CN107272640A - A kind of modeling quality control method and system based on model predictive controller - Google Patents
A kind of modeling quality control method and system based on model predictive controller Download PDFInfo
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Abstract
The invention discloses a kind of modeling quality control method based on model predictive controller and system, the realization of wherein method includes：Utilize model predictive controller control closed-loop control system operation, gatherer process output, process input and process external drive；Obtain the tracking error of closed-loop control system；Kernel-based methods output, process external drive set up mixing high-order autoregression model and carry out rectangular projection, obtain process estimation interference renewal vector；The matrix model of process external drive is set up, process estimation interference is obtained and updates spread vector；Using process model quality-monitoring index and block mold quality index, process model mismatch and interference model mismatch in closed-loop control system are detected, and then monitor the modeling quality of closed-loop control system.The present invention has feasibility high, and processing consumption resource is few, the characteristics of monitored results degree of accuracy is high.
Description
Technical field
The invention belongs to Model Predictive Control field, more particularly, to a kind of modeling based on model predictive controller
Quality control method and system.
Background technology
Model Predictive Control (Model Predictive Control, MPC) is that one kind is widely used in industrial process control
The advanced control method based on model in field processed, with control effect is good, strong robustness, less demanding to model exactness
Advantage.
Practical application of the Model Predictive Control on industrial process, referred to as model predictive controller (Model
Predictive Controller, MPC Controller).MPC controller is with modeling is simple, dynamic control effect is good, Shandong
The characteristics of rod is strong, has good control performance initial stage in operation；However, over time, MPC controller performance meeting
It is gradually reduced, traditional PID control must not even be switched to finally.The principal element for causing controller performance to decline has noise to do
Disturb, model mismatch, valve viscous, perceptron deviation etc..
In recent years, the method based on data-driven is increasingly being applied to control system Performance Evaluation problem.Such as MPC
Historical performance index under framework, can make effectively evaluating to MPC performance, but it needs to obtain one-stage control system operation
Good data carry out Calculation Estimation benchmark, and the no standard of selection of this good operation phase, so that the application band to this method
Carry out certain limitation.In System design based on model technology, the quality of model for controller design and adjust and play pass
Key is acted on, and the performance of control system depends on the precision of process model, that is, is influenceed by model mismatch degree.
On the one hand, at this stage on modeling the deterioration that the technology of quality monitoring there is no method diagnosis to cause controller performance to be deteriorated
Root, it is impossible to be to be that model has a mismatch the reason for diagnosing controller degradation, or noise jamming, it is valve viscous,
In the factors such as perceptron deviation.On the other hand, the achievement in research predicted at this stage on model quality mostly makees model mismatch
To influence an overall factor of model quality, process model mismatch and interference model mismatch are not separated.
As can be seen here, prior art exist can not diagnosing controller degradation the reason for, not by process model mismatch and
Interference model mismatch separates, can not the low technical problem of effective monitoring model quality, the monitoring degree of accuracy.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, the invention provides a kind of based on model predictive controller
Model quality control method and system, thus solve prior art exist can not diagnosing controller degradation the reason for, will
Process model mismatch and interference model mismatch separate, can not the low technology of effective monitoring model quality, the monitoring degree of accuracy ask
Topic.
To achieve the above object, according to one aspect of the present invention, there is provided a kind of building based on model predictive controller
Mould quality control method, including：
(1) using model predictive controller control closed-loop control system operation, collection closed-loop control system running
The output of process, process input and process external drive；
(2) according to process external drive and the output of process, the tracking error of closed-loop control system is obtained；
(3) the high-order autoregression model of the output of process and the high-order autoregression model of process external drive are set up, was obtained
Journey exports the mixing high-order autoregression model with process external drive, and rectangular projection is carried out based on mixing high-order autoregression model,
Obtain process estimation interference renewal vector；
(4) matrix model of process external drive is set up, rectangular projection is carried out using the matrix model of process external drive,
Obtain process estimation interference and update spread vector；
(5) process is estimated to disturb the quadratic form of renewal vector and the ratio of the quadratic form of tracking error to be used as block mold
Quality index, process is estimated interference updates the quadratic form of spread vector and the ratio of the quadratic form of tracking error is used as process mould
Type quality-monitoring index；
(6) process in process model quality-monitoring index and block mold quality index, detection closed-loop control system is utilized
Model mismatch and interference model mismatch, and then monitor the modeling quality of closed-loop control system.
Further, the specific implementation for setting up the high-order autoregression model of the output of process is：
yp(k)=[y (k) y (k-1) ... y (k-p)]
Wherein, p represents the data window size that process estimation interference updates, and M represents the high-order autoregression mould of the output of process
The order of type, y (k) represents the output of process at k moment, and y (k-1) represents the output of process at (k-1) moment, and y (k-p) represents (k-
P) the output of process at moment, yp(k) 1 × (P+1) dimensional vector being made up of y (k), y (k-1) ..., y (k-p), y are representedp(k-
1) 1 × (P+1) dimensional vector being made up of y (k-1), y (k-2) ..., y (k-p-1), y are representedp(k-2) represent by y (k-2),
1 × (P+1) dimensional vector that y (k-3) ..., y (k-p-2) are constituted, yp(k-M) represent by y (k-M), y (k-M-1) ..., y
(k-p-M) 1 constituted × (P+1) dimensional vector, YM(k-1) the high-order autoregression model of the output of process is represented, is by yp(k-1),
yp..., y (k-2)p(k-M) M constituted × (P+1) ties up matrix.
