A two-stage online identification method and system for multivariable systems

Abstract

A two-stage online identification method and system for a multivariable system, the method comprising: obtaining continuous historical data of each control variable and each controlled variable in the multivariable system; constructing data samples using a CARMA model; obtaining the optimal pure lag time from each control variable to each controlled variable in the multivariable system and establishing an optimal pure lag CARMA model; obtaining the step response curve of each controlled variable when each control variable makes a step change based on the optimal pure lag CARMA model; obtaining the continuous change data of the step response curve as an identification sample, obtaining the optimal pure lag time from each control variable to any controlled variable in a single variable system based on a second-order pure lag CARMA model and establishing a second-order optimal pure lag CARMA model; and performing matrix combination on the second-order optimal pure lag CARMA model to obtain a multivariable system identification model. The present invention decouples and simplifies the multivariable model while ensuring the accuracy of the model, which is helpful for the realization of predictive control.

Description

Technical Field

[0001] The present invention belongs to the technical field of advanced process control, and more specifically, relates to a two-stage online identification method and system for a multivariable system. Background Art

[0002] In the field of advanced process control, system identification is one of the most active and rapidly developing topics. Like optimal control and adaptive control, system identification is one of the main pillars of modern control theory. The purpose of system identification is to fully grasp the motion law of the research object and describe the cause and effect relationship of the motion of things in mathematical language. System identification is modeling, that is, to establish an optimal model of a system based on the input-output data of the actual system. This model can be used for adaptive control, model predictive control, etc., and is the basis and foundation of control simulation.

[0003] In the prior art, the least squares algorithm is one of the important methods for system identification. It has a simple principle, is easy to program and has a wide range of applications. Among them, the recursive least squares algorithm can track the parameters of a time-varying system. The recursive algorithm is also called an online identification method. It does not contain any matrix inversion and can be calculated quickly, thus realizing the recursive identification of the system.

[0004] However, in existing actual control systems, the controlled object is usually a multivariable system with coupling characteristics. In order to improve the identification accuracy during model identification, the order needs to be increased. However, when the model order is increased, it is easy to cause overfitting, and the higher the order, the more roots the function has. When it is reflected on the curve, the high-order model is prone to fluctuations as the time domain changes. When it is discretized, it is manifested as a discontinuous and non-smooth curve, which affects the control accuracy. In addition, the high-order model increases the amount of calculation. For predictive control, the increase in model order will greatly increase the calculation workload and affect the control speed. Therefore, in real-time control systems, it is necessary to simplify the model without affecting the accuracy, so as to achieve high-speed and accurate control. Summary of the invention

[0005] In order to solve the deficiencies in the prior art, the purpose of the present invention is to provide a two-stage online identification method and system for a multivariable system. In the first stage, a high-order model is used to accurately obtain the characteristic curves of each control loop. In the second stage, a simplified model is used to realize identification and finally obtain a low-order model. While ensuring the accuracy of the model, the multivariable model is decoupled and simplified, which is conducive to the realization of predictive control.

[0006] The present invention adopts the following technical solution.

[0007] The present invention proposes a two-stage online identification method for a multivariable system, comprising:

[0008] Step 1, obtain the continuous historical data of each control variable and each controlled variable in the multivariable system; use the controlled autoregression and moving average model CARMA (Controlled Auto Regression and Moving Average) to construct the data sample for online identification; where the order of the CARMA model is proportional to the number of control variables;

[0009] Step 2: According to the preset time step, an exhaustive method is used to minimize the variance between the CARMA model simulation curve and the CARMA model measured curve, and the optimal pure lag time from each control variable to each controlled variable in the multivariable system is obtained; the optimal pure lag CARMA model is established using the parameter vector of the CARMA model corresponding to each controlled variable and the optimal pure lag time of the multivariable system;

[0010] Step 3, based on the optimal pure lag CARMA model, obtain the step response curve of each controlled variable when each control variable makes a step change;

