CN108803338A - A kind of chemical industry multistage batch process iterative learning control method - Google Patents
A kind of chemical industry multistage batch process iterative learning control method Download PDFInfo
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Abstract
The invention discloses a kind of chemical industry multistage batch process iterative learning control methods.The present invention initially sets up the switching system model of multistage batch process, it is then based on switching system model, further design the iterative learning controller of multistage batch process, obtain the maximum mean residence time of the minimum average B configuration residence time for stablizing subsystem and unstable stator system, finally according to the maximum mean residence time of unstable stator system, switch step is pushed ahead, asynchronised handover is eliminated and avoids the unstable of subsystem.Different from traditional control method, the present invention analyzes the subsystem stability of multistage batch process by selecting Piecewise Quadratic Functions.
Description
Technical field
The invention belongs to automatic industrial process control fields, are related to a kind of chemical industry multistage batch process iterative learning
Control.
Background technology
During modern industry controls, batch process is using very universal, iterative learning control also extensive use
In batch process, but single iterative learning control cannot be guaranteed the stability of system and good control accuracy.To protect
The product quality of batch process production is demonstrate,proved, enhances control accuracy and stability in batch process, avoids the asynchronised handover of system,
A kind of good control method is designed, is a problem to be solved.Traditional method is only applicable to the batch process of single phase, no
Suitable for multistage batch process.In view of this problem, it is proposed that a kind of multistage batch process iterative learning control method leads to
The problem of crossing this method, asynchronised handover can be eliminated, and the unstable of system is avoided, it ensure that the high-precision of batch process
Degree control.
Invention content
The purpose of the present invention is eliminating the asynchronised handover in controller and multistage batch process between active subsystem, and
And avoid the unstable of subsystem.
The present invention initially sets up the switching system model of multistage batch process, is then based on switching system model, into one
Step designs the iterative learning controller of multistage batch process, obtains the minimum average B configuration residence time for stablizing subsystem and shakiness
The maximum mean residence time of stator system, finally according to the maximum mean residence time of unstable stator system, by switch step
It pushes ahead, eliminate asynchronised handover and avoids the unstable of subsystem.
The present invention method and step include：
Step 1, the system model for establishing multistage batch process, comprise the concrete steps that：
1-1. establishing batch process System State Model, form is as follows：
Wherein, t and k is the time of running and operation batch respectively, and x (t, k), x (t+1, k) are t moment, t+1 moment respectively
The system mode of kth batch, u (t, k) are the system inputs of t moment kth batch, and y (t, k) is that the system of t moment kth batch is defeated
Go out, σ (t, k) is the switching signal of t moment kth batch, wσ(t,k)(t, k) is the external disturbance of t moment kth batch, Aσ(t,k)、
Bσ(t,k)、Cσ(t,k)It is the sytem matrix of appropriate dimension.
1-2. can be expressed as in the System State Model of i stage batch process：
Wherein, xi(t,k)、xi(t+1, k) is t moment, the system mode in t+1 moment kth batch i stages, u respectivelyi(t,
K) be the t moment kth batch i stages system input, yi(t, k) is the system output in t moment kth batch i stages, Ai、Bi、Ci
It is the sytem matrix of i stages appropriate dimension.
1-3. establishes multistage batch process system mode switching model, is divided into two kinds of situations, form according to system dimensions
It is as follows：
(1) system dimensions are identical：
Wherein,It is the switching time in kth batch i stages,It is respectivelyMoment kth batch
The system mode in secondary i stages, i+1 stages.
(2) system dimensions are different：
Wherein, JiIt is the systematic state transfer matrix in i stages.
1-4. sets switching time, and form is as follows：
Wherein,It is the switching time in kth batch i-1 stages, min is to be minimized,It is the kth batch starting stage
Switching time, Gi(x (t, k)) is switching condition associated with system mode under the t moment kth batch i stages.
