Separated-layer water injection underground fusion control system and method based on MPC and PID

Abstract

The invention relates to a separate-layer water injection underground fusion control system and method based on MPC and PID. The system comprises a central MPC controller, a PID decoupling control system, a fusion controller and an underground water distributor multivariable mathematical model. The PID decoupling control system comprises a multi-path PID controller, a cascade weight w and a decoupler, the multi-path PID controller, the cascade weight w and the decoupler form cascade control with the central MPC controller, the fusion controller is used for fusing an output control law of the central MPC controller and an output control law of the multi-path PID controller to obtain a fusion control law, and the fusion control law is connected with the central MPC controller. And the fusion control law acts on the multivariable mathematical model of the underground water distributor. The flow allocation efficiency of each layer is improved by designing a fusion control structure; the fusion control structure reduces the requirement of the MPC on the model parameter precision, and improves the adaptability of the fusion controller; and meanwhile, the system is provided with a flow decoupler, so that interlayer interference is reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of oilfield separate layer injection, and particularly relates to a separate layer injection downhole fusion control system and method based on MPC and PID. BACKGROUND

[0002] Domestic water drive reservoirs generally have heterogeneity, and interlayer interference is serious. In order to balance the progress, separate layer injection is generally used. The function of separate layer injection is to adjust the water distribution of each layer to the requirements of the development plan. The existing layer water quantity adjustment method mainly adopts a one-by-one measurement and adjustment method. Due to the influence of interlayer heterogeneity, when the water quantity of a layer is adjusted to be qualified, the adjustment of other layers will affect the flow of the layer that has been adjusted. In order to achieve the target, the injection distribution of each layer needs to be adjusted multiple times and repeatedly, which is time-consuming.

[0003] In view of the coupling problem existing in the downhole flow regulation process of the separate layer injection well, the existing control algorithm has the defects of large overshoot, weak universality and poor stability, and cannot meet the demand of efficient adjustment of the downhole layer water distributor opening. SUMMARY

[0004] In view of the downhole control of separate layer injection of multi-layer heterogeneous reservoirs, the application provides a separate layer injection downhole fusion control system and method based on MPC and PID, aiming to provide an efficient and energy-saving control method for separate layer injection of multi-layer heterogeneous reservoirs, realize efficient and energy-saving automatic measurement and adjustment of separate layer flow, and achieve the required injection distribution.

[0005] The technical scheme adopted by the application is as follows:

[0006] A separate layer injection downhole fusion control system based on MPC and PID, the system comprises a central MPC controller, a PID decoupling control system, a fusion controller and a downhole water distributor multivariable mathematical model; the PID decoupling control system comprises a multi-path PID controller, a cascade weight w and a decoupler, the multi-path PID controller, the cascade weight w and the decoupler form a cascade control with the central MPC controller, the fusion controller is used for fusing the output control law of the central MPC controller and the output control law of the multi-path PID controller to obtain a fusion control law, and the fusion control law is applied to the downhole water distributor multivariable mathematical model.

[0007] Further, the central MPC controller, the fusion controller and the downhole water distributor multivariable mathematical model are placed in the outer ring of the system, and the multi-path PID controller is placed in the inner ring of the system; the central MPC controller is used for providing the output control law of the central MPC controller to the multi-path PID controller.

[0008] Further, the multi-path PID controller is configured to assign a cascade weight w to the output control law of the multi-path PID controller and the output control law of the central MPC controller, and the cascade weight w is applied to the downhole water distributor multi-variable mathematical model after self-feedback processing; the central MPC controller is further configured to assign an MPC control law weight w' to the output control law of the central MPC controller, and the MPC control law weight w' is applied to the downhole water distributor multi-variable mathematical model, and the downhole water distributor multi-variable mathematical model is configured to feed back the fused control law to the central MPC controller.

[0009] Further, the PID decoupling control system is configured to perform internal feedback after being assigned the cascade weight w and decoupling processing.

[0010] Further, the downhole water distributor multi-variable mathematical model comprises a downhole water distributor open-loop control model, and the downhole water distributor open-loop control model comprises a continuous multi-variable coupling model and a discrete state space model.

