CN105700358A - Modeling quality monitoring method for model predictive controller (MPC) with drift interference - Google Patents

Abstract

The invention discloses a modeling quality monitoring method for a model predictive controller (MPC) with drift interference. The method comprises the following steps: an interference model for a closed loop control system is built; according to the actual condition of the closed loop control system and a given control target, a dynamic model predictive controller (MPC) for a process is designed; the interference model and the MPC are adopted for controlling the closed loop control system, and process data obtained by operation of the closed loop control system are acquired; according to the structure of the closed loop control system, orthogonal projection is carried out on process output and process input data, and process estimation interference update is acquired; according to an established reference signal of the closed loop control system and the process actual output, the actual tracking error of the closed loop control system is acquired; according to the process estimation interference update and the actual tracking error, a model quality index for the closed loop control system is acquired; and according to the structure of the closed loop control system, the model quality index is used for monitoring the modeling quality. The method of the invention has the advantages of high feasibility, few consumed resources for processing, and high evaluation result accuracy.

Description

A kind of modeling quality control method of the model predictive controller with drift interference

Technical field

The invention belongs to Model Predictive Control field, more particularly, to the modeling quality control method of a kind of model predictive controller with drift interference。

Background technology

Model Predictive Control (ModelPredictiveControl, MPC) is a kind of advanced control method based on model being widely used in industrial process control field, has effective, the strong robustness of control, to the less demanding advantage of model exactness。

Model Predictive Control practical application on industrial process, is referred to as model predictive controller (ModelPredictiveController, MPCController)。MPC controller has modeling and simply, dynamically controls feature effective, strong robustness, has good control performance at the operation initial stage；But, As time goes on, MPC controller performance can be gradually reduced, and finally even must not switch to traditional PID control。Cause that the principal element that controller performance declines has noise jamming, model mismatch, valve viscous, perceptron deviation etc.。Therefore, the performance of MPC controller being carried out real-time assessment and monitoring, find that in time its hydraulic performance decline is also reported to the police, and then diagnosis performance worsens root, to ensureing safe efficient, the high-quality of production process, low consumption runs has important practical significance。

In recent years, it is increasingly being applied to control System Performance Analysis problem based on the method for data-driven。Such as the historical performance index under MPC framework, the performance of MPC can be made effectively evaluating, but it needs the data obtaining one-stage control system operational excellence to carry out Calculation Estimation benchmark, and choosing of this good operation phase does not have standard, thus bringing certain limitation to the application of the method。In System design based on model technology, the quality of model plays a key effect for the design and adjusting of controller, and the performance controlling system depends on the precision of process model, that is is subject to the impact of model mismatch degree。

On the one hand, but in actual industrial process, interference tends to vary with the time and is slowly incremented by, and presents the feature of non-gaussian about technology many employings white noise of modeling quality monitoring as system interference noise source present stage；On the other hand, present stage there is no, about the technology of modeling quality monitoring, the deterioration root that method diagnosis causes controller performance to be deteriorated, cannot the reason of diagnosing controller degradation be in that model exists mismatch, or in the factor such as noise jamming, valve viscous, perceptron deviation。

Summary of the invention

Disadvantages described above or Improvement requirement for prior art, the invention provides the modeling quality control method of a kind of model predictive controller with drift interference, the conventional inputoutput data that its object is to only need to utilize closed-loop control system can effective monitoring model quality, thus raising modeling quality monitoring accuracy。

For achieving the above object, according to one aspect of the present invention, it is provided that the modeling quality control method of a kind of model predictive controller with drift interference, comprise the steps:

(1) interference model of closed-loop control system is set up；

(2) according to the practical situation of closed-loop control system and given control target, the MPC controller of acquisition process；

(3) when closed-loop control system is run under the control of described interference model and MPC controller, gather closed-loop control system and run the process data of gained；Described process data includes the output of process and the process input of closed-loop control system；

(4) according to closed-loop control system structure, described the output of process and process are inputted data and carries out rectangular projection, it is thus achieved that process estimates that interference updates；

(5) according to the actual output of closed-loop control system given reference signal and process, the actual tracking error of closed-loop control system is obtained；

(6) estimate that interference updates and described actual tracking error according to described process, it is thus achieved that the model quality index of closed-loop control system；

(7) according to closed-loop control system structure, utilize described model quality index that modeling quality is monitored。

Preferably, above-mentioned steps (1) includes following sub-step:

(1.1) according to closed-loop control system structure, the single order moving average model(MA model) of industrial process is set up, specific as follows:

d_k=d_k-1+ε_k-θε_k-1

Wherein, θ is white noise mean coefficient ,-1 < θ < 1；ε_k～N (0, σ_ε ²) represent white noise；σ_ε ²Represent white noise variance；D_kExpression process random disturbances noise；

