A Parameter Tuning Method for Internal Model PID Controller in a Chemcial Process with Multi-loop Coupling

Abstract

The present invention provides a method for tuning the parameters of an internal model PID controller for multi-loop coupling in a chemical process. The closed-loop step response test of each loop of the system is carried out by using multi-loop sequential testing; according to the static gain matrix of the system, the relative gain matrix of the system is obtained, and the correlation between each loop of the system is analyzed through the relative gain matrix; based on the inverse decoupling method, a decoupling compensation matrix is constructed to decouple the multi-loop system into a diagonal system matrix composed of multiple single loops, and its diagonal elements are used as the internal model, and a multivariable internal model controller is designed; the all-pole approximation is introduced to handle the pure time-delay link in the object model, and combined with the Maclaurin formula to obtain the parameter tuning formula of the internal model PID controller, and the PID controller parameters of each loop are calculated. The present invention solves the problem of parameter tuning of the multi-loop coupling PID controller in the industrial process and can simultaneously meet the requirements of robustness and tracking performance of multi-loop control.

Description

Technical Field

[0001] The present invention relates to the technical field of PID control, and particularly but not limited to a method for tuning the parameters of an internal model PID controller for multi-loop coupling in a chemical process. Background Art

[0002] At present, in industrial process control, the proportional-integral-derivative (PID) control strategy is the most common and widely used. However, most PID controllers are for single-loop control, and there is no coupling or very little coupling between each loop. Moreover, the selection of PID control parameters has a great impact on the performance of the loop. Good parameters can ensure the stable operation of the industrial process, while improper parameters may cause the loop to oscillate or even diverge, thus affecting the industrial production process. Therefore, the tuning of PID parameters is crucial in process control.

[0003] In the field of modern industrial process control, pure single-loop systems are rare, and more are multi-loop systems. There is a strong coupling effect between loops, and there are also characteristics such as multiple time delays. Therefore, multi-loop systems are more complex than single-loop systems and often cannot be simply controlled by using the control methods of single-loop systems. Moreover, each loop in a multi-loop system is interrelated, and it is necessary to first decouple the coupling of the system and then study the control of the system.

[0004] In view of this, a new method for tuning the parameters of an internal model PID controller for multi-loop coupling in a chemical process is needed to help solve the problem of tuning the parameters of a multi-loop coupling PID controller in an industrial process, which can simultaneously meet the requirements of robustness and tracking of multi-loop control. Summary of the Invention

[0005] Aiming at one or more problems in the prior art, the present invention proposes a method for tuning the parameters of an internal model PID controller for multi-loop coupling in a chemical process, which solves the problem of tuning the parameters of a multi-loop coupling PID controller in an industrial process and simultaneously meets the requirements of robustness and tracking of multi-loop control.

[0006] The technical solution for achieving the object of the present invention is as follows:

[0007] A method for tuning the parameters of an internal model PID controller for multi-loop coupling in a chemical process, the method comprising the following steps:

[0008] (1) Performing a closed-loop step response test on each loop of the multi-loop system in sequence by using multi-loop sequential testing;

[0009] (2) Calculating the relative gain matrix of the multi-loop system according to the static gain matrix of the multi-loop system, and analyzing the correlation between each loop of the multi-loop system according to the reasonable pairing principle of the relative gain matrix;

[0010] (3) Construct the decoupling compensation matrix of the multi-loop system, decouple the multi-loop system, and obtain a diagonal system matrix composed of multiple single loops;

[0011] (4) Use the diagonal elements of the diagonal system matrix as the internal model, introduce a filter, and obtain a multi-loop internal model controller;

[0012] (5) For the time lag existing in the complex chemical process, use the all-pole approximation method to process the pure lag links in the multi-loop system, and combine with the Maclaurin formula to obtain the parameter tuning formula of the internal model PID controller, and calculate the PID controller parameters of each loop in turn according to this formula.