[0011] Further, the open-loop control model of the downhole water distributor is composed of the structural characteristics of the water distributor throttling element, the interlayer flow interference characteristics, and the flow change delay characteristics, and is loaded into the internal model of the central MPC controller as a controlled object.

[0012] Further, the cascade weight w and the MPC control law weight w' have the following algebraic relationship:

[0013]

[0014] The output control law u of the MPC controller is:

[0015]

[0016] wherein, represents a unit vector matrix with the column being 1, and the number of rows is the number of layered water injection intervals; u c is the output control law of the central MPC controller; u m is the cascade MPC-PID output control law.

[0017] Further, the input transformation matrix M of the decoupler and the state feedback matrix K have the following relationship:

[0018]

[0019] wherein, T is a decoupling canonical transformation matrix, is a pole placement matrix; C m1j , C m2j , C mNjrespectively represent the coupling response state matrix of the first, second, and Nth layer to the jth layer in the multivariable mathematical model of the downhole water distributor, A m A represents the state space model matrix of the multivariable mathematical model of the downhole water distributor; B m B represents the state space model matrix of the multivariable mathematical model of the downhole water distributor; N represents the layer order of the state space matrix of the multivariable mathematical model of the downhole water distributor; F represents the structure characteristic index matrix;

[0020] T -1 (A-BMF) T =A * , T -1 BM=B * , CT=C * ;

[0021] A, B, and C represent the multivariable state space model matrix of the downhole water distributor adapted to the central MPC controller; A ＊ , E ＊ , C ＊ represent the multivariable state space model matrix of the downhole water distributor adapted to the central MPC controller after decoupling and normalization;

[0022] The state space model matrix after decoupling is as follows:

[0023] A ^ =A m -B m K,B ^ =MB m , C^=C m ;

[0024] A ^ , B ^ , C^ represent the multivariable state space model matrix of the downhole water distributor after decoupling; C m C represents the state space model matrix C of the multivariable mathematical model of the downhole water distributor.

[0025] Further, the related state variables of the multi-path PID controller matrix are denoted as [A p , B p ,...], and the discrete transformation period is t e ; in addition to the central MPC controller, the multi-path PID controller, the decoupler, the cascade weight w, the MPC control law weight w', and the controlled object are all regarded as generalized objects, and the discrete model of the generalized objects can be obtained according to the linear operation property of the state space as follows:

[0026] x0(k+1)=A0x0(k)+B0u(k);

[0027] y0(k) = C0x0(k) + D0u(k);

[0028] wherein x0(k+1) represents the state response of the downhole water distributor at the k+1 step, wherein k represents any step; x0(k) represents the state response of the downhole water distributor at the k step; u(k) represents the control law input to the downhole water distributor at the k step; y0(k) represents the output response of the downhole water distributor at the k step; A0, B0, C0, D0 represent the state space matrix of the downhole fusion control system of the separate layer;

[0029] The generalized object state space model is:

[0030]

[0031]

[0032] wherein the state vector group x0, x l and the control vector group u are respectively:

[0033]

[0034] The x po , x mo , x co in the generalized object correspond to the outputs y po , y mo , y co of the PID controller, the cascade weight part system and the MPC weight part system respectively: the cascade weight part refers to the cascade weight w and the decoupler; the MPC weight part system refers to the MPC control law weight w'; x l represents the state vector group of the PID controller; x l(1) represents the state variable of the cascade weight part system at the l layer; x l(n*N) represents the state variable of the MPC weight part system at the N layer at the n step; β (1) , β (N) respectively represent the opening control amount of the downhole water distributor input at the l layer and the N layer;

[0035] y po = C p x po + D p u, y mo = C m x mo , y co = C m x co ;

[0036] q v(1) , q v(N)respectively represent the flow response of the downhole water distributor output of the first layer, the Nth layer; C p , D p represents the output state space matrix of the PID controller part; C m represents the output state space matrix of the cascade weight part.

