CN110069016A - A kind of industrial process prediction linear quadratic advanced control method - Google Patents
A kind of industrial process prediction linear quadratic advanced control method Download PDFInfo
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Abstract
The invention discloses a kind of industrial process to predict linear quadratic advanced control method, includes the following steps: step 1, establishes system two dimension handoff procedure spatial model；Step 2, designing system course prediction Linear Quadratic Control device.The present invention proposes a kind of industrial process prediction linear quadratic advanced control method by means such as data acquisition, model foundation, prediction mechanism, optimizations, and this method can effectively improve the control performance of system.
Description
Technical field
The invention belongs to fields of automation technology, are related to a kind of industrial process prediction linear quadratic advanced control method.
Background technique
In actual industrial processes, advanced industrial production technology can fast and efficiently realize the big of product
Amount production.Due to the prolonged and repeated work of industrial equipment, therefore a possibility that industrial equipment breaks down, is increasing.Control system
Major failure include actuator failures, sensor fault and internal system failure, and system control is influenced maximum to be to hold
Row device failure.Actuator once breaks down, and system will be uncontrolled, and equipment damage, property loss are even caused when serious.For
Loss brought by device fails is avoided, while in order to reduce the potential risk of production equipment system, then proposing one
The method that actuator failures can be effectively treated in kind is particularly important.
Summary of the invention
The purpose of the invention is to preferably handle actuator failures problem in industrial control process, and propose one kind
Industrial process predicts linear quadratic advanced control method.This method according to having input delay model, introduces new variable first
Be converted to a kind of state-space model of no time lag；Secondly, introducing iterative learning control law, the state error of systematic procedure is defined
And output tracking error, establish system two dimension handoff procedure spatial model；Then, according to the Control performance standard letter of two-dimentional system
Number, the linear secondary controller of the prediction of designing system process.Finally, being said by taking ethane cracking furnace fire door temperature controlled processes as an example
The actuator failures problem of the industrial process can not only be effectively treated in bright this method, and to the stability and accuracy of system
All improve.
The step of the method for the present invention includes:
Step 1 establishes system two dimension handoff procedure spatial model, the specific steps are as follows:
1.1 initially set up the system state space model with input delay, and System describe is as follows:
Wherein, i=1,2, k, t are the time at current time, and k is batch, and d is the time lag of batch process, xi(t,k),yi
(t, k) is respectively the state variable and output variable in t moment k batch i stage, xi(t+1, k) is the t+1 moment k batch i stage
State variable, ui(t-d, k) is the input variable in t-d moment k batch i stage,Respectively indicate appropriate dimension
Coefficient matrix.
Model conversation in step 1.1 is obtained a kind of system state space model of no time lag by 1.2, there is following form:
Wherein,
T is the transposition symbol of matrix,With0For the null vector of appropriate dimension,When respectively t
Carve the system state space variable that time lag is free of with the t+1 moment k batch i stage, αiFor system actuators fault compression, ui(t,k)
For the input variable in t moment k batch i stage, ui(t-1,k)T, ui(t-2,k)T... ui(t-d,k)TRespectively indicate t-1, t-
2 ... the Input matrix variable transposition in t-d batch i stage at moment k.
1.3 introduce following iterative learning control law:
Wherein, ui(t, 0) is t moment i stage iterative initial value, is arranged to 0, ri(t, k) is the t moment k batch i stage
More new law, ui(t, k-1) is the input variable in t moment k-1 batch i stage, TiIt is the knot of each process and phase process section
Beam time point.
1.4 define state error and output tracking error in systematic procedure, as follows:
In conjunction with step 1.2 and step 1.3, further the state error of systematic procedure and output error can be rewritten are as follows:
Wherein,For the desired output setting value in t moment i stage, δ (xi(t, k)) it is t moment k batch i stage to be
System state error, xi(t, k-1) is the state variable in t moment k-1 batch i stage, ei(t, k), ei(t+1, k) is respectively t moment
With the output tracking error in t+1 batch i stage at moment k, ei(t+1, k-1) is the output tracking in t+1 moment k-1 batch i stage
Error,Respectively t moment and t+1 moment k batch i stage system are missed without the state of time lag
Difference.