[0011] Step 4, obtain the continuously changing data of the step response curve as the identification sample, repeat step 2 based on the second-order pure lag CARMA model, that is, use the exhaustive method according to the preset time step to minimize the variance between the simulation curve of the second-order pure lag CARMA model and the measured curve of the second-order pure lag CARMA model, and obtain the optimal pure lag time from each control variable to any controlled variable in the single variable system; use the parameter vector of the second-order pure lag CARMA model corresponding to any controlled variable and the optimal pure lag time of the single variable system to establish a second-order optimal pure lag CARMA model;

[0012] Step 5: Matrix-combining the second-order optimal pure lag CARMA model to obtain a multivariable system identification model, and use the multivariable system identification model to perform two-stage online identification of the multivariable system.

[0013] Preferably, in step 1, the order of the CARMA model is twice the number m of control variables, that is, it satisfies the following relationship:

[0014] n=2×m

[0015] Where n is the order of the CARMA model.

[0016] Preferably, step 1 comprises:

[0017] Step 1.1, determine the length of the historical data vector of the controlled variable and the controlled variable according to the order n of the single-loop CARMA model in the discrete control system, where the historical data vector of the controlled variable and the controlled variable at the kth moment is Satisfies the following relationship:

[0018]

[0019] In the formula,

[0020] y(ki) is the controlled variable at the ki-th moment, where i=1, 2, ..., n,

[0021] u j (kd j -i′) is the kd j -i′ is the jth control quantity at time, where j=1, 2, ..., m, m is the number of control quantities, i′=0, 1, 2, ..., n,

[0022] w(kh) is the error at the khth moment, h = 1, ..., nc, nc is the order of the error,

[0023] d j is the pure lag time of the jth control quantity acting on each controlled quantity;

[0024] Step 1.2: Based on the historical data vector of the controlled and controlled quantities at the kth moment Determine that the data sample φ(k) used for online identification of multivariable systems satisfies the following relationship:

[0025]

[0026] In the formula, is the historical data vector of the lth controlled variable and control variable at the kth moment, where l=1, 2, ..., L, and L is the number of controlled variables in the CARMA model of the multivariable system.

[0027] Preferably, step 2 comprises:

[0028] Step 2.1: Determine each control variable u according to the historical curve of the CARMA model j Act on each controlled quantity y l The longest pure lag time D jl ;

[0029] Step 2.2, set the time step to an integer multiple of the sampling period;

[0030] Step 2.3: According to the time step, the pure lag time of each control variable acting on each controlled variable is increased from 0 to the maximum pure lag time D by using the exhaustive method. jl , thus obtaining different pure lag times;

[0031] Step 2.4, each time the value is incremented, the pure lag time obtained by the current increment is substituted into the historical data vector, and the parameter vector of the CARMA model is identified using the recursive least squares method to satisfy the following relationship:

[0032]

[0033] In the formula,

[0034] is the parameter vector of the CARMA model identified at the kth moment,

[0035] is the historical data vector of the controlled and controlled quantities formed by replacing the error with the error estimate at the kth moment,

[0036] y(k) is the controlled variable at the kth moment,

[0037] K(k) is the first identification parameter for rolling update at the kth moment,

[0038] P(k) is the second identification parameter that is updated at the kth moment;

[0039] Step 2.5, using the identified parameter vector of the CARMA model, the simulation curve of the CARMA model under the current pure lag time is obtained, which satisfies the following relationship:

[0040]

[0041] In the formula,

[0042] is the lth controlled variable at the kth moment on the CARMA model simulation curve,

[0043] is the parameter vector set of the identified CARMA model. The elements in the parameter vector set are the parameter vectors of the CARMA model identified at each moment.

[0044] Step 2.6, according to the time step, the simulation curve of the CARMA model The minimum variance between the measured curve and the CARMA model is the objective function, and the effect of each control variable uj on each controlled variable y is obtained by exhaustive method. l The optimal pure lag time d jl , that is, it satisfies the following relationship:

[0045]

[0046] In the formula,

[0047] AIM is the objective function,

[0048] y l (k) is the lth controlled variable at the kth moment on the measured curve of the CARMA model.