[0037] Further, the optimal output of the fusion controller is derived according to the state space model; the generalized object is discretized, and the sampling period is t e ; according to the MPC control algorithm, the state vector after N p step length predicted by the 0th step can be obtained as follows:

[0038]

[0039] wherein, is the superimposed state transition vector matrix:

[0040]

[0041] wherein, N p represents the prediction step number of the MPC controller; N m represents the control step length parameter of the MPC controller, and the prediction output of the 0th step can be obtained according to the state space model as follows:

[0042]

[0043] Take the error cost function matrix J as follows:

[0044]

[0045] wherein, R w(1) (N p ), R w(2) (N p ), R w(N) (N p ) respectively represent the target set value of the first, second, and Nth layer sections; respectively represent the prediction output of the 0th step of the first, second, and Nth layer sections; Q is the error weight matrix of the central type MPC controller; R is the control weight matrix of the central type MPC controller; Δu M is the optimal prediction control increment:

[0046]

[0047] wherein, L is the transposed matrix;

[0048] The discretized control law u * (z) of the fusion controller when the weight is fixed is as follows: ​​

[0049]

[0050] wherein, t e is a discrete transform period, I is a unit matrix.

[0051] In addition, the application also provides a layered water injection downhole fusion control method based on MPC and PID realized by using the system, and the method comprises the following steps: a central MPC controller provides an output control law of the central MPC controller to a multi-path PID controller; the multi-path PID controller assigns an output control law of the multi-path PID controller and the output control law of the central MPC controller to a cascade weight w; the central MPC controller assigns the output control law of the central MPC controller to an MPC control law weight w'; a fusion controller fuses the output control laws of the central MPC controller and the multi-path PID controller, and applies a fusion control law to a downhole water distributor multivariable mathematical model; and the downhole water distributor multivariable mathematical model feeds back the fusion control law to the central MPC controller.

[0052] Further, the multi-path PID controller is internally fed back after being assigned to the cascade weight w and being decoupled.

[0053] The layered water injection downhole fusion control system and method based on MPC and PID are designed, the deployment efficiency of the flow of each layer is improved through the design of the fusion control structure, the fusion control structure reduces the requirement of MPC on the precision of model parameters, and the adaptability of the fusion controller is improved; meanwhile, the system is provided with a flow decoupler, and the interlayer interference is reduced.

[0054] Other features and advantages of the present application will be set forth in the following description, and in part will become apparent to those skilled in the art from the following description, or can be learned by practice of the present application. The objects and other advantages of the present application can be achieved and obtained by means of the instrumentalities and combinations pointed out in the following description. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0056] Figure 1 It is a topological structure diagram of the layered water injection downhole fusion control system based on MPC and PID.

[0057] Figure 2 It is a design flow diagram of the layered water injection downhole fusion control system based on MPC and PID.

[0058] Figure 3 A flow chart of a layered injection downhole fusion control method based on MPC and PID. DETAILED DESCRIPTION

[0059] To make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0060] In the embodiments of the present application, Figure 1 A layered injection downhole fusion control system topology structure based on MPC and PID is shown; Figure 2 A design flow diagram of the layered injection downhole fusion control system based on MPC and PID is shown, combined with Figure 1 and Figure 2 The layered injection downhole fusion control system based on MPC (Model Predictive Control) and PID (proportional-integral-derivative control) is composed of three parts, including a central MPC controller, a PID decoupling control system, a fusion controller and a downhole water distributor multivariable mathematical model. The MPC controller is responsible for providing a predicted optimal reference value under an optimal index and eliminating the coupling effect of parameter variation of a layer on other layers, so as to realize independent optimization of the response performance of each layer. The PID decoupling control system includes a multi-channel PID controller, a cascade weight w and a decoupler. The multi-channel PID controller, the cascade weight w and the decoupler form a cascade control with the MPC controller. The fusion controller is used to fuse the output control law of the MPC controller and the output control law of the multi-channel PID controller to obtain a fusion control law. The fusion control law is applied to the downhole water distributor multivariable mathematical model. The downhole water distributor multivariable mathematical model is used to feed back the fusion control law to the MPC controller to correct and optimize the control law output of the MPC. The downhole water distributor multivariable mathematical model is a controlled object, and its function is to convert the input opening into an output flow response.

[0061] The central MPC controller and the downhole water distributor multivariable mathematical model are placed in the outer ring of the system, and the multi-path PID controller is placed in the inner ring of the system; the central MPC controller in the outer ring is used to provide the main set value to the multi-path PID controller in the inner ring, and the main set value is the set value of the bottom layer PID controller, that is, the output control law of the central MPC controller. The central MPC controller is also used to assign the output control law of the central MPC controller to the MPC control law weight w', and the MPC control law weight w' acts on the downhole water distributor multivariable mathematical model. The above setting ensures the stability of the control output and the robustness of the system.

