CN103425048A - Multi-model generalized predictive control system based on dynamic optimization and control method thereof - Google Patents

Multi-model generalized predictive control system based on dynamic optimization and control method thereof Download PDF

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CN103425048A
CN103425048A CN2013101919019A CN201310191901A CN103425048A CN 103425048 A CN103425048 A CN 103425048A CN 2013101919019 A CN2013101919019 A CN 2013101919019A CN 201310191901 A CN201310191901 A CN 201310191901A CN 103425048 A CN103425048 A CN 103425048A
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CN103425048B (en
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王昕�
宋治强
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Shanghai Jiaotong University
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Abstract

A multi-model generalized predictive control system based on dynamic optimization comprises a dynamic optimization layer, an MPC layer and a basic control layer. The dynamic optimization layer is located in the upper layer and calculates the optimization value of a critical control variable as the optimal set value of the MPC layer; the MPC layer is located in the lower layer and adjusts a to-be-optimized variable based on a rolling optimization prediction algorithm on the condition that the to-be-optimized variable satisfies a model dynamic behavior, thereby tracking the optimal set value obtained in the S1; the basic control layer is located in the bottom layer and transmits the final optimization value of the to-be-optimized variable to an actuating mechanism. According to the present invention, the cost consumption of the system is reduced, the economic benefit of the system is improved, the transient performance and the model parameter jump adjusting capability of the system can be improved, at the same time, the interference of disturbance on the output of the system can be eliminated effectively.

Description

A kind of multi-model generalized predictable control system and control method thereof based on dynamic optimization
Technical fieldThe present invention relates to control the optimization field, relate in particular to a kind of method for designing of the multi-model generalized predictable control system based on dynamic optimization.
Background technology
The market competition of production globalization aggravation makes reducing cost consumption, and the requirement of increasing economic efficiency is more and more higher.The operating performance optimization of process can be that enterprise produces and create huge interests, therefore needs more effectively, more advanced optimization and control strategy be applied in relevant commercial unit.Conventional procedure optimisation technique based on steady-state model has obtained outstanding achievements, and becoming not strong process during for model has good effect of optimization.But, in actual industrial, the phenomenon smartened while often model occurring, cause being difficult to meet based on traditional optimisation technique of steady-state model the requirement of modernization industry.Dynamic optimization can process preferably have when strong become, industrial process that reaction mechanism is comparatively complicated, and a lot of scholars are combined dynamic optimization composition layer-stepping PREDICTIVE CONTROL structure commercial unit are optimized with Model Predictive Control, and have obtained good ground effect.
Traditional dynamic optimization is combined with Model Predictive Control and is formed in layer-stepping PREDICTIVE CONTROL structure, and the MPC layer adopts the single model predictive controller more, but, in actual industrial process, the situation of procedure parameter with the production run saltus step often occur.Because actual production process is very complicated, be difficult to set up a succinct overall situation and control model, the still requirement in good state of a control of system when therefore the predictive controller of single model is difficult to meet parameter time varying or saltus step.The method of multi-model can effectively be processed many working points and the parameter time varying problem in complex industrial process, and many scholars have also applied to the multi-model PREDICTIVE CONTROL fields such as chemical industry, pharmacy, electric power, and obtain good effect.But because the existence of random noise makes conventional multi-model be difficult to be complementary with the real process feature.Therefore controller how to set up a regulating power can consider that economic benefit can guarantee again the transient performance of system and saltus step the time as a problem special procuring at present solution.
Summary of the invention
1. for solving an above-mentioned difficult problem, the invention provides a kind of multi-model generalized predictable control system based on dynamic optimization, it is characterized in that, comprise dynamic optimization layer, MPC layer and base control layer;
Described dynamic optimization layer is positioned at upper strata, and it adopts the track in conjunction with the optimal value of the economic goal function being carried out to dynamic optimization acquisition key variables of control vector parametrization and particle swarm optimization algorithm, and this optimal value is as the Optimal Setting value of described MPC layer;
Described MPC layer is positioned at lower floor, and it meets the prediction algorithm that adopts rolling optimization under the condition of model dynamic behaviour treats optimized variable and regulated at variable to be optimized, makes it follow the tracks of described optimal setting;
Described base control layer is positioned at bottom, and it delivers to topworks for the final optimization pass value by variable to be optimized.