[0013] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0014] 1. The parameter tuning method of the internal model PID controller for multi-loop coupling in the chemical process of the present invention solves the problem of parameter tuning of the multi-loop coupling PID controller in the industrial process.

[0015] 2. The parameter tuning method of the internal model PID controller for multi-loop coupling in the chemical process of the present invention introduces a filter, meeting the requirements of robustness and tracking performance of multi-loop control. Description of the Drawings

[0016] The drawings are used to provide a further understanding of the present invention, and are used together with the description to explain the embodiments of the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0017] Figure 1 Shows the flow chart of the parameter tuning method of the internal model PID controller for multi-loop coupling in the chemical process of the present invention.

[0018] Figure 2 Shows the schematic diagram of the step response test of the present invention.

[0019] Figure 3 Shows the structural diagram of the decoupling compensation matrix of the present invention.

[0020] Figure 4 Shows the reverse decoupling schematic diagram of the 2×2 system of the present invention.

[0021] Figure 5 Shows the schematic diagram of the internal model control structure with a filter of the present invention.

[0022] Figure 6 Shows the schematic diagram of the control scheme of a certain distillation column in the embodiment of the present invention.

[0023] Figure 7Shows the dynamic response diagram of the flow rate of the cooling water of a certain distillation column according to an embodiment of the present invention.

[0024] Figure 8 Shows the dynamic response diagram of the top temperature of a certain distillation column according to an embodiment of the present invention.

[0025] Figure 9 Shows the dynamic response diagram of the liquid level of the top tank of a certain distillation column according to an embodiment of the present invention. Detailed implementation manners

[0026] To further understand the present invention, the preferred implementation manners of the present invention will be described below in conjunction with embodiments. However, it should be understood that these descriptions are only for further explaining the features and advantages of the present invention, rather than limiting the claims of the present invention.

[0027] The description of this part only focuses on typical embodiments, and the present invention is not limited to the scope described in the embodiments. Combinations of different embodiments, mutual substitution of some technical features in different embodiments, and mutual substitution of the same or similar prior art means and some technical features in the embodiments are also within the scope of description and protection of the present invention.

[0028] A method for tuning the parameters of an internal model PID controller for multi-loop coupling in a chemical process, as Figure 1 shown, the method includes the following steps:

[0029] S1) Use the multi-loop sequential test method to perform a closed-loop step response test on multiple loops of the system. As Figure 2 shown, the test process is as follows:

[0030] 1) Input a step signal with an amplitude of Δr1 at the set value r1 end of the first loop, keep the set values of other loops unchanged, and record the system input output and error of each loop until all loops of the system enter a steady state;

[0031] 2) According to the method of the first step, input a step signal with an amplitude of Δr w at the set value r w end of each loop from the second to the nth loop in turn, keep the set values of other loops unchanged from the previous step signal, and record the system input output and error v = 1, 2,..., n, w = 1, 2,..., n until all loops of the system enter a steady state.

[0032] S2) According to the static gain matrix of the system, obtain the relative gain matrix of the system, and analyze the correlation between the loops of the multivariable system through the reasonable pairing principle of the relative gain matrix.

[0033] For a controlled process with both the number of manipulated variables and the number of controlled variables being n, its relative gain matrix can be obtained through the following formula:

[0034]

[0035] where Λ represents the relative gain matrix of the multi-loop system, G(0) is the static gain matrix of the system, and the value of λ ij reflects the relative value of the effect of the j-th input on the i-th output, which is called the relative gain. * represents the dot product, that is, the product of the elements in the same position of the two matrices.

[0036] The reasonable pairing principle of the relative gain matrix is as follows:

[0037] 1) The value of λ ij in the relative gain matrix is in [0.5, 1]: It indicates that there is coupling of different strengths between the u j -to-y i loop and other loops. When λ ij is closer to 1, the u j -y i loop is less affected by other loops under this pairing, and this loop pairing is correct.