[0062] The multi-path PID controller is used to assign the output control law of the multi-path PID controller and the output control law of the MPC controller to the cascade weight w, and after self-feedback processing, it acts on the downhole water distributor multivariable mathematical model. This setting can be used to enhance the adjustment efficiency of the fusion controller and the universality of the system. At the same time, the decoupler is used to weaken the coupling influence of the single-path PID controller parameter adjustment on other branches. The PID decoupling control system is used for internal feedback after being assigned to the cascade weight w and decoupling processing.

[0063] As shown in Figure 2 The downhole water distributor multivariable mathematical model includes a downhole water distributor open-loop control model, which includes a continuous multivariable coupling model and a discrete state space model. The open-loop control model of the downhole water distributor is loaded into the internal model of the central MPC controller as the controlled object. The open-loop control model of the downhole water distributor is mainly composed of the structural characteristics of the water distributor throttling element, the interlayer flow interference characteristics and the delay characteristics of the flow change, which completely describes the dynamic process of the water distributor injection, and at the same time, in order to facilitate the loading of the central MPC controller, the open-loop control model of the downhole water distributor needs to be discretized. Figure 2The well down water distributor control optimization realizes the rapid response of the well down water distributor valve group, thereby establishing a well down water distributor model; through the well down water distributor model and a multi-path PID controller, a decoupler, a central MPC controller and weight optimization jointly participate in the calculation of a fusion control algorithm, and the fusion control law is directly output to an open loop control model of the well down water distributor. The central MPC controller is in an outer ring, is responsible for providing a reference value of predicted optimization under an optimal index, guarantees the traceability and accuracy of system output, eliminates the coupling influence of single loop parameter variation on other loops, thereby realizing the independent optimization of each layer water distributor control. The pressure and flow characteristics of each layer are affected by real-time working conditions and the formation characteristics of each layer, so the central MPC controller does not have the feasibility of real-time optimization parameter adjustment. The fusion control system places a cascade PID control link in an inner ring, which is simple in structure and fast in operation, weakens the defects of slow MPC operation and high parameter adjustment accuracy under a complex model, improves the response speed of the well down water distributor and reduces the requirement of the controller on the parameter adjustment accuracy. Finally, the fusion controller fuses the output control law of the MPC and the PID, improves the dynamic response performance of the well down water distributor, improves the robustness of the system when the model parameters change, and enhances the accuracy of the opening adjustment of the well down water distributor in abnormal working conditions.

[0064] The present application uses a dynamic decoupling algorithm to process a multi-variable coupling model, so that the input transformation matrix M of the decoupler and the state feedback matrix K for decoupling satisfy the following relationship:

[0065]

[0066] wherein T is a decoupling canonical transformation matrix, is a pole assignment matrix, which is generally set in the negative half of the root locus plane to ensure the stability of the system; C m1j , C m2j , C mNj respectively represent the coupling response state matrix of the 1st, 2nd, Nth layer to the jth layer in the multi-variable mathematical model of the well down water distributor, A m represents the state space model matrix A of the multi-variable mathematical model of the well down water distributor, and the state space model matrix refers to a set of state transformation matrices composed of A, B, C and D matrices, wherein the D matrix is generally 0; B m represents the state space model matrix B of the multi-variable mathematical model of the well down water distributor; represents the layer number order of the state space matrix of the multi-variable mathematical model of the well down water distributor; F represents a structure characteristic index matrix;

[0067] T -1 (A-BMF)T=A * ,T -1 BM=B * ,CT=C * ;

[0068] Wherein, A, B, C represent the downhole water distributor multivariable state space model matrix matched with the central type MPC controller; A ＊ , B ＊ , C ＊ represent the downhole water distributor multivariable state space model matrix matched with the central type MPC controller after decoupling canonical transformation;

[0069] The state space model matrix after decoupling action is as follows:

[0070] A ^ = A m -B m K, B ^ = MBm ， C^ = C m ;

[0071] A ^ , B ^ , C^ represent the downhole water distributor multivariable state space model matrix after decoupling processing; C m represent the state space model matrix C of the downhole water distributor multivariable mathematical model.

