CN109799802A - Sensor fault diagnosis and fault tolerant control method in a kind of control of molecular weight distribution - Google Patents

Sensor fault diagnosis and fault tolerant control method in a kind of control of molecular weight distribution Download PDF

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CN109799802A
CN109799802A CN201811489086.3A CN201811489086A CN109799802A CN 109799802 A CN109799802 A CN 109799802A CN 201811489086 A CN201811489086 A CN 201811489086A CN 109799802 A CN109799802 A CN 109799802A
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molecular weight
indicate
fault
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CN109799802B (en
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姚利娜
王豪
李立凡
梁占红
武亚威
顾照玉
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Zhengzhou University
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Abstract

The invention proposes sensor fault diagnosis and fault tolerant control methods in a kind of control of molecular weight distribution, step are as follows: obtain the distribution of chemical reaction process molecular weight online by mass spectrometer or laser measurement technology, output probability density function is obtained, approaches output probability density function with B-spline neural network;The state-space model for establishing system obtains the parameter of state-space model, design learning fault diagnosis observer after scanning identification method transformation;Fault message is estimated in time when faulty generation using the study whether faulty generation of fault diagnosis observer real-time monitoring sensing device;The output weight of system is compensated using the fault message of estimation;By designed control signal input system, make the distribution of system output molecular weight distribution tracking desired molecular weight.The present invention can be that the reliability and safety in system operation provide safeguard, and escort for the life security and property safety of relevant enterprise personnel.

Description

Sensor fault diagnosis and fault tolerant control method in a kind of control of molecular weight distribution
Technical field
The present invention relates to the technical fields more particularly to a kind of molecular weight distribution control of sensor fault diagnosis and faults-tolerant control Sensor fault diagnosis and fault tolerant control method in system.
Background technique
The control of system molecular weight distribution is typical stochastic distribution control systematic difference in Chemical Engineering Process Control, and at it Endure attention to the fullest extent in relevant field.The concept of random distribution system by being proposed in paper industry production process, extend to later ore grinding, The fields such as boiler combustion, chemical reaction, since it is using very extensive, so enduring associated specialist and scholar to the fullest extent in its related fields Attention.Since the limited relevant industries of production environment mostly use greatly mechanization and intelligent production line, wherein needing largely to pass The components such as sensor actuator, and under such production environment for a long time, non-stop run inevitably break down, if cannot and When diagnosis be out of order and carry out faults-tolerant control and will cause serious consequence.The control object of random distribution system is whole system Output probability density function, input, noise and fault type might not Gaussian distributed, stochastic variable is non-gaussian Type, be a kind of non-Gaussian SDC systems.Disturbance suffered by random distribution system is mostly non-gaussian, and distribution is difficult to retouch It states, influences the performance of fault diagnosis.
And traditional method for diagnosing faults is mainly based upon modelling observer or filter carries out fault diagnosis.It is existing Fault diagnosis and fault-tolerant control method carry out fault diagnosis and fault-tolerant control just for the actuator of non-Gaussian SDC systems System does not consider to carry out fault diagnosis and faults-tolerant control to sensor when sensor failure.
Summary of the invention
Fault diagnosis and fault-tolerant control is carried out just for actuator for existing non-Gaussian SDC systems, is not considered The technical issues of status of sensor failure, the present invention propose in a kind of control of molecular weight distribution sensor fault diagnosis with Fault tolerant control method solves the problems, such as the sensor fault diagnosis of non-Gaussian and random control system, solve non-gaussian with Faults-tolerant control problem when machine distribution control system sensor failure.
In order to achieve the above object, the technical scheme of the present invention is realized as follows: being passed in a kind of control of molecular weight distribution Sensor fault diagnosis and fault-tolerant control method, its step are as follows:
Step 100: obtain the distribution of chemical reaction process molecular weight online by mass spectrometer or laser measurement technology, Output probability density function is obtained, approaches output probability density function with B-spline neural network;
Step 200: the state-space model of system is established according to the output probability density function approached, through scanning identification method The parameter of state-space model, design learning fault diagnosis observer are obtained after transformation;
Step 300: designed study fault diagnosis observer is realized that whether is real-time monitoring sensing device on computers Faulty generation learns fault diagnosis observer and estimates fault message in time when faulty generation;
Step 400: when system is faulty, the diagnostic observations device that breaks down accurately estimates fault message, utilize estimation therefore Barrier information compensates the output weight of system;
Step 500: designed control signal input system is made into system output molecular weight distribution tracking desired molecular weight Distribution.