[0049] Furthermore, in step 2.4, the error estimate used to replace the error at the kth moment in the recursive least squares method is Satisfies the following relationship:

[0050]

[0051] In the formula,

[0052] y(k) is the controlled variable at the kth moment,

[0053] is the controlled variable at the kth moment obtained by model simulation.

[0054] Preferably, in step 3, when any control variable u j When making a step change, keep other controlled variables unchanged and use the best pure lag CARMA model to obtain each controlled variable y l In the control quantity u j Step response curve for step change Satisfies the following relationship:

[0055]

[0056] In the formula, is the controlled quantity y at the kth moment l In the control quantity u j Step response curve for step change.

[0057] Furthermore, the step response curve is the l About the control quantity u j A univariate response curve to a step change.

[0058] Furthermore, step 5 also includes eliminating model errors before matrix combination.

[0059] On the other hand, the present invention also proposes a two-stage online identification system for a multivariable system, and implements a two-stage online identification method for a multivariable system.

[0060] The beneficial effect of the present invention is that, compared with the prior art, while ensuring the model identification accuracy, the decoupling and order reduction of the multivariable system can be achieved, which can effectively avoid the problem of discontinuous and non-smooth model curves that are easy to appear when the high-order model is discretized due to the large number of roots, and the low-order model can effectively reduce the amount of calculation of the model control and improve the control speed. At the same time, the decoupled model can realize the free combination of the control quantity and the controlled quantity, which is convenient for the analysis and research of the control strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of a two-stage online identification method of a multivariable system of the present invention;

[0062] Figure 2 is the y of the multivariable control system for two-stage identification in the embodiment of the present invention. 1 To u 1 Step response curve of

[0063] Figure 3 is the y of the multivariable control system for two-stage identification in the embodiment of the present invention. 2 To u 1 Step response curve of

[0064] Figure 4 is the y of the multivariable control system for two-stage identification in the embodiment of the present invention. 1 To u 2 Step response curve of;

[0065] Figure 5 is the y of the multivariable control system for two-stage identification in the embodiment of the present invention. 2 To u 2 Step response curve of . DETAILED DESCRIPTION

[0066] The present application is further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present application.

[0067] On the one hand, the present invention proposes a two-stage online identification method for a multivariable system, such as Figure 1 As shown, steps 1 to 5 are included.

[0068] Step 1, obtain the continuous historical data of each control variable and each controlled variable in the multivariable system; use the controlled autoregressive moving average model CARMA to construct the data sample for online identification; where the order of the CARMA model is proportional to the number of control variables.

[0069] When using the historical data of the controlled and controlled quantities to construct data samples and use them for identification, it is necessary to first determine the order of the model used. If the order of the model is too high, the workload of the identification calculation will increase, and if the order is too low, the accuracy of the system identification will be affected. In this embodiment, the order of the model is considered to ultimately obtain a second-order pure lag model. Therefore, the order of the CARMA model is twice the number of controlled quantities m, that is, it satisfies the following relationship:

[0070] n=2×m

[0071] Where n is the order of the CARMA model.

[0072] It is worth noting that in this embodiment, the model order is twice the number of controlled quantities, which is a non-restrictive and preferred choice, and those skilled in the art can select a reasonable model order as needed.

[0073] In a single-loop system in a discrete control system, the CARMA model satisfies the following relationship:

[0074]

[0075] In the formula,

[0076] y(k) is the controlled variable at the kth moment,

[0077] is the continuous historical data vector of the controlled quantity and the control quantity at the kth moment,

[0078] u j (k) is the control quantity of the jth path at the kth moment,

[0079] w(k) is the error at the kth moment,

[0080] θ is the parameter vector of the CARMA model,

[0081] a i is the model parameter corresponding to the controlled quantity,

[0082] is the model parameter corresponding to the control quantity,

[0083] c h is the model parameter corresponding to the error.