Preferably, described model dynamic behaviour comprises that model parameter changes and disturbing effect.
Preferably, described MPC layer adopts the walk abreast dynamic perfromance of identification system of a plurality of fixed models and adaptive model.
Preferably, described base control layer comprises a PID controller, and described PID controller is for suppressing, eliminate the impact of disturbance on exporting of the process that enters into.
The present invention also provides the method for work of planting the multi-model generalized predictable control system based on dynamic optimization, and it comprises the following steps:
S1: described dynamic optimization layer obtains the optimal value track of key variables for the method for the combination of the economic goal function of system and alter an agreement at that time Shu Caiyong control vector parametrization and particle swarm optimization algorithm, and will be as the optimal setting reference locus of the MPC of lower floor layer using this track;
S2: the prediction algorithm that described MPC layer adopts rolling optimization variable to be optimized in process is met to model parameter changes and the condition of disturbing effect dynamic behaviour under regulated, make its optimal setting track of following the tracks of this variable drawn in S1, and adopt the walk abreast dynamic perfromance of identification system of a plurality of fixed models and adaptive model;
S3: described basal layer suppresses, eliminates the impact of the disturbance of the process that enters on output by the PID effect, and the final optimization pass value of this variable is delivered to execution architecture.
Preferably, the acquisition process of the optimal value track of described key variables comprises the following steps:
S11: at first by time interval
Figure 2013101919019100002DEST_PATH_IMAGE001
Be divided into identical multistage, every section with piecewise constant track near-optimization track, obtains a plurality of control parameters to be optimized;
S12: population initialization: population is set
Figure 853685DEST_PATH_IMAGE002
, dimension
Figure 2013101919019100002DEST_PATH_IMAGE003
, two study factors
Figure 832267DEST_PATH_IMAGE004
, the position bound
Figure 2013101919019100002DEST_PATH_IMAGE005
And maximum iteration time
Figure 899449DEST_PATH_IMAGE006
, initial position, initial velocity, initialization globally optimal solution gBest and locally optimal solution pBest;
S13: calculate each particle fitness, upgrade local optimum and global optimum;
S14: calculate renewal speed and upgrade position, if position surpasses bound is set as boundary value;
S15: judge whether to reach maximum iteration time, if do not return to c) continue to calculate, export current optimal value if satisfy condition.
Preferably, in step S2, controlled device is:
Figure DEST_PATH_IMAGE007
, the multi-model set representations is:
Figure 963483DEST_PATH_IMAGE008
Figure DEST_PATH_IMAGE009
Wherein
Figure 587362DEST_PATH_IMAGE010
；
Adaptive model adopts following least square method of recursion to carry out the identification of system dynamic characteristic:
Figure 918986DEST_PATH_IMAGE012
Figure DEST_PATH_IMAGE013
Figure 658534DEST_PATH_IMAGE014
In formula For forgetting factor,
Figure 770716DEST_PATH_IMAGE016
For weight factor,
Figure DEST_PATH_IMAGE017
For the positive definite covariance battle array;
Multi-model switching index expression is:
Above formula is model
Figure DEST_PATH_IMAGE019
Constantly
Figure 84551DEST_PATH_IMAGE020
Performance index, wherein Be
Figure 41006DEST_PATH_IMAGE019
Individual model exists
Figure 141948DEST_PATH_IMAGE020
Output error constantly,
Figure 107630DEST_PATH_IMAGE022
With
Figure DEST_PATH_IMAGE023
Current and past error weight constantly,
Figure 476163DEST_PATH_IMAGE024
For the error forgetting factor,
Figure DEST_PATH_IMAGE025
For the moment in past error length,
Figure 557514DEST_PATH_IMAGE020
Constantly, can be according to performance index
Figure 129441DEST_PATH_IMAGE026
Minimum is switched to corresponding model.
Preferably, the performance optimization index of described PID is
Figure 882502DEST_PATH_IMAGE028
，
In formula
Figure 121854DEST_PATH_IMAGE029
For mathematical expectation,
Figure 748007DEST_PATH_IMAGE030
For the output expectation value,
Figure 557962DEST_PATH_IMAGE031
For controlling time domain,
Figure 865447DEST_PATH_IMAGE032
For controlling weighting coefficient, k means constantly;
The expectation value of object output is
Figure 943310DEST_PATH_IMAGE034
, in formula
Figure 240562DEST_PATH_IMAGE035
The key variables setting value of giving for the upper strata dynamic optimization,
Figure 148475DEST_PATH_IMAGE036
For optimizing time domain, stop constantly.