1.5 according to step 1.4, and available system two dimension handoff procedure spatial model is as follows:
Wherein, IiIndicate the unit matrix of appropriate dimension,
Step 2, designing system course prediction Linear Quadratic Control device, the specific steps are as follows:
2.1 determine the Control performance standard function of two-dimentional system, and form is as follows:
Wherein, min is minimum value meaning, ΩiFor performance index function, QiFor the weighting matrix of process status, RiFor process
The weighted input matrix of state,Function f is respectively indicated from j=1 respectively to j=P and to j=M natural number
Between in the state of functional value cumulative, zi(t+j | t, k) it is respectively that k batch i stage t moment cuts t+j moment systematic procedure
Change the prediction of sytem matrix, ri(t+j-1 | t, k) it is respectively k batch i stage t moment to t+j-1 moment systematic procedure more new law
The prediction of matrix.
2.2 can be as follows in the hope of the more new law of system according to step 2.1:
Wherein, KiIndicate more new law coefficient matrix, riFor i stage more new law, ΨiIndicate the appropriate dimension of i stage system process
Matrix number, EiIndicate the unit matrix of appropriate dimension,It respectively indicates updated process status weighting matrix and input adds
Weight matrix,Indicate k batch i stage t moment to t+1 moment state error and t+P moment Output error systems
The prediction of process switching system matrix.
2.3 according to step 1.3 and step 2.2, available linear quadratic Predictive control law, and form is as follows:
2.4 arrive step 2.3 according to step 2.1, and it is first based on a kind of industrial process prediction linear quadratic to take turns doing circulation solution
Into the control amount u of controli(t, k), then acted on controlled device.
It is pre- to propose a kind of industrial process by means such as data acquisition, model foundation, prediction mechanism, optimizations by the present invention
Linear secondary advanced control method, this method can effectively improve the control performance of system.
Specific embodiment
The present invention is described further below.
It is illustrated with ethane cracking furnace fire door temperature controlled processes in real process:
Wherein, Ethylene Cracking Furnace Tubes outlet temperature is the controlled device of ethane cracking furnace, and with In Cracking Feedstock mouth
Flow adjusts the control amount as ethane cracking furnace fire door temperature controlled processes.Pass through the adjusting control to pyrolysis furnace feed inlet flow
System, to realize effective control to ethane cracking furnace fire door temperature.
Step 1 establishes two dimension switching ethane cracking furnace fire door temperature controlled processes spatial model, the specific steps are as follows:
1.1 initially set up the ethane cracking furnace fire door temperature controlled processes state-space model with time lag, System describe
It is as follows:
Wherein, i=1,2, k, t are the time at current time, and k is the batch of ethane cracking furnace fire door temperature controlled processes, d
It is the time lag of ethane cracking furnace fire door temperature controlled processes, xi(t,k),yi(t, k) is respectively the ethylene in t moment k batch i stage
Pyrolysis furnace fire door temperature controlled processes state variable and temperature variable, xi(t+1, k) is that the ethylene in t+1 moment k batch i stage is split
Solve furnace fire door temperature controlled processes state variable, ui(t-d, k) is the ethane cracking furnace feed inlet in t-d moment k batch i stage
Flow adjusts control amount,Respectively indicate the coefficient matrix of appropriate dimension.
Model conversation in step 1.1 is obtained a kind of ethane cracking furnace fire door temperature controlled processes shape of no time lag by 1.2
State space model has following form:
Wherein,
T is the transposition symbol of matrix,With0For the null vector of appropriate dimension,When respectively t
Carve the ethane cracking furnace fire door temperature controlled processes state space variable that time lag is free of with the t+1 moment k batch i stage, αiFor second
The alkene pyrolysis furnace fire door temperature controlled processes actuator failures factor, ui(t, k) be the t moment k batch i stage ethane cracking furnace into
The flow of material mouth adjusts control amount, ui(t-1,k)T, ui(t-2,k)T... ui(t-d,k)TT-1, t-2 are respectively indicated ... t-d
The flow of the matrix ethane cracking furnace feed inlet in batch i stage at moment k adjusts control amount transposition.
1.3 introduce following ethane cracking furnace fire door temperature controlled processes iterative learning control law:
Wherein, ui(t, 0) is that the flow of t moment i stage ethylene pyrolysis furnace fire door temperature controlled processes feed inlet adjusts control
Initial value processed, is arranged to 0, ri(t, k) is the ethane cracking furnace fire door temperature controlled processes more new law in t moment k batch i stage, ui
(t, k-1) is that the flow of the ethane cracking furnace feed inlet in t moment k-1 batch i stage adjusts control amount, TiIt is that each ethylene is split
Solve the end time point of furnace fire door temperature controlled processes and phase process section.