Output probability density function is to provide in the step 100:
Wherein, φi(y) indicate that i-th of B-spline basic function, n indicate the number of B-spline basic function, y indicates the defeated of system Out, t indicates the time, and u (t) is control input, ωiIt (t) is the weight of i-th of B-spline basic function;
Since output probability density function γ (y, u (t)) is equal to 1 in the integral of its interval of definition [a, b], using B-spline Neural network approaches its output probability density function with linear B-spline basis function neural network are as follows:
γ (y, u (t))=C (y) V (t)+T (y);
Wherein, linear radial basic functionWithParameterφ1(y),φ2(y),φ3(y) be system output y line Property B-spline basic function;V (t)=[ω1(t),ω1(t),…ω3(t)]TTo export weight vector, ωiIt (t) is i-th of B-spline The weight of basic function, i=1,2,3.
The state-space model of system is established in the step 200 according to the probability density function approached are as follows:
A new state variable is introduced using the output weight of systemThe then shape of system State space model becomes:
Wherein, x (t) is the state variable of original system, and u (t) is control input, and f (t) is fault vectors, and V (t) is weight Vector,Indicate the first derivative of state variable x (t), AsIt indicates and unit matrix of the state variable with dimension, xs(t) it indicates State variable related with output weight,Indicate state variable xs(t) first derivative, A, B, D and G are respectively parameter square Battle array;
New stateThe state-space model of system are as follows:
Wherein, the state variable of new system isParameter matrix is respectivelyIpIndicate that P ties up unit matrix;
Design learning fault diagnosis observer is as follows:
Wherein,Indicate the first derivative of new system state variable observation,Indicate the sight of new system state variable Measured value,Indicate that observer gain matrix, ε (t) indicate that observation and actual value obtain residual error,Indicate observation weight,Observation probability density function, Z (t) expression and failure are indicated with the vector of dimension, Z (t- τ) indicates the τ of vector Z (t) Value before moment, ε (t- τ) indicate the residual error before the τ moment, K1、K2Observation system parameter is indicated with W,Indicate fault observation value Derivative.
It is compensated in the step 400 using output weight of the fault message of estimation to system are as follows:Wherein, Vc (t) is compensated output weight.
The probability density function of desired molecular weight is expressed as γ (y, u (t))=C (y) Vg+T (y), Vg in the step 500 It is expected weight;It designs following switching function and control law realizes the molecular weight distribution tracking desired distribution after failure:
It is as follows to design switching function:
Wherein, H and K indicates the parameter of switching function, and S (t) indicates switching function,Table Show weight error vector;
The control law of system is adjusted after detecting that the system failure occurs are as follows:
Wherein, K3, M is the parameter for meeting system stable condition,For the derivative of fault observation value, α, which indicates to meet, to be stablized The parameter of condition;
Pass through the following linear matrix inequality of computer solving:
0 < (6+3 σ) K1 TK1≤I;
P2(A1+MK3)+(A1+MK3)TP2+Q2≤0;
It solves the fault diagnosis observer parameter of the condition of satisfaction and meets the control input condition of the given distribution of tracking Parameter realizes faults-tolerant control and tracks the purpose of desired molecular weight distribution;Wherein, R1,Q1,Q2,P1,P2It is symmetrical for suitable dimension positive definite Matrix, σ, γ1For small normal number, A1=DAD-1, I is one-dimensional unit matrix;∑ indicates 1 × 2 matrix.