Further, the specific implementation for setting up the high-order autoregression model of process external drive is：
rp(k)=[r (k) r (k-1) ... r (k-p)]
Wherein, p represents the data window size that process estimation interference updates, and N represents that the high-order of process external drive is returned certainly
Return the order of model, r (k) represents the process external drive at k moment, and r (k-1) represents the process external drive at (k-1) moment, r
(k-p) the process external drive at (k-p) moment, r are representedp(k) represent by r (k), r (k-1) ..., r (k-p) constituted 1 ×
(P+1) dimensional vector, rp(k-1) 1 × (P+1) dimensional vector being made up of r (k-1), r (k-2) ..., r (k-p-1), r are representedp
(k-2) 1 × (P+1) dimensional vector being made up of r (k-2), r (k-3) ..., r (k-p-2), r are representedp(k-N) represent by r (k-
N), 1 × (P+1) dimensional vector that r (k-N-1) ..., r (k-p-N) are constituted, RN(k-1) high-order of process external drive is represented
Autoregression model is by rp(k-1), rp..., r (k-2)p(k-N) N constituted × (P+1) ties up matrix.
Further, mixing high-order autoregression model is set upSpecific implementation be：
Further, process estimation interference renewal vector is：
To matrixMake QR decomposition, i.e.,Obtain orthogonal matrix Q1And Q2,
Diagonal matrix R11, diagonal matrix R22With row vector R21；According to orthogonal matrix Q1And Q2, diagonal matrix R11, diagonal matrix R22And row
Vectorial R21Between relation, the results are as follows：
Acquisition process estimation interference renewal vector：
Further, the specific implementation of step (4) is：
The matrix model of process external drive is set up, rectangular projection is carried out using the matrix model of process external drive, obtains
Spread vector is updated to process estimation interference
Wherein, ep(k)=[e (k) e (k-1) ... e (k-p)], represents the tracking error vector of 1 × (P+1) dimensions, e (k)
The tracking error at k moment is represented, e (k-1) represents the tracking error at (k-1) moment, and e (k-p) represents that the tracking at (k-p) moment is missed
Difference, I represents the unit matrix of (P+1) × (P+1) dimensions, Xp(k) matrix model of process external drive is represented, by rp(k), rp(k-
..., r 1)p(k-M) M constituted × (P+1) ties up matrix, rp(k-M) represent by r (k-M), r (k-M-1) ..., r (k-p-M)
1 constituted × (P+1) dimensional vector.
Further, the specific implementation of step (6) is：
Evaluation modeling quality is combined according to process model quality-monitoring index MDI and block mold quality index MQI；
MQI span for (0,1], block mold quality index shows that the modeling quality of closed-loop control system is got over closer to 1
Good, block mold quality index shows that the modeling quality of closed-loop control system is poorer closer to 0, when MDI values in relatively close proximity to
1 and MQI values in relatively close proximity to 0, show that block mold is second-rate and process model quality preferably, then understand interference model quality
It is poor, there is mismatch condition.
It is another aspect of this invention to provide that there is provided a kind of modeling Quality Monitoring Control System based on model predictive controller,
Including：
Gathered data module, for using model predictive controller control closed-loop control system operation, gathering closed-loop control
The output of process, process input and the process external drive of system operation；
Obtain tracking error module, for according to process external drive and the output of process, obtain closed-loop control system with
Track error；
Acquisition process estimation interference renewal vector module, for setting up outside the high-order autoregression model and process of the output of process
The high-order autoregression model of portion's excitation, obtains the output of process and the mixing high-order autoregression model of process external drive, based on mixed
Close high-order autoregression model and carry out rectangular projection, obtain process estimation interference renewal vector；
Acquisition process estimation interference updates spread vector module, and the matrix model for setting up process external drive is utilized
The matrix model of process external drive carries out rectangular projection, obtains process estimation interference and updates spread vector；
Index module is obtained, for estimating process to disturb the ratio of the quadratic form of renewal vector and the quadratic form of tracking error
Process is estimated that interference updates the quadratic form of spread vector and the quadratic form of tracking error as block mold quality index by value
Ratio is used as process model quality-monitoring index；
Monitoring modeling quality module, for utilizing process model quality-monitoring index and block mold quality index, detection
Process model mismatch and interference model mismatch in closed-loop control system, and then monitor the modeling quality of closed-loop control system.
Further, the specific implementation of monitoring modeling quality module is：
Evaluation modeling quality is combined according to process model quality-monitoring index MDI and block mold quality index MQI；
MQI span for (0,1], block mold quality index shows that the modeling quality of closed-loop control system is got over closer to 1
Good, block mold quality index shows that the modeling quality of closed-loop control system is poorer closer to 0, when MDI values in relatively close proximity to
1 and MQI values in relatively close proximity to 0, show that block mold is second-rate and process model quality preferably, then understand interference model quality
It is poor, there is mismatch condition.
In general, by the contemplated above technical scheme of the present invention compared with prior art, it can obtain down and show
Beneficial effect：
(1) the modeling quality control method that the present invention is provided, using the conventional closed loop feeder number of current closed-loop control system
Estimate according to being updated to process interference, it is not necessary to which process time lag or Interactive matrix etc. are difficult the additional letter of the ring opening process obtained
Breath so that this method feasibility is high, consumption resource is few needed for processing, the reason for can be with diagnosing controller degradation, effectively prison
Control model quality and monitor degree of accuracy height.