1.4 define ethane cracking furnace fire door temperature controlled processes state error and output temperature tracking error, as follows:
In conjunction with step 1.2 and step 1.3, can further by ethane cracking furnace fire door temperature controlled processes state error and
Output temperature tracking error is rewritten are as follows:
Wherein,For the ethane cracking furnace fire door temperature controlled processes desired output desired temperature in t moment i stage,
δ(xi(t, k)) be the t moment k batch i stage ethane cracking furnace fire door temperature controlled processes state error, xiWhen (t, k-1) is t
Carve the ethane cracking furnace fire door temperature controlled processes state variable in k-1 batch i stage, ei(t, k), eiWhen (t+1, k) is respectively t
Carve the ethane cracking furnace fire door temperature controlled processes output temperature tracking error with the t+1 moment k batch i stage, ei(t+1,k-1)
For the ethane cracking furnace fire door temperature controlled processes output temperature tracking error in t+1 batch i stage at moment k-1,The respectively ethane cracking furnace furnace of t moment and t+1 moment k batch i stage system without time lag
Mouth temperature controlled processes state error.
1.5 switch the spatial model of ethane cracking furnace fire door temperature controlled processes according to step 1.4, available two dimension,
It is as follows:
Wherein, IiIndicate the unit matrix of appropriate dimension,
Step 2, the flow adjusting controller for designing ethane cracking furnace feed inlet, the specific steps are as follows:
2.1 determine the Control performance standard function of two-dimentional ethane cracking furnace fire door temperature controlled processes, and form is as follows:
Wherein, min is minimum value meaning, ΩiFor ethane cracking furnace fire door temperature controlled processes performance index function, QiFor
The weighting matrix of ethane cracking furnace fire door temperature controlled processes state, RiControl amount is adjusted for the flow of ethane cracking furnace feed inlet
Weighting matrix,Function f is respectively indicated from j=1 respectively to j=P and to the state j=M natural number
Cumulative, the z of minor function valuei(t+j | t, k) it is that k batch i stage t moment controlled t+j moment ethane cracking furnace fire door temperature
The prediction of journey switching system matrix, ri(t+j-1 | t, k) it is k batch i stage t moment to t+j-1 moment ethane cracking furnace fire door
The prediction of temperature controlled processes more new law matrix.
2.2 can be as follows in the hope of the more new law of ethane cracking furnace fire door temperature controlled processes according to step 2.1:
Wherein, KiIndicate ethane cracking furnace fire door temperature controlled processes more new law coefficient matrix, riFor the cracking of i stage ethylene
Furnace fire door temperature controlled processes more new law, ΨiIndicate the appropriate dimension square of i stage ethylene pyrolysis furnace fire door temperature controlled processes
Battle array, EiIndicate the unit matrix of appropriate dimension,Respectively indicate updated ethane cracking furnace fire door temperature controlled processes shape
The flow of state weighting matrix and In Cracking Feedstock mouth adjusts control amount weighting matrix,Indicate k batch i stage t
Moment is to t+1 moment state error and t+P moment output temperature error ethane cracking furnace fire door temperature controlled processes switching system
The prediction of matrix.
The 2.3 pre- observing and controlling of linear quadratic adjusted according to step 1.3 and step 2.2, available In Cracking Feedstock mouth flow
System rule, form are as follows:
2.4 arrive step 2.3 according to step 2.1, take turns doing circulation and solve the prediction of ethane cracking furnace fire door temperature controlled processes
The ethane cracking furnace feed inlet flow of linear quadratic Dynamic matrix control adjusts control amount ui(t, k), then acted on cracking of ethylene
Furnace fire door controlled target temperature.
Claims (3)
1. a kind of industrial process predicts linear quadratic advanced control method, include the following steps:
Step 1 establishes system two dimension handoff procedure spatial model；
Step 2, designing system course prediction Linear Quadratic Control device.