Beneficial effect of the invention: designed fault diagnosis observer carries out event to non-Gaussian SDC systems sensor The faults-tolerant control scheme of barrier diagnosis, design can be compensated effectively after sensor fault occurs for system, export system Probability density function track desired output.It is available that the present invention can be used for the outputs such as chemical reaction, papermaking, ore grinding, boiler combustion The sensor fault diagnosis and faults-tolerant control of the random process of probability density function description, are related to being high temperature height mostly due to it The production environments such as pressure, toxic, the present invention can be that the reliability and safety in system operation provide safeguard, and be relevant enterprise The life security and property safety of personnel escorts.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with It obtains other drawings based on these drawings.
Fig. 1 is flow chart of the invention;
Fig. 2 is polymerization process molecular weight distribution closed-loop control schematic diagram.
Fig. 3 is failure and Fault Estimation figure of the invention;
Fig. 4 is present system desired output probability density function (PDF) figure;
Fig. 5 is present system without faults-tolerant control output probability density function (PDF) figure;
Fig. 6 is that present system has faults-tolerant control output probability density function (PDF) figure;
Fig. 7 is expectation probability density function and reality output probability density function two dimension when present system has faults-tolerant control Effect picture.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art are obtained every other under that premise of not paying creative labor Embodiment shall fall within the protection scope of the present invention.
As shown in Figure 1, a kind of chemical process middle-molecular-weihydroxyethyl distributed controll sensor fault diagnosis and fault-tolerant method, step It is rapid as follows:
Step 100: chemical reaction process molecular weight distribution is obtained by mass spectrometer or laser measurement technology online Probability density function approaches its probability density function with B-spline neural network.
Approximation theory is as follows, and probability density function is given by:
Wherein, φi(y) indicate that i-th of B-spline basic function, n indicate the number of B-spline basic function, y indicates the defeated of system Out, t indicates the time, and u (t) is control input, ωiIt (t) is the weight of i-th of B-spline basic function.Due to output probability density letter Number γ (y, u (t)) is equal to 1 in the integral of its interval of definition [a, b], it may be assumed that
ω1(t)φ1(y)+ω2(t)φ2(y)…+ωn(t)φn(y)=1 (2)
Its probability density function specifically is approached using following 3 linear B-spline basis function neural networks, i.e., in formula (2) N=3, linear B-spline basic function is expressed as follows:
Wherein,Due toLinear radial base FunctionWithWherein, parameter Then probability density function can also indicate are as follows:
γ (y, u (t))=C (y) V (t)+T (y) (4)
Wherein, V (t)=[ω1(t),ω1(t),ω3(t)]TTo export weight vector, a, b indicate probability density function Interval of definition.
Step 200: establishing the state-space model of system according to probability density function, obtained after scanning identification method transformation The parameter of state-space model, design learning fault diagnosis observer.
The state-space model of system is as follows:
A new state variable is introduced using the output weight of system
Wherein, x (t) is the state variable of original system, and u (t) is control input, and f (t) is fault vectors, and V (t) is weight Vector,Indicate the first derivative of state variable x (t), AsIt indicates and unit matrix of the state variable with dimension, xs(t) it indicates State variable related with output weight,Indicate state variable xs(t) first derivative, A, B, D and G are respectively parameter square Battle array.
Scan the transformed new state of identification methodSystem are as follows:
Wherein, the state variable of new system isParameter matrix is respectively
Design learning fault diagnosis observer is as follows:
Wherein,Indicate the first derivative of new system state variable observation,Indicate the sight of new system state variable Measured value,Indicate that observer gain matrix, ε (t) indicate that observation and actual value obtain residual error,Indicate observation weight,Observation probability density function, Z (t) expression and failure are indicated with the vector of dimension, Z (t- τ) indicates the τ of vector Z (t) Value before moment, ε (t- τ) indicate the residual error before the τ moment, K1、K2Observation system parameter is indicated with W,Indicate fault observation value Derivative.
Step 300: designed study fault diagnosis observer being realized into the algorithm on computers, concrete principle is logical It crosses original system input/output information and constructs an observation system, the state of the state approach original system of observation system, when faulty When generation, the difference of the output based on original system and observation system constructs residual error, estimates fault message using residual error.Pass through calculating The whether faulty generation of machine real-time monitoring sensing device learns fault diagnosis observer and estimates to be out of order in time when faulty generation Information.