Compared with prior art, beneficial effect of the present invention is as follows:
1. reduce system cost consumption, improve the systematic economy benefit;
2. improve the system transient modelling performance;
3. improve the regulating power of system model parameter saltus step;
4. can effectively eliminate the interference of disturbance to system output.
The accompanying drawing explanation
The structural representation of the controller that Fig. 1 provides for the embodiment of the present invention;
The multi-model switching construction schematic diagram that Fig. 2 provides for the embodiment of the present invention;
The controller simulation result schematic diagram that Fig. 3 provides for the embodiment of the present invention.
Specific embodiment
The invention provides a kind of multi-model generalized predictable control system based on dynamic optimization, as shown in Figure 1, comprise dynamic optimization layer, MPC layer and base control layer; Described dynamic optimization layer is positioned at upper strata, and it calculates the optimal setting of the optimal value of key control variable as the MPC layer; Described MPC layer is positioned under lower floor meets model dynamic behaviour condition at this variable to be optimized and adopts the prediction algorithm of rolling optimization to be regulated this variable to be optimized, makes it follow the tracks of the optimal setting drawn in S1; Described base control layer is positioned at bottom, and the final optimization pass value of this variable to be optimized is delivered to topworks.
The concrete control procedure of the present invention comprises the following steps: comprise the following steps:
S1: described dynamic optimization layer obtains the optimal value track of key variables for the method for the combination of the economic goal function of system and alter an agreement at that time Shu Caiyong control vector parametrization and particle swarm optimization algorithm, and will be as the reference locus of the MPC of lower floor layer using this track;
S2: the prediction algorithm that described MPC layer adopts rolling optimization variable to be optimized in process is met to model parameter changes and the condition of disturbing effect dynamic behaviour under regulated, make its optimal setting track of following the tracks of this variable drawn in S1, and adopt the walk abreast dynamic perfromance of identification system of a plurality of fixed models and adaptive model;
S3: described basal layer suppresses, eliminates the impact of the disturbance of the process that enters on output by the PID effect, and the final optimization pass value of this variable is delivered to execution architecture.
In step S1, the optimal value track step that dynamic optimization is asked for key variables is as follows:
S11 is at first by time interval
Figure 96839DEST_PATH_IMAGE037
Be divided into identical N section, every section with piecewise constant track near-optimization track, obtains the control parameter to be optimized of N.
S12 population initialization: population is set
Figure 251746DEST_PATH_IMAGE002
, dimension
Figure 285561DEST_PATH_IMAGE003
, two study factors
Figure 685580DEST_PATH_IMAGE038
, the position bound
Figure 488451DEST_PATH_IMAGE039
And maximum iteration time
Figure 627309DEST_PATH_IMAGE006
, initial position, initial velocity, initialization globally optimal solution gBest and locally optimal solution pBest
S13 calculates each particle fitness, upgrades local optimum and global optimum.
S14 calculates renewal speed and upgrades position.If surpassing bound, position is set as boundary value
S15 judges whether to reach maximum iteration time, if do not return to c) continue to calculate.Export current optimal value if satisfy condition
As follows about the design of multi-model generalized predictive controller in step S2
Controlled device is expressed as:
Figure 397687DEST_PATH_IMAGE040
(1)
Wherein
Figure 850666DEST_PATH_IMAGE041
Figure 258775DEST_PATH_IMAGE042
In formula
Figure 506217DEST_PATH_IMAGE043
For backward shift operator;
Figure 763892DEST_PATH_IMAGE044
Be respectively the output of system, the white noise sequence that input and average are zero;
Figure 817299DEST_PATH_IMAGE045
For difference operator.
The multi-model set representations is:
Figure 594762DEST_PATH_IMAGE046
(2)
Figure 763837DEST_PATH_IMAGE009
Wherein
Figure 38010DEST_PATH_IMAGE011
When
Figure 669979DEST_PATH_IMAGE048
The time,
Figure 263816DEST_PATH_IMAGE049
For the steady state value of fixed model, with respect to single model, m fixed model can improve the transient performance of system.
