CN107992112A - A kind of control loop performance estimating method and system based on arrangement entropy - Google Patents
A kind of control loop performance estimating method and system based on arrangement entropy Download PDFInfo
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Abstract
The invention discloses a kind of control loop performance estimating method and system based on arrangement entropy, this method collection natural gas line control loop outlet pressure data;Suitable Embedded dimensions and time delay are selected respectively, and outlet pressure data sequence is reconstructed, obtains restructuring matrix;Component will each be reconstructed in restructuring matrix to be arranged according to numerical values recited, each component that reconstructs can obtain a symbol sebolic addressing;The probability of each symbol sebolic addressing appearance is calculated, the formula for substituting into arrangement entropy calculates the arrangement entropy of outlet pressure data;Arrangement entropy is normalized, obtains the control loop performance based on arrangement plan method assessment.Using this kind of method and system, when there is pressure control loop hydraulic performance decline trend or electric control valve breaks down, the device automatically in time can prompt administrative staff, this will mitigate the labor intensity of personnel significantly, operational management efficiency is lifted, pressure oscillation existing for Natural Gas Station is excessive and the generation of industrial accident so as to avoid or reduce.
Description
Technical field
The present invention relates to Natural Gas Pipeline Transportation technical field, more particularly to natural gas line control loop Performance Evaluation skill
Art field, in particular to a kind of control loop performance estimating method and system based on arrangement entropy towards Natural Gas Station.
Background technology
Natural gas has evolved into one of big main force's energy in the world three as a kind of high-quality, efficient clean energy resource.Naturally
Gas uses pipeline, and the natural gas that pressure is steady, safe and reliable is provided for the defeated user in downstream point.The natural gas warp of long distance pipeline
Excessive high pressure, high pressure station enter urban pipe network.Natural Gas Station is to divide gas transmission body to set to user along gas pipeline
The yard put, in order to ensure that high-pressure natural gas enters safely downstream line, and keeps lasting supply, point defeated station needs to pass through pressure regulation
System adjustment pressure, it is ensured that system downstream pressure is no more than the pressure allowed, while ensures when voltage adjusting device breaks down, energy
Carry out safety cut-off.
In recent years, Frequent Accidents during natural gas transportation, the Qingdao sinopec " 11-22 " in such as in January, 2014 are especially big
Accident causes 62 people wrecked altogether, and 136 people are injured, 7.5 hundred million yuan of direct economic loss.Therefore this clean and effective of natural gas is being applied
The energy at the same time, it is necessary to ensure natural gas operation safety.During natural gas transportation, due in each urban pipe network
All there are substantial amounts of industry and commerce user, civilian users, particularly industry and commerce user since not enough pipelines can be used as buffering
Gas storage, if discharge pressure fluctuation is too big or stops the supple of gas or steam, will directly affect the production of industrial user, cause great economic loss and
Security incident, therefore it is the key technology for ensureing natural gas safe operation that point defeated station pressure, which is adjusted,.
But since work regulating valve will cause regulating valve hydraulic performance decline to go out in harsh conditions such as high/low temperature, high pressure, corrosion
Existing nonlinear operation characteristic, simultaneously because other exterior interference (such as Inlet pressure change), controller architecture or parameter are unreasonable
Etc. reason, the performance of control loop will deteriorate even oscillation circuit, cause natural gas accident safe for operation.Thus it is guaranteed that control
It is necessary that controller performance, which is stablized, in circuit processed.
Due to the fast development of Gas Industry, point defeated station control loop is more and more.Run with Zhejiang Province's natural gas public
Exemplified by department, its provincial gas distributing system managed 2015 year end estimated lengths of pipeline will more than 1700 kilometers, gas transmission station 55,
Unmanned Remote Control Station 21, valve chamber 83, be related to point defeated station pressure control loop reach hundreds of, pressure-regulating valve reach thousands of
It is a.For so many control loop and valve arrangement, the yard management and maintenance personnel for natural gas operation enterprise,
It is a huge challenge.
The content of the invention
The shortcomings that present invention is in order to overcome the above-mentioned prior art is, and it is an object of the present invention to provide a kind of assessment is simple, is accurately based on
The control loop performance estimating method and system of entropy are arranged, when there is pressure control loop hydraulic performance decline trend or electric control valve
When breaking down, this method can quickly and accurately assess the control loop performance drawn in gas pipeline, and can automatically and
When administrative staff are prompted, this will significantly mitigate personnel labor intensity, lifted operational management efficiency so that avoid or
Reduce existing for Natural Gas Station that pressure oscillation is excessive and the generation of industrial accident.