Step 400: when system is faulty, the diagnostic observations device that breaks down accurately estimates fault message, as shown in figure 3, sharp It is compensated with output weight of the fault message of estimation to system:
Step 500: designed control signal input system is made into system output molecular weight distribution tracking desired distribution.Such as Shown in Fig. 4-7.
Vg is desired weight, and the probability density function of desired molecular weight is represented by γ (y, u (t))=C (y) Vg+T (y), It designs following switching function and control law realizes the molecular weight distribution tracking desired distribution after failure:
It is as follows to design switching function:
H and K indicates the parameter of switching function, and S (t) indicates switching function,Indicate power It is worth error vector.
The control of system input is adjusted to formula (10) after detecting that the system failure occurs, realize faults-tolerant control and with The purpose of track desired molecular weight distribution:
Wherein, K3For the parameter for meeting system stable condition,For fault observation value, α indicates the ginseng for meeting stable condition Number.
By computer solving linear matrix inequality (11), (12), (13) and (14), the failure for solving the condition of satisfaction is examined Disconnected observer parameter and the parameter for meeting the given control input condition being distributed of tracking are as follows:
0 < (6+3 σ) K1 TK1≤I (12)
P2(A1+MK3)+(A1+MK3)TP2+Q2≤0 (14)
Wherein, R1,Q1,Q2,P1,P2For suitable dimension positive definite symmetric matrices, σ, γ1For small normal number, A1=DAD-1, M=DB, I is one-dimensional unit matrix.The control for solving the fault diagnosis observer parameter of the condition of satisfaction and meeting the given distribution of tracking is defeated Enter the parameter of condition, realize faults-tolerant control and track the purpose of desired molecular weight distribution to get arriving:
K1=0.07, K2=-0.5, H=[0.4-0.1], K3=[12.1635 0.0389]
Modeling and control method of the invention is controlled applied to Bulk Polymerization of Styrene dynamic process molecular weight distribution shape. Polymerization process molecular weight distribution closed-loop control schematic diagram is as shown in Figure 2.
System model can indicate are as follows:
Wherein,It is the mean residence time of reactant;I0It is the initial concentration (molml of initiator-1);I is to draw Send out agent concentration (molml-1);M0It is the initial concentration (molml of monomer-1);M is the concentration (molml of monomer-1);Ki, Kp,KtrmIt is reaction rate constant;Kd,KI,KMIt is constant relevant to control input;Ri(i=1,2 ..., q) it is free radical.
Choose state variableThen system parameter matrix is expressed asWithK1,K2For the relevant parameter of failure.Through sweeping Retouch identification method can obtain state-space model parameter it is as follows:
Temperature sensor failure in such as reaction kettle, actual temperature is not inconsistent in measured temperature and kettle, it will shadow The injection rate of each reacted constituent or the dosage of heating oil are rung, the molecular weight distribution of product in kettle is then influenced.After failure occurs Designed observer can obtain rapidly the fault message, and feed back to control system.Control system will be switched in advance The control input type (10) of design carries out faults-tolerant control.By changing the injection rate of monomer or initiator, the dosage of heating oil, stirring Mixing rate etc. is suitble to the ratio of proper temperature in the chemical reaction kettle, reactant, it is expected reaction product molecular weight distribution Distribution.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.

Claims (5)

1. sensor fault diagnosis and fault tolerant control method in a kind of molecular weight distribution control, which is characterized in that its step are as follows:
Step 100: obtaining the distribution of chemical reaction process molecular weight online by mass spectrometer or laser measurement technology, obtain Output probability density function approaches output probability density function with B-spline neural network;
Step 200: the state-space model of system is established according to the output probability density function approached, through scanning identification method transformation The parameter of state-space model, design learning fault diagnosis observer are obtained afterwards;
Step 300: designed study fault diagnosis observer being realized on computers, whether real-time monitoring sensing device has event Barrier occurs, and when faulty generation, learns fault diagnosis observer and estimates fault message in time;
Step 400: when system is faulty, the diagnostic observations device that breaks down accurately estimates fault message, utilizes the failure letter of estimation Breath compensates the output weight of system;
Step 500: designed control signal input system is made to point of system output molecular weight distribution tracking desired molecular weight Cloth.