(2) the modeling quality control method that the present invention is provided, need not be to current closed-loop control system in processing procedure
Make any adjustment, thus minimum are influenceed on industrial processes, significantly reduce monitoring cost, improve the production of industrial process
Quality and security of system, it is maintainable.
(3) the modeling quality control method that the present invention is provided, is proposed a kind of using the feedback invariant principle for disturbing sequence
Block mold quality index MQI, can have found whether the model in control system is sent out in time according to block mold quality index MQI
Raw mismatch, realizes the Real-Time Evaluation to control system performance；And due to process estimation interference update with process tracking error it
Between relation, the uncontrolled device regulation parameters of block mold quality index MQI change and closed-loop control system interference model becomes
The influence of change, relative to traditional KPI indexs, MQI indexs more accurately can will influence control outside model quality
The factor of device entirety control performance makes a distinction, so as to more accurately and effectively characterize modeling quality.
(4) the modeling quality control method that the present invention is provided, is proposed a kind of using the feedback invariant principle for disturbing sequence
Process model quality-monitoring index MDI, the index and block mold quality index MQI are combined, and can be achieved process model
Mismatch and interference model detection of mismatch are separated.
Brief description of the drawings
Fig. 1 is a kind of flow of modeling quality control method based on model predictive controller provided in an embodiment of the present invention
Figure；
Fig. 2 is closed-loop system principle schematic diagram in the embodiment of the present invention；
Fig. 3 is Wood-Berry rectifying column principle schematics in the embodiment of the present invention 1.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below
Not constituting conflict each other can just be mutually combined.
As shown in figure 1, a kind of modeling quality control method based on model predictive controller, including：
(1) using model predictive controller control closed-loop control system operation, collection closed-loop control system running
The output of process, process input and process external drive；
(2) according to process external drive and the output of process, the tracking error of closed-loop control system is obtained；
(3) the high-order autoregression model of the output of process and the high-order autoregression model of process external drive are set up, was obtained
Journey exports the mixing high-order autoregression model with process external drive, and rectangular projection is carried out based on mixing high-order autoregression model,
Obtain process estimation interference renewal vector；
(4) matrix model of process external drive is set up, rectangular projection is carried out using the matrix model of process external drive,
Obtain process estimation interference and update spread vector；
(5) process is estimated to disturb the quadratic form of renewal vector and the ratio of the quadratic form of tracking error to be used as block mold
Quality index, process is estimated interference updates the quadratic form of spread vector and the ratio of the quadratic form of tracking error is used as process mould
Type quality-monitoring index；
(6) process in process model quality-monitoring index and block mold quality index, detection closed-loop control system is utilized
Model mismatch and interference model mismatch, and then monitor the modeling quality of closed-loop control system.
Further, step (1) also includes：
(1-1) defines related controlled variable CV, manipulating variable MV, disturbance variable DV according to given control targe；Its
In, DV refers to measurable disturbance influential on CV, but can not manipulate；
(1-2) obtains each controlled variable CV's by doing Spline smoothing to the manipulating variable MV and disturbance variable DV
Dynamic changing data, utilizes the dynamic Model Prediction controller of identification algorithm acquisition process；And utilize parameter selection rule configuration
Model predictive controller；
(1-3) gathers closed-loop control system running using model predictive controller control closed-loop control system operation
The output of process, process input and process external drive.
Further, the specific implementation of step (2) is：
According to process external drive and the output of process, the tracking error of closed-loop control system is obtained：
E (k)=y (k)-r (k)；
Wherein, e (k) represents the tracking error of k moment closed-loop control systems, and r (k) represents the process external drive at k moment,
Y (k) represents the output of process at k moment.