When The time, but model is an adaptive model and an assignment adaptive model.The online real-time identification systematic parameter of adaptive model not only can be eliminated the stability that steady-state error has guaranteed the convergence of system but also can guarantee system, but the introducing of the adaptive model of initialize has further improved the transient performance of system, increased the rapidity of system.Can adopt following Recursive Least Squares to carry out the identification of model parameter
Figure 377769DEST_PATH_IMAGE013
Figure 137915DEST_PATH_IMAGE052
(3)
In formula
Figure 93363DEST_PATH_IMAGE015
For forgetting factor;
Figure 229947DEST_PATH_IMAGE016
For weight factor;
Figure 898825DEST_PATH_IMAGE017
For the positive definite covariance battle array
Multi-model switching index expression is:
Figure 79140DEST_PATH_IMAGE018
(4)
Formula (4) is model Constantly
Figure 196580DEST_PATH_IMAGE020
Performance index, in formula
Figure 657648DEST_PATH_IMAGE021
Be
Figure 274443DEST_PATH_IMAGE019
Individual model exists
Figure 516069DEST_PATH_IMAGE020
Output error constantly;
Figure 728875DEST_PATH_IMAGE022
With It is current and past error weight constantly;
Figure 333611DEST_PATH_IMAGE024
For the error forgetting factor;
Figure 249483DEST_PATH_IMAGE025
For the moment in past error length.
Figure 265981DEST_PATH_IMAGE020
Constantly, can be according to performance index
Figure 763958DEST_PATH_IMAGE026
Minimum is switched to corresponding model.
The controller design:
Figure 224021DEST_PATH_IMAGE020
Performance optimization index constantly is
Figure 112342DEST_PATH_IMAGE054
(5)
In formula
Figure DEST_PATH_IMAGE055
For mathematical expectation;
Figure 119482DEST_PATH_IMAGE056
For the output expectation value;
Figure DEST_PATH_IMAGE057
For controlling time domain; For controlling weighting coefficient
The expectation value of object output is
Figure 40612DEST_PATH_IMAGE033
Figure 665498DEST_PATH_IMAGE034
(6)
In formula
Figure 23798DEST_PATH_IMAGE035
The key variables setting value (model output setting value) of giving for the upper strata dynamic optimization,
Figure 184783DEST_PATH_IMAGE036
For optimizing time domain, stop constantly.
In order to utilize formula (1) to calculate the rear prediction of output value of i step, at first introduce Diophantine equation
Figure 235916DEST_PATH_IMAGE058
(7)
Figure DEST_PATH_IMAGE059
(8)
In formula
Figure 348097DEST_PATH_IMAGE060
Figure DEST_PATH_IMAGE061
Figure 198503DEST_PATH_IMAGE062
Figure DEST_PATH_IMAGE063
Figure 384634DEST_PATH_IMAGE064
(9)
In formula
Figure 668985DEST_PATH_IMAGE065
Figure 19195DEST_PATH_IMAGE066
Figure 747328DEST_PATH_IMAGE067
Can obtain thus actual output controlled quentity controlled variable is
Figure 866594DEST_PATH_IMAGE068
。
Embodiment
S1 dynamic optimization layer is made as following process mathematical model:
Figure 243217DEST_PATH_IMAGE069
Figure 80723DEST_PATH_IMAGE070
Figure 335249DEST_PATH_IMAGE071
Figure 636918DEST_PATH_IMAGE072
(11)
In formula, For the economic goal function,
Figure 509245DEST_PATH_IMAGE074
For with key variables
Figure 816729DEST_PATH_IMAGE075
Two relevant parameters.
Time interval is divided into to identical 10 sections, and then the PSO parameter arranges population and gets
Figure 395740DEST_PATH_IMAGE076
, dimension
Figure 130478DEST_PATH_IMAGE077
, the study factor , maximum iteration time is 500. by dynamic optimization, to obtain the setting value of key variables the reference locus using this setting value as the multi-model generalized predictive controller.
