CN110045617A - A kind of industrial process constrained forecast advanced control method - Google Patents
A kind of industrial process constrained forecast advanced control method Download PDFInfo
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- CN110045617A CN110045617A CN201910431825.1A CN201910431825A CN110045617A CN 110045617 A CN110045617 A CN 110045617A CN 201910431825 A CN201910431825 A CN 201910431825A CN 110045617 A CN110045617 A CN 110045617A
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
Abstract
The invention discloses a kind of industrial process constrained forecast advanced control methods, include the following steps: step 1, establish industrial process single-input single-output model；Step 2, design industrial process control.The present invention devises infant industry process constraints prediction advanced control method by means such as model foundation, controller design, algorithm designs.With comprehensive considering various effects and the control performance of system can be improved using this method.
Description
Technical field
The invention belongs to automatic industrial process control fields, are related to a kind of industrial process constrained forecast Dynamic matrix control side
Method.
Background technique
With the development of industry, chemical process is to manufacture high-value product and be widely used in every field.But due to mould
Type and equipment mismatch will lead to actuator failure.If cannot use restraint to model, it is difficult to control accurately industry
Process, it is difficult to timely and effectively solve these problems.It not only will lead to production process reduced performance, also will cause serious property
Loss, or even threaten the life security of producers.From the angle of safety and production performance, a kind of industrial mistake is studied
Journey constrained forecast advanced control method is necessary.
Summary of the invention
Object of the present invention is to when actuator breaks down in industrial process, propose a kind of novel advanced control of constrained forecast
Method processed.This method initially sets up the model of industrial process, is extended to incremental form after introducing state error and output error
State-space model.And objective function and constraint condition are introduced, optimal more new law and control amount are obtained and acts on controller.No
It is same as traditional control strategy, Novel Control proposed by the invention considers actuator failure, objective function
And the connection between constraint condition three.By increasing constraint condition energy preferably Matching Model and equipment to manufacturing forecast,
Reach better control performance.
Method and step of the invention includes:
Step 1 establishes industrial process single-input single-output model, comprises the concrete steps that:
It is as follows that 1-1. establishes single-input single-output model:
X (k+1)=A (k) x (k)+B (k) u (k)
Y (k+1)=Cx (k+1)
Wherein k indicates sampling instant；X (k), x (k+1) respectively indicate the state at system kth moment ,+1 moment of kth；y(k+
1) output at+1 moment of system kth is indicated；U (k) indicates the control input of system kth moment；A (k), B (k) respectively indicate system
The corresponding parameter matrix of two of k moment；C is the sytem matrix with appropriate dimension.
Control amount input form of the 1-2. when partial fault occurs in actuator is as follows:
uF(k)=α u (k)
Wherein 0≤α≤1 indicates actuator failures degree；uFIt (k) is that the kth moment, there are control amount inputs when failure.
1-3. obtains new model by step 1-1 and step 1-2:
X (k+1)=A (k) x (k)+B (k) uF(k)
Y (k+1)=Cx (k+1)
It is as follows that step 1-3 is extended to incremental form by 1-4.:
xm(k+1)=Am(k)xm(k)+Bm(k)uF(k)
ym(k+1)=Cmxm(k+1)
WhereinCm=[0,1],
xm(k)=[Δ x (k) y (k)]；Am(k)、Bm(k) the incremental form parameter matrix at system kth moment is respectively indicated,
CmIndicate the incremental form sytem matrix with appropriate dimension；xm(k)、xm(k+1) when respectively indicating system kth moment, kth+1
The incremental form state at quarter；ym(k+1) the incremental form output at+1 moment of system kth is indicated, Δ x (k) indicates the shape at kth moment
State increment；The output at y (k) expression kth moment.
It is as follows that 1-5. introducing objective function comes track reference track:
Wherein J∞(k) objective function is indicated；Expression belongs in A (k+i) or B (k+i)
J under the conditions of certain dimension matrix Ω and Δ u (k+i | k) maximum value∞(k) minimum value；T indicates transposition symbol；I indicates a certain
It anticipates the period,Indicate cumulative from 0 period to infinite time section；Y (k+i | k), Δ u (k+i | k) indicate to inscribe when kth
The reality output at kth+i moment and actually enter increment；yr(k+i) the prediction output at kth+i moment is indicated；Q indicate output with
The weight matrix of track error；R indicates the weight matrix of control input increment.