[0038] 2) The value of λ ij in the relative gain matrix is in [0, 0.5]: It indicates that if the process channel is under this loop pairing, the effect of this loop is not obvious. The closer λ ij is to 0, that is, u j has no effect on y i and cannot control the change of y i , and the influence of this loop on other loops is weaker. Therefore, this loop pairing should not be adopted.

[0039] 3) If the value of λ ij in the relative gain matrix > 1, then there must be an element with λ ij < 0 in the same row or column. This indicates that there is an unstable coupling relationship between the process channels. When designing the decoupling method or controlling the loop, corresponding tuning measures must be taken.

[0040] 4) If the values of the elements in the same row or the same column of the relative gain matrix are equal or relatively close, it indicates that there is strong coupling between the loops, and the decoupling control method must be adopted.

[0041] S3) Based on the inverse decoupling method, by constructing a decoupling compensation matrix, the transfer function matrix of the multi-loop system is decoupled into a diagonal system matrix composed of multiple single loops. Among them, the multivariable decoupling compensation matrix D(s) is expressed as follows:

[0042] D(s) = G(s) -1 Q(s)

[0043] where G(s) is the controlled object and Q(s) is the expected transfer function after decoupling.

[0044] The entire decoupling matrix D(s) is divided into two matrices D d (s) and D o (s), as Figure 3 shown, where D d (s) is on the forward channel and D o (s) is the feedback channel between the process output and the controller output. Since the signal transmission directions of D d (s) and D o (s) are opposite, the elements at the positions corresponding to the non-zero elements in D o (s) in D d (s) are taken as zero. The decoupling matrices D d (s) and D o (s) jointly form the decoupling matrix D(s) through positive feedback. Through transfer function equivalence, the expression of the decoupling matrix is as follows:

[0045] D(s) = D d (s)(1 - D o (s)D d (s)) -1

[0046] The inverse matrix of the decoupling matrix in the above formula is expressed as follows:

[0047] D -1 (s) = (1 - D o (s)D d (s))D d (s) -1 = D d (s) -1 - D o (s)

[0048] That is, we can get:

[0049] D d (s) -1 - D o (s) = Q(s) -1 G(s)

[0050] In some cases, the forward channel matrix D d (s) does not satisfy the non - singularity condition. It is necessary to add a dynamic link N(s) to the system to ensure that the decoupler can be realized. The new model is expressed as follows:

[0051] G N (s) = G(s)N(s)

[0052] Where n1, n2, …, n i represent the time - delay parameters of the added dynamic link, making each element in the lag - time matrix of the new model G N (s) greater than or equal to 0, and n1, n2, …, n i all take the minimum values that satisfy the conditions. The corresponding n1, n2, …, n i are obtained according to the following formula:

[0053]

[0054] Where is the element in the lag - time matrix of the new model G N (s), and τ ij is a non - negative time - delay parameter.

[0055] For an n×n system, in the D d (s) matrix, only one element in each row is non - zero, and the other elements are 0. Its non - zero element such as dd ij represents the direct control action of the j - th input on the i - th output. Therefore, there are n! ways to select D d (s). For example, in a 3×3 system, there are 6 pairing methods. The non - zero positions of D d (s) can be determined according to the pairing principle of the control channels in the actual process. If the elements of the D d (s) matrix can be determined, then the element do o in the feedback channel D ij (s) matrix should satisfy the following formula:

[0056] If dd ij ≠0, i, j ≤ n; then do ij = 0, i, j ≤ n

[0057] As Figure 4 shown, taking a 2×2 system as an example, it is expressed in matrix form as follows:

[0058]

[0059] D d (s) If it is {1 - 2} paired, then according to the system matrix, we can get:

[0060]

[0061] According to the principle of equal corresponding terms, the element values of the two decoupling matrices can be obtained:

[0062]

