CN115933594A - Method for evaluating performance of MIMO control system based on subspace projection - Google Patents

Abstract

The invention discloses a performance evaluation method of an MIMO control system based on subspace projection, and belongs to the field of industrial process control performance evaluation. According to the method, through the subspace projection method between the output data, the additional system identification step is avoided, the actual operation data capable of reflecting the system model information is fully utilized, the problem that the existing performance evaluation process excessively depends on the system model is solved, and the purpose of conveniently and accurately evaluating the performance of the controller is achieved. Meanwhile, the evaluation method provided by the invention only needs to collect relevant input and output data of a factory, and does not need field engineers to test delay information of a large number of loops one by one to obtain priori knowledge, so that the influence of the evaluation process on the normal production flow is avoided, and the production efficiency is improved.

Description

Method for evaluating performance of MIMO control system based on subspace projection

Technical Field

The invention relates to a performance evaluation method of an MIMO control system based on subspace projection, belonging to the field of industrial process control performance evaluation.

Background

The MIMO (multiple input multiple output) control system is widely used in industrial processes such as petroleum, chemical engineering and the like, and the quality of the performance of the control system directly influences the safety and economic benefit of a factory. These control systems are typically carefully regulated during the initial period of production, but over time, the control performance may degrade over time due to various links that make up the control system, such as changes in process objects, wear on actuators, signal acquisition disturbances, and miscorrection of control parameters. In order to ensure the best industrial control performance, the system control performance needs to be evaluated and optimized in time.

Control performance evaluation often uses a performance benchmark to evaluate current control performance, and Harris proposed a Minimum Variance (MV) benchmark that is still widely used in 1989. Computing the MV reference for a SISO system from conventional closed-loop data requires only a priori knowledge of the process delay. However, in a multivariable system, this simplicity disappears and the single delay information is generalized into a correlation matrix that can characterize the system delay. There are many evaluation methods focusing on how to derive the correlation matrix problem, some of which try to extract the diagonal correlation matrix from each control loop delay information; other methods attempt to estimate the Markov parameters of the process model and extract unitary correlation matrices from them. Although the introduction of the delay matrix avoids the dependence on all or part of the information of the process model to some extent, it is difficult to obtain the delay between each pair of input and output in the case of a large number of control loops in industrial application.

In practical industrial control, in the face of a large number of loops needing to be evaluated, the most feasible evaluation scheme still depends on data driving, so that the increase of the calculation amount can be completely compensated by the calculation power of a computer, and whether the control performance evaluation process is delayed a priori by information becomes less important. Meanwhile, some existing evaluation processes assume that the set point of the system is constant or zero, and then model a noise model or a noise-driven closed-loop model. For example, ko et al time series modeling of noise models under the assumption that the set values are constant (see Ko B-S, edgar T F. Performance assessment of multivariable feedback control systems [ J ]. Automatic,2001,37 (6): 899-905.); huang et al estimate the closed-loop Markov parametric model assuming that the setpoint value changes are uncorrelated with the incoming noise signal (see Huang B, shah S L, fujii H. The unity internal matrix and estimation closed-loop data [ J ]. Journal of Process Control,1997,7 (3): 195-207.).

Practice shows that when the set value changes randomly, the recognition result of the noise model has a small deviation from the real model, and the accuracy is low (see the Estimation of the dynamic matrix and noise model for model predictive control used closed-loop data [ J ]. 2002,41 (4): 842-852.). Such model mismatch may result from the time-varying nature of the disturbances, with inaccurate model information being one of the primary reasons for failure of control system performance evaluation. Therefore, how to reduce or avoid the excessive dependence of the evaluation process on the system model is a problem to be solved.