In order to achieve the object of the present invention, in a kind of control loop Performance Evaluation side based on arrangement entropy that this is provided
Arrangement entropy is normalized in method, this method, judges control loop performance according to normalization result, specifically includes following
Step:
Step 1:Data acquisition, the pressure data that acquisition control circuit each exports, forms set A, A={ X (i), i=
1,2,3n };
Step 2:Reconstruct, is reconstructed set A, forms restructuring matrix;
Step 3:Symbol sebolic addressing, the element in every a line in restructuring matrix is ranked up according to numerical values recited, sequence
One symbol sebolic addressing S (l) of every behavior afterwards;
Step 4:Probability is calculated, calculates the probability P z that each symbol sebolic addressing occurs;
Step 5:Calculated permutations entropy, the arrangement entropy Hp in restructuring matrix is calculated according to arrangement entropy formula;
Step 6:Normalized, is normalized arrangement entropy Hp, and it is 0~1 to obtain normalization result H, H value
Then there is failure in control loop, and sends prompt tone prompting related personnel, on the contrary then control loop is functional;
Step 6:Circulation performs step 1 to step 5.
Arrangement entropy is normalized in appraisal procedure provided by the present invention, improves the accurate of assessment result
Degree, and circulate and perform each step, realize assessment monitoring function, and being sent out in time when something goes wrong in control loop in real time
Go out prompt tone prompting related personnel.
Specifically, the model of the restructuring matrix described in the step 2 is as follows:
Wherein:M and τ represents Embedded dimensions and time delay respectively, and K=n- (m-1) τ, wherein n represent times of collection.
Specifically, symbol sebolic addressing S (l) expression formulas are as follows:
S (l)=(j1,j2,···,jm) (2)
In formula:j1﹑ j2And jmThe index of each element column in every a line in restructuring matrix is represented respectively;L=1,2,
3, k, k≤m!, m expression Embedded dimensions.
Specifically, the arrangement entropy Hp is obtained by following formula:
In formula:k≤m!, m expression Embedded dimensions;Ln Pz represent the logarithm using e as bottom Pz.
Specifically, the normalization result H is obtained by following formula:
H=Hp/ln (m!) (4)
In formula:ln(m!) represent using e as bottom ln (m!) logarithm, m!Represent m factorials, m represents Embedded dimensions.
In addition, a kind of control loop performance evaluation system based on arrangement entropy provided by the present invention, the system include:
Data acquisition module, the pressure data for acquisition control circuit outlet;
Database module, for storing collected pressure data;
Data reconstruction module, for selecting suitable Embedded dimensions and time delay, carries out outlet pressure data sequence
Reconstruct, obtains restructuring matrix;
Symbol sebolic addressing module, arranges, each reconstruct point for will each reconstruct component in restructuring matrix according to numerical values recited
Amount can obtain a symbol sebolic addressing;
Control loop performance Index Calculation module, for calculating the probability of each symbol sebolic addressing appearance, substitutes into arrangement entropy
Formula calculate outlet pressure data arrangement entropy, control loop performance indicator is obtained by normalized;
Reminding module, for sending prompt tone when failure occurs in control loop.
Further, which further includes human-computer interaction module, and the network for being built based on Django frames establishes people
Border interactive interface, control loop performance Index Calculation result and warning message are issued by the human-computer interaction interface.
The beneficial effects of the invention are as follows:Appraisal procedure improves the accuracy of assessment result, and circulates and perform each step,
Realize assessment monitoring function in real time.
Assessment system can utilize more personal computers, by using Django and MySQL open source softwares, with based on row
Based on the control loop performance estimating method of row entropy, the control loop outlet pressure data to gather in real time are built to assess control
The on-line monitoring network of loop performance processed;Natural gas line pressure control loop can be monitored in real time, mitigate personnel's
Labor intensity, lifts operational management efficiency, so that it is excessive and safe to avoid or reduce pressure oscillation existing for natural gas line
The generation of production accident.
Brief description of the drawings
Fig. 1 is the flow chart of appraisal procedure of the present invention.
Embodiment
In order to which technical solution provided by the present invention is better described, it is described further herein with reference to attached drawing.