Further, step (3) includes：
(3-1) sets up the high-order autoregression model of the output of process according to closed-loop control system structure：
yp(k)=[y (k) y (k-1) ... y (k-p)]
Wherein, p represents the data window size that process estimation interference updates, and M represents the high-order autoregression mould of the output of process
The order of type, y (k) represents the output of process at k moment, and y (k-1) represents the output of process at (k-1) moment, and y (k-p) represents (k-
P) the output of process at moment, yp(k) 1 × (P+1) dimensional vector being made up of y (k), y (k-1) ..., y (k-p), y are representedp(k-
1) 1 × (P+1) dimensional vector being made up of y (k-1), y (k-2) ..., y (k-p-1), y are representedp(k-2) represent by y (k-2),
1 × (P+1) dimensional vector that y (k-3) ..., y (k-p-2) are constituted, yp(k-M) represent by y (k-M), y (k-M-1) ..., y
(k-p-M) 1 constituted × (P+1) dimensional vector, YM(k-1) the high-order autoregression model for representing the output of process is by yp(k-1),
yp..., y (k-2)p(k-M) M constituted × (P+1) ties up matrix；
(3-2), according to closed-loop control system structure, the high-order autoregression model for setting up process external drive is as follows：
rp(k)=[r (k) r (k-1) ... r (k-p)]
Wherein, p represents the data window size that process estimation interference updates, and N represents that the high-order of process external drive is returned certainly
Return the order of model, r (k) represents the process external drive at k moment, and r (k-1) represents the process external drive at (k-1) moment, r
(k-p) the process external drive at (k-p) moment, r are representedp(k) represent by r (k), r (k-1) ..., r (k-p) constituted 1 ×
(P+1) dimensional vector, rp(k-1) 1 × (P+1) dimensional vector being made up of r (k-1), r (k-2) ..., r (k-p-1), r are representedp
(k-2) 1 × (P+1) dimensional vector being made up of r (k-2), r (k-3) ..., r (k-p-2), r are representedp(k-N) represent by r (k-
N), 1 × (P+1) dimensional vector that r (k-N-1) ..., r (k-p-N) are constituted, RN(k-1) high-order of process external drive is represented
Autoregression model, is by rp(k-1), rp..., r (k-2)p(k-N) N constituted × (P+1) ties up matrix；
(3-3) sets up the mixing high-order autoregression of the output of process and process external drive according to closed-loop control system structure
Model：
Wherein,It is that (M+N) × (P+1) ties up matrix to represent mixing high-order autoregression model；
(3-4) is based on mixing high-order autoregression model and carries out rectangular projection, obtains process estimation interference renewal vector：
Wherein,Represent that the process estimation of 1 × (P+1) dimensions is dry
Renewal vector is disturbed, e ° (k) represents that the process estimation interference at k moment updates, and e ° (k-1) represents that the process estimation at (k-1) moment is dry
Renewal is disturbed, e ° (k-p) represents that the process estimation interference at (k-p) moment updates, and I represents the unit matrix of (P+1) × (P+1) dimensions.
Because closed-loop data has high correlation, thereforeIt is ill, causes gained process estimation
It is unreliable that interference updates.
Preferably, step (3-4) solution to this problem further comprises following sub-step：
(3-4-1) is to matrixMake QR decomposition, i.e.,Obtain orthogonal matrix
Q1And Q2, diagonal matrix R11, diagonal matrix R22With row vector R21；
(3-4-2) is according to orthogonal matrix Q1And Q2, diagonal matrix R11, diagonal matrix R22With row vector R21Between relation,
The results are as follows：
(3-4-3) obtains reliable process estimation interference renewal vector：
Further, the specific implementation of step (4) is：
The matrix model of process external drive is set up, rectangular projection is carried out using the matrix model of process external drive, obtains
Spread vector is updated to process estimation interference
Wherein, ep(k)=[e (k) e (k-1) ... e (k-p)], represents the tracking error vector of 1 × (P+1) dimensions, e (k)
The tracking error at k moment is represented, e (k-1) represents the tracking error at (k-1) moment, and e (k-p) represents that the tracking at (k-p) moment is missed
Difference, I represents the unit matrix of (P+1) × (P+1) dimensions, Xp(k) matrix model of process external drive is represented, by rp(k), rp(k-
..., r 1)p(k-M) M constituted × (P+1) ties up matrix, rp(k-M) it is expressed as by r (k-M), r (k-M-1) ..., r (k-p-
M 1) constituted × (P+1) dimensional vector.
Further, step (5) also includes：
(5-1) defines Key Performance Indicator KPI according to output weight matrix Q and input weight matrix S：
Wherein, JnKey Performance Indicator KPI is represented, n represents sampled data length needed for asking for index, when y (k) represents k
The output of process is carved, r (k) represents the process external drive at k moment, Δ u*(k)=u (k)-u (k-1) represents k etching process input u
(k) and (k-1) etching process input u (k-1) difference；
(5-2) estimates process to disturb the quadratic form of renewal vector and the ratio of the quadratic form of tracking error to be used as overall mould
Type quality index MQI：
(5-3) estimates process interference updates the quadratic form of spread vector and the ratio of the quadratic form of tracking error is used as mistake
Journey model quality monitoring index MDI：
Further, the specific implementation of step (6) is：
According to the Key Performance Indicator KPI evaluation model predictive controller performances of the closed-loop control system：KPI value is got over
It is small, represent that model predictive controller performance is better；
According to the process model quality-monitoring index MDI of the closed-loop control system and block mold quality index MQI phases
Combining assessment models quality；MQI span for (0,1], block mold quality index shows closed-loop control closer to 1
The modeling quality of system is better, and block mold quality index shows that the modeling quality of closed-loop control system is poorer closer to 0,
When MDI values in relatively close proximity to 1 and MQI values in relatively close proximity to 0, show that block mold is second-rate and process model quality preferably,
Then understand that interference model is second-rate, has mismatch condition, therefore process model quality index MDI and block mold quality are referred to
Mark MQI is combined and can separate process model mismatch and interference model detection of mismatch.
As shown in Fig. 2 being the closed-loop control system structure chart used in the embodiment of the present invention, u (k), y (k) difference table
Show process input and the output of process at closed-loop control system k moment, r (k) represents to swash outside the process at closed-loop control system k moment
Encourage, Gc is the transmission function of LTI controller, be MPC controller in embodiment, G ° is process transmission function, and H ° is
Disturbance transfer function, the process estimation interference of e ° (k) to represent the k moment updates.
Embodiment 1
Wood-Berry rectifying columns are the typical mimo systems having compared with large time delay；Process such as Fig. 3 institutes
Show, be output as overhead concentration XD(s) with bottom of towe liquid concentration XB(s), steamed by overhead reflux amount R (s) and tower bottom reboiler
Vapour amount S (s) is controlled；Process model is：
Wherein, s represents Laplace operator.
