CN111176155A - Process model mismatch detection method of closed-loop model predictive control system - Google Patents

Process model mismatch detection method of closed-loop model predictive control system Download PDF

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CN111176155A
CN111176155A CN201911328557.7A CN201911328557A CN111176155A CN 111176155 A CN111176155 A CN 111176155A CN 201911328557 A CN201911328557 A CN 201911328557A CN 111176155 A CN111176155 A CN 111176155A
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mismatch
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郑英
唐祎
万一鸣
王彦伟
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Huazhong University of Science and Technology
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Abstract

The invention belongs to the field of model predictive control monitoring, and particularly discloses a process model mismatch detection method of a closed-loop model predictive control system, which comprises the following steps: calculating a system residual value and an interference updating sequence of the control system based on input data and output data of the closed-loop model prediction control system and each transfer function in the control system; calculating the variance ratio of the system residual value and the interference updating sequence to serve as a quality index value of an actual process model in the control system, judging whether model mismatch exists or not based on the quality index value, and identifying all subspace matrixes of the control system by adopting a subspace identification method if the model mismatch exists; and carrying out singular value decomposition on the subspace matrix corresponding to the state variable, calculating the ratio of the maximum singular value and the minimum singular value obtained by decomposition, and judging whether the actual process model is mismatched or not based on the ratio. The method can effectively detect and distinguish the actual mismatch model from various factors influencing the control performance by only utilizing input and output data, and is efficient and reliable.

Description

Process model mismatch detection method of closed-loop model predictive control system
Technical Field
The invention belongs to the field of model predictive control monitoring, and particularly relates to a process model mismatch detection method of a closed-loop model predictive control system.
Background
Model Predictive Control (MPC) belongs to the field of advanced Control technology, and an MPC controller has the characteristics of simple and convenient modeling, quick dynamic Control effect, strong robustness and the like, and is widely applied to actual industrial process Control.
In recent years, the performance of MPC has become more and more demanding for industrial processes, and MPC performance monitoring technology has become a hot spot in the research of advanced control technologies. The process model mismatch problem is a significant cause of MPC performance degradation, and a large number of scholars have contributed to the research for detecting process model mismatch problems over the last two decades. Currently, methods for model mismatch detection can be divided into four major categories:
(1) the robust control-based method comprises the following steps: badwe et al calculate the boundary range of the mismatch effect from the design sensitivity function and the relative sensitivity function using the concept of model uncertainty. The method has larger conservation, and can not reflect the direction of the change of the control performance by the expression of norm form;
(2) method based on relationships between variables: stanfelj et al, which detects whether there is a mismatch or not by correlation between variables and residuals, does not need to identify the part of the mismatch. Badwe et al further propose a method for locating mismatched channels using a partial correlation system. The method based on the relation between variables still has the defects in the aspects of quantifying the mismatch size, evaluating the influence of mismatch and the like, and other methods are needed;
(3) the method based on system identification comprises the following steps: qin et al distinguishes models according to their autocorrelation function order, Sun et al estimates the minimum variance basis of the residual model from closed-loop data and evaluates the model quality accordingly. The method based on system identification is based on a specific model, so that the severity of mismatch can be conveniently quantified, only closed-loop input and output data are needed, the method has the defect that the system identification usually needs sufficient excitation, but the method is still used generally in the process industry;
(4) indirect methods: the method is mainly used for processing the mismatch problem of the nonlinear model, and the mismatch of the model is detected by establishing a nonlinear state space model and a nonlinear ARMA model with external input and utilizing mutual information of an excitation signal and a model residual error. This method requires more constraints and is less studied.
Through the above explanation, it can be found that the existing model mismatch detection method still has the technical problems of difficult detection, excitation requirement, high cost, low safety and the like in the industrial practical process.
Disclosure of Invention
The invention provides a process model mismatch detection method of a closed-loop model predictive control system, which is used for solving the technical problem that the specific mismatch model in the control system cannot be accurately determined due to the complex required data and insufficient detection in the conventional model mismatch detection method.
The technical scheme for solving the technical problems is as follows: a process model mismatch detection method for a closed-loop model predictive control system includes:
calculating a system residual value and an interference updating sequence of the control system based on input data and output data of a closed-loop model prediction control system and each transfer function in the control system;
calculating the variance ratio of the system residual value and the interference updating sequence to serve as a quality index value of an actual process model in the control system, judging whether model mismatch exists or not based on the quality index value, and identifying all subspace matrixes of the control system by adopting a subspace identification method if the model mismatch exists;
and carrying out singular value decomposition on the subspace matrix corresponding to the state variable, calculating the ratio of the maximum singular value and the minimum singular value obtained by decomposition, judging whether the actual process model is mismatched or not based on the ratio and the threshold value thereof, and finishing mismatch detection.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, the method for acquiring the input data and the output data comprises the following steps:
setting input initial data of the control system and inputting the initial data into the control system;
acquiring output initial data of the actual process model, and calculating the output initial data of a prediction process model in the control system based on the set input initial data;
and respectively carrying out centralized processing on the set input initial data and the two output initial data to obtain processed input data and output data.