It is as follows that objective function is extended to incremental form by 1-6.:
Wherein xm(k+i | k) indicate the virtual condition increment that the kth+i moment is inscribed when kth；xr(k+i) kth+i moment is indicated
Predicted state increment；Indicate the weight matrix of status tracking error.
Step 2, design industrial process control, comprise the concrete steps that:
2-1. defines tracking error:
E (k)=y (k)-yr(k)
Wherein e (k) indicates the output error at kth moment, y (k), yr(k) reality output at kth moment and pre- is respectively indicated
Survey output.
2-2. changes the formula of step 2-1 for prediction form:
E (k+1)=e (k)+CA (k) Δ x (k)+CB (k) Δ u (k)
Wherein e (k+1) indicates the output error at+1 moment of kth；Δ x (k) indicates the state increment at kth moment, Δ u (k)
Indicate the input increment at kth moment.
2-3. is according to the available delta state spatial model of step 2-2:
Z (k+1)=Az(k)z(k)+Bz(k)Δu(k)
Δ y (k+1)=Czz(k+1)
WhereinCz=[C 0]；Az(k)、Bz(k) it respectively indicates
The corresponding parameter matrix of two of the kth moment of delta state spatial model；CzIt is state-space model with appropriate dimension
Sytem matrix；The incremental form state of etching system when z (k), z (k+1) are kth moment, kth+1；When Δ y (k+1) indicates kth+1
The output increment at quarter.
2-4. combination step 1-6 and 2-3 propose objective function track reference value:
Wherein z (k+1 | k) indicates the prediction extended mode that+1 moment of kth is inscribed when kth.
2-5. introduces constraint condition:
Wherein | Δ u (k+i | k) |, | Δ y (k+i | k) inscribes the kth+i moment and inputs increment absolute value when respectively indicating kth
With output increment absolute value；Δumax、ΔymaxRespectively indicate the maximum upper limit output and input.
It is as follows that 2-6. by step 2-3, step 2-4 and step 2-5 can obtain more new law Δ u (k+i | k):
Δ u (k+i | k)=F (k) z (k+i | k)
Wherein F (k)=YS-1It is the gain factor matrix at kth moment；Y,S-1Be two is according to objective function value
Matrix number.
The available industrial process optimal control law Δ u of 2-7. combination step 2-1 to step 2-6 (k+i | k) and act on
Controlled device.
It is pre- to devise infant industry process constraints by means such as model foundation, controller design, algorithm designs by the present invention
Survey advanced control method.With comprehensive considering various effects and the control performance of system can be improved using this method.
Specific embodiment
The invention will be further described below.
By taking high pressure polyethylene process as an example:
High pressure polyethylene process is ethylene polymerization, to guarantee that reaction has higher conversion, needs constantly to control former
Expect that input quantity keeps reactor pressure to stablize.Here using the pressure in polyethylene reactor as controlled device, with raw material input quantity
For control amount.By adjusting and controlling to raw material input quantity, realizes the control to reactor pressure, increase the conversion ratio of polyethylene
It is high.
Step 1 establishes high pressure polyethylene process single-input single-output model, comprises the concrete steps that:
It is as follows that 1-1. establishes refining high pressure polyethylene process single-input single-output model:
X (k+1)=A (k) x (k)+B (k) u (k)
Y (k+1)=Cx (k+1)
Wherein k indicates the high pressure polyethylene process sampling moment；X (k), x (k+1) respectively indicate high pressure polyethylene process kth
The state at moment ,+1 moment of kth；The tank reactor pressure at y (k+1) expression+1 moment of system kth；U (k) indicates system kth
Moment raw material input quantity；A (k), B (k) respectively indicate two corresponding parameter matrixs at high pressure polyethylene process kth moment；C is tool
There is the sytem matrix of appropriate dimension.
1-2. raw material input form when partial fault occurs in actuator is as follows:
uF(k)=α u (k)
Wherein uFIt (k) is the kth moment there are fault degree when failure, α is the system diagonal matrix with appropriate dimension.