2. industrial process as described in claim 1 predicts linear quadratic advanced control method, it is characterised in that:
The step 1 is specific as follows:
1.1 establish the system state space model with input delay, and System describe is as follows:
Wherein, i=1,2 ... k, t are the time at current time, and k is batch, and d is the time lag of batch process, xi(t,k),yi(t,
K) be respectively the t moment k batch i stage state variable and output variable, xi(t+1, k) is the shape in t+1 moment k batch i stage
State variable, ui(t-d, k) is the input variable in t-d moment k batch i stage,Respectively indicate appropriate dimension is
Matrix number；
Model conversation in step 1.1 is obtained a kind of system state space model of no time lag by 1.2, there is following form:
Wherein,
T is the transposition symbol of matrix,With0For the null vector of appropriate dimension,Respectively t moment and
The t+1 batch i stage at moment k is free of the system state space variable of time lag, αiFor system actuators fault compression, ui(t, k) is t
The input variable in batch i stage at moment k, ui(t-1,k)T, ui(t-2,k)T... ui(t-d,k)TT-1, t-2 are respectively indicated,
... the Input matrix variable transposition in t-d batch i stage at moment k；
1.3 introduce following iterative learning control law:
Wherein, ui(t, 0) is t moment i stage iterative initial value, is arranged to 0, ri(t, k) is the update in t moment k batch i stage
Rule, ui(t, k-1) is the input variable in t moment k-1 batch i stage, TiAt the end of being each process and phase process section
Between point；
1.4 define state error and output tracking error in systematic procedure, as follows:
In conjunction with step 1.2 and step 1.3, further the state error of systematic procedure and output error can be rewritten are as follows:
Wherein,For the desired output setting value in t moment i stage, δ (xi(t, k)) be the t moment k batch i stage system shape
State error, xi(t, k-1) is the state variable in t moment k-1 batch i stage, ei(t, k), ei(t+1, k) is respectively t moment and t+
The output tracking error in 1 batch i stage at moment k, ei(t+1, k-1) is the output tracking error in t+1 moment k-1 batch i stage,The respectively state error of t moment and t+1 moment k batch i stage system without time lag；
1.5 according to step 1.4, and available system two dimension handoff procedure spatial model is as follows:
Wherein, IiIndicate the unit matrix of appropriate dimension,
3. industrial process as claimed in claim 2 predicts linear quadratic advanced control method, it is characterised in that:
The step 2 is specific as follows:
2.1 determine the Control performance standard function of two-dimentional system, and form is as follows:
Wherein, min is minimum value meaning, ΩiFor performance index function, QiFor the weighting matrix of process status, RiFor process status
Weighted input matrix,Function f is respectively indicated from j=1 respectively to j=P and to j=M natural number
In the state of functional value cumulative, zi(t+j | t, k) it is respectively that k batch i stage t moment switches system to t+j moment systematic procedure
The prediction of system matrix, ri(t+j-1 | t, k) it is respectively k batch i stage t moment to t+j-1 moment systematic procedure more new law matrix
Prediction；
2.2 can be as follows in the hope of the more new law of system according to step 2.1:
Wherein, KiIndicate more new law coefficient matrix, riFor i stage more new law, ΨiIndicate the appropriate dimension square of i stage system process
Battle array, EiIndicate the unit matrix of appropriate dimension,Respectively indicate updated process status weighting matrix and weighted input square
Battle array,Indicate k batch i stage t moment to t+1 moment state error and t+P moment Output error systems process
The prediction of switching system matrix；
2.3 according to step 1.3 and step 2.2, available linear quadratic Predictive control law, and form is as follows:
2.4 arrive step 2.3 according to step 2.1, take turns doing circulation and solve based on a kind of prediction advanced control of linear quadratic of industrial process
The control amount u of systemi(t, k), then acted on controlled device.
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| CN109212971A (en) * | 2018-10-11 | 2019-01-15 | 海南师范大学 | Multistage batch process 2D linear quadratic tracks fault tolerant control method |
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| CN109212971A (en) * | 2018-10-11 | 2019-01-15 | 海南师范大学 | Multistage batch process 2D linear quadratic tracks fault tolerant control method |
Non-Patent Citations (3)
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| LIMIN WANG，WEIPING LUO: "Linear Quadratic Predictive Fault-Tolerant Control for Multi-Phase Batch Processes", 《IEEE ACCESS》 * |
| WEIPING LUO，LIMIN WANG，RIDONG ZHANG，FURONG GAO: "2D Switched Model-Based Infinite Horizon LQ Fault-Tolerant Tracking Control for Batch Process", 《INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH》 * |
| 王立敏，卢丽彬，高福荣，周东华: "多阶段间歇过程无穷时域优化线性二次容错控制", 《化工学报》 * |
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