[0063] D d (s) If it is a {2 - 1} pairing, then according to the system matrix, we can get:

[0064]

[0065] According to the principle of equal corresponding terms, the element values of the two decoupling matrices can be obtained:

[0066]

[0067] Select D d (s) to be a diagonal matrix to simplify the calculation for application, then the main diagonal elements of D o (s) are 0, and the diagonal elements D d (s) and the off - diagonal elements D ii of D o (s) and the off - diagonal elements D ii of D

[0068]

[0069]

[0070] Then the decoupled diagonal system matrix Q(s), the forward - channel matrix D d (s) and the feedback - channel matrix D o (s) are obtained;

[0071] S4) According to the decoupled diagonal system matrix, take its diagonal elements as the internal - model to design a multivariable internal - model controller. The specific process is as follows:

[0072] Decompose the internal - model into the part containing the minimum - phase part and the remaining part In the part, introduce a filter to meet the requirements of system stability and robustness, and design the obtained model according to the steps of the internal - model controller to obtain the multivariable internal - model controller C(s), as Figure 5 shown.

[0073] The internal - model of the internal - model controller is:

[0074]

[0075] The design steps of the multivariable internal model controller include:

[0076] 1) First, design the diagonal elements \(C_{11}(s)\) and \(C_{22}(s)\) of the controller matrix, and decompose the diagonal elements of the model into two parts: 11 \(C_{11}(s)\) and 22 \(C_{22}(s)\), which are decomposed into two parts:

[0077]

[0078] where are all \(i\) right-half plane zeros, \(\tau\) is the time delay parameter of the model time delay link, contains all time delay links and right-half plane zeros, is the stable part with minimum phase characteristics.

[0079] 2) Introduce a filter to ensure system stability and controller realizability. The diagonal element \(C_{ii}(s)\) of the controller matrix is the inverse of the diagonal element of the model multiplied by the filter. The filter expression is as follows: ii \(C_{ii}(s)\) is the inverse of the diagonal element of the model multiplied by the filter, and the filter expression is as follows:

[0080]

[0081] where \(n\) i is taken so that each element in the \(i\)-th row of the internal model controller matrix can be realized, \(\lambda\) ii is the design parameter of the low-pass filter, and \(n\) i is the order of the filter.

[0082] 3) The multivariable internal model controller \(C(s)\) is:

[0083] \(C(s)=\text{diag}\{C_{11}(s),C_{22}(s),\cdots,C_{nn}(s)\}\) 11 \(C_{11}(s)\), \(C_{22}(s)\), \(\cdots\), \(C_{nn}(s)\) 22 \(C_{22}(s)\), \(\cdots\), \(C_{nn}(s)\) nn \(C_{nn}(s)\)

[0084] where

[0085] S5) To address the time lag problem in complex chemical processes, introduce the method of all-pole approximation to handle the pure time lag link in the object model, and combine with the Maclaurin formula to obtain the parameter tuning formula for the internal model PID controller. Calculate the PID controller parameters for each loop according to the formula in turn.

[0086] Taking the first-order lag model as an example, the first-order lag model is expressed by the following formula:

[0087]

[0088] The all-pole approximation method can be expressed by the following formula:

[0089] e -θs ≈1 / (1 + θs + 0.5θ 2 s 2 )

[0090] The model decomposition gives:

[0091]

[0092]

[0093] Take the filter model as: f ii (s) = 1 / (1 + λ ii s)

[0094] The transfer function of the controller can be expressed by the following formula:

[0095]

[0096] Expanding F(s) by Maclaurin's formula, it can be expressed by the following formula:

[0097]

[0098] where, (K c ) ii = Q ii ′(0),

[0099] The above formula can be converted to:

[0100]

[0101] where:

[0102] p ii (s) = 0.5τ 2 s 3 +(aτ + 0.5bτ 2 )s 2 +(a + bτ)s + b

[0103] q ii (s) = 0.5τ 2 λ ii s 2 +(λ ii τ + 0.5τ 2 )s + (λ ii + τ)