Further, the system residual e (t) of the control system is represented as:
e(t)＝(Ho)-1[y(t)-Gou(t)]
wherein HoFor a transfer function, G, of a predicted process disturbance model corresponding to a predicted process model in the control systemoFor the transfer function of the prediction process model, y (t) is equal to RnFor process output data, u (t) is e.g. RnFor process input data, n represents the dimension of the matrix and t is the current time.
Further, the calculation of the interference update sequence is specifically obtained by evaluating by an orthogonal projection method.
Further, the calculating of the interference update sequence comprises:
respectively establishing a system residual error of a control system and an extended matrix for setting input data, and establishing a total extended matrix obtained by combining the two extended matrices, wherein the system residual error is a function related to the input data and the output data of the control system;
and solving to obtain an interference update sequence by adopting an orthogonal projection method based on the extension matrix of the system residual error and the total extension matrix.
Further, the interference update sequence is represented as:
Figure BDA0002329006180000031
wherein E isP(t) represents the total spreading matrix for time t,
Figure BDA0002329006180000032
represents EP(t) projection onto its orthogonal subspace,
Figure BDA0002329006180000033
represents an estimated P x 1-dimensional interference update sequence, P being the window size of the spreading matrix,
Figure BDA0002329006180000034
and controlling the external interference value of the system for the estimated t moment.
Further, the determining whether there is a model mismatch based on the index value specifically includes:
and according to the size of the actual process model quality index value, if the size of the actual process model quality index value is larger than 0.95 +/-0.05, model mismatch does not exist, and otherwise, model mismatch exists.
Further, the subspace matrix corresponding to the state variable is:
ΓNLz；
ΓN＝[C′ C′A′ … C′A′N-1]′；
Lz＝[(AN-1K AN-2K … K),(AN-1B AN-2B … B)]；
a, B, C and K are state space matrixes in the expression of the control system based on the state space respectively, and N represents a prediction time domain.
Further, the threshold specifically is:
acquiring the distribution of process model identification indexes based on multiple control operations under the mismatch-free condition, and taking the upper limit of the distribution control limit as the threshold;
judging whether the actual process model is mismatched specifically as follows:
if the ratio is less than the threshold, then no mismatch exists, otherwise, mismatch exists.
The invention also provides a storage medium, wherein the storage medium stores instructions, and when the instructions are read by a computer, the computer is enabled to execute the process model mismatch detection method of any closed-loop model predictive control system.
In general, by the above technical solution of the present invention, the following beneficial effects can be obtained:
(1) the method collects closed-loop input and output data under normal working conditions, and can obtain the quality index of the process model only by using the closed-loop data so as to detect whether the model predictive control system has the problem of unmatched models. Because only closed-loop operation data are needed, specific control model parameters are not needed, and experimental data are acquired by the method, the method provided by the invention has the characteristics of simplicity in operation, no influence on the actual industrial process, strong practicability and the like.
(2) The invention utilizes the relation between the process model residual error and the estimated interference update sequence when establishing the process model quality index. The quality index of the process model provided by the invention is a detection process specially aiming at the system model, and can effectively separate other control performance degradation factors such as the change of controller parameters and the like, thereby only detecting whether the model of the model predictive control system has the situation of model mismatch.
(3) The invention provides a detection method based on subspace identification when detecting that the model has mismatch, and the method only researches the mismatch influence related to the process model aiming at the subspace matrix which is only related to the control variable and is obtained by identification, and can distinguish the mismatch of the process model from the mismatch of the interference model. Compared with a subspace identification method, other identification methods such as a prediction error algorithm (PEM) and an auxiliary variable method (IVM) have the defects of iterative optimization and the like, the subspace identification method only needs to identify a process model system and judge whether the process model is mismatched, the method does not need iterative optimization, only needs to carry out a least square method estimation process once, and meanwhile is not sensitive to initial conditions, so that the operation in industrial process monitoring is reduced, and the production cost is saved.
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FIG. 1 is a block flow diagram of a process model mismatch detection method for a closed-loop model predictive control system according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method for process model mismatch detection for a closed-loop model predictive control system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a closed-loop model predictive control system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an actual process control system in a closed-loop model predictive control system according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a predictive process control system architecture in a closed-loop model predictive control system according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a Wood-Berry binary rectification column according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Example one
A method 100 for process model mismatch detection in a closed loop model predictive control system, as shown in fig. 1, includes:
step 110, predicting input data and output data of the control system and each transfer function in the control system based on a closed-loop model, and calculating a system residual value and an interference updating sequence of the control system;
step 120, calculating a variance ratio of the system residual value and the interference update sequence to serve as a quality index value of an actual process model in the control system, judging whether model mismatch exists or not based on the index value, and if the model mismatch exists, identifying all subspace matrixes of the control system by adopting a subspace identification method;
and step 130, performing singular value decomposition on the subspace matrix corresponding to the state variable, calculating the ratio of the maximum singular value to the minimum singular value obtained by decomposition, judging whether the actual process model is mismatched or not based on the ratio and the threshold value thereof, and finishing mismatch detection.