The process transfer function matrix of Wood-Berry rectifying columns is：
Wherein, s represents Laplace operator.
The process sampling time is 1min/ times, and the process transfer function matrix after discretization is：
Wherein, q is that a mathematical operator represents discretization.
Interference model takes following diagonal matrix：
The improved modeling quality control method based on model predictive controller provided using the present invention is to Wood-
Berry rectifying column processes are modeled quality monitoring process, specific as follows：
(1) according to industrial process actual interference situation, the interference model of closed-loop control system is set up,
The interference model of Wood-Berry rectifying column processes is as follows：
It is stated that following common version：
Order
It is preferred that, σ1 2=7.62, σ2 2=0.142。
Preferably to represent process model mismatch and interference model mismatch condition, orderRepresent process model,
Represent interference model
Wherein, Δ KpRepresent process model gain delta, Δ DpRepresent process model time delay increment, Δ TpExpression process mould
Type time constant increment, Δ K1Represent interference model gain delta.
(2) according to the actual conditions of closed-loop control system, design a model predictive controller MPC, utilizes MATLAB tool boxes
In existing MPC Toolbox design MPC controller；MPC controller parameter takes prediction time domain P=100, controls time domain M=10,
Sampled data length takes N=500 needed for index.To realize minimum variance principle, weight matrix be set to Q=diag 1,
100 }, S=0；Process external drive is：R (k)=[0.9*sin (k) 0.05*sin (k)].
(3) closed-loop control system is controlled according to above-mentioned MPC controller, and gathers closed-loop control system operation gained process
Output and process input data；
When closed-loop control system is normally run, the sampling time is set as 1min/ times, collection closed-loop control system Wood-
Berry rectifying columns operation gained the output of process data, including overhead concentration XDWith bottom of towe liquid concentration XB, it is designated as respectively
y1And y2；Process input data, including top capacity of returns R and tower bottom reboiler quantity of steam S, are designated as u respectively1And u2；The sample of collection
Number N is set to 500.
(4) according to the external drive of closed-loop control system process and the output of process, the tracking error of closed-loop control system is obtained：
According to the structure of closed-loop system, the tracking error of system is obtained：
E (k)=y (k)-r (k)
Wherein, e (k) represents the actual tracking error of k moment closed-loop control systems, and r (k) represents to swash outside k etching process
Encourage, y (k) represents the output of k etching process, k=1,2 ... ..., 500.
(5) according to closed-loop control system structure, rectangular projection is carried out to gained the output of process and process input data, obtained
Process estimation interference updates：
Gained the output of process and process input data are run according to closed-loop control system, the high-order for setting up the output of process is returned certainly
Return model as follows：
yp(k)=[y (k) y (k-1) ... y (k-p)]
The high-order autoregression model for setting up process external drive is as follows：
rp(k)=[r (k) r (k-1) ... r (k-p)]
Wherein, process external drive is r (k), is set as in embodiment：R (k)=[0.9*sin (k) 0.05*sin
(k)]；P represents the data window size that process estimation interference updates, and M represents the order of the output of process high-order autoregression model, N
The order of expression process external drive high-order autoregression model；
The output of process and the mixing high-order autoregression model of process external drive are set up, it is specific as follows：
To matrixMake QR decomposition, i.e.,Obtain orthogonal matrix Q1And Q2,
Diagonal matrix R11, diagonal matrix R22With row vector R21；
Pass through orthogonal projection algorithm, acquisition process estimation interference renewal vector：
Wherein,Represent that the process estimation of 1 × (P+1) dimensions is dry
Renewal vector is disturbed, e ° (k) represents that process estimation interference updates obtained by the k moment, and I represents the unit matrix of (P+1) × (P+1) dimensions.
According to orthogonal matrix Q1And Q2, diagonal matrix R11, diagonal matrix R22With row vector R21Between relation, obtain it is as follows
As a result：
Final reliable process estimation interference is obtained to update：
In embodiment, k=1,2 ... ..., 500, the sample number N of collection is set to 500, predicts time domain P=100, controls time domain
M=10.
The high-order autoregression model for setting up process external drive signal is as follows：
rp(k)=[r (k) r (k-1) ... r (k-p)]
Wherein, p represents the data window size that process estimation interference updates, and N represents that the high-order of process external drive is returned certainly
Return the order of model, r (k) represents the process external drive at k moment, and r (k-1) represents the process external drive at (k-1) moment, r
(k-p) the process external drive at (k-p) moment, r are representedp(k) represent by r (k), r (k-1) ..., r (k-p) constituted 1 ×
(P+1) dimensional vector, rp(k-1) 1 × (P+1) dimensional vector being made up of r (k-1), r (k-2) ..., r (k-p-1), r are representedp
(k-2) 1 × (P+1) dimensional vector being made up of r (k-2), r (k-3) ..., r (k-p-2), r are representedp(k-N) represent by r (k-
N), 1 × (P+1) dimensional vector that r (k-N-1) ..., r (k-p-N) are constituted, Xp(k) represent by rp(k-1), rp(k-2) ...,
rp(k-M) M constituted × (P+1) ties up matrix；
According to above-mentioned high-order autoregression model, by orthogonal projection algorithm, acquisition process estimation interference update expanded type to
Amount：
Wherein, ep(k)=[e (k) e (k-1) ... e (k-p)], represents the model residual vector of 1 × (P+1) dimensions, e (k)
Model residual error obtained by the k moment is represented, I represents the unit matrix of (P+1) × (P+1) dimensions, Xp(k) represent by rp(k), rp(k-
..., r 1)p(k-M) M constituted × (P+1) ties up matrix.