S2 MPC layer controlled device is expressed as:
Figure 99757DEST_PATH_IMAGE079
Control step number and be taken as 300,
Figure 48122DEST_PATH_IMAGE080
, ,
Figure 738308DEST_PATH_IMAGE082
,
Figure 636863DEST_PATH_IMAGE083
, systematic parameter generation saltus step when 150 step.Saltus step is
Figure 502051DEST_PATH_IMAGE084
,
Figure 578591DEST_PATH_IMAGE085
, Remain unchanged.
Figure 37834DEST_PATH_IMAGE087
For
Figure 210058DEST_PATH_IMAGE088
Equally distributed white noise fixed model is taken as
Figure 457500DEST_PATH_IMAGE089
,
Figure 216639DEST_PATH_IMAGE090
,
Figure 270046DEST_PATH_IMAGE082
, Totally 10, the adaptive model initial parameter value all is taken as 0.1.Corresponding multi-model switching index is:
Figure 715120DEST_PATH_IMAGE091
Concrete switching execute form as shown in Figure 2, is switched to the model of corresponding model as object output according to the switching index
Figure 945244DEST_PATH_IMAGE020
Performance optimization index constantly go into
Figure 490757DEST_PATH_IMAGE092
The expectation value of object output.Be that reference locus in MPC has following formula to obtain
Figure 122727DEST_PATH_IMAGE094
In formula
Figure DEST_PATH_IMAGE095
The reference locus (model output setting value) of the key variables that () obtained for S1,
Figure 898922DEST_PATH_IMAGE036
For optimizing time domain, stop constantly.
Introduce diophantus side
1=E j(z -1)A(z -1)Δ+z -jF j(z -1)
E j(z -1)B(z -1)=G j(z -1)+z -jH j(z -1)
That
Δu ( k ) = Q T ( w r - F ( z - 1 ) y ( k ) - H ( z - 1 ) Δu ( k - 1 ) ) Q T Q + λ ( 1 + β 2 + · · · β 2 ( N u - 1 ) )
Can obtain thus actual output controlled quentity controlled variable is
u(k)=u(k-1)+Δu(k|k)
From the simulated effect of Fig. 3, can find out, before reaching stable state, the transient performance of the present invention's design is more excellent, output quantity changes milder, less, better for the tracking performance of reference locus with the fluctuation of disturbing, the control performance after the 150th step generation saltus step also is significantly improved.
Compared with prior art, the present invention reduces system cost consumption, improves the systematic economy benefit, and can improve the regulating power of system transient modelling performance and the saltus step of system model parameter, can also effectively eliminate the interference of disturbance to system output simultaneously.
The above disclosed preferred embodiment of the present invention is just for helping to set forth the present invention.Preferred embodiment does not have all details of detailed descriptionthe, and also not limiting this invention is only described embodiment.Obviously, according to the content of this instructions, can make many modifications and variations.These embodiment are chosen and specifically described to this instructions, is in order to explain better principle of the present invention and practical application, thereby under making, the technical field technician can understand and utilize the present invention well.The present invention only is subject to the restriction of claims and four corner and equivalent.

Claims (8)

1. the multi-model generalized predictable control system based on dynamic optimization, is characterized in that, comprises dynamic optimization layer, MPC layer and base control layer;
Described dynamic optimization layer is positioned at upper strata, and it adopts the track in conjunction with the optimal value of the economic goal function being carried out to dynamic optimization acquisition key variables of control vector parametrization and particle swarm optimization algorithm, and this optimal value is as the Optimal Setting value of described MPC layer;
Described MPC layer is positioned at lower floor, and it meets the prediction algorithm that adopts rolling optimization under the condition of model dynamic behaviour treats optimized variable and regulated at variable to be optimized, makes it follow the tracks of described optimal setting;
Described base control layer is positioned at bottom, and it delivers to topworks for the final optimization pass value by variable to be optimized.
2. the multi-model generalized predictable control system based on dynamic optimization as claimed in claim 1, is characterized in that, described model dynamic behaviour comprises that model parameter changes and disturbing effect.
3. the multi-model generalized predictable control system based on dynamic optimization as claimed in claim 1, is characterized in that, described MPC layer adopts the walk abreast dynamic perfromance of identification system of a plurality of fixed models and adaptive model.
4. the multi-model generalized predictable control system based on dynamic optimization as claimed in claim 1, is characterized in that, described base control layer comprises a PID controller, and described PID controller is for suppressing, eliminate the impact of disturbance on exporting of the process that enters into.