Disclosure of Invention

In order to solve the problem of excessive dependence on a process model and a noise model of a system in the performance evaluation process of the MIMO control system, the invention provides a performance evaluation method of the MIMO control system based on subspace projection, and the technical scheme is as follows:

a first object of the present invention is to provide a method for evaluating performance of a MIMO control system, comprising:

the method comprises the following steps: judging whether the controlled system is a system with a constant set value:

if the set value is constant, a noise signal is superposed on the output of the controller or the set value is artificially changed into a step change signal;

if the set value changes randomly, no processing is carried out;

step two: collecting input and output data of the controlled system, and constructing a historical database, wherein the steps of:

for the controlled system with the constant set value, acquiring the noise signal or the step change signal, and acquiring system output data;

for the controlled system with the set value changing randomly, directly acquiring system input data and output data;

step three: estimating Markov parameters of the process object according to the historical data, and extracting a unitary incidence matrix D (q) from the Markov parameters;

step four: constructing a multivariable time delay matrix L based on the unitary incidence matrix D (q), and then filtering output data by utilizing the multivariable time delay matrix L;

step five: calculating a theoretical minimum output variance of the controlled system, wherein the theoretical minimum output variance is as follows: projection of the filtered output data vector space on the orthogonal complement space of the original output data;

step six: and calculating the ratio of the theoretical minimum output variance to the actual output variance, namely the performance index of the controlled system.

Optionally, the fifth step includes:

step 51: constructing an output matrix after filtering, and outputting the output vector after filtering in the fourth step

The expansion is as follows:

step 52: constructing an original output matrix, and constructing a matrix for an original output vector:

Z _r,N ＝[y _r-1 (k-r+1) y _r-1 (k-r+2)…y _r-1 (k-r+N)]

wherein r is the number of impulse response coefficients of the closed-loop system;

step 53: and (3) calculating the theoretical minimum output variance of the controlled system by using a data projection mode:

wherein, the first and the second end of the pipe are connected with each other,

is the theoretical minimum output variance, sign->

Pseudo-inverse calculation of the representation matrix, i.e.

Optionally, the performance index of the controlled system is:

optionally, the process of extracting the unitary incidence matrix D (q) in step three includes:

step 31: f of each estimated controlled object model parameter _i Markov parameter matrix G combined into MIMO system _i There is a process model transfer function matrix:

the matrix is then constructed byG：

Step 32: fixing the order;

matrix ofGThe size of the middle d needs to be determined through singular value decomposition, and the value of the middle d is the order of the unitary correlation matrix; sequentially setting d to 0,1,2 \8230, constructing matrixes of different sizesG(ii) a For each kind separatelyGPerforming singular value decomposition:

assuming process objects as m-dimensional inputs, p-dimensional outputs, i.e.

Let V ₂₁ Is a V ₂ The upper m rows of (a); if rank(s) are satisfied at the same timeG) = min (m, p), and V ₂₁ If m is not less than 0, the value of d is the required value;

step 33: based on the determined order d value, by means of an iterative method, through G _i The first D term of (c) estimates the unitary correlation matrix D (q).

Optionally, the fourth step includes:

expanding the unitary incidence matrix D (q) as:

D(q)＝D ₁ q+D ₂ q ² +...+D _d q ^d

then constructing a multivariate delay matrix L:

L＝[D ₁ ,...,D _d ]

constructing an output matrix for the output data:

wherein the content of the first and second substances,

is the output vector at time k + i, y _d-1 (k + 1) represents a vector composed of outputs y (k + 1) at the time k +1 to y (k + d) at the time k + d;

filtering the output data by using the multivariate delay matrix L:

wherein, the first and the second end of the pipe are connected with each other,

is the filtered output vector.

Optionally, the noise signal superimposed in the first step is a white noise signal.

Optionally, when the set value is constant, the third step estimates the Markov parameter of the process object by using a data correlation analysis method.

Optionally, when the set value changes randomly, estimating a Markov parameter of the process object by using a subspace identification method in the third step.

A second objective of the present invention is to provide a parameter optimization method for a MIMO control system, which first evaluates the system performance by using the performance evaluation method for the MIMO control system, and then determines whether to perform parameter optimization on the MIMO control system according to the evaluation result.

A third objective of the present invention is to provide a MIMO control system, which utilizes the performance evaluation method of the MIMO control system to evaluate the system performance.

The invention has the beneficial effects that:

according to the performance evaluation method of the MIMO control system, disclosed by the invention, through the subspace projection method for the output data, an additional system identification step is avoided, actual operation data capable of reflecting system model information is fully utilized, the problem that the existing performance evaluation process excessively depends on a system model is solved, and the purpose of conveniently and accurately evaluating the performance of the controller is achieved. Meanwhile, the evaluation method provided by the invention only needs to collect relevant input and output data of a factory, and does not need field engineers to test delay information of a large number of loops one by one to obtain priori knowledge, so that the influence of the evaluation process on the normal production flow is avoided, and the production efficiency is improved.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a flowchart illustrating the implementation steps of the method for evaluating the performance of the MIMO control system based on subspace projection according to the present invention.