The method comprises the steps of collecting closed-loop input and output data obtained in an industrial process, analyzing the data, and obtaining a process model quality index to detect whether the model has a mismatch condition; by definition, the value of the process model quality indicator is between 0 and 1 and is not affected by variations in the regulator regulation parameters; if the process model quality index is close to 1, the models are considered to be matched; if the quality index of the process model is far less than 1, the model is considered to be unmatched, and for the unmatched model, the mismatch of the actual process model or the mismatch of the interference model corresponding to the model is distinguished by using a subspace identification method. The method adopts a subspace identification method to effectively distinguish the influence of model mismatch from various factors influencing the control performance, can separate the influence of the interference model mismatch detection process, and realizes the problem of model mismatch in the detection process, wherein the flow is shown in fig. 2. The control model aimed at by the method is a model prediction control system, only input and output data in an industrial process are used, whether the model is mismatched or not can be detected, the internal structure of the system is not required to be influenced, the cost of the control process is effectively reduced, and the safety of the control process is improved.
Preferably, the method for acquiring the input data and the output data comprises:
setting input initial data of a setting control system and inputting the initial data into the control system;
acquiring output initial data of an actual process model, and calculating the output initial data of a prediction process model in the control system based on the set input initial data;
and respectively carrying out centralized processing on the set input initial data and the two output initial data to obtain processed input data and output data.
The specific formula for centralizing the input data and the output data is as follows:
Figure BDA0002329006180000071
Figure BDA0002329006180000072
wherein T represents the total sampling times, T is the current time, u0(t) and y0(t) is respectively the input and output values of the system at the t moment, u (t) and y (t) are respectively the input and output values of the system at the t moment after centralization
Further, the system residual e (t) of the control system is expressed as:
e(t)＝(Ho)-1[y(t)-Gou(t)]
wherein HoFor transfer functions of a predicted process disturbance model corresponding to a predicted process model in a control system, GoTo predict the transfer function of a process model, y (t) is equal to RnFor process output data, u (t) is e.g. RnFor process input data, n represents the dimension of the matrix. And t is the current time.
Further, the calculation of the interference update sequence is specifically obtained by evaluating by an orthogonal projection method.
Preferably, the calculation of the interference update sequence comprises:
respectively establishing a system residual error of a control system and an extended matrix for setting input data, and establishing a total extended matrix obtained by combining the two extended matrices, wherein the system residual error is a function related to the input data and the output data of the control system; and solving to obtain an interference update sequence by adopting an orthogonal projection method based on the extension matrix and the total extension matrix of the system residual error.
According to the system residual e (t) and the set input data r (t), establishing an extended data matrix as follows:
eP(t)＝[e(t-1) e(t-2) … e(t-P)]，
rP(t)＝[r(t-1) r(t-2) … r(t-P)]，
EP(t)＝[e′p(t-1),e′p(t-2),…,e′p(t-L),rp′(t-1),rp′(t-2),…,rp′(t-M)]′，
where P is the size of the spreading matrix and window, then eP(t) denotes a P x 1 dimensional matrix of model residual values, rP(t) represents a P × 1 dimensional matrix composed of set values, E, which is the output of the process after the centering processP(t) is represented by eP(t) and rP(t) a (L + M) × P dimensional matrix of formation; denotes the transposition of the matrix.
Estimating an interference update sequence of a process model by combining an extension matrix and a total extension matrix of system residual errors and utilizing an orthogonal projection method, wherein the expression is as follows:
Figure BDA0002329006180000081
wherein the content of the first and second substances,
Figure BDA0002329006180000082
represents EP(t) projection onto its orthogonal subspace,
Figure BDA0002329006180000083
represents an estimated P x 1-dimensional interference update sequence, P being the window size of the spreading matrix,
Figure BDA0002329006180000084
and controlling the external interference value of the system for the estimated time t.
Specifically, the method for estimating the interference update sequence of the process model specifically includes:
according to EP(t)E′PSingular characteristics of the values of (t), pair matrix
Figure BDA0002329006180000085
As QR decomposition, i.e.