[0084] Specifically, step 1 includes:

[0085] Step 1.1, determine the length of the historical data vector of the controlled variable and the controlled variable according to the order n of the single-loop CARMA model in the discrete control system, where the historical data vector of the controlled variable and the controlled variable at the kth moment is Satisfies the following relationship:

[0086]

[0087] In the formula,

[0088] y(ki) is the controlled variable at the ki-th moment, where i=1, 2, ..., n,

[0089] u j (kd j -i′) is the kd j -i′ is the jth control quantity at time, where j=1, 2, ..., m, m is the number of control quantities, i′=0, 1, 2, ..., n,

[0090] w(kh) is the error at the khth moment, h = 1, ..., nc, nc is the order of the error,

[0091] d j is the pure lag time of the jth control quantity acting on each controlled quantity;

[0092] The CARMA model of a multivariable system satisfies the following relationship:

[0093]

[0094] In the formula,

[0095] Y(k) is the controlled variable matrix at the kth moment, and the elements of this matrix are the lth controlled variable y at the kth moment. l (k)

[0096] φ(k) is the continuous historical data matrix of the controlled and controlled quantities at the kth moment. The elements of this matrix are the historical data vectors of the lth controlled and controlled quantities at the kth moment.

[0097] θ is the parameter matrix of the CARMA model, and the elements of this matrix are the parameter vectors θ of the CARMA model of the lth controlled variable at the kth moment. l ,

[0098] W(k) is the error matrix at the kth moment, and the elements of this matrix are the error w of the lth controlled quantity at the kth moment. l (k).

[0099] Step 1.2: Based on the historical data vector of the controlled and controlled quantities at the kth moment Determine that the data sample φ(k) used for online identification of multivariable systems satisfies the following relationship:

[0100]

[0101] In the formula, is the historical data vector of the lth controlled variable and control variable at the kth moment, where l=1, 2, ..., L, and L is the number of controlled variables in the CARMA model of the multivariable system.

[0102] Step 2: According to the preset time step, an exhaustive method is used to minimize the variance between the CARMA model simulation curve and the CARMA model measured curve, and the optimal pure lag time from each control variable to each controlled variable in the multivariable system is obtained; the optimal pure lag CARMA model is established using the parameter vector of the CARMA model corresponding to each controlled variable and the optimal pure lag time of the multivariable system.

[0103] Specifically, step 2 includes:

[0104] Step 2.1: Determine each control variable u according to the historical curve of the CARMA model jAct on each controlled quantity y l The longest pure lag time D il ;

[0105] Step 2.2, set the time step to an integer multiple of the sampling period;

[0106] For discrete systems, since each sampling is fixed-period sampling, its period is consistent with the sampling period when forming the identification sample. Therefore, when setting the time step, it should be selected as an integer multiple of the sampling period. In this embodiment, the time step is consistent with the sampling period.

[0107] Step 2.3: According to the time step, the pure lag time of each control variable acting on each controlled variable is increased from 0 to the maximum pure lag time D by using the exhaustive method. jl , thus obtaining different pure lag times;

[0108] Step 2.4, each time the value is incremented, the pure lag time obtained by the current increment is substituted into the historical data vector, and the parameter vector of the CARMA model is identified using the recursive least squares method to satisfy the following relationship:

[0109]

[0110] In the formula,

[0111] is the parameter vector of the CARMA model identified at the kth moment,

[0112] is the historical data vector of the controlled and controlled quantities formed by replacing the error with the error estimate at the kth moment,

[0113] y(k) is the controlled variable at the kth moment,

[0114] K(k) is the first identification parameter for rolling update at the kth moment,

[0115] P(k) is the second identification parameter that is updated at the kth moment;

[0116] Furthermore, since the error cannot be measured and can only be replaced by an error estimate, in step 2.4, the error estimate used to replace the error at the kth moment in the recursive least squares method is Satisfies the following relationship:

[0117]

[0118] In the formula,

[0119] y(k) is the controlled variable at the kth moment,

[0120] is the controlled variable at the kth moment obtained by model simulation.