1-3. obtains new model by step 1-1 and step 1-2:
X (k+1)=A (k) x (k)+B (k) uF(k)
Y (k+1)=Cx (k+1)
It is as follows that step 1-3 is extended to incremental form by 1-4.:
xm(k+1)=Am(k)xm(k)+Bm(k)uF(k)
ym(k+1)=Cmxm(k+1)
WhereinCm=[0,1],
xm(k)=[Δ x (k) y (k)]；Am(k)、Bm(k) the incremental form parameter matrix at system kth moment is respectively indicated,
CmIndicate the incremental form sytem matrix with appropriate dimension；xm(k)、xm(k+1) when respectively indicating system kth moment, kth+1
The incremental form state at quarter；ym(k+1) the incremental form reactor pressure at+1 moment of system kth is indicated；When Δ x (k) indicates kth
The state increment at quarter；The reactor pressure at y (k) expression kth moment.
It is as follows that 1-5. introducing objective function comes track reference track:
Wherein J∞(k) objective function is indicated；Expression belongs in A (k+i) or B (k+i)
J under the conditions of certain dimension matrix Ω and Δ u (k+i | k) maximum value∞(k) minimum value；T indicates transposition symbol；I indicates a certain
It anticipates the period,Indicate cumulative from 0 period to infinite time section；Y (k+i | k), Δ u (k+i | k) indicate to inscribe when kth
The actual reactor pressure and raw material at kth+i moment input increment；yr(k+i) the prediction reactor pressure at kth+i moment is indicated；
The weight matrix of Q expression reactor pressure tracking error；R indicates the weight matrix of raw material input increment.
It is as follows that objective function is extended to incremental form by 1-6.:
Wherein xm(k+i | k) indicate the virtual condition increment that the kth+i moment is inscribed when kth；xr(k+i) kth+i moment is indicated
Predicted state increment；Indicate the weight matrix of reactor pressure tracking error.
Step 2, design high pressure polyethylene process controller, comprise the concrete steps that:
2-1. defines tracking error:
E (k)=y (k)-yr(k)
Wherein e (k) indicates the reactor pressure error at kth moment, y (k), yr(k) the practical anti-of kth moment is respectively indicated
Answer device pressure and prediction reactor pressure.
2-2. changes the formula of step 2-1 for prediction form:
E (k+1)=e (k)+CA (k) Δ x (k)+CB (k) Δ u (k)
Wherein e (k+1) indicates the reactor pressure error at+1 moment of kth；Δ x (k) indicates the state increment at kth moment,
Δ u (k) indicates that the raw material at kth moment inputs increment.
2-3. is according to the available delta state spatial model of step 2-2:
Z (k+1)=Az(k)z(k)+Bz(k)Δu(k)
Δ y (k+1)=Czz(k+1)
WhereinCz=[C 0]；Az(k)、Bz(k) it respectively indicates
The corresponding parameter matrix of two of the kth moment of state-space model；CzIt is the system with appropriate dimension of state-space model
Matrix；The incremental form state of etching system when z (k), z (k+1) are kth moment, kth+1；Δ y (k+1) indicates+1 moment of kth
Reactor pressure increment.
2-4. combination step 1-6 and 2-3 propose objective function track reference value:
Wherein z (k+1 | k) indicates the prediction extended mode that+1 moment of kth is inscribed when kth.
2-5. introduces constraint condition:
Wherein | Δ u (k+i | k) |, | Δ y (k+i | k) | it is exhausted that kth+i moment raw material input increment is inscribed when respectively indicating kth
To value and reactor pressure increment absolute value；Δumax、ΔymaxRespectively indicate the maximum upper limit of raw material input and reactor pressure.
It is as follows that 2-6. by step 2-3, step 2-4 and step 2-5 can obtain more new law Δ u (k+i | k):
Δ u (k+i | k)=F (k) z (k+i | k)
Wherein F (k)=YS-1It is the gain factor matrix at kth moment；Y,S-1Be two is according to objective function value
Matrix number.
The available high pressure polyethylene process raw material input quantity Δ u of 2-7. combination step 2-1 to step 2-6 (k+i | k), then
Acted on polymerization process.
Claims (3)
1. a kind of industrial process constrained forecast advanced control method, includes the following steps:
Step 1 establishes industrial process single-input single-output model；
Step 2, design industrial process control.