Figure BDA0002329006180000086
Obtaining a diagonal matrix R according to the orthogonal characteristic of QR decomposition11And R22A row vector R21And quadrature matrix [ Q'1Q′2]′；
According to [ Q'1Q′2]' is a feature of orthogonal matrix, and can be expressed as matrix eP(t)E′P(t) and matrix EP(t)E′P(t) are respectively expressed as:
eP(t)E′P(t)＝R21R′11；
EP(t)E′P(t)＝R11R′11；
according to matrix eP(t)E′P(t) and matrix EP(t)E′P(t), the process interference update sequence can be expressed as:
Figure RE-GDA0002432122270000091
preferably, the determining whether there is a model mismatch based on the index value specifically includes:
according to the size of the actual process model quality index value, if the size of the actual process model quality index value is larger than 0.95 +/-0.05, model mismatch does not exist, and otherwise, model mismatch exists.
specifically, according to the system residual error and the interference update sequence, the ratio of the variance value of the system residual error and the interference update sequence is used for representing the process model quality index etaMDIi.e. ηMDIExpressed as:
Figure BDA0002329006180000092
wherein e isP(t) representing an expansion matrix formed by model residual values;
Figure BDA0002329006180000093
representing an estimated interference update sequence; q is the weight matrix of the output, which is already determined at the stage of model predictive controller design; t represents the total number of samples.
According to the above eP(t) and
Figure BDA0002329006180000094
the relationship of (1), the process model quality index ηMDIthe actual value of (b) is in the range of etaMDI∈(0,1](ii) a If the actual process model quality index value is larger than 0.95 +/-0.05, model mismatch does not exist, otherwise, model mismatch exists.
Preferably, the subspace matrix corresponding to the state variable is:
ΓNLz；
ΓN＝[C′ C′A′ … C′A′N-1]′；
Lz＝[(AN-1K AN-2K … K),(AN-1B AN-2B … B)]；
a, B, C and K are state space matrixes in the expression of the control system based on the state space respectively, and N represents a prediction time domain.
Specifically, according to an expression of a closed-loop model predictive control system based on a state space:
Figure BDA0002329006180000101
wherein x (t) ∈ Rn、u(t)∈Rm、y(t)∈RrAnd v (t) ∈ RrRespectively representing state variables, input variables, output variables and white noise of the control system at the time t, wherein A, B, C, D and K are state space matrixes corresponding to the control system, and n, m and r represent the dimensionality of the matrixes;
establishing a subspace matrix-based matrix equation of the control system, wherein the subspace matrix-based matrix equation is expressed as follows:
Yf＝ΓNxf+HNUf+GNYf+Vf，
where N represents the prediction time domain, f represents the future, p represents the past, and the matrix xf∈RnN×L、Yf∈RrN×L、Uf∈RmN×L、Vf∈RrN×LIs changed from a state variable x (t) and an outputThe quantity y (T), the input variable u (T) and the white noise v (T) respectively form a Hankel matrix, L is T-p-f +1, T represents the total sampling frequency, and ΓN、HN、GNIs a subspace matrix, and the definition forms are respectively:
ΓN＝[C′ C′A′ … C′A′N-1]′，
Figure BDA0002329006180000103
Figure BDA0002329006180000104
according to the characteristics of the state variable x (t), xfExpressed as:
xf＝ANxp+LNZp，
wherein L isN＝[(AN-1K AN-2K … K),(AN-1B AN-2B … B)]，ZP＝[YP′,UP′]′， Yp∈Rrp×L、Up∈Rmp×LThe Hankel matrix is composed of an output variable y (t) and an input variable u (t); due to the matrix ANIs a Helvelz matrix, then when N is large enough, we can ignore ANxpI.e. the subspace matrix equation can be approximated as:
Yf≈ΓNLNZp+HNUf+GNYf+Vf
estimating the subspace matrix [ (gamma) in the subspace matrix equation by using a least square methodNLN),HN,GN]The specific calculation form is as follows:
Figure BDA0002329006180000111
wherein | | xi | purpleFThe F-norm of the matrix is expressed.
Preferably, the threshold is specifically:
based on control operation under the condition of no mismatch for multiple times, acquiring the distribution of process model identification indexes, and taking the upper limit of the distribution control limit as the threshold;
then, the above-mentioned determining whether the actual process model is mismatched specifically includes:
if the ratio is less than the threshold, then no mismatch exists, otherwise, mismatch exists.
Based on the subspace matrix [ (gamma) obtained as described aboveNLN),HN,GN]Analysis by singular value decomposition with a weighted matrix (gamma)NLN) The process of decomposition can be expressed as:
W1(ΓNLN)W2＝USVT
wherein the weight matrix
Figure BDA0002329006180000112
According to the calculation characteristics of the singular value decomposition method of the weighted matrix, the elements of the matrix S diagonal which are not 0 form a matrix (gamma)NLz) Is arranged in descending order as sigma1,…,σgwhere g is the number of singular values, the process model identification indicator ηSSIThe calculation expression of (a) is:
Figure BDA0002329006180000113
the indicator η can be identified from the process model according to the characteristics of the subspace identification methodSSIthe value of (a) is used to determine whether the process model has a mismatch, and the specific process can be expressed as taking an adjustable positive integer β, if the process model identification index eta isSSIif the values of the parameters are less than β, the process model has no mismatch and only has interference model mismatch, and if the process model identification index eta is less than β, the process model identification index eta has no mismatchSSIif there is a value greater than β, then the case of model mismatch also includes process model mismatch.