(6) updated and above-mentioned actual tracking error, acquisition closed loop according to the estimation interference of the process of above-mentioned closed-loop control system
The block mold quality index of control system；
Key Performance Indicator KPI is defined according to output weight matrix Q and input weight matrix S：
Wherein, JnRepresent that Key Performance Indicator KPI, n represent sampled data length needed for asking for index, be set to 500；y(k)
Represent k etching process reality outputs：Overhead concentration XDWith bottom of towe liquid concentration XB, y is designated as respectively1And y2；Outside process
Excitation r (k) is set to：
R (k)=[0.9*sin (k) 0.05*sin (k)]；Δu*(k)=u (k)-u (k-1) represents the control of k etching process
Input and the difference of (k-1) etching process control input, output weight matrix Q=diag { 1,100 }, input weight matrix S=0.
E ° (k) and actual tracking error e (k) are updated according to process estimation interference, the model matter of closed-loop control system is obtained
Figureofmerit MQI：
Wherein, n refers to be 500 in sampled data length needed for asking for index, embodiment；E (k) represents k moment closed loop controls
The actual tracking error of system processed, e ° (k) represents that the process estimation interference of k moment closed-loop control systems updates, and Q represents output power
In weight matrix, embodiment, Q=diag { 1,100 }.
Expanded type is updated according to process estimation interferenceWith actual tracking error e (k), closed-loop control system is obtained
Process model quality-monitoring index MDI：
Wherein, n represents sampled data length needed for asking for index,Represent the process of k moment closed-loop control systems
Estimation interference updates expanded type, and e (k) represents the actual tracking error of k moment closed-loop control systems, and Q represents to export weight matrix.
(7) according to closed-loop control system structure, block mold quality index and process model quality-monitoring index pair are utilized
Modeling quality is monitored；In embodiment 1, having for model quality index MDI and MQI is verified by following six kinds of different situations
Effect property.
Situation one：Process model and interference model is made all to match first, Gp(s)=G (s), Hp(q)=H (q).Now, ηMDI
And ηMQIValue is respectively 0.96 and 0.96, all close to 1, shows that mismatch is not present in process-interference built-up pattern.
Situation two：Only there is mismatch in process model, and be mismatched for gain.
First in process model gain mismatch (Δ Kp＞ 0 or Δ Kp＜ 0) and other parameters are matched, i.e. Δ Tp=0, Δ Dp
When=0, η is obtainedMDI, ηMQIWith KPI value.The process model gain different by setting i.e. Δ KpValue, obtain in process mould
There is KPI, MQI and the MDI index in the case of different degrees of gain mismatch in type, as shown in table 1.
Table 1：η during process model gain mismatchMDI, ηMQI, KPI
From the acquired results of table 1, no matter Δ Kp＞ 0 or Δ Kp＜ 0, Δ KpDistance 0 is bigger, ηMDIAnd ηMQIValue is smaller.Example
Such as, as Δ KpWhen=- 0.5, ηMDI=0.44, ηMQI=0.42；As Δ KpWhen=- 0.2, ηMDI=0.84, ηMQI=0.83, compare
ΔKpCloser to 1 when=- 0.5.Therefore, this method can detect process model mismatch feelings when being mismatched comprising model gain
Condition.
Situation three：Only there is mismatch in process model, and be mismatched for time constant.Lost first in process model time constant
With (Δ Tp＞ 0 or Δ Tp＜ 0) and other parameters are matched, i.e. Δ Kp=0, Δ DpWhen=0, η is obtainedMDI, ηMQIWith KPI value.It is logical
Cross and set different process model time constants i.e. Δ TpValue, obtain there is different degrees of time constant mismatch in process model
In the case of MDI, MQI and KPI index, as shown in table 2.
Table 2：η during process model time constant mismatchMDI, ηMQI, KPI
From the acquired results of table 2, no matter Δ Tp＞ 0 or Δ Tp＜ 0, Δ TpDistance 0 is bigger, ηMDIAnd ηMQIValue is smaller.Example
Such as, as Δ TpWhen=- 0.4, ηMDI=0.47, ηMQI=0.46；As Δ TpWhen=- 0.2, ηMDI=0.83, ηMQI=0.82, compare
ΔTpCloser to 1 when=- 0.4.Therefore, this method can detect that process model when being mismatched comprising model time constant loses
With situation.
Situation four：All there is mismatch condition in process model gain and time constant.
First in process model gain mismatch and time constant mismatch (Δ Kp＞ 0 or Δ Kp＜ 0, Δ Tp＞ 0 or Δ Tp＜
0) other parameters matching, i.e. Δ DpWhen=0, η is obtainedMDI, ηMQIWith KPI value.The process model gain different by setting
ΔKpWith time constant Δ TpValue, obtain existing under different degrees of gain and time constant mismatch condition in process model
MDI, MQI and KPI index, as shown in table 3.