2. industrial process constrained forecast advanced control method as described in claim 1, it is characterised in that:
The step is specific as follows:
It is as follows that 1-1. establishes single-input single-output model:
X (k+1)=A (k) x (k)+B (k) u (k)
Y (k+1)=Cx (k+1)
Wherein k indicates sampling instant；X (k), x (k+1) respectively indicate the state at system kth moment ,+1 moment of kth；Y (k+1) table
Show the output at+1 moment of system kth；U (k) indicates the control input of system kth moment；When A (k), B (k) respectively indicate system kth
The two corresponding parameter matrixs carved；C is the sytem matrix with appropriate dimension；
Control amount input form of the 1-2. when partial fault occurs in actuator is as follows:
uF(k)=α u (k)
Wherein 0≤α≤1 indicates actuator failures degree；uFIt (k) is that the kth moment, there are control amount inputs when failure；
1-3. obtains new model by step 1-1 and step 1-2:
X (k+1)=A (k) x (k)+B (k) uF(k)
Y (k+1)=Cx (k+1)
It is as follows that step 1-3 is extended to incremental form by 1-4.:
xm(k+1)=Am(k)xm(k)+Bm(k)uF(k)
ym(k+1)=Cmxm(k+1)
WhereinCm=[0,1], xm(k)=[Δ x (k) y (k)]；
Am(k)、Bm(k) the incremental form parameter matrix at system kth moment, C are respectively indicatedmIndicate the incremental form with appropriate dimension
Sytem matrix；xm(k)、xm(k+1) the incremental form state at system kth moment ,+1 moment of kth is respectively indicated；ym(k+1) it indicates
The incremental form at+1 moment of system kth exports, and Δ x (k) indicates the state increment at kth moment；Y (k) indicates the defeated of kth moment
Out；
It is as follows that 1-5. introducing objective function comes track reference track:
Wherein J∞(k) objective function is indicated；Expression belongs to centainly in A (k+i) or B (k+i)
J under the conditions of dimension matrix Ω and Δ u (k+i | k) maximum value∞(k) minimum value；T indicates transposition symbol；When i indicates a certain any
Between section,Indicate cumulative from 0 period to infinite time section；Y (k+i | k), Δ u (k+i | k) indicate to inscribe kth+i when kth
The reality output at moment and actually enter increment；yr(k+i) the prediction output at kth+i moment is indicated；Q indicates output tracking error
Weight matrix；R indicates the weight matrix of control input increment；
It is as follows that objective function is extended to incremental form by 1-6.:
Wherein xm(k+i | k) indicate the virtual condition increment that the kth+i moment is inscribed when kth；xr(k+i) the pre- of kth+i moment is indicated
Survey state increment；Indicate the weight matrix of status tracking error.
3. industrial process constrained forecast advanced control method as claimed in claim 2, it is characterised in that:
Step 2 is specific as follows:
2-1. defines tracking error:
E (k)=y (k)-yr(k)
Wherein e (k) indicates the output error at kth moment, y (k), yr(k) it respectively indicates the reality output at kth moment and predicts defeated
Out；
2-2. changes the formula of step 2-1 for prediction form:
E (k+1)=e (k)+CA (k) Δ x (k)+CB (k) Δ u (k)
Wherein e (k+1) indicates the output error at+1 moment of kth；Δ x (k) indicates that the state increment at kth moment, Δ u (k) indicate
The input increment at kth moment；
2-3. is according to the available delta state spatial model of step 2-2:
Z (k+1)=Az(k)z(k)+Bz(k)Δu(k)
Δ y (k+1)=Czz(k+1)
WhereinCz=[C 0]；Az(k)、Bz(k) increment is respectively indicated
The corresponding parameter matrix of two of the kth moment of state-space model；CzIt is the system with appropriate dimension of state-space model
Matrix；The incremental form state of etching system when z (k), z (k+1) are kth moment, kth+1；Δ y (k+1) indicates+1 moment of kth
Output increment；
2-4. combination step 1-6 and step 2-3 propose objective function track reference value:
Wherein z (k+1 | k) indicates the prediction extended mode that+1 moment of kth is inscribed when kth；
2-5. introduces constraint condition:
Wherein | Δ u (k+i | k) |, | Δ y (k+i | k) | inscribing the kth+i moment when respectively indicating kth inputs increment absolute value and defeated
Increment absolute value out；Δumax、ΔymaxRespectively indicate the maximum upper limit output and input；
It is as follows that 2-6. by step 2-3, step 2-4 and step 2-5 can obtain more new law Δ u (k+i | k):
Δ u (k+i | k)=F (k) z (k+i | k)
Wherein F (k)=YS-1It is the gain factor matrix at kth moment；Y,S-1It is two coefficient squares according to objective function value
Battle array；
2-7. combination step 2-1 to step 2-6 obtains industrial process optimal control law Δ u (k+i | k) and acts on controlled device.
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