[0104] Then there is:

[0105]

[0106]

[0107]

[0108] In summary, the general formula for tuning the parameters of the internal model PID controller can be obtained:

[0109] K c = diag{Q ii ′(0)}

[0110]

[0111]

[0112] Example 1

[0113] Taking a certain distillation column as an example, as Figure 6 shown, it includes the flow control loop of the cooling water in the top tank, the temperature control loop at the top, and the liquid level control loop of the top tank, and introduces the method for tuning the parameters of the internal model PID controller for the multi-loop coupling of the chemical process of this solution.

[0114] The flow control loop of the reflux drum is cooled and condensed by the cooling water in the condenser. The flow rate of the cooling water affects the temperature of the reflux drum and is also the main interference to the top temperature. Therefore, it is necessary to set up a flow control loop for the cooling water to accurately control the flow rate of the cooling water. The temperature control loop at the top is directly related to the quality of the product withdrawn from the top. In order to maintain the top temperature at the critical boiling point, overcome the interference from the cooling water and the reflux liquid in the reflux drum, and keep the top temperature stably controlled is very necessary. Considering that the distillation process cannot be completed at one time, when it is observed that the top temperature remains constant, the reflux metering pump will not act because there is no deviation, so the product pump can be determined when to draw the product from the reflux drum by setting the liquid level of the top tank.

[0115] First, perform a step response test in the order of multi-loops. Perform a step response test on the three control loops, including the flow control loop of the cooling water, the temperature control loop at the top, and the liquid level control loop of the top tank, obtain the step response test data, and obtain the transfer function matrix of the system according to this data:

[0116]

[0117] The static gain matrix of the system is:

[0118]

[0119] The relative gain matrix of the system can be obtained:

[0120]

[0121] According to the pairing principle of the relative gain matrix, the pairing of this system is {1-2-3}, which conforms to the actual control scheme of the actual distillation column. However, negative elements appear in the relative gain matrix, so decoupling methods must be adopted.

[0122] To ensure that the decoupler can be implemented, a dynamic link N(s) = diag{e -s , 1, e -3s} is added, and the new model is expressed as follows:

[0123]

[0124] According to the pairing principle of the relative gain matrix, the pairing of this system is {1-2-3}. Taking D d (s) = I in the inverse decoupling control, the expression of D o (s) can be obtained as follows:

[0125]

[0126] From this, the corresponding internal model controller can be calculated, and the expression is as follows:

[0127]

[0128]

[0129]

[0130] To ensure the rapidity and robust stability of the system, the filter parameters are taken as λ 11 = 10, λ 22 = 20, λ 33 = 0.7. According to the PID conversion formula, the parameters of the internal model controller can be calculated as follows:

[0131]

[0132]

[0133]

[0134] Such as Figures 7 - 9As shown, it is a schematic diagram of the dynamic response when the set value of the top temperature y2 increases by 10% and the set value of the liquid level y3 in the top tank increases by 10% of a certain distillation column under the multi-loop reverse decoupling PID control method at t = 300 s and t = 600 s. It can be seen from the figure that when the top temperature y2 changes, the liquid level y3 in the top tank is not affected. It can be seen that this method has good decoupling performance, and the output of the decoupled controller is small. The output of the controller can represent the opening degrees of the regulating valves and metering pumps of the distillation column. A small adjustment range of the regulating valve or pump can effectively protect the instruments and equipment. At the same time, the tuned internal model control system has good tracking performance and robustness, and can maintain a good control effect.