1-5. switching sequence models are as follows：
Wherein, Σ indicates switching sequence,It is kth0The starting point of 1 stage of batch switching,It is kth0The tie point that 1 stage of batch switches to 2 stages,It is kth0
The tie point that the batch p-1 stages switch to the p stages,It is kth0The end point that the batch p stages switch is also
With kth1The tie point of batch；It is kth1The starting point of 1 stage of batch switching；It is kthkThe tie point that the batch stage p-1 stages switch to the p stages；
It is kthkThe end point of batch stage p switchings is also the tie point with next batch.
Step 2 is based on switching system model, designs new iterative learning controller, comprises the concrete steps that：
2-1. design iteration controlled quentity controlled variables：
ui(t, k)=ui(t,k-1)+ri(t,k)
ui(t, 0)=0
Wherein, ui(t, 0) is the initial value of t moment iteration control amount, ri(t, k) is the iteration update of t moment kth batch
Rule, ui(t, k) is the iteration control amount in t moment kth batch i stages, ui(t, k-1) is changing for -1 batch i stages of t moment kth
For controlled quentity controlled variable.
2-2. output error is defined as follows with state error：
Wherein,It is the reference value exported in the i stages, e (t, k) is the output error of t moment kth batch,It is t
The state error in kth batch i stages at moment.
2-3. combination steps 1-4, step 2-1, step 2-2 are obtained：
The error of integrated system, form are as follows：
Wherein,It is the state error in t+1 moment kth batch i stages, ei(t+1, k) is t moment kth batch
The output error in secondary i stages, ei(t+1, k-1) is the output error in -1 batch i stages of t+1 moment kth,It is t moment
The output error that kth batch i stage augmentation forms indicate.
2-4. combination step 2-3 obtain the augmentation switching model of multistage batch process iterative learning control, as follows：
Wherein,It is the output error that+1 batch i stage augmentation forms of t moment kth indicate,IiIt is the unit matrix of appropriate dimension.
The system mode transition form of 2-5. switching models is as follows：
Wherein, Ci+1It is constant matrices known to the i+1 stages,It is the output reference value in i+1 stages,
It isThe state error in kth batch i+1 stages at moment,It isMoment kth batch i+1 stage augmentation form it is defeated
Go out error,It isThe state error in kth batch i stages at moment,It is the reference value exported in the i+1 stages,It isThe system mode in -1 batch i stages of moment kth, I, EiIt is the unit matrix of appropriate dimension respectively,
2-6. iteration update rule is designed to：
Wherein, KiIt is known gain matrix.
2-7. repeats step 2-1 to step 2-6, obtains iteration control amount u in subsequent timei(t, k), then acted on
In controlled device, recycle successively.
Beneficial effects of the present invention：Different from traditional control method, the present invention is divided by selecting Piecewise Quadratic Functions
Analyse the subsystem stability of multistage batch process.The technical scheme is that passing through model foundation, controller design, algorithm
The means such as design, it is proposed that it is existing can to eliminate nonsynchronous controller switching for a kind of multistage batch process iterative learning control program
As reducing the run time of entire batch, avoiding the unstable of subsystem.
Specific implementation mode
By taking injection molding process as an example：
Here it is described by taking nozzle exit pressure control in injection molding process as an example, regulating measure is to control the valve of proportioning valve
Door aperture.
Step 1, the system model for establishing injection molding multistage batch process, comprise the concrete steps that：
1-1. establishes injection molding batch process System State Model, and form is as follows：
Wherein, t and k is the time of running and the operation batch of injection molding respectively, when x (t, k), x (t+1, k) are t respectively
It carves, the system mode of t+1 moment kth batch injection moldings, u (t, k) is the valve opening of t moment kth batch injection molding, y
(t, k) is the nozzle exit pressure of t moment kth batch injection molding, and σ (t, k) is the switching signal of t moment kth batch injection molding,
wσ(t,k)(t, k) is the external disturbance of t moment kth batch injection molding, Aσ(t,k)、Bσ(t,k)、Cσ(t,k)It is the system of appropriate dimension
Matrix.
1-2. injection moldings can be expressed as in the System State Model of i stage batch process：
Wherein, xi(t,k)、xi(t+1, k) be respectively t moment, t+1 moment kth batch i stage injection moldings system shape
State is the system mode of t+1 moment kth batch i stage injection moldings, ui(t, k) is t moment kth batch i stage injection moldings
Valve opening, yi(t, k) is the nozzle exit pressure of t moment kth batch i stage injection moldings, Ai、Bi、CiIt is suitably to tie up in the i stages
The sytem matrix of degree.