For a better illustration of the invention, specific examples are given below:
as shown in fig. 3, which is a structural diagram of the model predictive control system employed in the present example, Q (Q) represents a transfer function of the model predictive controller, G (Q) and G (Q) represent transfer functions of an actual process model and a predicted process model, respectively, and H (Q) represents a transfer function of an interference process model; and u (t) and y (t) respectively represent the control input and the control output of the closed-loop process at the time t, r (t) represents a set input value of the closed-loop process at the time t, and epsilon (t) represents white noise of the closed-loop control system at the time t.
The schematic diagram of the process control model in a closed loop control system is shown in fig. 4, while the predictive process control model therein is shown in fig. 5.ε (t) and e (t) represent the white noise at time t of the closed-loop system model and the residual error at time t of the process model, respectively.
In the following, a Wood-Berry binary rectification tower industrial process is taken as an example to carry out simulation design.
The Wood-Berry rectification column process is illustrated in FIG. 6, which is a typical two input two output system with hysteresis, wherein the two outputs are the overhead concentration YTAnd the liquid phase concentration Y at the bottom of the columnBThe two are controlled by two input quantities of tower top reflux quantity R and tower bottom reboiler steam quantity S, and a transfer function matrix of the established process model is as follows:
Figure BDA0002329006180000121
wherein s is a Laplace operator, and the rate of the manipulated variable tower top reflux R is 1 b/m; the speed of the manipulated variable steam flow S is 1 b/m; the output is the overhead concentration YTAnd the liquid phase concentration Y at the bottom of the columnBThe units are mol%.
Establishing an interference model, and taking a diagonal matrix as follows:
Figure BDA0002329006180000131
wherein, theta1And theta2Interference parameters representing interference models, in the embodiment, theyThe values are 0.5 and 0.7 respectively. When the MPC controller is designing parameters, the prediction time domain P is 100, the control time domain M is 10, and the weight matrix Q is diag {1,100 }. The controller process set points are: r (k) ═ 90 mol% 5 mol%]。
The Wood-Berry binary rectifying tower process in the embodiment is tested by using the method for detecting the mismatching problem of the process model of the closed-loop model predictive control system.
Assuming a real model transfer function of
Figure BDA0002329006180000132
The process model transfer function is
Figure BDA0002329006180000133
Wherein, K and KoGain coefficients, D and D, of transfer functions of the system actual model and the system process model, respectivelyoTime lag factors, T and T, of the transfer functions of the system actual model and the system process model, respectivelyoThe gain coefficients of the transfer functions of the system actual model and the system process model are respectively. The process of model mismatch is divided into four categories, which are respectively:
(1) process gain change:
Figure BDA0002329006180000134
(2) the time constant changes:
Figure BDA0002329006180000135
(3) the time lag factor changes:
Figure BDA0002329006180000136
(4) interference model change:
Figure BDA0002329006180000137
further, the specific process is as follows:
(1) and collecting input data and output data of the closed-loop model predictive control system.
In the MPC control process, setting sampling time for one minute, collecting 5000 groups of closed-loop input data samples, and firstly carrying out centralized processing on the 5000 groups of data samples, wherein the calculation formula is as follows:
Figure BDA0002329006180000141
then, the MPC control process was operated to obtain 5000 sets of corresponding control output data, which was also centered:
Figure BDA0002329006180000142
(2) model residual values of the control process are calculated.
According to the calculation expression of the residual value of the control process model:
e(t)＝(Q(q))-1[y(t)-yo(t)]，
wherein Q (Q) is a transfer function of the controller in the process of model predictive control, and y (t) belongs to RnIs the actual system output value at time t, yo(t)∈RnAnd the output value of the process model at the time t, t is the current time, and n represents the dimension of the matrix.
Knowing the operating data and process models in an MPC process, the system residual values e (t) of the in-process control process can be directly calculated. Subsequently, the system residual value e (t) is also subjected to centering processing.
(3) An interference update sequence of the process model is estimated.
Combining the residual value of the system, the formula for estimating the interference update by using the orthogonal projection method is as follows:
Figure BDA0002329006180000143
wherein the content of the first and second substances,
Figure BDA0002329006180000144
represents EP(k) Projection on its orthogonal subspace，
Figure BDA0002329006180000145
Represents an estimated P x 1-dimensional interference update sequence, P being the window size of the spreading matrix,
Figure BDA0002329006180000146
and controlling the external interference value of the system for the estimated time t.