(1.2) in above-mentioned single order moving average model(MA model), add drift, obtain the single order moving average model(MA model) with drift interference, specific as follows:

d_k=d_k-1+ε_k-θε_k-1+δ

Wherein, δ is drift, d_kExpression process random disturbances noise。

Preferably, above-mentioned steps (2) includes following sub-step:

(2.1) according to given control target, the controlled variable CV, manipulation variable MV, the disturbance variable DV that are correlated with are defined；Wherein, DV refers to measurable disturbance that CV is influential, but can not handle；

(2.2) (2.2) are by doing Spline smoothing to described manipulation variable MV and disturbance variable DV, it is thus achieved that the dynamic changing data of each controlled variable CV, utilize the dynamic Model Prediction controller of identification algorithm acquisition process；And utilize parameter to select rule configuration controller。

Preferably, above-mentioned steps (3) includes following sub-step:

(3.1) according to the requirement controlling system, generating the process settings of closed-loop control system, this setting value is constant, is designated as r (k), and wherein k represents kth sampling instant；

(3.2) run closed-loop control system, obtain process input u (k) and the output of process y (k) of closed-loop control system。

Preferably, above-mentioned steps (4) includes following sub-step:

(4.1) according to closed-loop control system structure, the high-order autoregression model setting up the output of process is as follows:

y_p(k)=[y (k) y (k-1) ... y (k-p)]

$Y_M(k-1)=\left[\begin{array}{c}{y}_p(k-1)\\ y_p(k-2)\\ .\\ .\\ .\\ y_p(k-M)\end{array}\right]$

Wherein, p represents that process estimates the data window size that interference updates, and M represents the order of the output of process high-order autoregression model；Y (k) represents that the k moment gathers gained the output of process, and y (k-1) represents that (k-1) moment gathers gained the output of process ..., y (k-p) represents that (k-p) moment gathers gained the output of process, y_pK () represents by y (k), y (k-1) ..., 1 × (P+1) that y (k-p) is constituted ties up matrix；Y_M(k-1) represent by y_p(k-1), y_p(k-2) ..., y_p(k-M) M constituted × (P+1) ties up matrix；

(4.2) according to closed-loop control system structure, the high-order autoregression model setting up process settings is as follows:

r_p(k)=[r (k) r (k-1) ... r (k-p)]

$R_N(k-1)=\left[\begin{array}{c}{r}_p(k-1)\\ r_p(k-2)\\ .\\ .\\ .\\ r_p(k-N)\end{array}\right]$

Wherein, p represents that process estimates the data window size that interference updates, and N represents the order of process settings high-order autoregression model；

R (k) represents that the k moment gathers gained process settings, and r (k-1) represents that (k-1) moment gathers gained process settings ..., r (k-p) represents that (k-p) moment gathers gained process settings, r_pK () represents by r (k), r (k-1) ..., 1 × (P+1) that r (k-p) is constituted ties up matrix；R_N(k-1) represent by r_p(k-1), r_p(k-2) ..., r_p(k-N) N constituted × (P+1) ties up matrix；

(4.3) according to closed-loop control system structure, the mixing high-order autoregression model setting up the output of process and process settings is as follows:

$\stackrel{\&OverBar;}{Z_p}\left(k\right)=\left[\begin{array}{c}{Y}_M(k-1)\\ R_N(k-1)\end{array}\right]$

Wherein,Tieing up matrix for (M+N) × (P+1), front M row is by the high-order autoregression model Y of the output of process_M(k-1) composition, rear N row is by the high-order autoregression model R of process settings_N(k-1) composition；

(4.4) according to above-mentioned high-order autoregression model, by orthogonal projection algorithm, acquisition process estimates that interference updates vector:

$e_p\left(k\right)=y_p\left(k\right)(I-\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T{\&lsqb;\stackrel{\&OverBar;}{Z_p}\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T\&rsqb;}^{-1}\stackrel{\&OverBar;}{Z_p}(k\left)\right)$

Wherein, e_p(k)=[e (k) e (k-1) ... e (k-p)], represent that 1 × (P+1) process tieed up estimates that interference updates vector, e (k) represents that k moment gained process estimates that interference updates, and I represents (P+1) × (P+1) unit matrix tieed up；

Owing to closed-loop data has high correlation, thereforeBeing ill, interference renewal is unreliable to cause gained process to be estimated。

Preferably, step (4.4) solution to this problem farther includes following sub-step:

(4.4.1) to matrixMake QR to decompose, namelyObtain orthogonal matrix Q₁And Q₂, diagonal matrix R₁₁, diagonal matrix R₂₂With row vector R₂₁；

(4.4.2) according to orthogonal matrix Q₁And Q₂, diagonal matrix R₁₁, diagonal matrix R₂₂With row vector R₂₁Between relation, it is thus achieved that following result:

$y_p\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T=R_{21}{R_{11}}^T;$

$\stackrel{\&OverBar;}{Z_p}\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T=R_{11}{R_{11}}^T;$