1-3. establishes the system mode switching model of injection molding process, and form is as follows：
Wherein,It is the switching time in kth batch i stages,It is respectivelyMoment kth batch
The system mode in i stages, i+1 stages, JiIt is the state-transition matrix of injection stage and the switching of packaging holding stage.
The switching time of 1-4. injection molding processes, form are as follows：
Wherein,It is the switching time of kth batch injection molding process, min is to be minimized,It is the injection molding of kth batch
Molding initial time, Gi(x (t, k)) is switching associated with injection molding system state under the t moment kth batch i stages
Condition.
The switching sequence model of 1-5. injection molding processes is as follows：
Wherein, Σ indicates switching sequence,It is kth0The starting point of 1 stage of batch switching,It is kth0The tie point that 1 stage of batch switches to 2 stages,It is kth0
The tie point that the batch p-1 stages switch to the p stages,It is kth0The end point that the batch p stages switch is also
With kth1The tie point of batch；It is kth1The starting point of 1 stage of batch switching；It is kthkThe tie point that the batch stage p-1 stages switch to the p stages；
It is kthkThe end point of batch stage p switchings is also the tie point with next batch.
Step 2 is based on switching system model, and the new iterative learning controller of design injection molding process comprises the concrete steps that：
2-1. designs the valve opening of injection molding process proportioning valve first：
ui(t, k)=ui(t,k-1)+ri(t,k)
ui(t, 0)=0
Wherein, ui(t, 0) is the initial value of the valve opening of proportioning valve, ri(t, k) is the iteration update of t moment kth batch
Rule, ui(t, k) is the valve opening of t moment kth batch i stage proportioning valves, ui(t, k-1) is -1 batch i stages of t moment kth
The valve opening of proportioning valve.
The output error of 2-2. injection molding processes is defined as follows with state error：
Wherein,It is the reference value of i stage delivery nozzle pressure, e (t, k) is the output error of kth batch injection molding；It is the state error of t moment kth batch i stage injection moldings.
2-3. combination steps 1-4, step 2-1, step 2-2 are obtained
The augmented error of injection molding is defined, form is as follows：
Wherein,It is the state error of t+1 moment kth batch i stage injection moldings, eiWhen (t+1, k) is t
Carve the output error of kth batch i stage injection moldings, ei(t+1, k-1) is -1 batch i stage injection moldings of t+1 moment kth
Output error,It is the output error that t moment kth batch i stage injection molding augmentation forms indicate.
2-4. combination step 2-3 obtain the enhancing switching model of injection molding multistage batch process iterative learning control,
It is as follows：
Wherein,It is the output error that+1 batch i stage injection molding augmentation forms of t moment kth indicate,IiIt is the unit matrix of appropriate dimension.
2-5. the system mode transition form of injection molding switching model is as follows：
Wherein, Ci+1It is constant matrices known to injection molding,It is the output reference value of i+1 stage injection moldings,It isThe state error of kth batch i+1 moment, injection molding stage,It isMoment kth batch i+1
The output error that stage injection molding augmentation form indicates,It isThe state of kth batch i moment, injection molding stage
Error,It isThe system mode of -1 batch i stage injection moldings of moment kth, I, EiIt is appropriate dimension respectively
Unit matrix,
2-6. the iteration update rule of injection molding is designed to：
Wherein, KiIt is known gain matrix.
2-7. repeats step 2-1 to step 2-6, obtains the valve opening u of proportioning valve in subsequent timei(t, k), then will
It acts on injection molding process, recycles successively.