[0121] Step 2.5, using the identified parameter vector of the CARMA model, the simulation curve of the CARMA model under the current pure lag time is obtained, which satisfies the following relationship:

[0122]

[0123] In the formula,

[0124] is the lth controlled variable at the kth moment on the CARMA model simulation curve,

[0125] is the parameter vector set of the identified CARMA model. The elements in the parameter vector set are the parameter vectors of the CARMA model identified at each moment.

[0126] Step 2.6, according to the time step, the simulation curve of the CARMA model The minimum variance between the measured curve and the CARMA model is the objective function, and the control variables u are obtained by exhaustive method. j Act on each controlled quantity y l The optimal pure lag time d jl , that is, it satisfies the following relationship:

[0127]

[0128] In the formula,

[0129] AIM is the objective function,

[0130] y l (k) is the lth controlled variable at the kth moment on the measured curve of the CARMA model.

[0131] Through steps 1 and 2, the model identification results of the first stage of the multivariable system are obtained, that is, the model parameter variables and the optimal pure lag time corresponding to each controlled quantity are obtained. However, the model parameter variable format obtained at this time is It is a high-order model that includes various control variables and errors, so a second stage of identification is required to decouple and reduce the order of the model.

[0132] Step 3: Based on the optimal pure lag CARMA model, obtain the step response curve of each controlled variable when each control variable makes a step change.

[0133] Specifically, in step 3, when any control variable u j Keep other control variables unchanged when making step changes.

[0134] Using the optimal pure lag CARMA model, we can get the controlled variables y l In the control quantity u j Step response curve for step change Satisfies the following relationship:

[0135]

[0136] In the formula, is the controlled quantity y at the kth moment l In the control quantity u j Step response curve for step change.

[0137] Furthermore, the step response curve obtained after step 3 is the controlled quantity y l About the control quantity u j The single variable response curve with step change converts the identification problem of multivariable system into the identification problem of multiple single-loop systems, thus realizing the decoupling of the model.

[0138] Step 4, obtain the continuously changing data of the step response curve as the identification sample, and repeat step 2 based on the second-order pure lag CARMA model, that is, use the exhaustive method according to the preset time step to minimize the variance between the simulation curve of the second-order pure lag CARMA model and the measured curve of the second-order pure lag CARMA model, and obtain the optimal pure lag time from each control variable to any controlled variable in the single variable system; use the parameter vector of the second-order pure lag CARMA model corresponding to any controlled variable and the optimal pure lag time of the single variable system to establish a second-order optimal pure lag CARMA model.

[0139] The model obtained through the second stage identification is a second-order optimal pure lag discrete model, which realizes the order reduction of the multivariable system. The second-order optimal pure lag CARMA model satisfies the following relationship:

[0140]

[0141] In the formula,

[0142] is the lth controlled variable corresponding to the jth controlled variable at the kth moment,

[0143] is the continuous historical data vector of the j-th control quantity and the l-th controlled quantity at the k-th moment,

[0144] is the parameter vector of the CARMA model of the j-th control variable and the l-th controlled variable,

[0145] is the error between the jth control quantity and the lth controlled quantity at the kth moment,

[0146] is the lth controlled variable at the kith moment, where i = 1, 2,

[0147] For kd j -i time point j-th control quantity, where j = 1, 2, ..., m, m is the number of control quantities, i' = 0, 1, 2, ..., n,

[0148] is the error between the jth control quantity and the lth controlled quantity at the khth moment, h = 1, 2,

[0149] is the pure lag time of the jth control quantity acting on the lth controlled quantity;

[0150] is the model parameter corresponding to the lth controlled quantity,

[0151] is the model parameter corresponding to the j-th control quantity,

[0152] is the model parameter corresponding to the error between the j-th controlled variable and the l-th controlled variable.