Table 3：Process model gain, η during time constant mismatchMDI, ηMQI, KPI
From the acquired results of table 3, as Δ Kp=0.5, Δ TpWhen=- 0.5, ηMDI=0.51, ηMQI=0.49.As Δ Tp
=-0.5 keeps constant, Δ KpWhen being changed into 0.9 from 0.5, ηMDI=0.41, ηMQI=0.36.As Δ Kp=0.5 keeps constant, Δ Tp
When being changed into 0.5 from -0.5, ηMDI=0.65, ηMQI=0.62.|ΔKp| or | Δ Tp| bigger, Δ ηMDIAlso it is bigger, therefore, should
Method can detect process model mismatch condition when all being mismatched comprising model gain and time constant.
Situation five：Process model gain mismatch, interference model matching, controller parameter is different.
First in process model gain mismatch (Δ Kp=0.5) and in the case of interference model matching, obtain in different controls
η during device parameter processedMDI, ηMQIWith KPI value.MPC1 is process model gain mismatch (Δ Kp=0.5) matched with interference model
In the case of, output weight matrix and input weight matrix are respectively Q=diag { 1,100 } and S=0.Correspondingly, MPC2 output
Weight matrix and input weight matrix are respectively Q=diag { 0.5,100 } and S=0.MPC3 output weight matrix and input are weighed
Weight matrix is respectively Q=diag { 2,100 } and S=diag { 0.5,0 }.
Table 4：Process model gain mismatch, η during different controller parametersMDI, ηMQI, KPI
From the acquired results of table 4, in the case where output weight matrix Q and input weight matrix S changes, ηMDI
And ηMQIAll keep constant, respectively 0.75 and 0.72, and KPI value is increased to 153.89 from 88.37.This result shows, controls
Device adjusting parameter processed has significant impact to control performance, and proposed model quality Testing index ηMDIValue not
The influence of controlled device adjusting parameter.
Situation six：There is different degrees of matching in process model gain and time constant mismatch, interference model.
First in process model gain and time constant mismatch (Δ Kp=-0.5, Δ Tp=0.5) other parameters matching,
That is Δ Dp=0, when there is different degrees of mismatch condition in interference model, ηMDI, ηMQIWith KPI value.The different interference by setting
Model gain AK1Value, obtain in process model gain and time constant mismatch, interference model has different degrees of mismatch condition
Under MDI, MQI and KPI index, as shown in table 5.
Table 5：Process model is matched, η during interference model mismatchMDI, ηMQI, KPI
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, it is not used to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the invention etc., it all should include
Within protection scope of the present invention.
Claims (9)
1. a kind of modeling quality control method based on model predictive controller, it is characterised in that including：
(1) using model predictive controller control closed-loop control system operation, the process of closed-loop control system running is gathered
Output, process input and process external drive；
(2) according to process external drive and the output of process, the tracking error of closed-loop control system is obtained；
(3) the high-order autoregression model of the output of process and the high-order autoregression model of process external drive are set up, process is obtained defeated
Go out the mixing high-order autoregression model with process external drive, rectangular projection is carried out based on mixing high-order autoregression model, obtained
Process estimation interference renewal vector；
(4) matrix model of process external drive is set up, rectangular projection is carried out using the matrix model of process external drive, obtains
Process estimation interference updates spread vector；
(5) process is estimated to disturb the quadratic form of renewal vector and the ratio of the quadratic form of tracking error to be used as block mold quality
Index, process is estimated interference updates the quadratic form of spread vector and the ratio of the quadratic form of tracking error is used as process model matter
Measure monitoring index；
(6) process model in process model quality-monitoring index and block mold quality index, detection closed-loop control system is utilized
Mismatch and interference model mismatch, and then monitor the modeling quality of closed-loop control system.
2. a kind of modeling quality control method based on model predictive controller as claimed in claim 1, it is characterised in that institute
The specific implementation for stating the high-order autoregression model for setting up the output of process is：
yp(k)=[y (k) y (k-1) ... y (k-p)]
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Wherein, p represents the data window size that process estimation interference updates, and M represents the high-order autoregression model of the output of process
Order, y (k) represents the output of process at k moment, and y (k-1) represents the output of process at (k-1) moment, when y (k-p) represents (k-p)
The output of process at quarter, yp(k) 1 × (P+1) dimensional vector being made up of y (k), y (k-1) ..., y (k-p), y are representedp(k-1) table
Show by y (k-1), 1 × (P+1) dimensional vector that y (k-2) ..., y (k-p-1) are constituted, yp(k-2) represent by y (k-2), y (k-
3) ..., 1 × (P+1) dimensional vectors that are constituted of y (k-p-2), yp(k-M) represent by y (k-M), y (k-M-1) ..., y (k-p-
M 1) constituted × (P+1) dimensional vector, YM(k-1) the high-order autoregression model for representing the output of process is by yp(k-1), yp(k-
..., y 2)p(k-M) M constituted × (P+1) ties up matrix.