Claims (1)
1. a kind of chemical industry multistage batch process iterative learning control method, it is characterised in that this method is specifically：
Step 1, the system model for establishing multistage batch process, comprise the concrete steps that：
1-1. establishes batch process System State Model, and form is as follows：
Wherein, t and k is the time of running and operation batch respectively, and x (t, k), x (t+1, k) are t moment, t+1 moment kth batch respectively
Secondary system mode, u (t, k) are the system inputs of t moment kth batch, and y (t, k) is the system output of t moment kth batch, σ
(t, k) is the switching signal of t moment kth batch, wσ(t,k)(t, k) is the external disturbance of t moment kth batch, Aσ(t,k)、Bσ(t,k)、
Cσ(t,k)It is the sytem matrix of appropriate dimension；
1-2. is expressed as in the System State Model of i stage batch process：
Wherein, xi(t,k)、xi(t+1, k) is t moment, the system mode in t+1 moment kth batch i stages, u respectivelyi(t, k) is t
The system in kth batch i stages at moment inputs, yi(t, k) is the system output in t moment kth batch i stages, Ai、Bi、CiIt is i ranks
The sytem matrix of the appropriate dimension of section；
1-3. establishes multistage batch process system mode switching model, is divided into two kinds of situations according to system dimensions, form is as follows：
(1) system dimensions are identical：
Wherein,It is the switching time in kth batch i stages,It is respectivelyMoment kth batch i ranks
Section, the system mode in i+1 stages；
(2) system dimensions are different：
Wherein, JiIt is the systematic state transfer matrix in i stages；
1-4. sets switching time, and form is as follows：
Wherein,It is the switching time in kth batch i-1 stages, min is to be minimized,It is cutting for kth batch starting stage
It changes the time, Gi(x (t, k)) is switching condition associated with system mode under the t moment kth batch i stages；
1-5. switching sequence models are as follows：
Wherein, Σ indicates switching sequence,It is kth0The starting point of 1 stage of batch switching,It is kth0The tie point that 1 stage of batch switches to 2 stages,It is kth0
The tie point that the batch p-1 stages switch to the p stages,It is kth0The end point that the batch p stages switch
It is and kth1The tie point of batch；It is kth1The starting point of 1 stage of batch switching；It is kthkThe tie point that the batch stage p-1 stages switch to the p stages；
It is kthkThe end point of batch stage p switchings is also the tie point with next batch；
Step 2 is based on switching system model, designs new iterative learning controller, comprises the concrete steps that：
2-1. design iteration controlled quentity controlled variables：
ui(t, k)=ui(t,k-1)+ri(t,k)
ui(t, 0)=0
Wherein, ui(t, 0) is the initial value of t moment iteration control amount, ri(t, k) is the iteration update rule of t moment kth batch,
ui(t, k) is the iteration control amount in t moment kth batch i stages, ui(t, k-1) is the iteration control in -1 batch i stages of t moment kth
Amount processed；
2-2. defines output error and state error：
Wherein,It is the reference value exported in the i stages, e (t, k) is the output error of t moment kth batch,It is t moment
The state error in kth batch i stages；
2-3. combination steps 1-4, step 2-1, step 2-2 are obtained：
The error of integrated system, form are as follows：
Wherein,It is the state error in t+1 moment kth batch i stages, ei(t+1, k) is t moment kth batch i ranks
The output error of section, ei(t+1, k-1) is the output error in -1 batch i stages of t+1 moment kth,It is t moment kth batch
The output error that secondary i stages augmentation form indicates；
2-4. combination step 2-3 obtain the augmentation switching model of multistage batch process iterative learning control, as follows：
Wherein,It is the output error that+1 batch i stage augmentation forms of t moment kth indicate,IiIt is the unit matrix of appropriate dimension；
The system mode transition form of 2-5. switching models is as follows：
Wherein, Ci+1It is constant matrices known to the i+1 stages,It is the output reference value in i+1 stages,It is
The state error in kth batch i+1 stages at moment,It isThe output of moment kth batch i+1 stage augmentation form misses
Difference,It isThe state error in kth batch i stages at moment,It is- 1 batch i stages of moment kth
System mode, I, EiIt is the unit matrix of appropriate dimension respectively,
The update of 2-6. iteration is designed as：
Wherein, KiIt is known gain matrix；
2-7. repeats step 2-1 to step 2-6, obtains iteration control amount u in subsequent timei(t, k), then acted on controlled
Object recycles successively.
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