As shown in Figure 1, a kind of control loop performance estimating method based on arrangement entropy provided by the present invention, this method pair
Arrangement entropy is normalized, and judges control loop performance according to normalization result, specifically includes following steps:
Step 1:Data acquisition, the pressure data that acquisition control circuit each exports, forms set A, A={ X (i), i=
1,2,3n };Wherein, X (i) represents that the pressure value in each exit of control loop (refers to unit area (1cm2)
The size of upper pressure, unit are Pa (pa)), i represents the pressure value that the one outlet that ith collects goes out;It is assumed herein that set A
In element be respectively 3Pa, 4Pa, 6Pa, 1Pa, 3Pa, 5Pa, 7Pa, 2Pa, 9Pa, represent to it is a certain outlet acquire altogether 9 times,
Pressure value each time as above, then set A={ 3Pa, 4Pa, 6Pa, 1Pa, 3Pa, 5Pa, 7Pa, 2Pa, 9Pa };
Step 2:Reconstruct, is reconstructed set A, forms restructuring matrix;The restructuring matrix can be any type mould
Type, it is used herein, it is such as drag:
Wherein:M and τ represents Embedded dimensions and time delay respectively, and K=n- (m-1) τ, wherein n represent the number of collection,
Assuming that n is 9, Embedded dimensions m is 3, and delay time τ is 2, K=9- (3-1) * 2=5, and it is as follows to obtain restructuring matrix model:
X (1), x (2), x (3), x (4), x (5), x (6), x (7), x (8) and x (9) correspond to set A respectively in above matrix
In the 1st element, the 2nd element, the 3rd element, the 4th element, the 5th element, the 6th element, the 7th element, the 8th
Element and the 9th element, therefore set A is reconstructed, obtained restructuring matrix B is as follows:
Step 3:Symbol sebolic addressing, can regard every a line in restructuring matrix as a reconstruct component, then share K reconstruct
Component, by each reconstruct component is rearranged according to numerical values recited according to ascending order in restructuring matrix:x(j1)≤x(j2)≤···
≤x(jm), wherein, j1,j2···,jmRepresent the index of each element column in reconstruct component;If deposited in reconstruct component
In equal value, such as:x(j1)=x (j2), at this time just according to index j1、j2The size of value sorts, such as:Work as j1< j2When, then regard
For x (j1) < x (j2);One symbol sebolic addressing S (l) of every behavior after sequence;The expression formula of symbol sebolic addressing S (l) is as follows:
S (l)=(j1,j2,···,jm) (2)
In formula:j1﹑ j2And jmThe index of each element column in every a line in restructuring matrix is represented respectively;L=1,2,
3, k, k≤m!, m expression Embedded dimensions;Wherein l represents the line number of restructuring matrix, herein by taking matrix B as an example.
Every a line in matrix is regarded as a reconstruct component, then 5 reconstruct components are shared in matrix B.Then will
Element in each reconstruct component, rearranges according to ascending order according to numerical values recited, extracts each element in original weight structure component
The index of column, obtains following symbol sebolic addressing S (l):
S (1)=(1,3,2), the 1st element numerical value is minimum in the first row of representing matrix B, the 3rd element numerical value secondly,
2nd element numerical value is maximum;
S (2)=(2,1,3), the 2nd element numerical value is minimum in the first row of representing matrix B, the 1st element numerical value secondly,
3rd element numerical value is maximum;
S (3)=(2,1,3), the 2nd element numerical value is minimum in the first row of representing matrix B, the 1st element numerical value secondly,
3rd element numerical value is maximum;
S (4)=(1,3,2), the 1st element numerical value is minimum in the first row of representing matrix B, the 3rd element numerical value secondly,
2nd element numerical value is maximum;
S (5)=(1,2,3), the 1st element numerical value is minimum in the first row of representing matrix B, the 2nd element numerical value secondly,
3rd element numerical value is maximum.
Step 4:Probability is calculated, calculates the probability P z that each symbol sebolic addressing occurs;Z=1,2,3, k, k≤
m!, m represent Embedded dimensions, Pz can use existing any type calculation calculate, such asWherein X represents a certain
The quantity of kind (i.e. the identical symbol sebolic addressing of element) symbol sebolic addressing, Y represent the sum of all symbol sebolic addressings.Pass throughCalculate
The relative frequency for obtaining each ordered mode is respectively P(1,2,3)=1/5, P(1,3,2)=2/5, P(2,1,3)=2/5, P(2,3,1)=0,
P(3,2,1)=0 and P(3,1,2)=0.