[0153] Step 5: Matrix-combining the second-order optimal pure lag CARMA model to obtain a multivariable system identification model, and use the multivariable system identification model to perform two-stage online identification of the multivariable system.

[0154] Step 5 also includes eliminating the model error before matrix combination, because the error is unmeasurable in actual use. The model after error elimination satisfies the following relationship:

[0155]

[0156] The multivariable system identification model finally obtained in this embodiment satisfies the following relationship:

[0157]

[0158] Where Y(k) is the controlled quantity vector at the kth moment obtained by identification.

[0159] Figures 2 to 5, which is a comparison of the first-stage identification results and the second-stage identification results obtained by using the method proposed in the present invention to perform two-stage identification on a 2×2 multivariable control system. It can be seen that when the two-stage identification proposed in the present invention is adopted, the accuracy of the model does not decrease compared with the one-stage identification. At the same time, due to the high order of the model in the one-stage identification process, there are discontinuous jumps on the curve of the obtained model, and the model achieves smoothing of the curve during the two-stage identification, so the identification result is closer to the actual model.

[0160] On the other hand, the present invention also proposes a two-stage online identification system for a multivariable system, and implements a two-stage online identification method for a multivariable system.

[0161] The beneficial effect of the present invention is that, compared with the prior art, while ensuring the model identification accuracy, the decoupling and order reduction of the multivariable system can be achieved, which can effectively avoid the problem of discontinuous and non-smooth model curves that are easy to appear when the high-order model is discretized due to the large number of roots, and the low-order model can effectively reduce the amount of calculation of the model control and improve the control speed. At the same time, the decoupled model can realize the free combination of the control quantity and the controlled quantity, which is convenient for the analysis and research of the control strategy.

[0162] The applicant of the present invention has made a detailed explanation and description of the implementation examples of the present invention in conjunction with the drawings in the specification. However, those skilled in the art should understand that the above implementation examples are only preferred implementation schemes of the present invention, and the detailed description is only to help readers better understand the spirit of the present invention, but not to limit the scope of protection of the present invention. On the contrary, any improvements or modifications based on the inventive spirit of the present invention should fall within the scope of protection of the present invention.

Claims

1. A two-stage online identification method for a multivariable system, characterized in that: The online identification method comprises: Step 1, obtain the continuous historical data of each control variable and each controlled variable in the multivariable system; use the controlled autoregressive moving average model CARMA to construct the data sample for online identification; wherein the order of the CARMA model is proportional to the number of control variables; Step 2: According to the preset time step, an exhaustive method is used to minimize the variance between the CARMA model simulation curve and the CARMA model measured curve, and the optimal pure lag time from each control variable to each controlled variable in the multivariable system is obtained; the optimal pure lag CARMA model is established using the parameter vector of the CARMA model corresponding to each controlled variable and the optimal pure lag time of the multivariable system; Step 3, based on the optimal pure lag CARMA model, obtain the step response curve of each controlled variable when each control variable makes a step change; Step 4, obtain the continuously changing data of the step response curve as the identification sample, repeat step 2 based on the second-order pure lag CARMA model, that is, use the exhaustive method according to the preset time step to minimize the variance between the simulation curve of the second-order pure lag CARMA model and the measured curve of the second-order pure lag CARMA model, and obtain the optimal pure lag time from each control variable to any controlled variable in the single variable system; use the parameter vector of the second-order pure lag CARMA model corresponding to any controlled variable and the optimal pure lag time of the single variable system to establish a second-order optimal pure lag CARMA model; Step 5: Matrix-combining the second-order optimal pure lag CARMA model to obtain a multivariable system identification model, and use the multivariable system identification model to perform two-stage online identification of the multivariable system.

2. The two-stage online identification method for multivariable systems according to claim 1, characterized in that: In step 1, the order of the CARMA model is twice the number of control variables m, that is, it satisfies the following relationship: n=2×m Where n is the order of the CARMA model.