[0072] Suppose the cascade weight is w, and according to the mathematical principle of MPC calculating the control law, the coupling action among the multiple outputs can be offset, so the MPC control does not need to be decoupled, so the output is directly applied to the object, and the MPC control law is given a weight w'. There is an algebraic relationship among the weight matrices as follows:

[0073]

[0074] The output control law u of the MPC controller is:

[0075]

[0076] Wherein, represents a unit vector matrix with column 1, and the number of rows is the number of layered water injection intervals; u c is the output control law of the central type MPC controller; u m is the cascade MPC-PID output control law.

[0077] The output of the PID control algorithm does not depend on the model, so it can be equivalent to multiple parallel independent models and as part of the generalized system, and the parameters are determined by the PID controller parameters; the related state variables of the PID controller matrix are denoted as [A p , B p ,...], and the discrete transformation period is t eThe prediction controller is the main control unit, responsible for controlling all aspects including PID controller, decoupler, weight and controlled object. Figure 1 In addition to the central MPC controller, other aspects are regarded as MPC generalized objects. The discrete model of the generalized object can be obtained from the linear operational properties of the state space as follows:

[0078] x0(k+1) = A0x0(k) + B0u(k);

[0079] y0(k) = C0x0(k) + D0u(k);

[0080] where x0(k+1) represents the state response of the downhole water distributor at step k+1, where k represents any step; x0(k) represents the state response of the downhole water distributor at step k; u(k) represents the control law input to the downhole water distributor at step k; y0(k) represents the output response of the downhole water distributor at step k; A0, B0, C0, D0 represent the state space matrix of the layered injection downhole fusion control system;

[0081] The generalized object is divided into two parts by transformation, and the weight corresponding to each part corresponds to the weight of the control algorithm. From the above analysis, the state space model of the generalized object under MPC control is:

[0082]

[0083]

[0084] where the state vector group x0, x l and the control vector group u are:

[0085]

[0086] x po , x mo , x co in the generalized object correspond to the outputs y po , y mo , y co of the PID controller, the cascade weight part system and the MPC weight part system respectively: the cascade weight part refers to the cascade weight w and the decoupler; the MPC weight part system refers to the MPC control law weight w'; x l represents the state vector group of the PID controller; x l(1) represents the state variable of the cascade weight part system at the lth layer; x l(n*N) represents the state variable of the MPC weight part system at the Nth layer at the nth step; β (1) , β (N) represent the opening control amount of the downhole water distributor input at the lth layer and the Nth layer respectively.

[0087] y po = C p x po + D p u, y mo = C m x mo , y co = C m x co ;

[0088] q v(1) , q v(N) represent the flow response of the downhole water distributor output of the lth layer, the Nth layer, respectively; C p , D p represent the output state space matrix of the PID controller part; C m represents the output state space matrix of the cascade weight part.

[0089] According to the state space model, the optimal output of the fusion controller is derived; the generalized object is discretely processed, and the sampling period is t e ; according to the MPC control algorithm, the state vector after N p step length prediction from the 0th step is:

[0090]

[0091] Wherein, is the superposition state transition vector matrix:

[0092]

[0093] Wherein, N p represents the prediction step number of the MPC controller; N m represents the control step length parameter of the MPC controller, and the prediction output of the 0th step is obtained according to the state space model:

[0094]

[0095] Take the error cost function matrix J as:

[0096]

[0097] Wherein, R w(1) (N p ), R w(2) (N p ), R w(N) (N p ) represent the target set value of the 1st, 2nd, Nth layer, respectively; ​respectively represent the prediction output of the 0th step of the 1st, 2nd and Nth layer; Q is the error weight matrix of the central MPC controller; R is the control weight matrix of the central MPC controller; Δu M is the optimal prediction control increment:

[0098]

[0099] wherein L is a transposed matrix;

[0100] solving the discrete control law u of the fusion controller with fixed weights * (z) is:

[0101]

[0102] wherein t e is a discrete transformation period, and I is a unit matrix.