Step 5:Calculated permutations entropy, the arrangement entropy Hp in restructuring matrix is calculated according to arrangement entropy formula;Arranging entropy Hp can be with
Calculated using the existing computational methods of any type, used calculation formula is as follows herein:
In formula:k≤m!, m expression Embedded dimensions;Ln Pz represent the logarithm using e as bottom Pz;
Step 6:Normalized, is normalized the arrangement entropy Hp obtained by formula 3, obtains normalizing
Change result H, H value and failure occur for 0~1 control loop, and send prompt tone prompting related personnel, on the contrary then control loop
It is functional;Wherein, normalized can use existing any of which, the application used normalization side herein
Formula is as follows:
H=Hp/ln (m!) (4)
In formula:ln(m!) represent using e as bottom ln (m!) logarithm, m!Represent m factorials, m represents Embedded dimensions.
Step 6:Circulation performs step 1 to step 5.
Can utilize above appraisal procedure to a certain exit of control loop or some exits or whole exit into
Row assessment.The accuracy of assessment result is improved, and circulates and performs each step, realizes assessment monitoring function in real time.
Above appraisal procedure can realize that used system is as follows herein by the application by any type system:
Based on the control loop performance evaluation system of arrangement entropy, including following function module:
Data acquisition module, for the pressure data of acquisition control circuit outlet, the pressure data gathered passes through wireless
Network is uploaded to host computer (computer);The data acquisition module is arranged at control loop to exit, including pressure sensor
With 2.4G wireless communication modules, the pressure value that pressure sensor is collected is uploaded to host computer by 2.4G wireless communication modules
In (computer) and the memory module being stored in host computer (computer);
Database module, for storing collected pressure data;
Data reconstruction module, for selecting suitable Embedded dimensions and time delay, carries out outlet pressure data sequence
Reconstruct, obtains restructuring matrix;
Symbol sebolic addressing module, arranges, each reconstruct point for will each reconstruct component in restructuring matrix according to numerical values recited
Amount can obtain a symbol sebolic addressing;
Control loop performance Index Calculation module, for calculating the probability of each symbol sebolic addressing appearance, substitutes into arrangement entropy
Formula calculate outlet pressure data arrangement entropy, control loop performance indicator is obtained by normalized;
Reminding module, for sending prompt tone when failure occurs in control loop, which can use buzzing
The hardware such as device, loudspeaker;
Wherein, data library module ﹑ data reconstructions module, symbol sebolic addressing module and control loop performance Index Calculation module collection
Into in development system, existing any type development system can be used, and development system is then used by the application
Django and MySQL open source softwares.
In addition, the system further includes human-computer interaction module, the network for being built based on Django frames establishes interpersonal friendship
Mutual interface, control loop performance Index Calculation result and warning message are issued by the human-computer interaction interface.
System Working Principle provided herein is as follows:
First, natural gas line control loop outlet pressure data (can be gathered by PLC), the data after collection are gathered
It is uploaded to host computer (computer);Secondly, Django the and MySQL open source softwares being installed on host computer, He Duotai are recycled
Computer carries out distributed storage;Then, suitable Embedded dimensions and time delay are selected, outlet pressure data sequence is carried out
Reconstruct, obtains restructuring matrix;Being arranged again by will each reconstruct component in restructuring matrix according to numerical values recited, each reconstructing component
It can obtain a symbol sebolic addressing;Then, the probability of each symbol sebolic addressing appearance is calculated, the formula for substituting into arrangement entropy calculates
The arrangement entropy of mouth pressure data, control loop performance indicator is obtained by normalized;In man-machine interface, using WEB shapes
Formula inquires about control loop outlet pressure and control loop performance, and control loop performance is monitored in real time, works as monitoring
After value exceedes given threshold, alarm.
Using the control loop performance estimating method and system towards Natural Gas Station of the invention, more individuals are utilized
Computer, by using Django and MySQL open source softwares, using the control loop performance estimating method based on arrangement entropy as base
Plinth, builds the control loop outlet pressure data to gather in real time to assess the on-line monitoring network of control loop performance;Can
Natural gas line pressure control loop is monitored in real time, mitigates the labor intensity of personnel, lifts operational management efficiency, so that
Avoid or reduce that pressure oscillation existing for natural gas line is excessive and the generation of industrial accident.
