CN106896721B - A centralized control method for a binary distillation column - Google Patents

Abstract

The invention discloses a centralized control method and system for a binary rectification tower. By identifying the channel transfer function between each controlled variable and the control variable, the model of the binary distillation column is established. Obtain and analyze the frequency domain characteristics of the inverse model of the obtained binary distillation tower model to determine the filter parameters in the centralized PID controller, and then determine the adjustment parameters of the PID controller according to the expected dynamic performance and robustness . The calculated centralized PID controller is used to adjust the control signal, so that the purity of the light components and heavy components at the top and bottom of the binary distillation column can meet the requirements. The method has a simple idea and is easy to implement, and can effectively control the binary rectification column with coupling effect.

Description

A centralized control method for a binary distillation column

technical field

The invention belongs to the field of automatic control of petrochemical distillation towers, in particular to a centralized control method and system for binary distillation towers.

Background technique

Rectification is the most widely used mass transfer process in the petrochemical industry, and about 90% of the product purification and recovery is accomplished through rectification. The mechanism of rectification separation is mainly to use the different volatilities of different components in the mixture to separate. After the mixture passes through the rectification tower, the product extracted from the top or bottom of the tower meets certain purity requirements. The binary distillation column is mainly used to separate the mixture containing two components. The binary distillation column is a multi-variable process with complex internal mechanism, slow dynamic response and serious coupling between the control variable and the controlled variable. Therefore, higher requirements are put forward for the control scheme. In the control scheme of the rectification tower, it is relatively simple to divide the multivariable rectification process into multiple single loops for control by the method of variable pairing. This method is more effective in single-end component control, but its The coupling effect between variables is not effectively compensated, and the pairing criterion is often based on the static relative gain matrix (RGA). Therefore, when controlling the components at both ends of the tower, it is necessary to conduct a comprehensive analysis of the process. Decoupling control is a good way to eliminate the coupling between variables. However, in the existing decoupling control, although static decoupling is easy to implement, it also faces the problem of ignoring the dynamic information of the process, while dynamic solutions such as ideal decoupling or simple decoupling It is difficult to obtain the decoupler or decoupling process of the coupling method, which brings difficulty to the design of the controller. About 90% of the controllers in the industry are still PID controllers. How to design an effective PID controller to control the binary distillation column well is a problem worth studying.

Contents of the invention

In view of this, the main purpose of the present invention is to provide a centralized control method for a binary rectification tower. Include the following steps:

S1. Measure the values of each input and each output of the binary distillation tower, and transmit the measured values into electrical signals;

S2. Store the electrical signal obtained in step S1, and transmit the electrical signal to the system identification module after the storage time t;

S3. Using the least squares identification algorithm to identify the transfer function of each control channel, and establishing the transfer function matrix model of the binary distillation column;

S4. Calculate the frequency characteristics of the normalized inverse model according to the transfer function model obtained in step S3, and then design a filter by analyzing the frequency characteristics of the inverse model.

S5. According to the transfer function model obtained in step S3 and the filter obtained in step S4, calculate the PID controller parameters according to the given robustness and dynamic performance requirements, and determine the final centralized PID controller;

S6. Using the centralized PID controller obtained in step S5 to adjust the input.

The storage time t is the time period from the moment when the step signal for identifying each channel is added to the time when the output reaches a new steady-state value.

The specific process of S3 is: according to the amplitude h of the step signal, the sampling period Ts and the output Y(k) of the acquisition object, the parameters in the transfer function of each channel are calculated according to the following formula

θ＝(P ^T ·P) ^-1 P ^T Z

Where P and Z are coefficient matrices composed of h, Ts, and Y(k) respectively, and θ is a parameter used to identify the transfer function of each branch.

The specific steps of S4 are:

S401. Obtain the steady-state gain inverse matrix K of the process.

S402. According to the process transfer function matrix, calculate the minimum time lag τ _{1 in all channels corresponding to output 1} and the minimum time delay τ 2 in all channels corresponding to output ₂ .

