaining a historical sample training set and a corresponding prediction label set of the first data set, and a historical sample training set and a corresponding prediction label set of the second data set;

[0014] 2.2) using the historical sample training set and the corresponding prediction label set of the first data set, and the historical sample training set and the corresponding prediction label set of the second data set, respectively establishing a time series autoregressive model.

[0015] Further, the method for dividing the historical sample training set and the corresponding prediction label set of the data set in step 2.1) is:

[0016] The output value of the system at time k is represented as y(k), the output values of the system at time k and n historical times before time k, and the output values of the system at N future times after time k constitute a group of data samples, represented as:

[0017] X k ={y(k-n),y(k-n+1),...,y(k-1),y(k),y(k+1),...,y(k+N)}

[0018] Wherein, X k represents the sample data group corresponding to time k, n represents the historical length before time k, and N represents the future length after time k;

[0019] Taking the output value of the system at time k as a demarcation point, taking the output value set of time k and its historical time as the historical sample training set of time k, denoted as X kl ; taking the output value set of future time of time k as the prediction label set of time k, denoted as X kr ;

[0020] The same processing is performed on the data sample group X k , k = 1, 2, …, T, to obtain the historical sample training set and the corresponding prediction label set of the first data set, and the historical sample training set and the corresponding prediction label set of the second data set, respectively; wherein T represents the total sampling duration, T > N + n + 1.

[0021] Further, the time series autoregressive model in step 2.2) is established by using a prediction error algorithm, and the model is represented as:

[0022] y(k) + a1y(k-1) + … + a n y(k-n) = e(k)

[0023] Taking minimizing the prediction error as an optimization objective;

[0024] Wherein y(k) represents the output value of the system at time k, y(k-n) represents the output value at the n th time before time k, i.e. the output value at the k-n th time of the system, and n represents the historical duration before time k; a n represents the n th parameter of the time series autoregressive model, and e(k) represents the white noise value of the system at time k.

[0025] Further, when solving the time series autoregressive model, it is converted into a least squares optimization proposition for solving.

[0026] Further, the model metric value calculation formula of the two continuous domain autoregressive models is:

[0027]

[0028] Wherein G1(s) and G2(s) respectively represent the continuous domain autoregressive model above the candidate split point and the continuous domain autoregressive model below the candidate split point, δ(·) represents the model metric value, and the value range is [0, 1], and the closer to 0 indicates that the split range control system performance is better; j represents an imaginary unit, ω represents a frequency, R represents a real number domain, and sup(.) represents a minimum upper bound.

[0029] Further, by adjusting the value of the candidate split point, the model metric value of the split range control system is within the range of [0, 0.1], and the optimal candidate split point that meets the performance requirements of the split range control system is obtained.

[0030] The present application has the beneficial effects of:

[0031] The present application perfects the split-range control loop evaluation method, fills the gap of split-range control system evaluation by using system identification method, and has practical application value for the evaluation and maintenance of split-range control system in actual industrial manufacturing. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 It is the overall flow schematic diagram of the split-range control system performance evaluation method based on model metric index shown in the embodiment of the present application. DETAILED DESCRIPTION

[0033] In order to describe the present application more specifically, the technical solutions of the present application are described in detail below in combination with the drawings and specific embodiments.

[0034] The present application is applicable to a split-range control system in which the output signals of a controller are used to control two split-range valves respectively, such as Figure 1 As shown, the split-range control system performance evaluation method based on model metric index mainly includes the following steps:

[0035] Step one, the output value of the split-range control system, the controller output value of the split-range control system, and the candidate split-range point value of the split-range control system are collected, and according to the comparison result of the controller output value of the split-range control system and the candidate split-range point value, the output value of the split-range control system obtained in the sampling time period is divided into a first data set and a second data set.

[0036] In this step, if the controller output value of the split-range control system at a certain time is less than the candidate split-range point value, the controller output value at this time is divided into the first data set, otherwise, the controller output value at this time is divided into the second data set.

[0037] Step two, a prediction error algorithm is used to respectively establish two time series autoregressive models according to the first data set and the second data set.

[0038] In this step, the first data set and the second data set are preprocessed first to obtain the historical sample training set and the corresponding prediction label set of the first data set, and the historical sample training set and the corresponding prediction label set of the second data set;

[0039] For example, the output value of the system at time k is represented as y(k), then the output values of the system at time k and n historical times before time k, and the output values of the system at N future times after time k constitute a group of data samples, represented as:

[0040] X k= {y(k - n), y(k - n + 1),..., y(k - 1), y(k), y(k + 1),..., y(k + N)}

[0041] The data samples are divided into two segments with the output value of the system k time as the demarcation point, and are represented as:

[0042] X kl = {y(k - n), y(k - n + 1),..., y(k)}

[0043] X kr = {y(k + 1), y(k + 2),..., y(k + N)}

[0044] wherein, X k represents the sample data group corresponding to the system k time, X kl represents the output value set of k time and its historical time, as the k time historical sample training set; X kr represents the output value set of the future time of k time, as the k time prediction label set, n represents the historical length before k time, and N represents the future length after k time.