Further:
(3.1) establishing the following spreading matrix:
eP(t)＝[e(t-1) e(t-2) … e(t-P)]，
rP(t)＝[r(t-1) r(t-2) … r(t-P)]，
combining the two to obtain:
EP(t)＝[e′p(t-1),e′p(t-2),…,e′p(t-L),rp′(t-1),rp′(t-2),…,rp′(t-M)]′
in this example, k is 5000, P is 4950, and L and M are 50.
(3.2) due to EP(t)E′PThe singular nature of the values of (t), the difficulty of calculation, the need for matrices
Figure BDA0002329006180000151
Performing QR decomposition, and further:
(3.2.1) order
Figure BDA0002329006180000152
Obtaining a diagonal matrix R11And R22Row vector R21And quadrature matrix [ Q'1Q′2]′；
(3.2.2) separately determining the matrix e by the following equationP(t)E′P(t) and matrix EP(t)E′P(t)：
eP(t)E′P(t)＝R21R′11；
EP(t)E′P(t)＝R11R′11；
(3.2.3) the process interference update sequence can be expressed as:
Figure RE-GDA0002432122270000153
from the above equation, an estimated interference update sequence can be obtained
Figure BDA0002329006180000154
(4) And detecting whether the model has mismatch according to the value of the process model quality index.
calculating a process model quality index eta according to the interference update sequence and the model residual valueMDIThe expression of (1) is:
Figure BDA0002329006180000161
wherein e isP(t) representing an expansion matrix formed by model residual values;
Figure BDA0002329006180000162
representing the estimated interference update sequence; q is the weight matrix of the output, which is already determined at the stage of model predictive controller design; t denotes the total number of samples.
Thus, the value of the model quality index can be based on eP(t) and
Figure BDA0002329006180000163
it is worth explaining that the process model quality index ηMDIthe actual value of (b) is in the range of etaMDI∈(0,1]。
Further, the process of determining whether the model has a mismatch is as follows:
and if the actual process model quality index value is larger than 0.95 +/-0.05, model mismatch does not exist, otherwise, model mismatch exists.
The process model quality indicators for different model mismatch scenarios are given in Table 1criterion etaMDI。
TABLE 1 detection results of different model mismatch scenarios
Situation(s) Variation of parameter ηMDI Judgment of
S0 Without change 0.9885 Model Normal
S1 ΔK＝0.5 0.8249 Model mismatch
S2 ΔT＝0.5 0.6991 Model mismatch
S3 ΔD＝0.5 0.4470 Model mismatch
D1 ΔK1＝0.5 0.9332 Model mismatch
D2 ΔK1＝0.2 0.8774 Model mismatch
As can be seen from Table 1, in the case of S0, the process model quality indicator ηMDIis 0.9885, which is greater than 0.95, the model is determined to be normal, and the cases S1, S2 and S3 respectively represent the cases that the gain, the time constant and the hysteresis factor in the transfer function of the process model have mismatch, in the three cases, the quality index eta of the process model has mismatchMDIa value of less than 0.95, it can be determined that there is a model mismatch, and the cases D1 and D2, in which the process model quality indicator η is changed, change the parameters of the interference modelMDI0.9332 and 0.8774, which are close to 1, but have a certain difference from 0.95, because of the process model quality indicator ηMDIThe method is influenced by the mismatch of the interference model, but the influence effect is not large, so the specific result needs to be further analyzed.
(5) If the models are mismatched, identifying the whole process model by using a subspace identification method, which specifically comprises the following steps:
(5.1) according to the structure of the closed-loop model prediction control system, establishing a subspace matrix-based matrix equation of the control system, wherein the subspace matrix equation is expressed as:
Yf＝ΓNxf+HNUf+GNYf+Vf
where N represents the prediction time domain, f represents the future, p represents the past, and the matrix xf∈RnN×L、Yf∈RrN×L、Uf∈RmN ×L、Vf∈RrN×LFor the purpose of being formed by a state variable x ∈ RnAnd inputThe variable u ∈ RmThe output variable y belongs to RrWhite noise v ∈ RrRespectively forming a Hankel matrix, wherein L is T-p-f +1, T represents the total sampling times, n, m and r represent the dimensionality of the matrix, and gamma isN、HN、GNIs a subspace matrix, and is defined by gammaN＝[C′ C′A′ … C′A′N-1]′，
Figure BDA0002329006180000171
Figure BDA0002329006180000172
(5.2) characteristics according to the state variable x (t), xfExpressed as:
xf＝ANxp+LNZp
wherein L isN＝[(AN-1K AN-2K … K),(AN-1B AN-2B … B)]Zp＝[YP′,UP′]′；
Due to the matrix ANIs a Helveltz matrix, then when N is large enough, A can be ignoredNxpThen the subspace matrix equation can be approximated as:
Yf≈ΓNLNZp+HNUf+GNYf+Vf
(5.3) estimating the subspace matrix [ (gamma) therein by using the least square method according to the subspace matrix equation of (5.2)NLN),HN,GN]The specific calculation form is as follows:
Figure BDA0002329006180000181
(6) obtaining a process model identification indicator etaSSIAnd determines whether a mismatch exists in the process model.