S403. After reducing the time-delay parts of all channels corresponding to output 1 by τ ₁ and reducing the time-delay parts of all channels corresponding to output 2 by τ ₂ , a model G ₀ for designing a filter is obtained.

S404. Select the maximum frequency ω _max , and draw each element of the normalized inverse model on the frequency range [0, ω _max ] The frequency characteristic curve (Nyquist diagram). The maximum frequency ω _max must satisfy the frequency characteristic curves of all elements of the normalized inverse model in the right half plane of the complex plane. The frequency characteristics of the normalized inverse model elements are obtained by the following formula

Among them, j is the imaginary number unit, ω is the frequency, K is the steady-state gain inverse matrix of the process, is the inverse model frequency characteristic matrix, is the normalized inverse model frequency characteristic matrix, and the subscripts i and k represent the elements in row i and column k of the matrix, respectively.

S405. Analyze the frequency characteristic curves of the elements of the normalized inverse model column by column to determine the value of the controller parameter γ _k , the subscript k indicates that the parameter γ _k corresponds to the k-th column element of the normalized inverse model, and the parameter γ _k The selection criterion of is to choose a smaller value so that the frequency characteristic curves of all elements in the k-th column of the normalized inverse model after compensation are in the stable region, and the k-th column elements of the normalized inverse model are compensated according to the following formula

Among them, j is the imaginary number unit, ω is the frequency, γ _k is the corresponding controller parameter, is the normalized inverse model frequency characteristic matrix, is the normalized inverse model frequency characteristic matrix after compensation, and the subscripts i and k represent the elements of the i-th row and k-th column of the matrix, respectively,

S406. Using the obtained normalized inverse model after compensation, take N points on the frequency characteristic curve of each element, and the frequencies corresponding to these points are ω ₁ , ω ₂ , ... ω _N , where ω ₁ =0. Then use the method of complex curve fitting to get the transfer function of the corresponding filter

Among them, Q _ik (s) is the filter obtained by fitting the i-th row and k-column element of the compensated normalized inverse model, A _ik and B _ik are the parameter values corresponding to the filter, and K _ik is the process The i-th row and k-th column element of the steady-state gain inverse matrix, s is the Laplacian operator, and the parameters are calculated according to the following complex curve fitting method:

Among them, Q _ik (jω _m ) is the element in the i-th row and the k-th column, the complex number corresponding to the frequency on the frequency characteristic curve when the frequency is ω _m , |Q _ik (jω _m )| is the modulus value of the complex number, Re( Q _ik (jω _m )) is to obtain the real part of the complex number, Im(Q _ik (jω _m )) is to obtain the imaginary part of the complex number, N is the number of selected frequency points, a, b, c, d is an intermediate variable.

The specific process of S5 is

S501, given the value of the robustness index Ms, the controller adjustment parameters λ ₁ and λ ₂ are obtained according to the following formula

S502. Calculate sub-PID controller parameters

Among them, K _p is the proportional gain, K _I is the integral gain, K _d is the differential gain, and T _f is the filter time constant. The specific calculation methods of these parameters are as follows:

The final centralized PID controller with filter can be obtained as:

Among them, C is the overall centralized PID controller, C ₁ and C ₂ are the sub-PID controllers obtained above, and Q _ik is the filter obtained before.

In the second aspect, the present invention provides a centralized control system for a binary distillation column, which includes a measurement transmitter and a data storage and output unit connected sequentially, and a system identification unit and a parameter analysis unit are sequentially connected after the data storage and output unit. unit and controller unit, where

Measuring transmitters for collecting input and output signals;

The data storage and output unit stores the data transmitted by the measuring transmitter and outputs it to the system identification unit;

The system identification unit uses an identification algorithm to identify the transfer function of each channel to form a transfer function matrix;

The parameter analysis unit analyzes the transfer function matrix of the process, designs a centralized filter, and calculates the parameters of the PID controller by using a certain robustness index;

The controller unit uses the obtained filter parameters and PID controller parameters to form a centralized PID controller, thereby outputting control signals.