Fig. 2 is a block diagram of a mimo system according to an embodiment of the present invention.

FIG. 3 is a graph showing the variation of the output before and after the minimum variance control is applied in the embodiment of the present invention.

FIG. 4 is a graph comparing a theoretically calculated multivariate overall performance index with a projectively calculated multivariate overall performance index calculated by a projection method as a function of a process object model in an embodiment of the invention.

Fig. 5 is a comparison graph of a single-output performance index calculated by a theoretical calculation and a single-output performance index calculated by a projection method according to a change in a process object model in the embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The first embodiment is as follows:

the embodiment provides a performance evaluation method of a MIMO control system, comprising:

the method comprises the following steps: judging whether the controlled system is a system with a constant set value:

if the set value is constant, a noise signal is superposed on the output of the controller or the set value is artificially changed into a step change signal;

if the set value changes randomly, no processing is carried out;

step two: collecting input and output data of the controlled system, and constructing a historical database, wherein the historical database comprises the following steps:

for the controlled system with a constant set value, acquiring the noise signal or the step change signal, and acquiring system output data;

for the controlled system with the set value changing randomly, directly acquiring system input data and output data;

step three: estimating Markov parameters of the process object according to the historical data, and extracting a unitary incidence matrix D (q) from the Markov parameters;

step four: constructing a multivariable time delay matrix L based on the unitary incidence matrix D (q), and then filtering output data by using the multivariable time delay matrix L;

step five: calculating a theoretical minimum output variance of the controlled system, wherein the theoretical minimum output variance is as follows: projection of the filtered output data vector space on the orthogonal complement space of the original output data;

step six: and calculating the ratio of the theoretical minimum output variance to the actual output variance, namely the performance index of the controlled system.

Example two:

the embodiment provides a performance evaluation method of a MIMO control system, comprising:

the method comprises the following steps: judging whether the controlled system is a system with a constant set value:

if the set value is constant, a noise signal is superposed on the output of the controller or the set value is artificially changed into a step change signal; if the set value changes randomly, no processing is carried out;

for a system with a constant setpoint, the control loop does not have sufficient excitation signal, and it is difficult to estimate an accurate model by data analysis or identification. Within the allowable range of the control system, a certain white noise signal can be superposed on the output of the controller, and the model impulse response coefficient of a partial closed-loop system is obtained through the correlation analysis of the simple noise signal and the system output signal. For practical devices, a random jitter signal may not be allowed. For this case, the setting value can be changed appropriately as a series of simple step change signals within an allowable range.

For a control loop in which the set value itself is constantly changing, no additional measures need to be taken.

Step two: collecting input and output data of the controlled system, and constructing a historical database, wherein the historical database comprises the following steps:

and acquiring data according to the two conditions in the step one. If the set value is constant, collecting a dither signal a applied to the system according to whether the random dither white noise signal is allowed to be applied or not ₁ And (t) or acquiring a set value signal r (t) which is changed artificially. If the set value itself is continuously changed, it is collected. Simultaneously, the output signal y (t) is acquired. Due to the requirement of correlation analysis, the collected signal data amount depends on the model order of the actual controlled object.

Step three: estimating Markov parameters of the process object according to the historical data, and extracting a unitary incidence matrix D (q) from the Markov parameters;

two methods of estimating the model Markov parameters can be referenced.

The first is data correlation analysis: with a constant setpoint of 0, the autoregressive process of the process model for a single loop can be expressed as:

y(t)＝(f ₀ +f ₁ q ^-1 +f ₂ q ^-2 +…f _d-1 q ^-d-1 +…)a ₁ (t) (1)

a ₁ (t) is applied white noise with a variance of

Are known. The Markov parameter can then be obtained by:

if the set value is constant and not 0, the data is only needed to be centralized, i.e. the average value of each output is subtracted.

When the set value is randomly changed, a in equation (1) is changed ₁ (t) becomes r (t) and the model parameters can be estimated using a least squares identification method.