[0135] The description and application of the present invention here are illustrative and not intended to limit the scope of the present invention to the above embodiments. The related descriptions of effects or advantages in the specification may not be reflected in actual experimental examples due to uncertainties in specific condition parameters or other factors. The related descriptions of effects or advantages are not used to limit the scope of the invention. Deformations and changes of the disclosed embodiments here are possible, and various replacements and equivalent components of the embodiments are known to those of ordinary skill in the art. Those skilled in the art should clearly understand that without departing from the spirit or essential characteristics of the present invention, the present invention can be implemented in other forms, structures, arrangements, proportions, and with other components, materials, and parts. Other deformations and changes can be made to the disclosed embodiments here without departing from the scope and spirit of the present invention.

Claims

1. A method for tuning the parameters of an internal model PID controller for multi-loop coupling in a chemical process, characterized in that, Including the following steps: Step 1: Perform closed-loop step response tests on each loop of the multi-loop system in sequence using multi-loop sequential testing; Step 2: Calculate the relative gain matrix of the multi-loop system based on the static gain matrix of the multi-loop system, and analyze the correlation between each loop of the multi-loop system according to the reasonable pairing principle of the relative gain matrix; among them, for a controlled process with both the number of manipulated variables and the number of controlled variables being n, the relative gain matrix of the multi-loop system is: where, Λ represents the relative gain matrix of the multi-loop system, G(0) represents the static gain matrix of the multi-loop system, * represents dot multiplication, and λ ij represents the relative value of the effect of the j-th input on the i-th output; Analyzing the correlation between each loop of the multi-loop system according to the reasonable pairing principle of the relative gain matrix specifically means: 1) If λ in the relative gain matrix ij ∈[0.5, 1], it means that there is coupling of varying strengths between the u j- y i loop and other loops. When λ ij is closer to 1, the u j- y i loop is less affected by other loops; 2) If λ in the relative gain matrix ij ∈ [0, 0.5], it means that the effect of the u j -y i loop is not obvious. When λ ij is closer to 0, that is, u j has no effect on y i and cannot control the change of y i , and the weaker the influence of the u j -y i loop on other loops; 3) If λ in the relative gain matrix ij > 1, then there must be an element with λ ij < 0 in the same row or the same column, indicating the existence of an unstable coupling relationship between process channels. When designing a decoupling method or a loop for control, corresponding tuning measures should be taken; 4) If the values of the elements in the same row or the same column of the relative gain matrix are equal or close, it indicates that there is strong coupling between the loops, and a decoupling control method is adopted; Step 3: Construct a decoupling compensation matrix for the multi-loop system, decouple the multi-loop system, and obtain a diagonal system matrix composed of multiple single loops; Step 4: Use the diagonal elements of the diagonal system matrix as the internal model, introduce a filter, and obtain the internal model controller of the multi-loop system; Step 5: For the time lag existing in the complex chemical process, use the all-pole approximation method to process the pure-lag link in the multi-loop system, and combine with the Maclaurin formula to obtain the parameter tuning formula of the internal model PID controller, and calculate the PID controller parameters of each loop in sequence according to this formula.

2. The parameter tuning method of the internal model PID controller for multi-loop coupling in the chemical process according to claim 1, characterized in that, Step 1 specifically includes: Close the first loop, keep other loops open-loop, and perform a step response test on the first loop; While keeping the first loop closed, close the second loop, keep other loops open-loop, and perform a step response test on the second loop; And so on until step response tests are completed for all loops of the multi-loop system.

3. The internal model PID controller parameter tuning method for multi-loop coupling in a chemical process according to claim 2, characterized in that, The step response test of the w-th loop specifically includes: At the setpoint terminal r of the w-th loop w Add a step signal with an amplitude of Δr w while keeping the setpoint signals of other loops unchanged from the previous step signals, and record the input output and error where n is the total number of loops and t represents time until all loops of the multi-loop system reach a steady state.