[0045] The same processing is performed on the data sample group X k corresponding to all time points in the first data set and the second data set, k = 1, 2,..., T, to obtain the historical sample training set and the corresponding prediction label set of the first data set, and the historical sample training set and the corresponding prediction label set of the second data set; wherein, T represents the total sampling length, T > N + n + 1.

[0046] Then, a time series autoregressive model is established using the historical sample training set and the corresponding prediction label set of the first data set, and the historical sample training set and the corresponding prediction label set of the second data set, and the model is represented as:

[0047] y(k) + a1y(k - 1) + … + a n y(k - n) = e(k)

[0048] The optimization objective is:

[0049]

[0050]

[0051] wherein y(k) represents an output value of the system at time k, y(k-n) represents an output value at the nth time before the time k, i.e., an output value of the system at the k-nth time, n represents a history length before the time k, y(k+i) represents an output value at the ith time after the time k, i.e., an output value of the system at the k+i-th time, and N represents a future length after the time k;a n represents an nth parameter of the time series autoregressive model, e(k) represents a white noise value at the time k, and represents a model parameter matrix, V N represents a prediction error function. represents a predicted output result at the k+i-th time obtained according to an output value at the k+i-1-th time, represents a set of negative values of output values at the corresponding historical times of the k+i-th time of the system, the superscript T represents transposition, and V N represents a prediction error function.

[0052] In this embodiment, when the time series autoregressive model is solved, it is converted into a least square optimization proposition represented by the following formula:

[0053]

[0054] wherein

[0055]

[0056]

[0057] The solution of the least square optimization proposition is a solution of the following normal equation:

[0058] Φ T Φθ=Φ T Y

[0059] θ=[Φ T Φ] -1 Φ T Y

[0060] wherein J represents a least square optimization function, Y represents a reference matrix, and represents a historical output matrix, represents a square of an L2 norm.

[0061] Step three, converting the two time series autoregressive models from a discrete domain to a continuous domain to obtain a continuous domain autoregressive model above the candidate split point and a continuous domain autoregressive model below the candidate split point, respectively.

[0062] Step four, with the candidate split range point as a boundary, the model metric index values of two continuous domain autoregressive models are calculated, the model metric index reflects the performance of the split range control system, so as to determine whether the candidate split range point is reasonable, and determine the optimal candidate split range point;

[0063] In the embodiment, the model metric index value calculation formula of the two continuous domain autoregressive models is:

[0064]

[0065] Wherein, G1(s), G2(s) respectively represent the continuous domain autoregressive model above the candidate split range point and the continuous domain autoregressive model below the candidate split range point, j represents the imaginary unit, ω represents the frequency, R represents the real number domain, sup(.) represents the minimum upper bound; δ(·) represents the model metric index value, the value range is [0, 1], the closer to 0, the better the performance of the split range control system, in the embodiment, by adjusting the value of the candidate split range point, the model metric index value of the split range control system is in the range of [0, 0.1], and the optimal candidate split range point meeting the performance requirement of the split range control system is obtained.

[0066] Taking the split range control system of the opposite direction valve combination as an example, the implementation effect of the application is described.

[0067] Considering the opposite direction valve combination, the control valve A is air-off type, the control valve B is air-on type, the valve flow characteristics are the same, and the valve action relationship diagram of the reaction controller is used, the horizontal axis is the PID output, and the vertical axis is the single valve opening, wherein: the cooling water control valve A is air-off valve with negative gain; the steam quantity control valve B is air-on valve with positive gain.

[0068] The temperature rising section: the temperature in the reactor is low, the controller output is a large signal, and the controller signal decreases with the increase of the temperature, then the valve A is closed, the valve B has a large opening, and the valve B is gradually closed with the increase of the temperature in the reactor;

[0069] The reaction section: the reaction heat is removed, the temperature in the reactor reaches the reaction temperature, the signal decreases with the increase of the temperature, and the valve B is completely closed. With the progress of the exothermic reaction, the temperature in the reactor increases, the controller output signal decreases, and the opening of the valve A gradually increases.

[0070] In the embodiment, the performance of the split range control system in the range of 20%-80% of the split range point is tested, and the test results are shown in Table 1:

[0071] Table 1 experimental results

[0072]

[0073]

[0074] From the above results, it is seen that the system performance is optimal at a split point of 40% to 60%, with 50% being optimal.