The second method is a subspace identification method, which is suitable for parameter estimation when the set value is randomly changed, and the specific implementation steps are shown in the reference document' Kadali R, huang B.

After estimating Markov parameters of an object model, referring to a unitary incidence matrix extraction method proposed by Huang B, shah S L, fujii H.

Step 31: combining the Markov parameters of each controlled object model estimated in the third step into a Markov parameter of the MIMO systemMatrix G _i Then the MIMO process model transfer function matrix T can be written as:

the matrix is then constructed in the following mannerG:

Step 32: step (3) fixing: matrix arrayGThe size of d in (1) needs to be determined by singular value decomposition, which is the order of the unitary correlation matrix. Sequentially setting d to 0,1,2 \8230, constructing matrixes of different sizesG. For each kind of the medicine respectivelyGPerforming singular value decomposition:

assuming process objects as m-dimensional inputs, p-dimensional outputs, i.e.

Let V ₂₁ Is a V ₂ The upper m rows of. If rank (G) = min (m, p) is satisfied at the same time, and V ₂₁ If =0 (m ≧ p), the value of d at this time is the desired value.

Step 33: calculating a unitary correlation matrix D (q): with reference to "Rogozinski M, panenski a, gibbard m.an algorithm for the calculation of a ni ilpotential interactive matrix for linear multivariable systems," a method of calculating a unitary correlation matrix is proposed in which the right matrix score of the transfer function matrix T:

the following steps are used:

instead, the remaining steps are not changed, i.e. a unitary correlation matrix D (q) is obtained, which generally has the following properties:

D ^T (q ^-1 )D(q)＝I

where K is a full rank (row full rank or column full rank) constant matrix and I is a unit matrix.

Step four: constructing a multivariable time delay matrix L based on the unitary incidence matrix D (q), and then filtering output data by utilizing the multivariable time delay matrix L;

the unitary correlation matrix calculated in step three can be expanded as:

D(q)＝D ₁ q+D ₂ q ² +...+D _d q ^d (6)

constructing a multivariate delay Matrix (MTD):

L＝[D ₁ ,...,D _d ] (7)

further, for facilitating subsequent derivation, a property lemma of the unitary incidence matrix is given:

constructing an output matrix for the output data:

wherein

Is the output vector at the k + i time, symbol y _i (j) Represents a vector composed of i +1 data from time j to time j + i, namely: y is _d-1 (k + 1) represents the time from the output y (k + 1) at the time of k +1 to the output y (k + d) at the time of k + dThe vectors of the components. Filtering the output data using a matrix L:

step five: calculating a theoretical minimum output variance of the controlled system, wherein the theoretical minimum output variance is as follows: projection of the filtered output data vector space on the orthogonal complement space of the original output data;

before data projection, two data output matrices are constructed. On one hand, the filtered output vector in step four is utilized

The expansion is as follows:

in the formula

Namely, k in the formula (9) is replaced with k + i.

And on the other hand, a matrix is constructed for the original output vector:

Z _r,N ＝[y _r-1 (k-r+1) y _r-1 (k-r+2)…y _r-1 (k-r+N)] (11)

where r is the number of impulse response coefficients of the closed loop system, and the magnitude should be large enough to approximately describe the original system. N in the two formulas is large enough to satisfy mathematical statistics.

In order to estimate the theoretical optimal performance of the MIMO control system, the minimum output is calculated by means of data projection:

wherein

Is the theoretical minimum output variance, sign->

Is a pseudo-inverse of the matrix, having

The calculation of such a data projection is geometrically understood to be: theoretical minimum output variance

Outputting vector space for a filtered system>

In historical output data Z _r,N Orthogonal complement space of (a).

Step six: and calculating the ratio of the theoretical minimum output variance to the actual output variance, namely the performance index of the controlled system.

Defining the Minimum Variance (MV) index η as the ratio of the theoretical minimum output variance to the actual output variance, the performance index is calculated using the following equation:

example three:

this embodiment mainly explains how the theoretically optimal performance (MV output) should be achieved under what control action, why it can be used as a reference for evaluating the control performance, and how the effect under the minimum variance control is.