(4.4.3) by above-mentioned (4.4.2) acquired results, obtain reliable process and estimate that interference updates:

$e_p\left(k\right)=y_p\left(k\right)-R_{21}{R_{11}}^T\stackrel{\&OverBar;}{Z_p}\left(k\right).$

Preferably, above-mentioned steps (5) is specific as follows:

According to closed-loop control system given reference signal (or control signal) and the actual output of process, obtain the actual tracking error of closed-loop control system:

$\stackrel{\&OverBar;}{e}\left(k\right)=y\left(k\right)-r\left(k\right);$

Wherein,Representing the actual tracking error of k moment closed-loop control system, r (k) represents k moment given reference signal, and y (k) represents the actual output of k etching process。

Preferably, above-mentioned steps (6) includes following sub-step:

(6.1) Key Performance Indicator KPI is defined according to output weight matrix Q and input weight matrix S:

$J_N=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}\&lsqb;{||y\left(k\right)-r\left(k\right)||}_Q^2+{||\mathrm{\&Delta;}u*\left(k\right)||}_S^2\&rsqb;$

Wherein, J_NRepresenting that Key Performance Indicator KPI, N represent and ask for sampled data length needed for index, y (k) represents the actual output of k etching process, and r (k) represents k moment given reference signal, Δ u^*K ()=u (k)-u (k-1) represents that k etching process controls the difference of input and the control input of (k-1) etching process；

(6.2) process obtained according to step (4) estimates that interference updates e (k) the actual tracking error obtained with step (5)Obtain the model quality index MQI of closed-loop control system:

$\mathrm{\&eta;}=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}e{\left(k\right)}^{T}Qe\left(k\right)}{\underset{k=1}{\overset{N}{\&Sigma;}}\stackrel{\&OverBar;}{e}{\left(k\right)}^{T}Q\stackrel{\&OverBar;}{e}\left(k\right)}$

Wherein, N represents and asks for sampled data length needed for index,Representing the actual tracking error of k moment closed-loop control system, e (k) represents that the process of k moment closed-loop control system estimates that interference updates, and Q represents output weight matrix。

Preferably, above-mentioned steps (7) is specific as follows:

Key Performance Indicator KPI according to above-mentioned closed-loop control system evaluates controller performance: KPI value is more little, represents that controller performance is more good；Model quality index MQI according to above-mentioned closed-loop control system evaluates modeling quality；The span of MQI be η ∈ (0,1], model quality index η is closer to 1, and the modeling quality of closed-loop control system is more good, and model quality quality index is closer to 0, and the modeling quality of closed-loop control system is more poor。

In general, by the contemplated above technical scheme of the present invention compared with prior art, it is possible to obtain following beneficial effect:

(1) modeling quality control method provided by the invention, process is disturbed renewal to estimate by the conventional closed loop loop data adopting current closed-loop control system, do not need the additional information of the ring opening process of the very difficult acquisition such as process time lag or Interactive matrix, make the method feasibility high, process required consumption resource few；

(2) modeling quality control method provided by the invention, in order to describe the actual interference situation of industrial process, adopt IMA (1,1) the model description disturbance noise with drift, more conform to industrial process practical situation, thus the assessment result of modeling quality is more accurate；

(3) modeling quality control method provided by the invention, current closed-loop control system need not be done any adjustment by processing procedure, and any dynamic excitation signal need not be added, thus industrial processes impact is minimum, significantly reduce monitoring cost, improve product quality and the security of system of industrial process, maintainable；

(4) modeling quality control method provided by the invention, the feedback invariant principle utilizing disturbance sequence proposes a kind of model quality index MQI, according to whether the model that this index can find in control system in time there is mismatch, it is achieved to the Real-Time Evaluation controlling systematic function；And owing to process estimates that interference updates the relation between the actual tracking error of process, the uncontrolled device of model quality index MQI regulates parameter change and the impact of closed-loop control system interference model change, relative to traditional KPI index, the factor of the affected controller entirety control performance outside model quality can be made a distinction by MQI index more exactly, thus characterizing modeling quality more accurately and effectively。

Accompanying drawing explanation

Fig. 1 is the overall flow schematic diagram of the model quality monitoring method that the embodiment of the present invention provides；

Fig. 2 is the closed loop system structural principle schematic diagram in embodiment；

Fig. 3 is the Wood-Berry rectifying column principle schematic in embodiment；

Fig. 4 is the simulation result figure in embodiment based on Wood-Berry rectifying column gained process estimating interference noise sequence；

Fig. 5 is the simulation result figure in embodiment based on Wood-Berry rectifying column gained model residual sequence；

Fig. 6 is the simulation result figure exporting y1 and setting value r1 in embodiment based on Wood-Berry rectifying column gained model；