The controller designed according to this method can effectively reduce the influence of coupling on the system output, thereby effectively improving the quality of products extracted from the top and bottom of the tower. Moreover, the controller has a simple structure and is easy to implement, and the controller parameters can be obtained directly, avoiding the process of setting according to experience.

Description of drawings

Fig. 1 is a flowchart of a centralized control method for a binary distillation column according to an embodiment of the present invention.

Fig. 2 is a structural diagram of a centralized control system for a binary distillation column according to an embodiment of the present invention.

FIG. 3 is a frequency characteristic curve of each element of the normalized inverse model in a specified frequency band according to an embodiment of the present invention.

Fig. 4 is a schematic diagram of the stability judgment of each element of the normalized inverse model according to the embodiment of the present invention.

FIG. 5 is a frequency characteristic curve of each element of the normalized inverse model after compensation in a specified frequency band according to an embodiment of the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Taking a binary distillation column whose components are methanol and water as an example, the input (control variable) selected in this process is the reflux flow at the top of the tower and the steam flow at the bottom of the tower, and the output (controlled variable) is selected as the methanol group at the top of the tower. The mole fraction of points and the mole fraction of methanol at the bottom of the column. There is a strong coupling between the input and output of the process, and the control target is that the mole fraction of methanol in the products at the top and bottom of the tower must meet the set requirements. The embodiment of the centralized control method of the binary distillation tower is shown in Figure 1, comprising the following steps:

Step 1. Measure the return flow value at the top of the tower and the steam flow value at the bottom of the tower from the input end of the process, measure the mole fraction of methanol at the top and bottom of the tower from the output end of the process, and convert the flow value and mole fraction into electrical signals;

Step 2, storing the electrical signal in step 1, until the number required for identifying each channel is met, and then transmitting the electrical signal to the system identification module;

Step 3. Identify the transfer function of each channel according to the set least squares identification algorithm, and form the identified transfer function into a transfer function matrix;

After identification, the obtained transfer function matrix is:

Wherein, y ₁ and y ₂ are the mole fractions of methanol in the top and bottom products of the tower respectively, and R and S are the reflux flow at the top of the tower and the heating steam flow at the bottom of the tower respectively.

Step 4. Using the identified process model, analyze and design the centralized filter.

(1) First, the process steady-state gain inverse matrix K can be obtained

(2) The minimum time lag related to output 1 (the mole fraction of methanol in the product extracted from the top of the tower) is 1, and the minimum time lag related to output 1 (the mole fraction of methanol in the product extracted from the bottom of the tower) is 3 , that is, τ ₁ =1, τ ₂ =3.

(3) Reduce the time-delay of all channels corresponding to output 1 by τ ₁ , and reduce the time-delay of all channels corresponding to output 2 by τ ₂ , to obtain a model G ₀ for designing filters.

(4) Select the maximum frequency ω _max =10 ^-2 , and then on [0,ω _max ], draw the frequency characteristic curve of each element of the normalized inverse model according to G ₀ , as shown in FIG. 3 .

(5) Analyze the stability of the elements to determine the controller parameter γ _k , and judge the stability of the elements according to Fig. 4 . In Fig. 4, the real axis and the dotted line perpendicular to the real axis (a straight line composed of complex numbers whose real part is always 1) divides the right half plane of the complex plane into four regions. If the frequency characteristic curve of the normalized inverse model element is in In area II or area III, the elements are stable, if in area I or area IV, the elements are unstable, so the normalized inverse model should be compensated so that the frequency characteristic curves of all elements of the compensated normalized inverse model All are in Zone II or Zone III. The filter will then be derived using the compensated normalized inverse model. Since the introduction of the compensator will inevitably introduce unnecessary dynamics, it is necessary to offset this part of the dynamics as much as possible when designing the controller, so the compensator parameter γ _k will appear in the controller and become a controller parameter. The selection criterion of the parameter γ _k is to select a small value so that the frequency characteristic curves of all elements in the kth column of the compensated normalized inverse model are in the stable region, because the same compensator will compensate the original normalized inverse Models an entire column of elements, for example, a compensator with parameter γ1 will act on the two elements of the _first column, and _a compensator with parameter γ2 will act on the _two elements of the second column, so γ1 will be chosen as The smaller value that can make the two elements in the first column of the inverse model after compensation stable at the same time, γ ₂ will be selected as the smaller value that can make the two elements in the second column of the inverse model after compensation stable at the same time. In this example, after calculation, γ ₁ =2 and γ ₂ =10 are optional. From this, the frequency characteristic curves of the elements after compensation can be obtained as shown in FIG. 5 . As shown in FIG. 5 , after compensation, the frequency characteristic curves of all elements are in the stable region. The filter will therefore be fitted using the frequency characteristic curve of the compensated element.