In this description, the present invention is described with reference to its specific embodiment.But it is clear that it can still make
Various modifications and alterations are without departing from the spirit and scope of the present invention.Therefore, specification and drawings are considered as illustrative
It is and non-limiting.
Claims (7)
- A kind of 1. control loop performance estimating method based on arrangement entropy, it is characterised in that:This method returns arrangement entropy One change is handled, and is judged control loop performance according to normalization result, is specifically included following steps:Step 1:Data acquisition, the pressure data that acquisition control circuit each exports, formation set A, A=X (i), i=1,2, 3······n};Step 2:Reconstruct, is reconstructed set A, forms restructuring matrix;Step 3:Symbol sebolic addressing, the element in every a line in restructuring matrix is ranked up according to numerical values recited, after sequence Per one symbol sebolic addressing S (l) of behavior;Step 4:Probability is calculated, calculates the probability P z that each symbol sebolic addressing occurs;Step 5:Calculated permutations entropy, the arrangement entropy Hp in restructuring matrix is calculated according to arrangement entropy formula;Step 6:Normalized, is normalized arrangement entropy Hp, obtains normalization result H, H value as 0~1 control There is failure in circuit processed, and sends prompt tone prompting related personnel, on the contrary then control loop is functional;Step 6:Circulation performs step 1 to step 5.
- A kind of 2. control loop performance estimating method based on arrangement entropy as claimed in claim 1, it is characterised in that:The step The model of restructuring matrix described in rapid two is as follows:<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mo>(</mo> <mi>m</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>&tau;</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mrow></mrow> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mrow></mrow> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mrow></mrow> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>+</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>+</mo> <mo>(</mo> <mi>m</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>&tau;</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mrow></mrow> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mrow></mrow> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mrow></mrow> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>K</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>K</mi> <mo>+</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>K</mi> <mo>+</mo> <mo>(</mo> <mi>m</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>&tau;</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>Wherein:M and τ represents Embedded dimensions and time delay respectively, and K=n- (m-1) τ, wherein n represent times of collection.
- A kind of 3. control loop performance estimating method based on arrangement entropy as claimed in claim 2, it is characterised in that:Described Symbol sebolic addressing S (l) expression formulas are as follows:S (l)=(j1,j2,···,jm) (2)In formula:j1﹑ j2And jmThe index of each element column in every a line in restructuring matrix is represented respectively;L=1,2, 3, k, k≤m!, m expression Embedded dimensions.
- A kind of 4. control loop performance estimating method based on arrangement entropy as claimed in claim 3, it is characterised in that:Described Arrangement entropy Hp is obtained by following formula:<mrow> <mi>H</mi> <mi>p</mi> <mo>=</mo> <mo>-</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>z</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <mi>P</mi> <mi>z</mi> <mi>ln</mi> <mi>P</mi> <mi>z</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>In formula:k≤m!, m expression Embedded dimensions;Ln Pz represent the logarithm using e as bottom Pz.
- A kind of 5. control loop performance estimating method based on arrangement entropy as claimed in claim 4, it is characterised in that:It is described to return One change result H is obtained by following formula:H=Hp/ln (m!) (4)In formula:ln(m!) represent using e as bottom ln (m!) logarithm, m!Represent m factorials, m represents Embedded dimensions.
- 6. a kind of control loop performance evaluation system based on arrangement entropy, it is characterised in that the system includes:Data acquisition module, the pressure data for acquisition control circuit outlet;Database module, for storing collected pressure data;Data reconstruction module, for selecting suitable Embedded dimensions and time delay, is reconstructed outlet pressure data sequence, Obtain restructuring matrix;Symbol sebolic addressing module, arranges, each reconstruct component can for will each reconstruct component in restructuring matrix according to numerical values recited To obtain a symbol sebolic addressing;Control loop performance Index Calculation module, for calculating the probability of each symbol sebolic addressing appearance, substitutes into the public affairs of arrangement entropy Formula calculates the arrangement entropy of outlet pressure data, and control loop performance indicator is obtained by normalized;Reminding module, for sending prompt tone when failure occurs in control loop.
- 7. the control loop performance evaluation system according to claim 6 based on arrangement entropy, it is characterised in that further include:Human-computer interaction module, the network for being built based on Django frames establish interpersonal interactive interface, pass through the man-machine friendship Mutual interface issue control loop performance Index Calculation result and warning message.
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