Fig. 7 is the simulation result figure exporting y2 and setting value r2 in embodiment based on Wood-Berry rectifying column gained model。

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated。Should be appreciated that specific embodiment described herein is only in order to explain the present invention, is not intended to limit the present invention。As long as just can be mutually combined additionally, technical characteristic involved in each embodiment of invention described below does not constitute conflict each other。

The modeling quality control method of model predictive controller with drift interference that the embodiment of the present invention provides, its flow process is as it is shown in figure 1, specific as follows:

(1) according to industrial process actual interference situation, the interference model of closed-loop control system is set up；

(2) practical situation according to closed-loop control system, designs MPC controller；

(3) control closed-loop control system according to the interference model of above-mentioned closed-loop control system and above-mentioned MPC controller, and gather closed-loop control system operation gained the output of process and process input data；

(4) according to closed-loop control system structure, gained the output of process and process are inputted data and carries out rectangular projection, it is thus achieved that process estimates that interference updates；

(5) according to the actual output of closed-loop control system given reference signal (or control signal) and process, the actual tracking error of closed-loop control system is obtained；

(6) estimate that interference updates and above-mentioned actual tracking error according to the process of above-mentioned closed-loop control system, it is thus achieved that the model quality index of closed-loop control system；

(7) according to closed-loop control system structure, utilize above-mentioned model quality index that modeling quality is monitored；

Key Performance Indicator KPI according to gained closed-loop control system evaluates controller performance, and KPI value is more little, represents that controller performance is more good；Model quality index MQI according to gained closed-loop control system evaluates modeling quality, the span of MQI is η ∈ (0,1], model quality index η is closer to 1, the modeling quality of closed-loop control system is more good, model quality quality index is closer to 0, and the modeling quality of closed-loop control system is more poor。

Shown in Fig. 2, it it is the closed-loop control system structure chart adopted in the embodiment of the present invention, u (t), y (t) represent process input and the output of process of closed-loop control system respectively, r (t) represents the process settings of closed-loop control system, and d (t) represents the external interference of closed-loop control system；G_cFor the transmission function of the controller of general closed-loop control system, being MPC controller in embodiment, G is process transmission function。

Below with Wood-Berry rectifying column process for embodiment, the modeling quality control method of the model predictive controller with drift interference provided by the invention is described further。

In embodiment, Wood-Berry rectifying column is a mimo systems typically with relatively large time delay；Process is as it is shown on figure 3, be output as overhead concentration X_DWith liquid concentration X at the bottom of tower_B, overhead reflux amount R and tower bottom reboiler quantity of steam S control；Process model is:

$\left[\begin{array}{c}{X}_D\left(s\right)\\ X_B\left(s\right)\end{array}\right]=\left[\begin{array}{cc}\frac{12.8e^{-s}}{16.7s+1}& \frac{-18.9e^{-3s}}{16.7s+1}\\ \frac{6.6e^{-7s}}{10.9s+1}& \frac{-19.4e^{-3s}}{14.4s+1}\end{array}\right]\left[\begin{array}{c}R\left(s\right)\\ S\left(s\right)\end{array}\right]$

Wherein, input u₁Representing reflux rate, unit is 1b/min；Input u₂Representing steam flow, unit is 1b/min；Output y₁Representing overhead concentration, unit is mol%；Output y₂Representing liquid concentration at the bottom of tower, unit is mol%。

In embodiment, the process transfer function matrix of Wood-Berry rectifying column is:

$G\left(s\right)=\left[\begin{array}{cc}\frac{12.8e^{-s}}{16.7s+1}& \frac{-18.9e^{-3s}}{16.7s+1}\\ \frac{6.6e^{-7s}}{10.9s+1}& \frac{-19.4e^{-3s}}{14.4s+1}\end{array}\right]$

Wherein, s represents Laplace operator。

In embodiment, the process sampling time is 1min/ time, and the process transfer function matrix after discretization is:

$\stackrel{\&OverBar;}{G}\left(q\right)=\left[\begin{array}{cc}{q}^{-2}\frac{0.744}{1-0.9419q^{-1}}& q^{-4}\frac{-0.8789}{1-0.9535q^{-1}}\\ q^{-8}\frac{0.5786}{1-0.9123q^{-1}}& q^{-4}\frac{-1.302}{1-0.9329q^{-1}}\end{array}\right]$

In embodiment, interference model takes following diagonal matrix:

$\stackrel{\&OverBar;}{H}\left(q\right)=\left[\begin{array}{cc}\frac{1-0.5q^{-1}}{1-q^{-1}}& \\ & \frac{1-0.7q^{-1}}{1-q^{-1}}\end{array}\right]$

The Wood-Berry rectifying column process of embodiment is modeled quality monitoring process by the modeling quality control method utilizing the model predictive controller with drift interference provided by the invention, 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 process is as follows:

$\stackrel{\&OverBar;}{H}\left(q\right)=\left[\begin{array}{cc}\frac{1-0.5q^{-1}}{1-q^{-1}}& \\ & \frac{1-0.7q^{-1}}{1-q^{-1}}\end{array}\right]$

It is stated that following common version:

$\stackrel{\&OverBar;}{H}\left(q\right)=\left[\begin{array}{cc}\frac{1-(1-K_1)q^{-1}}{1-q^{-1}}& \\ & \frac{1-(1-K_2)q^{-1}}{1-q^{-1}}\end{array}\right]$

With the single order moving average model(MA model) (IMA (1,1)) of drift interference, it is expressed as follows:

d_k=d_k-1+ε_k-θε_k-1+δ

Wherein, δ represents drift, d_kExpression process random disturbances noise；

In formula,e_k～N (δ/(1-θ), σ_ε ²)。Make δ=0.005, θ=0.5, thenIn embodiment, σ²Respectively 7.6²With 0.14²；D_kIt is the interference model that Wood-Berry rectifying column process adopts, wherein, k=1,2 ..., 500。

(2) practical situation according to closed-loop control system, design a model predictive controller MPC, in embodiment, utilizes existing MPCToolbox in MATLAB workbox to design MPC controller；MPC controller parameter takes prediction time domain P=100, controls time domain M=10, and needed for index, sampled data length takes N=500。For realizing minimum variance principle, weight matrix is set to Q=diag{1,100}, S=0；Process settings is:

(3) control closed-loop control system according to the interference model of above-mentioned closed-loop control system and above-mentioned MPC controller, and gather closed-loop control system operation gained the output of process and process input data；

When closed-loop control system is properly functioning, the sampling time is set as 1min/ time, gathers closed-loop control system Wood-Berry rectifying column and runs gained the output of process data, including overhead concentration X_DWith liquid concentration X at the bottom of tower_B, it is designated as y respectively₁And y₂；Process input data, including fight back flow R and tower bottom reboiler quantity of steam S, are designated as u respectively₁And u₂；The sample number N gathered is set to 500。

(4) according to closed-loop control system structure, gained the output of process and process are inputted data and carry out rectangular projection, it is thus achieved that process estimates that interference updates:

Run gained the output of process and process input data according to closed-loop control system, the high-order autoregression model setting up the output of process is as follows:

y_p(k)=[y (k) y (k-1) ... y (k-p)]

$Y_M(k-1)=\left[\begin{array}{c}{y}_p(k-1)\\ y_p(k-2)\\ .\\ .\\ .\\ y_p(k-M)\end{array}\right]$

The high-order autoregression model setting up setting value is as follows:

r_p(k)=[r (k) r (k-1) ... r (k-p)]

$R_N(k-1)=\left[\begin{array}{c}{r}_p(k-1)\\ r_p(k-2)\\ .\\ .\\ .\\ r_p(k-M)\end{array}\right]$

Wherein, process settings r (k) is constant, is set as in embodiment:P represents that process estimates the data window size that interference updates, and M represents the order of the output of process high-order autoregression model, and N represents the order of process settings high-order autoregression model；

Set up the output of process and the mixing high-order autoregression model of process settings (or process input), specific as follows:

$\stackrel{\&OverBar;}{Z_p}\left(k\right)=\left[\begin{array}{c}{Y}_M(k-1)\\ R_N(k-1)\end{array}\right]$

To matrixMake QR to decompose, namelyObtain orthogonal matrix Q₁And Q₂, diagonal matrix R₁₁, diagonal matrix R₂₂With row vector R₂₁；

By orthogonal projection algorithm, acquisition process estimates that interference updates vector:

$e_p\left(k\right)=y_p\left(k\right)(I-\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T{\&lsqb;\stackrel{\&OverBar;}{Z_p}\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T\&rsqb;}^{-1}\stackrel{\&OverBar;}{Z_p}(k\left)\right)$

Wherein, e_p(k)=[e (k) e (k-1) ... e (k-p)], represent that 1 × (P+1) process tieed up estimates that interference updates vector, e (k) represents that k moment gained process estimates that interference updates, and I represents (P+1) × (P+1) unit matrix tieed up；

According to orthogonal matrix Q₁And Q₂, diagonal matrix R₁₁, diagonal matrix R₂₂With row vector R₂₁Between relation, it is thus achieved that following result:

$y_p\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T=R_{21}{R_{11}}^T$

$\stackrel{\&OverBar;}{Z_p}\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T=R_{11}{R_{11}}^T$

Obtain final process reliably and estimate that interference updates:

$e_p\left(k\right)=y_p\left(k\right)-R_{21}{R_{11}}^T\stackrel{\&OverBar;}{Z_p}\left(k\right)$

In embodiment, k=1,2 ..., 500, the sample number N of collection is set to 500, it was predicted that time domain P=100, controls time domain M=10。