4. The internal model PID controller parameter tuning method for multi-loop coupling of chemical processes according to claim 1, characterized in that, Step 3 specifically includes: Step 3-1: The transfer function matrix G(s) of the multi-loop system is: Among them, g ij (s) is stably rational, τ ij is a non - negative time - delay parameter, s is a complex variable, i is the number of rows of the transfer function matrix, and j is the number of columns of the transfer function matrix; The multivariable decoupling compensation matrix D(s) is: D(s) = G(s) -1 Q(s) Among them, G(s) is the controlled object of the multivariable decoupling compensation matrix, and Q(s) is the expected decoupled diagonal system matrix; Step 3-2: The multivariable decoupling compensation matrix D(s) is divided into a forward channel matrix D d (s) and a feedback channel matrix D o (s). Among them, D d (s) is in the forward channel, and D o (s) is the feedback channel between the process output and the controller output. The signal transmission directions of D d (s) and D o (s) are opposite. Then, the elements of D o (s) corresponding to the non-zero elements in D d (s) are taken as zero. D d (s) and D o (s) jointly form the decoupling compensation matrix D(s) through positive feedback. Through transfer function equivalence, the multivariable decoupling compensation matrix D(s) is expressed as: D(s) = D d (s)(1 - D o (s)D d (s)) -1 Step 3-3: In some cases, the forward channel matrix cannot meet the non-singular condition, so a dynamic link N(s) is added to the system to ensure the realization of the decoupler, and thus the new model G N (s) is as follows: G N (s) = G(s)N(s) Among them, n1, n2, …, n i represent the time-delay parameters of the added dynamic link, making each element in the lag time matrix in the new model G N (s) greater than or equal to 0, and n1, n2, …, n i all take the minimum values that meet the conditions, and the corresponding n1, n2, …, n i are obtained according to the following formula: wherein is the element in the lag time matrix of the new model G N (s), and τ ij is a non - negative time - delay parameter; Step 3-4: According to Step 3-1 and Step 3-2, obtain: D d (s) -1 -D o (s) = Q(s) -1 G(s) Step 3-5: To simplify the calculation for easier application, select the forward channel matrix D d (s) as a diagonal matrix, then the main diagonal elements of the feedback channel matrix D o (s) are all 0, and the diagonal elements D d (s) and the non-diagonal elements D ii and D o (s) of D ii are calculated as follows: Then the decoupled diagonal system matrix Q(s), forward channel matrix D d (s) and feedback channel matrix D o (s) are obtained.

5. The internal model PID controller parameter tuning method for multi-loop coupling in a chemical process according to claim 1, characterized in that, Step 4 specifically includes: Step 4-1: Use the diagonal elements of the diagonal system matrix as the internal model where s represents a complex variable, Q 11 (s), Q 22 (s), …, Q nn (s) are the diagonal elements of the diagonal system matrix; Step 4-2: Decompose the diagonal elements of the inner mold model to obtain: wherein, Re(β i ) > 0, are all i right half-plane zeros, τ is the time-delay parameter of the model time-delay link, contains all time-delay links and right half-plane zeros, and has a minimum-phase characteristic; Step 4-3: At section, introduce filter f ii (s): where, n i is chosen such that each element in the i-th row of the internal model controller matrix can achieve, λ ii is the design parameter of the low-pass filter, and n i is the order of the filter; Step 4-4: The diagonal element C of the controller matrix ii (s) is the inverse of the diagonal element of the internal model multiplied by the filter, and the multivariable internal model controller C(s) is obtained as follows: C(s) = diag{C 11 (s), C 22 (s), …, C nn (s)} Among them, 6. The internal model PID controller parameter tuning method for multi-loop coupling in a chemical process according to claim 1, characterized in that The general formula for tuning the parameters of the internal model PID controller: K c = diag{Q ii '(0)} where Q ii ′(0) is the diagonal element of the decoupled diagonal system matrix Q ii (s), the value of its first derivative at s = 0, Q ii (0) is Q ii (s), the value at s = 0, Q ii ″(0) is Q ii (s), the value of its second derivative at s = 0.

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