Introduction of basic theory: an open-loop MIMO process can be represented by a state space model in the form of an innovation:

in the formula

Respectively the state, input, output and white noise information vector of the process, K _f Is the kalman filter gain. The above equation can be written in the form of the following augmented equation:

in the formula:

where d is the order of the multivariate process correlation matrix, symbol u _i (j)、e _i (j) Represents a vector consisting of i +1 data from time j to time j + i, H _d The lower triangular Markov parameter matrix corresponding to the process model, namely: CA ⁱ B＝G _i (i＝0,1,…,d-1)。

In order to introduce a minimum variance control law, marking:

h _d 、

respectively represent a matrix H _d And &>

First row, e _d-1 (k + 1) represents a vector e _d (k) The last d rows, then:

wherein, the first and the second end of the pipe are connected with each other,

is a matrix->

The last d column of (1).

Filtering the output data with a multivariate delay Matrix (MTD) L:

according to the general property of unitary incidence matrix, where K = LH _d And K is a full rank constant matrix.

Can be seen as a pair of the original output vectors y _d-1 (k + 1) filtered output. The output can be divided into an optimal prediction-ahead part and a prediction error part after filtering:

wherein the optimal advanced prediction part

Prediction error part

The goal of the control law is to minimize the variance of the output excited by the initial state x (k) and the interfering signal e (k). At time k, e _d-1 The noise term in (k + 1) is unknown and cannot be compensated for by the control action u (k). Therefore, it is possible to obtain the same as that of equation (15)The first three terms are zero to implement the minimum variance control law, and the minimum variance solution can be expressed as:

wherein

Is a false inverse of K, since K column is full rank, is asserted>

Are present. The remaining feedback invariant terms constitute the minimum variance output:

the steps of this embodiment:

referring to the structural block diagram of the MIMO system shown in fig. 2, given a 2-input 2-output system, the mathematical models of the controlled object T and the noise model N are:

the two-dimensional white noise sequence a (k) follows a normal distribution, and the noise covariance ∑ is _a ＝I。

(1) Assuming the model is unknown, the process model gain K ₁₂ And (6). As shown in FIG. 2, the appropriate change settings are a series of simple step change signals, historical data is collected, a subspace identification method is used to estimate the model coefficient matrix and to estimate the Markov parameters of the process model and the noise model, and a matrix H is constructed from the parameters _d 、

(2) D (q) is obtained according to the method for estimating the unitary correlation matrix in the second embodiment, and a multivariable delay matrix L is constructed.

(3) From K = LH _d The matrix K is calculated.

(4) The recording system outputs data in an open loop, stimulated by noise, without the action of a controller.

(5) Using minimum variance control law in control loop

And forming a closed loop feedback system and recording the output of the system.

(6) The open loop output and the minimum variance control output are plotted in fig. 3.

In FIG. 3, the first two sub-graphs are respectively output 1 (y) under the action of initial control (no controller) ₁ (k) And output 2 (y) ₂ (k) The last two subgraphs respectively output 1 (y) under the action of a Minimum Variance (MV) controller _mv,1 (k) And output 2 (y) _mv,2 (k) Output data of). It can be found that the Minimum Variance (MV) control law adopted in step (5) has obvious effect and small output fluctuation, and the output variance caused by noise can be limited to a very low level. The minimum variance output is actually the theoretical lowest limit that the control system performance can reach, reflecting the maximum ability of an ideal controller to suppress noise interference. This example demonstrates the rationality of using the minimum variance criterion as the criterion for evaluating the performance of the MIMO control system.

Example four:

the embodiment mainly illustrates the principle and effectiveness of evaluating the performance of the MIMO control system by using the subspace projection method.

Introduction of basic theory: applying a time-invariant feedback controller to the controlled object model in the third theory of the embodiment:

in combination with the optimal prediction advance part and the controlled object model in the third embodiment, there is the following optimal prediction output system jointly excited by the original output and the closed loop state:

wherein:

for the new closed-loop model, it can be represented by a series of impulse responses, and the response coefficient matrix is:

Θ _r ＝[Θ _r Θ _r-1 … Θ ₁ ]

Θ ₁ ＝D _cl

assuming that the closed loop system is stable, the r outputs before the time k +1 are represented by a vector:

y _r-1 (k-r+1)＝[y ^T (k-r+1) … y(k) ^T ] ^T

when r is large enough, the optimal look ahead part has a finite impulse response:

the filtered system output is:

analysis y _r-1 (k-r + 1) and

it can be found that y _r-1 (k-r+ 1) depends on the output data preceding the instant k +1>

The two are independent of each other depending on the noise data from the time k +1 to the time k + d. This explains why equation (12) holds:

wherein, when N → ∞ is:

the above is the principle of estimating the minimum variance output for the projection method.