(5) according to the actual output of closed-loop control system given reference signal (or control signal) and process, the actual tracking error of closed-loop control system is obtained:

Structure according to closed loop system, obtains the tracking error of system:

$\stackrel{\&OverBar;}{e}\left(k\right)=y\left(k\right)-r\left(k\right)$

Wherein,Representing the actual tracking error of k moment closed-loop control system, r (k) represents k moment given reference signal, and y (k) represents the actual output of k etching process, k=1,2 ..., 500。

(6) estimate that interference updates and above-mentioned actual tracking error according to the process of above-mentioned closed-loop control system, it is thus achieved that the model quality index of closed-loop control system

Key Performance Indicator KPI is defined according to output weight matrix Q and input weight matrix S:

$J_N=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}\&lsqb;{||y\left(k\right)-r\left(k\right)||}_Q^2+{||\mathrm{\&Delta;}u*\left(k\right)||}_S^2\&rsqb;---\left(1\right)$

Wherein, J_NRepresent that Key Performance Indicator KPI, N represent and ask for sampled data length needed for index, be set to 500；Y (k) represents the actual output of k etching process: overhead concentration X_DWith liquid concentration X at the bottom of tower_B, it is designated as y respectively₁And y₂；Process settings r (k) is constant, is set to: Δu^*K ()=u (k)-u (k-1) represents that k etching process controls the difference of input and the control input of k-1 etching process, export weight matrix Q=diag{1,100}, input weight matrix S=0。

Estimate that interference updates e (k) and actual tracking error according to processObtain the model quality index MQI of closed-loop control system:

$\mathrm{\&eta;}=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}e{\left(k\right)}^{T}Qe\left(k\right)}{\underset{k=1}{\overset{N}{\&Sigma;}}\stackrel{\&OverBar;}{e}{\left(k\right)}^{T}Q\stackrel{\&OverBar;}{e}\left(k\right)}---\left(2\right)$

Wherein, N refers to and asks for sampled data length needed for index, is 500 in embodiment；Representing the actual tracking error of k moment closed-loop control system, e (k) represents that the process of k moment closed-loop control system estimates that interference updates, and Q represents output weight matrix, in embodiment, and Q=diag{1,100}。

(7) according to closed-loop control system structure, utilize model quality index that modeling quality is monitored；In embodiment, verified the effectiveness of model quality index MQI by following three kinds of different situations。

Situation one: process model mates, but interference model mismatch:

Making K1=0.5, K2=0.3, the situation that simulation process model and interference model all mate, by calculating formula (1) and formula (2), obtaining corresponding KPI desired value be 450.3286, MQI desired values is 0.9993；By setting different K1 and K2 values, obtain the KPI index under interference model exists mismatch condition in various degree and MQI index, as shown in table 1:

Table 1: process model mates, the parameter list under interference model mismatch condition

Can analyzing from table 1, the first row result is two CV variablees is all the white noise interference gained adding drift, due to the interference model that employing is more mated, MQI and KPI index all the increasing than the first row in second, three, four row results。

Simulation result is as shown in figs. 4-7；Can analyze from Fig. 4, estimated interference noise sequence is close to white noise but be not exclusively white noise, overall distribution has a small drift。Fig. 5 is model residual sequence, Fig. 6, and Fig. 7 is model output and setting value, can analyze from Fig. 6, Fig. 7, and the control effectiveness comparison of model is desirable, can overall tracking fixed valure and process tend towards stability。

Situation two: process model and interference model all match condition, but controller parameter is different:

In order to verify the uncontrolled device parameter impact of MQI index, and there is this defect in KPI index, when process model and interference model all mate, can carry out following three groups of contrast tests:

(I) fundamental test, i.e. K1=0.5, K2=0.3 in situation one；

(II) input weight matrix is set to S=diag{0.2,0.6}；

(III) namely reflux rate inputs u₁It is defined as u₁≤151b/min。

Simulation results is as follows:

Table 2: process model and the controller parameter list under the equal match condition of interference model

Can be analyzed by table 2 acquired results, all mate at process model and interference model, when controller parameter changes, KPI index generation respective change, but MQI index remains unchanged；Thus, demonstrate MQI index can the factor of the affected controller entirety control performance outside model quality be made a distinction exactly。

Situation three: process model and the equal mismatch condition of interference model:

When process model exists mismatch condition, it is assumed that in MPC, the steady-state gain of process model comprises the deviation of 20-40%, specific as follows:

$G\left(q\right)=\left[\begin{array}{cc}0.8q^{-2}\frac{0.744}{1-0.9419q^{-1}}& 0.6q^{-4}\frac{-0.8789}{1-0.9535q^{-1}}\\ q^{-8}\frac{0.5786}{1-0.9123q^{-1}}& 1.2q^{-4}\frac{-1.302}{1-0.9329q^{-1}}\end{array}\right]$