[0103] The first-step prediction value is substituted back into the prediction output expression of the 0th step, and the above steps are repeated to complete the cyclic prediction output of the fusion control, and the fusion control law solving is completed.

[0104] In addition, the application also provides a layered injection downhole fusion control method based on MPC and PID using the above system, as shown in Figure 3 The method comprises the following steps: the MPC controller provides the output control law of the MPC controller to the multi-path PID controller; the multi-path PID controller assigns the output control law of the multi-path PID controller and the output control law of the MPC controller with a cascade weight w; the MPC controller assigns the output control law of the MPC controller with an MPC control law weight w'; the fusion controller fuses the output control laws of the MPC controller and the multi-path PID controller, and applies the fusion control law to the downhole water distributor multivariable mathematical model; and the downhole water distributor multivariable mathematical model feeds back the fusion control law to the MPC controller.

[0105] Specifically, the multi-path PID controller is internally fed back after being assigned with the cascade weight w and decoupling processing.

[0106] Although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced with equivalent features, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the application.

Claims

1. A layered downhole water injection fusion control system based on MPC and PID, the system comprising a central MPC controller, a PID decoupling control system, a fusion controller, and a multivariable mathematical model of a downhole water distributor; the PID decoupling control system comprising a multi-channel PID controller, cascaded weights w, and a decoupler, wherein the multi-channel PID controller, cascaded weights w, and decoupler form a cascade control with the central MPC controller; the fusion controller is used to fuse the output control law of the central MPC controller and the output control law of the multi-channel PID controller to obtain a fusion control law, and apply the fusion control law to the multivariable mathematical model of the downhole water distributor.

2. The system according to claim 1, wherein, The central MPC controller, the fusion controller, and the downhole water distributor multivariate mathematical model are placed in the outer loop of the system, and the multi-channel PID controller is placed in the inner loop of the system. The central MPC controller is used to provide the output control law of the central MPC controller to the multi-channel PID controller.

3. The system according to claim 2, wherein, The multi-channel PID controller is used to assign cascade weight w to the output control law of the multi-channel PID controller and the output control law of the central MPC controller, and after self-feedback processing, it is applied to the multivariable mathematical model of the downhole water distributor. The central MPC controller is also used to assign the output control law of the central MPC controller to the MPC control law weight w′, and to apply the MPC control law weight w′ to the downhole water distributor multivariate mathematical model, wherein the downhole water distributor multivariate mathematical model is used to feed the fusion control law back to the central MPC controller.

4. The system according to claim 3, wherein, The PID decoupling control system is used for internal feedback after being assigned cascade weights w and undergoing decoupling processing.

5. The system according to any one of claims 1-4, wherein, The multivariate mathematical model of the downhole water distributor includes an open-loop control model of the downhole water distributor, which includes a continuous multivariate coupled model and a discrete state-space model.

6. The system according to claim 5, wherein, The open-loop control model of the downhole water distributor consists of the structural characteristics of the water distributor's throttling element, the inter-layer flow interference characteristics, and the flow change delay characteristics, which are loaded as the controlled object into the internal model of the central MPC controller.

7. The system according to claim 6, wherein, The cascade weight w and the MPC control law weight w′ have the following algebraic relationship: The output control law u of the MPC controller is: in, This represents a unit vector matrix with 1 column, where the number of rows corresponds to the number of stratified water injection layers; u c For the output control law of the central MPC controller; u m This is a cascaded MPC-PID output control law.

8. The system according to claim 7, wherein, The input transformation matrix M and the state feedback matrix K of the decoupler have the following relationship: Where T is the decoupling canonical transformation matrix. Configure the matrix for the poles; C m1j C m2j C mNj Let A represent the coupled response state matrices of the water distribution states of layers 1, 2, and N to layer j in the multivariate mathematical model of the downhole water distributor. m The state-space model matrix A and B represent the multivariable mathematical model of the downhole water distributor. m B represents the state-space model matrix of the multivariable mathematical model of the downhole water distributor; The order of the layer in the state space matrix of the multivariable mathematical model of the downhole water distributor is represented by F; F represents the structural characteristic index matrix. T -1 (A-BMF)T=A * ,T -1 BM=B * ,CT=C * ; Where A, B, and C represent the multivariable state-space model matrix of the downhole water distributor adapted to the central MPC controller; A ＊ B ＊ C ＊ This represents the multivariable state-space model matrix of the downhole water distributor adapted to the central MPC controller after decoupling canonical transformation; The state-space model matrix after decoupling is as follows: A ∧ = A m -B m K, B ∧ = MB m ,C^=C m ; B ∧ B ∧ C ^ C represents the multivariable state-space model matrix of the downhole water distributor after decoupling; m Let C represent the state-space model matrix of the multivariable mathematical model of the downhole water distributor.