The steps of this embodiment:

also with the object model, noise model and noise excitation in example three, a minimum variance controller representing the decoupled system was used:

forming a control loop. Assuming the loop setpoint is 0, let K ₁₂ The performance of the current controller was evaluated separately, varying from 0 to 7.

(1) Let K assume that the model is unknown ₁₂ =0. As shown in FIG. 2, the appropriate change settings are a series of simple step change signals, historical data are collected, a subspace identification method is used to estimate the model coefficient matrix and the Markov parameters of the process model, and a matrix H is constructed based on the parameters _d 。

(2) And determining the order D of the unitary correlation matrix according to the method in the third step, and estimating the unitary correlation matrix D (q).

(3) And (4) filtering the output data according to the fourth decomposition unitary incidence matrix D (q) which is a multivariable time delay Matrix (MTD) L.

(4) Constructing an extended output filter matrix according to the fifth step

Expanding the original output matrix Z _r,N . Calculating the optimal output performance, namely the minimum variance output:

(5) Calculating the MV performance index of the control loop according to the sixth step:

(6) On the one hand, the proportional gain K in the process model is changed ₁₂ 0,1,2 \82307, repeating steps one to five, calculating the performance index of the two-input two-output system in sequence, marking the index as a 'projection method', and using a circled dotted line in fig. 4. On the other hand, in the control loop, the minimum variance control action adopted in the formula (18) in the third theoretical basis of the embodiment is applied, the output data is collected as the minimum variance reference, the ratio of the calculated actual output variance to the output variance is used as a performance index, and the index is marked as 'theoretical calculation' and is represented by a solid line with a star in fig. 4.

(7) On one hand, extracting the minimum output variance and the actual output variance of each output in the step (5), and following K ₁₂ Variation of the values, calculating in turn the individual outputs (y) ₁ (k) And y ₂ (k) Performance index, marked as "projection method", represented by the circled dashed line in fig. 5; on the other hand, in the control loop, the minimum variance control action adopted in the formula (18) in the third theoretical basis of the embodiment is applied, the output data is collected as the minimum variance, and the minimum variance is compared with the controller Q (Q) ^-1 ) The outputs under action are compared and the performance index of the individual outputs is calculated, labeled "theoretical calculation" and represented in figure 5 by the solid line with the stars.

As can be seen from both fig. 4 and 5, the dashed line is very close to the solid line, i.e.: no matter the overall performance or single output performance of the control system, the performance index calculated by the projection method provided by the embodiment is very close to the theoretical calculation value, and the good accuracy of the evaluation method provided by the embodiment is reflected. For further analysis, when K ₁₂ On the other hand, when the temperature is → 0, the interaction between the two circuits is weakened, and the output performance index approaches 1. And with K ₁₂ The interaction between the two loops is enhanced, the performance is gradually deteriorated, and eta finally approaches to 0.

As can be seen from FIG. 5, y ₁ (k) Performance index value of with K ₁₂ Increase in (3) falls faster, reflecting y ₁ (k) Performance of (2) to K ₁₂ Is more sensitive to changes in the image. Comparing FIG. 4 with FIG. 5, it can be found that y ₁ (k) The performance change of the system seems to be more consistent with the MIMO performance change trend, and the total performance of the control system is influenced by y ₁ (k) The effect of (a) is more pronounced, which indicates that it is not sufficient to control a multivariable system using only two single-loop controllers.

The embodiment mainly explains the accuracy of the subspace projection performance evaluation method, and further analyzes the reason of poor performance of the MIMO control system. From the whole evaluation process, the performance evaluation is finished only by means of input and output data, the evaluation process is simple, and the model information is estimated and the control system performance evaluation is fused by processing conventional operation data without depending on any system model. This will bring great convenience to the control performance evaluation of an actual industrial control system.

Some steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.