3. a kind of modeling quality control method based on model predictive controller as claimed in claim 2, it is characterised in that institute
The specific implementation for stating the high-order autoregression model for setting up process external drive is：
rp(k)=[r (k) r (k-1) ... r (k-p)]
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Wherein, p represents the data window size that process estimation interference updates, and N represents the high-order autoregression mould of process external drive
The order of type, r (k) represents the process external drive at k moment, and r (k-1) represents the process external drive at (k-1) moment, r (k-p)
Represent the process external drive at (k-p) moment, rp(k) 1 × (P+1) being made up of r (k), r (k-1) ..., r (k-p) is represented
Dimensional vector, rp(k-1) 1 × (P+1) dimensional vector being made up of r (k-1), r (k-2) ..., r (k-p-1), r are representedp(k-2) table
Show by r (k-2), 1 × (P+1) dimensional vector that r (k-3) ..., r (k-p-2) are constituted, rp(k-N) represent by r (k-N), r (k-
N-1) ..., 1 × (P+1) dimensional vectors that are constituted of r (k-p-N), RN(k-1) the high-order autoregression mould of process external drive is represented
Type is by rp(k-1), rp..., r (k-2)p(k-N) N constituted × (P+1) ties up matrix.
4. a kind of modeling quality control method based on model predictive controller as claimed in claim 3, it is characterised in that institute
State foundation mixing high-order autoregression modelSpecific implementation be：
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5. a kind of modeling quality control method based on model predictive controller as claimed in claim 4, it is characterised in that institute
Stating process estimation interference renewal vector is：
To matrixMake QR decomposition, i.e.,Obtain orthogonal matrix Q1And Q2, to angular moment
Battle array R11, diagonal matrix R22With row vector R21；According to orthogonal matrix Q1And Q2, diagonal matrix R11, diagonal matrix R22With row vector R21
Between relation, the results are as follows：
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Acquisition process estimation interference renewal vector：
6. a kind of modeling quality control method based on model predictive controller as claimed in claim 5, it is characterised in that institute
The specific implementation for stating step (4) is：
The matrix model of process external drive is set up, rectangular projection is carried out using the matrix model of process external drive, obtained
Journey estimation interference updates spread vector
Wherein, ep(k)=[e (k) e (k-1) ... e (k-p)], represents the tracking error vector of 1 × (P+1) dimensions, and e (k) represents k
The tracking error at moment, e (k-1) represents the tracking error at (k-1) moment, and e (k-p) represents the tracking error at (k-p) moment, I
Represent the unit matrix of (P+1) × (P+1) dimensions, Xp(k) matrix model of process external drive is represented, by rp(k), rp(k-
..., r 1)p(k-M) M constituted × (P+1) ties up matrix, rp(k-M) represent by r (k-M), r (k-M-1) ..., r (k-p-M)
1 constituted × (P+1) dimensional vector.
7. a kind of modeling quality control method based on model predictive controller as claimed in claim 1, it is characterised in that institute
The specific implementation for stating step (6) is：
Evaluation modeling quality is combined according to process model quality-monitoring index MDI and block mold quality index MQI；MQI's
Span for (0,1], block mold quality index shows that the modeling quality of closed-loop control system is better closer to 1, overall
Model quality index shows that the modeling quality of closed-loop control system is poorer closer to 0, when MDI values in relatively close proximity to 1 and MQI
Value shows that block mold is second-rate and process model quality preferably, then understands that interference model is second-rate in relatively close proximity to 0,
There is mismatch condition.
8. a kind of modeling Quality Monitoring Control System based on model predictive controller, it is characterised in that including：
Gathered data module, for using model predictive controller control closed-loop control system operation, gathering closed-loop control system
The output of process, process input and the process external drive of running；
Tracking error module is obtained, for according to process external drive and the output of process, the tracking for obtaining closed-loop control system to be missed
Difference；
Swash outside acquisition process estimation interference renewal vector module, the high-order autoregression model and process for setting up the output of process
The high-order autoregression model encouraged, obtains the output of process and the mixing high-order autoregression model of process external drive, high based on mixing
Rank autoregression model carries out rectangular projection, obtains process estimation interference renewal vector；
Acquisition process estimation interference updates spread vector module, and the matrix model for setting up process external drive utilizes process
The matrix model of external drive carries out rectangular projection, obtains process estimation interference and updates spread vector；
Index module is obtained, for estimating process to disturb the quadratic form of renewal vector and the ratio of the quadratic form of tracking error to make
For block mold quality index, process is estimated that interference updates the ratio of the quadratic form of spread vector and the quadratic form of tracking error
It is used as process model quality-monitoring index；
Monitoring modeling quality module, for utilizing process model quality-monitoring index and block mold quality index, detects closed loop
Process model mismatch and interference model mismatch in control system, and then monitor the modeling quality of closed-loop control system.
9. a kind of modeling Quality Monitoring Control System based on model predictive controller as claimed in claim 8, it is characterised in that institute
State monitoring modeling quality module specific implementation be：
Evaluation modeling quality is combined according to process model quality-monitoring index MDI and block mold quality index MQI；MQI's
Span for (0,1], block mold quality index shows that the modeling quality of closed-loop control system is better closer to 1, overall
Model quality index shows that the modeling quality of closed-loop control system is poorer closer to 0, when MDI values in relatively close proximity to 1 and MQI
Value shows that block mold is second-rate and process model quality preferably, then understands that interference model is second-rate in relatively close proximity to 0,
There is mismatch condition.
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| CN108536127B (en) * | 2018-04-20 | 2019-08-13 | 华中科技大学 | A kind of model mismatch diagnostic method of the multivariable control system of data-driven |
| CN111176155A (en) * | 2019-12-20 | 2020-05-19 | 华中科技大学 | Process model mismatch detection method of closed-loop model predictive control system |
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