(6) Take 100 points one by one on the frequency characteristic curve of each element after compensation, and the frequencies corresponding to these points are ω ₁ , ω ₂ , ... ω ₁₀₀ , ω ₁ =0. Taking the elements in the first row and the first column as an example, the obtained filter parameters are:

According to this method, the entire filter matrix can be obtained as:

Step 5. Determine the parameters of the PID controller based on the obtained process transfer function matrix and the designed filter.

(1) Given the robustness index Ms = 1.6, from the obtained minimum time lag τ ₁ = 1, τ ₂ = 3 related to each output, another set of parameters to determine the controller can be obtained:

(2) Using the obtained parameters λ ₁ and λ ₂ , and γ ₁ and γ ₂ obtained in step 4, the final PID parameters can be determined, which can be inserted into the formula:

Thus the final centralized PID controller is obtained as:

Step 6, using the obtained PID controller to adjust the system's top reflux flow and the amount of heating steam at the bottom of the tower.

This embodiment is a centralized control system for a binary rectification tower, and its structure is shown in FIG. 2 .

In addition to including a binary rectification tower, this embodiment also includes: a measuring transmitter for measuring the reflux flow at the top of the tower, the amount of heating steam at the bottom of the tower and the mole fraction of methanol extracted from the top and bottom of the tower, and the above Parameters are transmitted as electrical signals;

The data storage and output unit stores the signal from the measuring transmitter until the data volume required for identifying each channel is met, and then outputs the signal to the system identification unit;

The system identification unit is used to identify the transfer function of each branch through calculation;

The parameter analysis unit analyzes the transfer function matrix of the process, designs a centralized filter, and calculates the parameters of the PID controller by using a given robustness index;

The controller unit uses the obtained filter parameters and PID controller parameters to form a centralized PID controller, thereby outputting control signals.

The above-mentioned embodiment is only to demonstrate the spirit of the present invention, and the present invention is not limited to this embodiment.

Claims (4)