Claims (10)

1. A performance evaluation method of a MIMO control system, the performance evaluation method of the MIMO control system comprising:

the method comprises the following steps: judging whether the controlled system is a system with a constant set value:

if the set value is constant, a noise signal is superposed on the output of the controller or the set value is artificially changed into a step change signal;

if the set value changes randomly, no processing is carried out;

step two: collecting input and output data of the controlled system, and constructing a historical database, wherein the historical database comprises the following steps:

for the controlled system with the constant set value, acquiring the noise signal or the step change signal, and acquiring system output data;

for the controlled system with the set value changing randomly, directly acquiring system input data and output data;

step three: estimating Markov parameters of the process object according to the historical data, and extracting a unitary incidence matrix D (q) from the Markov parameters;

step four: constructing a multivariable time delay matrix L based on the unitary incidence matrix D (q), and then filtering output data by utilizing the multivariable time delay matrix L;

step five: calculating a theoretical minimum output variance of the controlled system, wherein the theoretical minimum output variance is as follows: projection of the filtered output data vector space on an orthogonal complement space of the original output data;

step six: and calculating the ratio of the theoretical minimum output variance to the actual output variance, namely the performance index of the controlled system.

2. The method of claim 1, wherein the step five comprises:

step 51: constructing an output matrix after filtering, and outputting the output vector after filtering in the fourth step

The expansion is as follows:

step 52: constructing an original output matrix, and constructing a matrix for an original output vector:

Z _r,N ＝[y _r-1 (k-r+1) y _r-1 (k-r+2)…y _r-1 (k-r+N)]

wherein r is the number of impulse response coefficients of the closed-loop system;

step 53: and (3) calculating the theoretical minimum output variance of the controlled system by using a data projection mode:

wherein the content of the first and second substances,

is the theoretical minimum output variance, sign->

Pseudo-inverse calculation of the representation matrix, i.e.

3. The method of claim 2, wherein the performance index of the controlled system is:

4. the method for evaluating the performance of the MIMO control system according to claim 1, wherein the step of extracting the unitary correlation matrix D (q) in three steps comprises:

step 31: f of each estimated controlled object model parameter _i Markov parameter matrix G combined into MIMO system _i There is a process model transfer function matrix:

matrix G is then constructed by:

step 32: fixing the rank;

matrix arrayGThe size of the middle d needs to be determined through singular value decomposition, and the value of the middle d is the order of the unitary correlation matrix; sequentially setting d to 0,1,2, 8230to form matrixes in different sizesG(ii) a For each kind separatelyGSingular value decomposition is carried out:

assuming process objects as m-dimensional inputs, p-dimensional outputs, i.e.

Let V ₂₁ Is a V ₂ The upper m rows of sections; if rank(s) are satisfied at the same timeG) = min (m, p), and V ₂₁ If m is not less than 0, the value of d is the required value;

step 33: based on the determined order d value, by means of an iterative method, through G _i The first D term of (a) estimates the unitary correlation matrix D (q).

5. The method of claim 1, wherein the step four comprises:

expanding the unitary incidence matrix D (q) as:

D(q)＝D ₁ q+D ₂ q ² +…+D _d q ^d

then constructing a multivariate delay matrix L:

L＝[D ₁ ,...,D _d ]

constructing an output matrix for the output data:

wherein the content of the first and second substances,

output vector at time k + i, y _d-1 (k + 1) represents a vector composed of outputs y (k + 1) at the time k +1 to y (k + d) at the time k + d;

filtering the output data by utilizing the multivariate time delay matrix L:

wherein the content of the first and second substances,

is the filtered output vector.

6. The method of claim 1, wherein the noise signal superimposed in the step-adding is a white noise signal.

7. The method for evaluating the performance of a MIMO control system according to claim 1, wherein the third step estimates the Markov parameter of the process object using a data correlation analysis method when the set value is constant.

8. The method of claim 1, wherein the step three is to estimate the Markov parameter of the process object by using a subspace identification method when the setting value is randomly changed.

9. A parameter optimization method for a MIMO control system, wherein the parameter optimization method for the MIMO control system first evaluates system performance by using the performance evaluation method for the MIMO control system according to any one of claims 1 to 8, and then determines whether to perform parameter optimization for the MIMO control system according to the evaluation result.

10. A MIMO control system, characterized in that the MIMO control system evaluates system performance using the performance evaluation method of the MIMO control system according to any one of claims 1 to 8.

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