[0075] The above only lists specific embodiments of the present application. Obviously, the present application is not limited to the above embodiments, and there can be many variations. All variations that can be directly derived or thought of by those of ordinary skill in the art from the disclosure of the present application should be considered to be within the scope of the present application.

Claims

1. A performance evaluation method for a split-range control system based on model metrics, characterized in that: The steps include: S1: collecting the output value of the split-range control system, the output value of the controller of the split-range control system, and the candidate split-range point value of the split-range control system, and dividing the output value of the split-range control system obtained during the sampling period into a first data set and a second data set based on the comparison result between the output value of the controller of the split-range control system and the candidate split-range point value; S2: Using the prediction error algorithm, two time series autoregressive models are established based on the first and second data sets respectively; The step S2 includes: 2.1) Preprocessing the first dataset and the second dataset to obtain a historical sample training set and a corresponding prediction label set for the first dataset, and a historical sample training set and a corresponding prediction label set for the second dataset; The method for dividing the data set into the historical sample training set and the corresponding prediction label set in step 2.1) is: The output value of the system at time k is expressed as y(k). Then the output value of the system at time k and the n historical moments before it, as well as the output value of the system at N future moments after time k, constitute a set of data samples, which can be expressed as: X k ={y(kn),y(k-n+1),...,y(k-1),y(k),y(k+1),...,y(k+N)} Among them, X k represents the sample data group corresponding to time k of the system, n represents the historical duration before time k, and N represents the future duration after time k; The output value of the system at time k is the demarcation point, and the output value set at time k and its historical moments is used as the historical sample training set at time k, denoted as X kl ; The output value set of the future time at time k is used as the predicted label set at time k, recorded as X kr ; For the data sample group X corresponding to all moments in the first and second data sets k , k=1,2,…,T, perform the same process to obtain the historical sample training set and the corresponding prediction label set of the first data set, and the historical sample training set and the corresponding prediction label set of the second data set respectively; where T represents the total sampling time, T>N+n+1; 2.2) Using the historical sample training set and the corresponding prediction label set of the first dataset, and the historical sample training set and the corresponding prediction label set of the second dataset, respectively, establish a time series autoregressive model; The time series autoregressive model in step 2.2) is established using a prediction error algorithm, and the model is expressed as: y(k)+a1y(k-1)+…+a n y(kn)=e(k) The optimization goal is: Among them, y(k) represents the output value of the system at time k, y(kn) represents the output value of the system at time n before time k, that is, the output value of the system at time kn, and n represents the historical length before time k; y(k+i) represents the output value of the system at time i after time k, that is, the output value of the system at time k+i, and N represents the future length after time k; n represents the nth parameter of the time series autoregressive model, e(k) represents the white noise value of the system at time k, θ represents the model parameter matrix, V N (θ) represents the prediction error function; It represents the predicted output result at the k+i moment obtained based on the output value of the system at the k+i-1 moment. It represents the transposition of the negative value of the output value set of the system at the historical moment corresponding to the k+i moment. The superscript T represents the transposition. V N (θ) represents the prediction error function; S3: Convert the two time series autoregressive models from discrete domain to continuous domain, and obtain the continuous domain autoregressive model above the candidate split point and the continuous domain autoregressive model below the candidate split point respectively; S4: Calculate the model metric index values ​​of the two continuous domain autoregressive models with the candidate split point as the boundary. The model metric index reflects the performance of the split control system, thereby judging whether the candidate split point selection is reasonable and determining the optimal candidate split point. The calculation formula of the model metric value of the two continuous domain autoregressive models is: Among them, G1(s) and G2(s) represent the continuous domain autoregressive model above the candidate split point and the continuous domain autoregressive model below the candidate split point, respectively. δ(·) represents the model metric value, which ranges from [0,1]. The closer it is to 0, the better the performance of the split-range control system. j represents the imaginary unit, ω represents the frequency, R represents the real number domain, and sup(.) represents the minimum upper bound.

2. A performance evaluation method for a split-range control system based on model metrics according to claim 1, characterized in that: In step S1, if the controller output value of the split-range control system at a certain moment is less than the candidate split-range point value, the controller output value at that moment is divided into a first data set; otherwise, the controller output value at that moment is divided into a second data set.

3. The performance evaluation method of a split-range control system based on model metrics according to claim 1, characterized in that: When solving the time series autoregressive model, it is converted into a least squares optimization problem for solution.

4. The performance evaluation method of a split-range control system based on model metrics according to claim 1, characterized in that: By adjusting the values ​​of the candidate split points, the model metric values ​​of the split-range control system are made within the range of [0, 0.1], and the optimal candidate split points that meet the performance requirements of the split-range control system are obtained.

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