1. a binary distillation column centralized control method, is characterized in that, comprises the following steps: S1. Measure the values of each input and each output of the binary distillation tower, and transmit the measured values into electrical signals; S2. Store the electrical signal obtained in step S1, and transmit the electrical signal to the system identification module after the storage time t; S3. Using the least squares identification algorithm to identify the transfer function of each control channel, and establishing the transfer function matrix model of the binary distillation column; S4. Calculate the frequency characteristics of the normalized inverse model according to the transfer function model obtained in the step S3, and then design a filter by analyzing the frequency characteristics of the inverse model, The frequency characteristic of described normalized inverse model is obtained as follows Among them, j is the imaginary number unit, ω is the frequency, K is the steady-state gain inverse matrix of the process, is the inverse model frequency characteristic matrix, is the normalized inverse model frequency characteristic matrix, and the subscripts i and k represent the elements of the ith row and the kth column of the matrix, respectively; The specific process of said S4 is: S401. Calculating the steady-state gain inverse matrix K of the process, S402. According to the process transfer function matrix, the minimum time delay τ 1 in all channels corresponding to output ₁ and the minimum time delay τ _2. in all channels corresponding to output 2 are calculated respectively, S403. After reducing the time-delay part of all channels corresponding to output ₁ by τ1, and reducing the time-delay part of all channels corresponding to output ₂ by _τ2 , a model G0 for designing a filter is obtained, S404. Select the maximum frequency ω _max , and draw each element of the normalized inverse model on the frequency range [0, ω _max ] The frequency characteristic curve of , that is, the Nyquist diagram, the maximum frequency ω _max must satisfy that the frequency characteristic curves of all elements of the normalized inverse model are in the right half plane of the complex plane, and the frequency characteristics of the elements of the normalized inverse model are obtained by the following formula out Among them, j is the imaginary number unit, ω is the frequency, K is the steady-state gain inverse matrix of the process, is the inverse model frequency characteristic matrix, is the normalized inverse model frequency characteristic matrix, the subscripts i and k represent the elements of the i-th row and k-th column of the matrix, respectively, S405. Analyze the frequency characteristic curves of the elements of the normalized inverse model column by column to determine the value of the controller parameter γ _k , the subscript k indicates that the parameter γ _k corresponds to the k-th column element of the normalized inverse model, and the parameter γ _k The selection criterion of is to choose a small value so that the frequency characteristic curves of all elements in the kth column of the normalized inverse model after compensation are in the stable region, and the kth column elements of the normalized inverse model are compensated according to the following formula Among them, j is the imaginary number unit, ω is the frequency, γ _k is the corresponding controller parameter, is the normalized inverse model frequency characteristic matrix, is the normalized inverse model frequency characteristic matrix after compensation, and the subscripts i and k represent the elements of the i-th row and k-th column of the matrix, respectively, S406. Using the obtained normalized inverse model after compensation, take N points on the frequency characteristic curve of each element, and the frequencies corresponding to these points are ω ₁ , ω ₂ , ... ω _N , where ω ₁ = 0, and then use the method of complex curve fitting to get the transfer function of the corresponding filter Among them, Q _ik (s) is the filter obtained by fitting the i-th row and k-column element of the compensated normalized inverse model, A _ik and B _ik are the parameter values corresponding to the filter, and K _ik is the process The i-th row and k-th column element of the steady-state gain inverse matrix, s is the Laplacian operator, and the parameters are calculated according to the following complex curve fitting method: Among them, Q _ik (jω _m ) is the i-th row k column element, the complex number corresponding to the frequency on the frequency characteristic curve when the frequency is ω _m , |Q _ik (jω _m )| is the modulus value of the complex number, Re( Q _ik (jω _m )) is to obtain the real part of the complex number, Im(Q _ik (jω _m )) is to obtain the imaginary part of the complex number, N is the number of selected frequency points, a, b, c, d is an intermediate variable, S5. According to the transfer function model obtained in step S3 and the filter obtained in step S4, calculate the PID controller parameters according to the given robustness and dynamic performance requirements, and determine the final centralized PID controller; S6. Using the centralized PID controller obtained in step S5 to adjust the input. 2. The centralized control method of binary distillation column according to claim 1, characterized in that, the storage time t is from the moment when the step signal for identifying each channel is added until the output reaches a new steady state The time period up to the value. 3. the binary rectification column centralized control method according to claim 1, is characterized in that, the concrete step of described S3 is: the amplitude h of step signal, sampling period Ts and the output Y(k of collection object ), according to the following formula to calculate the parameters in the transfer function of each channel θ＝(P ^T ·P) ^-1 P ^T Z Where P and Z are coefficient matrices composed of h, Ts, and Y(k) respectively, and θ is a parameter used to identify the transfer function of each branch. 4. binary rectification column centralized control method according to claim 1, is characterized in that, the concrete process of S5 is the value of S501, given robustness index Ms, controller adjustment parameter λ ₁ and λ ₂ all Obtain according to the following formula S502. Calculate sub-PID controller parameters Among them, K _p is the proportional gain, K _I is the integral gain, K _d is the differential gain, and T _f is the filter time constant. The specific calculation methods of these parameters are as follows: The final centralized PID controller with filter can be obtained as: Among them, C is the overall centralized PID controller, C ₁ and C ₂ are the sub-PID controllers obtained above, and Q _ik is the filter obtained before.