By setting different K1 and K2 values, make interference model there is mismatch condition in various degree, obtain result as shown in table 3。

Table 3: the parameter list of process model and the equal mismatch condition of interference model

Can be analyzed by table 3 acquired results, fix at process model mismatch condition, by setting different Kalman gains and obtain the interference model of different mismatch condition and when controller parameter does not change, along with successively decreasing of KPI index, MQI index is incremented by accordingly, thus, demonstrating MQI index can Efficient Characterization modeling quality。

Those skilled in the art will readily understand; the foregoing is only presently preferred embodiments of the present invention; not in order to limit the present invention, all any amendment, equivalent replacement and improvement etc. made within the spirit and principles in the present invention, should be included within protection scope of the present invention。

Claims (9)

1. the modeling quality control method of the model predictive controller with drift interference, it is characterised in that comprise the steps:

(1) interference model of closed-loop control system is set up；

(2) according to closed-loop control system parameter and given control target, the MPC controller of acquisition process；

(3) when closed-loop control system is run under the control of described interference model and MPC controller, gather closed-loop control system and run the process data of gained；Described process data includes the output of process and the process input of closed-loop control system；

(4) according to closed-loop control system structure, described the output of process and process are inputted data and carries out rectangular projection, it is thus achieved that process estimates that interference updates；

(5) according to the actual output of closed-loop control system given reference signal and process, the actual tracking error of closed-loop control system is obtained；

(6) estimate that interference updates and described actual tracking error according to described process, it is thus achieved that the model quality index of closed-loop control system；

(7) according to closed-loop control system structure, utilize described model quality index that modeling quality is monitored。

2. modeling quality control method as claimed in claim 1 is characterized in that, described step (1) includes following sub-step:

(1.1) according to closed-loop control system structure, the single order moving average model(MA model) of industrial process is set up, specific as follows:

d_k=d_k-1+ε_k-θε_k-1

Wherein, θ is white noise mean coefficient ,-1 < θ < 1；ε_k～N (0, σ_ε ²) represent white noise；σ_ε ²Represent white noise variance；D_kExpression process random disturbances noise；

(1.2) in above-mentioned single order moving average model(MA model), add drift, obtain the single order moving average model(MA model) with drift interference, specific as follows:

d_k=d_k-1+ε_k-θε_k-1+δ

Wherein, δ is drift, d_kExpression process random disturbances noise。

3. model quality control method as claimed in claim 1 or 2, it is characterised in that described step (2) includes following sub-step:

(2.1) according to given control target, definition controlled variable CV, manipulation variable MV and disturbance variable DV；

(2.2) by described manipulation variable MV and disturbance variable DV is done Spline smoothing, it is thus achieved that the dynamic changing data of each controlled variable CV, the MPC controller of identification algorithm acquisition process is utilized；And utilize parameter to select rule configuration controller。

4. model quality control method as claimed in claim 1 or 2, it is characterised in that described step (3) includes following sub-step:

(3.1) according to the requirement controlling system, process settings r (k) of closed-loop control system is generated；Described setting value is constant, and k represents kth sampling instant；

(3.2) run closed-loop control system, obtain process input u (k) and the output of process y (k) of closed-loop control system。

5. model quality control method as claimed in claim 1 or 2, it is characterised in that described step (4) includes following sub-step:

(4.1) according to closed-loop control system structure, the high-order autoregression model setting up the output of process is as follows:

y_p(k)=[y (k) y (k-1) ... y (k-p)]

$Y_M(k-1)=\left[\begin{array}{c}{y}_p(k-1)\\ y_p(k-2)\\ .\\ .\\ .\\ y_p(k-M)\end{array}\right]$

Wherein, p represents that process estimates the data window size that interference updates, and M represents the order of the output of process high-order autoregression model；Y (k) represents that the k moment gathers gained the output of process, and y (k-1) represents that the k-1 moment gathers gained the output of process ..., y (k-p) represents that (k-p) moment gathers gained the output of process, y_pK () represents by y (k), y (k-1) ..., 1 × (P+1) that y (k-p) is constituted ties up matrix；Y_M(k-1) represent by y_p(k-1), y_p(k-2) ..., y_p(k-M) M constituted × (P+1) ties up matrix；

(4.2) according to closed-loop control system structure, the high-order autoregression model setting up process settings is as follows:

r_p(k)=[r (k) r (k-1) ... r (k-p)]

$R_N(k-1)=\left[\begin{array}{c}{r}_p(k-1)\\ r_p(k-2)\\ .\\ .\\ .\\ r_p(k-N)\end{array}\right]$

Wherein, p represents that process estimates the data window size that interference updates, and N represents the order of process settings high-order autoregression model；