2. sensor fault diagnosis and fault tolerant control method in molecular weight distribution control according to claim 1, feature It is, output probability density function is to provide in the step 100:
Wherein, φi(y) indicate that i-th of B-spline basic function, n indicate the number of B-spline basic function, y indicates the output of system, t table Show the time, u (t) is control input, ωiIt (t) is the weight of i-th of B-spline basic function;
Since output probability density function γ (y, u (t)) is equal to 1 in the integral of its interval of definition [a, b], using B-spline nerve Network approaches its output probability density function with linear B-spline basis function neural network are as follows:
γ (y, u (t))=C (y) V (t)+T (y);
Wherein, linear radial basic functionWithParameterφ1(y),φ2(y),φ3(y) be system output y line Property B-spline basic function;V (t)=[ω1(t),ω1(t),…ω3(t)]TTo export weight vector, ωiIt (t) is i-th of B-spline The weight of basic function, i=1,2,3.
3. sensor fault diagnosis and fault tolerant control method in molecular weight distribution control according to claim 2, feature It is, establishes the state-space model of system in the step 200 according to the probability density function approached are as follows:
A new state variable is introduced using the output weight of systemThen the state of system is empty Between model become:
Wherein, x (t) is the state variable of original system, and u (t) is control input, and f (t) is fault vectors, and V (t) is weight vector,Indicate the first derivative of state variable x (t), AsIt indicates and unit matrix of the state variable with dimension, xs(t) indicate with it is defeated The related state variable of weight out,Indicate state variable xs(t) first derivative, A, B, D and G are respectively parameter matrix;
New stateThe state-space model of system are as follows:
Wherein, the state variable of new system isParameter matrix is respectivelyIpIndicate that P ties up unit matrix;
Design learning fault diagnosis observer is as follows:
Wherein,Indicate the first derivative of new system state variable observation,Indicate the observation of new system state variable Value,Indicate that observer gain matrix, ε (t) indicate that observation and actual value obtain residual error,Indicate observation weight,Observation probability density function, Z (t) expression and failure are indicated with the vector of dimension, Z (t- τ) indicates the τ of vector Z (t) Value before moment, ε (t- τ) indicate the residual error before the τ moment, K1、K2Observation system parameter is indicated with W,Indicate fault observation value Derivative.
4. sensor fault diagnosis and fault tolerant control method in molecular weight distribution control according to claim 3, feature It is, is compensated in the step 400 using output weight of the fault message of estimation to system are as follows:Wherein, Vc (t) is compensated output weight.
5. sensor fault diagnosis and fault tolerant control method in molecular weight distribution control according to claim 1, feature It is, the probability density function of desired molecular weight is expressed as γ (y, u (t))=C (y) Vg+T (y), Vg and is in the step 500 It is expected that weight;It designs following switching function and control law realizes the molecular weight distribution tracking desired distribution after failure:
It is as follows to design switching function:
Wherein, H and K indicates the parameter of switching function, and S (t) indicates switching function,Indicate power It is worth error vector;
The control law of system is adjusted after detecting that the system failure occurs are as follows:
Wherein, K3, M is the parameter for meeting system stable condition,For the derivative of fault observation value, α expression meets stable condition Parameter;
Pass through the following linear matrix inequality of computer solving:
0 < (6+3 σ) K1 TK1≤I;
P2(A1+MK3)+(A1+MK3)TP2+Q2≤0;
It solves the fault diagnosis observer parameter of the condition of satisfaction and meets the parameter of the control input condition of the given distribution of tracking, It realizes faults-tolerant control and tracks the purpose of desired molecular weight distribution;Wherein, R1,Q1,Q2,P1,P2Positive definite symmetric matrices is tieed up to be suitable, σ,γ1For small normal number, A1=DAD-1, I is one-dimensional unit matrix;∑ indicates 1 × 2 matrix.
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