3. The two-stage online identification method for multivariable systems according to claim 1, characterized in that: Step 1 includes: Step 1.1, determine the length of the historical data vector of the controlled variable and the controlled variable according to the order n of the single-loop CARMA model in the discrete control system, where the historical data vector of the controlled variable and the controlled variable at the kth moment is Satisfies the following relationship: In the formula, y(ki) is the controlled variable at the ki-th moment, where i = 1, 2, ..., n, u j (kd j -i′) is the kd j -i′ is the jth control quantity at time j, where j = 1, 2, ..., m, m is the number of control quantities, i′ = 0, 1, 2, ..., n, w(kh) is the error at the khth moment, h = 1,…,nc, nc is the order of the error, d j is the pure lag time of the jth control quantity acting on each controlled quantity; Step 1.2: Based on the historical data vector of the controlled and controlled quantities at the kth moment Determine that the data sample φ(k) used for online identification of multivariable systems satisfies the following relationship: In the formula, is the historical data vector of the lth controlled variable and control variable at the kth moment, where l = 1, 2, …, L, and L is the number of controlled variables in the CARMA model of the multivariable system.

4. The two-stage online identification method for multivariable systems according to claim 3 is characterized in that: Step 2 includes: Step 2.1: Determine each control variable u according to the historical curve of the CARMA model j Act on each controlled quantity y l The longest pure lag time D jl ; Step 2.2, set the time step to an integer multiple of the sampling period; Step 2.3: According to the time step, the pure lag time of each control variable acting on each controlled variable is increased from 0 to the maximum pure lag time D by using the exhaustive method. jl , thus obtaining different pure lag times; Step 2.4, each time the increment is made, the pure lag time obtained by the current increment is substituted into the historical data vector, and the parameter vector of the CARMA model is identified using the recursive least squares method to satisfy the following relationship: In the formula, is the parameter vector of the CARMA model identified at the kth moment, is the historical data vector of the controlled and controlled quantities formed by replacing the error with the error estimate at the kth moment, y(k) is the controlled variable at the kth moment, K(k) is the first identification parameter for rolling update at the kth moment, P(k) is the second identification parameter that is updated at the kth moment; Step 2.5, using the identified parameter vector of the CARMA model, the simulation curve of the CARMA model under the current pure lag time is obtained, which satisfies the following relationship: In the formula, is the lth controlled variable at the kth moment on the CARMA model simulation curve, is the parameter vector set of the identified CARMA model. The elements in the parameter vector set are the parameter vectors of the CARMA model identified at each moment. Step 2.6, according to the time step, the simulation curve of the CARMA model The minimum variance between the measured curve and the CARMA model is the objective function, and the control variables u are obtained by exhaustive method. j Act on each controlled quantity y l The optimal pure lag time d jl , that is, it satisfies the following relationship: In the formula, Aim is the objective function, y l (k) is the lth controlled variable at the kth moment on the measured curve of the CARMA model.

5. The two-stage online identification method for multivariable systems according to claim 4, characterized in that: In step 2.4, the error estimate used to replace the error at the kth moment in the recursive least squares method is Satisfies the following relationship: In the formula, y(k) is the controlled quantity at the kth moment, is the controlled variable at the kth moment obtained by model simulation.

6. The two-stage online identification method for multivariable systems according to claim 4, characterized in that: In step 3, when any control variable u j When making a step change, keep other controlled variables unchanged and use the best pure lag CARMA model to obtain each controlled variable y l In the control quantity u j Step response curve for step change Satisfies the following relationship: In the formula, is the controlled quantity y at the kth moment l In the control quantity u j Step response curve for step change.

7. The two-stage online identification method for multivariable systems according to claim 6, characterized in that: The step response curve is the l About the control quantity u j A univariate response curve to a step change.

8. The two-stage online identification method for multivariable systems according to claim 1, characterized in that: Step 5 also includes eliminating model errors before matrix combination.

9. A two-stage online identification system for a multivariable system, characterized in that: The system implements the two-stage online identification method for a multivariable system as described in any one of claims 1-8.

Images