R (k) represents that the k moment gathers gained process settings, and r (k-1) represents that (k-1) moment gathers gained process settings ..., r (k-p) represents that (k-p) moment gathers gained process settings, r_pK () represents by r (k), r (k-1) ..., 1 × (P+1) that r (k-p) is constituted ties up matrix；R_N(k-1) represent by r_p(k-1), r_p(k-2) ..., r_p(k-N) N constituted × (P+1) ties up matrix；

(4.3) according to closed-loop control system structure, the mixing high-order autoregression model setting up the output of process and process settings is as follows:

$\stackrel{\&OverBar;}{Z_p}\left(k\right)=\left[\begin{array}{c}{Y}_M(k-1)\\ R_N(k-1)\end{array}\right]$

Wherein,Dimension matrix, front M row is by the high-order autoregression model Y of the output of process_M(k-1) composition, rear N row is by the high-order autoregression model R of process settings_N(k-1) composition；

(4.4) according to above-mentioned high-order autoregression model, by orthogonal projection algorithm, acquisition process estimates that interference updates vector:

$e_p\left(k\right)=y_p\left(k\right)(I-\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T{\&lsqb;\stackrel{\&OverBar;}{Z_p}\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T\&rsqb;}^{-1}\stackrel{\&OverBar;}{Z_p}(k\left)\right)$

Wherein, e_p(k)=[e (k) e (k-1) ... e (k-p)], represent that 1 × (P+1) process tieed up estimates that interference updates vector, e (k) represents that k moment gained process estimates that interference updates, and I represents (P+1) × (P+1) unit matrix tieed up。

6. model quality control method as claimed in claim 5, it is characterised in that described step (4.4) includes following sub-step:

(4.4.1) to matrixMake QR to decompose, namelyObtain orthogonal matrix Q₁And Q₂, diagonal matrix R₁₁, diagonal matrix R₂₂With row vector R₂₁；

(4.4.2) according to orthogonal matrix Q₁And Q₂, diagonal matrix R₁₁, diagonal matrix R₂₂With row vector R₂₁Between relation, it is thus achieved that following result:

$y_p\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T=R_{21}{R_{11}}^T;$

$\stackrel{\&OverBar;}{Z_p}\left(k\right)\stackrel{\&OverBar;}{Z_p}{\left(k\right)}^T=R_{11}{R_{11}}^T;$

(4.4.3) by above-mentioned (4.4.2) acquired results, obtain reliable process and estimate that interference updates:

$e_p\left(k\right)=y_p\left(k\right)-R_{21}{R_{11}}^T\stackrel{\&OverBar;}{Z_p}\left(k\right).$

7. model quality control method as claimed in claim 1 or 2, it is characterised in that described step (5) is specific as follows:

According to closed-loop control system given reference signal and the actual output of process, obtain the actual tracking error of closed-loop control system:

$\stackrel{\&OverBar;}{e}\left(k\right)=y\left(k\right)-r\left(k\right);$

Wherein,Representing the actual tracking error of k moment closed-loop control system, r (k) represents k moment given reference signal, and y (k) represents the actual output of k etching process。

8. model quality control method as claimed in claim 7, it is characterised in that described step (6) includes following sub-step:

(6.1) Key Performance Indicator KPI is defined according to output weight matrix Q and input weight matrix S:

$J_N=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}\&lsqb;\left|\right|y\left(k\right)-r\left(k\right)|{|}_Q^2+|\left|{\mathrm{\&Delta;u}}^{*}\left(k\right)\right|{|}_S^2\&rsqb;$

Wherein, J_NRepresenting that Key Performance Indicator KPI, N represent and ask for sampled data length needed for index, y (k) represents the actual output of k etching process, and r (k) represents k moment given reference signal, Δ u^*K ()=u (k)-u (k-1) represents that k etching process controls the difference of input and the control input of (k-1) etching process；

(6.2) process obtained according to step (4) estimates that interference updates e (k) and described actual tracking errorObtain the model quality index MQI of closed-loop control system:

$\mathrm{\&eta;}=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}e{\left(k\right)}^{T}Qe\left(k\right)}{\underset{k=1}{\overset{N}{\&Sigma;}}\stackrel{\&OverBar;}{e}{\left(k\right)}^{T}Q\stackrel{\&OverBar;}{e}\left(k\right)}$

Wherein, N represents and asks for sampled data length needed for index,Representing the actual tracking error of k moment closed-loop control system, e (k) represents that the process of k moment closed-loop control system estimates that interference updates, and Q represents output weight matrix。

9. model quality control method as claimed in claim 8, it is characterised in that described step (7) is specific as follows:

Key Performance Indicator KPI according to described closed-loop control system evaluates controller performance: KPI value is more little, represents that controller performance is more good；

Model quality index MQI according to described closed-loop control system evaluates modeling quality；The span of MQI be η ∈ (0,1], model quality index is closer to 1, it was shown that the modeling quality of closed-loop control system is more good, and model quality quality index is closer to 0, it was shown that the modeling quality of closed-loop control system is more poor。