Further, the step (6) comprises:
(6.1) obtaining a subspace matrix [ (gamma) according to the subspace matrix [ (gamma) obtained in the step (5.3)NLN),HN,GN]Analysis by singular value decomposition with a weighted matrix (gamma)NLN) The process of decomposition can be expressed as:
W1(ΓNLN)W2＝USVT
wherein the weight matrix
Figure BDA0002329006180000182
(6.2) according to the calculation characteristics of the singular value decomposition method of the weighted matrix, the elements of the matrix S diagonal which are not 0 form a matrix (gamma)NLz) Is arranged in descending order as sigma1,…,σ4obtaining process model identification indicator eta by calculationSSIThe calculation process expression is as follows:
Figure BDA0002329006180000183
(6.3) according to the characteristics of the subspace identification method, the indicator eta can be identified by the process modelSSIthe value of (b) is used to judge whether the process model has mismatch, wherein the specific process can be expressed as that the distribution of the process model identification index is obtained based on control operation under the condition of no mismatch for a plurality of times, and the upper limit of the distribution control limit is used as the threshold (in the example, the threshold β is 10);
then, whether the actual process model is mismatched is judged based on the ratio and the threshold thereof, which specifically includes:
if the process model identifies the indicator ηSSIare all less than beta, then the process model order Nuif the process model identification index eta is equal to 0, no mismatch exists, only the interference model mismatch exists, and if the process model identification index eta is equal to 0SSIif the value of (d) is greater than beta, the process model order is NuNot equal to 0, the case of model mismatch also includes process model mismatch.
Table 2 gives the results of distinguishing process model mismatch from interference model mismatch in the case of known model mismatch.
Table 2 distinguishes process model mismatch from interference model mismatch
Situation(s) ηSSI Nu Judgment of
D1 2.5575 ＝0 Interference-only model mismatch
D2 2.5962 ＝0 Interference-only model mismatch
S1+D1 16.0026 >0 There is a process model mismatch
S2+D1 12.6205 >0 There is a process model mismatch
S3+D1 408.7128 >0 There is a process model mismatch
in Table 2, the process model identification index η for the case of process model mismatches D1 and D2 was first analyzedSSI2.5575 and 2.5962, respectively, both of which are seen to be much less than 10, and then, introducing a process model mismatch condition, the resulting process model identification indicator ηSSIare all greater than 0, and thus, according to ηSSIthe determination mode of (1) selects beta to be 10, the latter three conditions can determine the condition that the process model mismatch exists certainly, and the detection process of the process model mismatch is realized
Example two
A storage medium having instructions stored therein, which when read by a computer, cause the computer to perform a method of process model mismatch detection in a closed loop model predictive control system of any of the above-described types.
The related technical solution is the same as the first embodiment, and is not described herein again.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A process model mismatch detection method for a closed-loop model predictive control system, comprising:
calculating a system residual value and an interference updating sequence of the control system based on input data and output data of a closed-loop model prediction control system and each transfer function in the control system;
calculating the variance ratio of the system residual value and the interference updating sequence to serve as a quality index value of an actual process model in the control system, judging whether model mismatch exists or not based on the quality index value, and identifying all subspace matrixes of the control system by adopting a subspace identification method if the model mismatch exists;
and carrying out singular value decomposition on the subspace matrix corresponding to the state variable, calculating the ratio of the maximum singular value and the minimum singular value obtained by decomposition, judging whether the actual process model is mismatched or not based on the ratio and the threshold value thereof, and finishing mismatch detection.
2. The method of claim 1, wherein the method of collecting the input data and the output data comprises:
setting input initial data of the control system and inputting the initial data into the control system;
acquiring output initial data of the actual process model, and calculating the output initial data of a prediction process model in the control system based on the set input initial data;
and respectively carrying out centralized processing on the set input initial data and the two output initial data to obtain processed input data and output data.
3. The method of claim 1, wherein the system residual e (t) of the control system is expressed as:
e(t)＝(Ho)-1[y(t)-Gou(t)]
wherein HoFor a transfer function, G, of a predicted process disturbance model corresponding to a predicted process model in the control systemoFor the transfer function of the prediction process model, y (t) is equal to RnFor process output data, u (t) is e.g. RnFor process input data, n represents the dimension of the matrix and t is the current time.
4. The method as claimed in claim 1, wherein the calculation of the interference update sequence is evaluated by an orthogonal projection method.
5. The method of claim 4, wherein the calculating of the interference update sequence comprises:
respectively establishing a system residual error of a control system and an extended matrix for setting input data, and establishing a total extended matrix obtained by combining the two extended matrices, wherein the system residual error is a function related to the input data and the output data of the control system;
and solving to obtain an interference update sequence by adopting an orthogonal projection method based on the extension matrix of the system residual error and the total extension matrix.