5. the optimization method of the multi-model generalized predictable control system based on dynamic optimization, is characterized in that, comprises the following steps:
S1: described dynamic optimization layer obtains the optimal value track of key variables for the method for the combination of the economic goal function of system and alter an agreement at that time Shu Caiyong control vector parametrization and particle swarm optimization algorithm, and will be as the optimal setting reference locus of the MPC of lower floor layer using this track;
S2: the prediction algorithm that described MPC layer adopts rolling optimization variable to be optimized in process is met to model parameter changes and the condition of disturbing effect dynamic behaviour under regulated, make its optimal setting track of following the tracks of this variable drawn in S1, and adopt the walk abreast dynamic perfromance of identification system of a plurality of fixed models and adaptive model;
S3: described basal layer suppresses, eliminates the impact of the disturbance of the process that enters on output by the PID effect, and the final optimization pass value of this variable is delivered to execution architecture.
6. the optimization method of the multi-model generalized predictable control system based on dynamic optimization as claimed in claim 5, is characterized in that, the acquisition process of the optimal value track of described key variables comprises the following steps:
S11: at first by time interval Be divided into identical multistage, every section with piecewise constant track near-optimization track, obtains a plurality of control parameters to be optimized;
S12: population initialization: population is set
Figure 2013101919019100001DEST_PATH_IMAGE004
, dimension , two study factors
Figure DEST_PATH_IMAGE008
, the position bound
Figure DEST_PATH_IMAGE010
And maximum iteration time , initial position, initial velocity, initialization globally optimal solution gBest and locally optimal solution pBest;
S13: calculate each particle fitness, upgrade local optimum and global optimum;
S14: calculate renewal speed and upgrade position, if position surpasses bound is set as boundary value;
S15: judge whether to reach maximum iteration time, if do not return to c) continue to calculate, export current optimal value if satisfy condition.
7. the optimization method of the multi-model generalized predictable control system based on dynamic optimization as claimed in claim 5, is characterized in that, in step S2, controlled device is:
Figure DEST_PATH_IMAGE014
, the multi-model set representations is:
Figure DEST_PATH_IMAGE016
Figure DEST_PATH_IMAGE018
Wherein
Figure DEST_PATH_IMAGE020
Figure DEST_PATH_IMAGE022
；
Adaptive model adopts following least square method of recursion to carry out the identification of system dynamic characteristic:
Figure DEST_PATH_IMAGE026
Figure DEST_PATH_IMAGE028
In formula
Figure DEST_PATH_IMAGE030
For forgetting factor, For weight factor,
Figure DEST_PATH_IMAGE034
For the positive definite covariance battle array;
Multi-model switching index expression is:
Figure DEST_PATH_IMAGE036
Above formula is model
Figure DEST_PATH_IMAGE038
Constantly
Figure DEST_PATH_IMAGE040
Performance index, wherein
Figure DEST_PATH_IMAGE042
Be
Figure DEST_PATH_IMAGE038A
Individual model exists
Figure DEST_PATH_IMAGE040A
Output error constantly,
Figure DEST_PATH_IMAGE044
With Current and past error weight constantly,
Figure DEST_PATH_IMAGE048
For the error forgetting factor,
Figure DEST_PATH_IMAGE050
For the moment in past error length,
Figure DEST_PATH_IMAGE040AA
Constantly, can be according to performance index
Figure DEST_PATH_IMAGE052
Minimum is switched to corresponding model.
8. the optimization method of the multi-model generalized predictable control system based on dynamic optimization as claimed in claim 5, is characterized in that, the performance optimization index of described PID is
Figure DEST_PATH_IMAGE054
，
In formula
Figure DEST_PATH_IMAGE056
For mathematical expectation,
Figure DEST_PATH_IMAGE058
For the output expectation value, For controlling time domain,
Figure DEST_PATH_IMAGE062
For controlling weighting coefficient, k means constantly;
The expectation value of object output is
Figure DEST_PATH_IMAGE064
Figure DEST_PATH_IMAGE066
, in formula
Figure DEST_PATH_IMAGE068
The key variables setting value of giving for the upper strata dynamic optimization,
Figure DEST_PATH_IMAGE070
For optimizing time domain, stop constantly.
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