9. The system according to claim 8, wherein, The relevant state variables of the multi-path PID controller matrix are denoted as [A]. p B p [,…], the discrete transformation period is t e Besides the central MPC controller, the multi-channel PID controller, the decoupler, the cascade weights w, the MPC control law weights w′, and the controlled object are all considered as generalized objects. Based on the linear operational properties of the state space, the discrete model of the generalized object is: x0(k+1)=A0x0(k)+B0u(k); y0(k)=C0x0(k)+D0u(k); Where x0(k+1) represents the state response of the downhole water distributor at step k+1, where k refers to any step; x0(k) represents the state response of the downhole water distributor at step k; u(k) represents the control law input to the downhole water distributor at step k; y0(k) represents the output response of the downhole water distributor at step k; A0, B0, C0, and D0 represent the state space matrix of the stratified water injection downhole fusion control system. The generalized object state-space model is as follows: Among them, the state vector groups x0, x l The control vector set u is as follows: x in generalized objects po x om x co The outputs y of the PID controller, the cascade weighted system, and the MPC weighted system are respectively... po y mo y co The cascaded weights refer to the cascaded weights w and the decoupler; the MPC weights refer to the MPC control law weights w′; x l This represents the state vector group of the PID controller; x l(1) x represents the state variables of the cascaded weighted system at the l-th layer; l(n*N) β represents the state variable of the MPC weighted system at the nth step of the Nth layer; (1) β (N) These represent the opening control values ​​of the downhole water distributor input at the l-th and N-th layers, respectively. y po =C p x po +D p u,y mo =C m x mo ,y co =C m x co ; q v(1) q v(N) C represents the flow response output of the downhole water distributors at the 1st and Nth layers, respectively; p D p C represents the output state space matrix of the PID controller; m This represents the output state space matrix of the cascaded weights.

10. The system according to claim 9, wherein, The optimal output of the fusion controller is derived based on the state-space model; the generalized object is discretized with a sampling period of t. e According to the MPC control algorithm, N can be predicted from step 0. p State vector after step size for: in, The superimposed state transition vector matrix: Where, N p N represents the prediction steps of the MPC controller. m This represents the control step size parameter of the MPC controller. The predicted output for step 0 can be obtained from the state-space model. for: Let the error cost function matrix J be: Among them, R w(1) (N p ), R w(2) (N p ), R w(N) (N p ) represent the target settings for the 1st, 2nd, and Nth layers, respectively; These represent the predicted outputs at step 0 of layers 1, 2, and N, respectively; Q is the error weight matrix of the central MPC controller; R is the control weight matrix of the central MPC controller; Δu M To optimize the predictive control increment: Where L is the transpose matrix; Solving the discretized control law u of the fusion controller with fixed weights * (z) is: Among them, t e Let I be the discrete transformation period, and let I be the identity matrix.

11. A method for implementing stratified downhole water injection control based on MPC and PID using the system according to any one of claims 1-10, the method comprising the following steps: The central MPC controller provides the output control law of the central MPC controller to the multi-channel PID controller; The multi-channel PID controller assigns a cascade weight w to the output control law of the multi-channel PID controller and the output control law of the central MPC controller; The central MPC controller assigns a weight w′ to the MPC control law of the central MPC controller's output control law; The fusion controller integrates the output control laws of the central MPC controller and the multi-channel PID controller, and applies the fusion control law to the multivariable mathematical model of the downhole water distributor. The multivariable mathematical model of the downhole water distributor feeds the fusion control law back to the central MPC controller.

12. The method according to claim 11, wherein, The multi-channel PID controller performs internal feedback after being assigned cascade weights w and undergoing decoupling processing.

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