6. The method of claim 5, wherein the interference update sequence is expressed as:
Figure FDA0002329006170000021
wherein E isP(t) represents the total spreading matrix for time t,
Figure FDA0002329006170000022
represents EP(t) projection onto its orthogonal subspace,
Figure FDA0002329006170000023
represents an estimated P x 1-dimensional interference update sequence, P being the window size of the spreading matrix,
Figure FDA0002329006170000024
and controlling the external interference value of the system for the estimated t moment.
7. The method for detecting process model mismatch of a closed-loop model predictive control system according to claim 1, wherein the determining whether there is model mismatch based on the index value specifically comprises:
and according to the size of the actual process model quality index value, if the size of the actual process model quality index value is larger than 0.95 +/-0.05, model mismatch does not exist, and otherwise, model mismatch exists.
8. The method of any of claims 1 to 7, wherein the subspace matrix corresponding to the state variable is:
ΓNLz；
ΓN＝[C′ C′A′…C′A′N-1]′；
Lz＝[(AN-1K AN-2K…K),(AN-1B AN-2B…B)]；
a, B, C and K are state space matrixes in the expression of the control system based on the state space respectively, and N represents a prediction time domain.
9. The method of claim 8, wherein the threshold is specifically:
acquiring the distribution of process model identification indexes based on multiple control operations under the mismatch-free condition, and taking the upper limit of the distribution control limit as the threshold;
judging whether the actual process model is mismatched specifically as follows:
if the ratio is less than the threshold, then no mismatch exists, otherwise, mismatch exists.
10. A storage medium having stored therein instructions which, when read by a computer, cause the computer to perform a process model mismatch detection method for a closed loop model predictive control system as claimed in any one of claims 1 to 9.
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Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102183699A (en) * 2011-01-30 2011-09-14 浙江大学 Method for model mismatching detection and positioning of multivariate predictive control system in chemical process
US20120221124A1 (en) * 2008-01-31 2012-08-30 Fisher-Rosemount Systems, Inc. Using autocorrelation to detect model mismatch in a process controller
CN105700358A (en) * 2016-03-14 2016-06-22 华中科技大学 Modeling quality monitoring method for model predictive controller (MPC) with drift interference
CN105807611A (en) * 2016-03-05 2016-07-27 华中科技大学 Detection method for mismatching of model of closed-loop control system and object
CN107272640A (en) * 2017-06-12 2017-10-20 华中科技大学 A kind of modeling quality control method and system based on model predictive controller
CN108536127A (en) * 2018-04-20 2018-09-14 华中科技大学 A kind of model mismatch diagnostic method of the multivariable control system of data-driven
CN108646553A (en) * 2018-04-20 2018-10-12 华中科技大学 A method of statistics on-line monitoring closed-loop control system model quality
CN110244563A (en) * 2019-06-18 2019-09-17 华北电力大学 A kind of identification of neural Networks Internal Model Control device model mismatch and online updating method

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20120221124A1 (en) * 2008-01-31 2012-08-30 Fisher-Rosemount Systems, Inc. Using autocorrelation to detect model mismatch in a process controller
CN102183699A (en) * 2011-01-30 2011-09-14 浙江大学 Method for model mismatching detection and positioning of multivariate predictive control system in chemical process
CN105807611A (en) * 2016-03-05 2016-07-27 华中科技大学 Detection method for mismatching of model of closed-loop control system and object
CN105700358A (en) * 2016-03-14 2016-06-22 华中科技大学 Modeling quality monitoring method for model predictive controller (MPC) with drift interference
CN107272640A (en) * 2017-06-12 2017-10-20 华中科技大学 A kind of modeling quality control method and system based on model predictive controller
CN108536127A (en) * 2018-04-20 2018-09-14 华中科技大学 A kind of model mismatch diagnostic method of the multivariable control system of data-driven
CN108646553A (en) * 2018-04-20 2018-10-12 华中科技大学 A method of statistics on-line monitoring closed-loop control system model quality
CN110244563A (en) * 2019-06-18 2019-09-17 华北电力大学 A kind of identification of neural Networks Internal Model Control device model mismatch and online updating method

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
LEI LIU等: "Process model quality monitoring of model predictive controller", 《PROCEEDINGS OF THE 36TH CHINESE CONTROL CONFERENCE》 *
YING ZHENG等: "Model Quality Evaluation in Semiconductor", 《TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING》 *
凌丹: "基于数据的非侵入式闭环工业系统模型失配检测", 《中国博士学位论文全文数据库信息科技辑（月刊）》 *
李秋美: "多变量MPC控制器性能监控及模型失配检测方法研究", 《中国优秀硕士学位论文全文数据库信息科技辑（月刊）》 *

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