CN106896721A - A kind of binary distillation column centerized fusion method and system - Google Patents

Abstract

The present invention discloses a kind of binary distillation column centerized fusion method and system.By recognizing the channel transfer function between each controlled variable and control variables, the model of binary distillation column is set up.Binary distillation column model to obtaining is asked for and analyzes the frequency domain characteristic of its inversion model to determine the filter parameter in centralized PID controller, and the regulation parameter of PID controller is determined further according to desired dynamic property and robustness.Control signal is adjusted using the centralized PID controller for calculating so that two-component fractionation column overhead reaches requirement with bottom of towe light component with the purity of heavy constituent.This method thinking is simple, it is easy to accomplish, effective control can be implemented to the binary distillation column that there is coupling.

Description

A kind of binary distillation column centerized fusion method and system

Technical field

The invention belongs to the automation field of petrochemical industry rectifying column, particularly binary distillation column centerized fusion method And system.

Background technology

Rectifying is the mass transport process being most widely used in petrochemical industry, and purification and the recovery of about 90% product are to pass through Rectifying is completed.The mechanism that rectifying is separate mainly uses the volatility difference of different component in mixture to be separated.Mixture By after rectifying column, the product produced from tower top or bottom of towe meets certain purity requirement.Binary distillation column is mainly used to separate Containing two kinds of mixtures of component.Binary distillation column is a multivariable process, and internal mechanism is complicated, and dynamic response is slow and controls Coupling between variable and controlled variable is more serious, therefore requirement higher is proposed to control program.In rectifying column Control program in, relatively simple is that the distillation process of multivariable is split into multiple single loops by the method for variable pairing It is controlled, this method is more effective when single-ended component is controlled, but it is not carried out to the coupling between variable Effective compensation, and the criterion of pairing is often according to static Relative increasing rate (RGA), therefore when carrying out two ends to tower It is necessary to carry out comprehensive analysis to process during component control.Uneoupled control is a good method coupled between eliminating variable, but existing Uneoupled control in, though static decoupling easily realize, equally face ignore process dynamics information problem, and ideal decoupling or Process is difficult to ask for again after its decouplers of dynamic decoupling method such as simple decoupling or decoupling, and this all brings difficulty to design controller Degree.Now about 90% controller is still PID controller in the industry, how to design effective PID controller, it is controlled well Binary distillation column processed is a good problem to study.

The content of the invention

In view of this, the main object of the present invention is to provide a kind of binary distillation column centerized fusion method.Including following Step：

S1, each input of measurement binary distillation column and the numerical value of each output, and will measure the value pick-up for obtaining is electricity Signal；

S2, the electric signal that S1 steps are obtained is stored, by after storage time t, electric signal being sent into system and being distinguished Know module；

S3, the transmission function that each control passage is recognized using linear least squares method algorithm, set up the biography of binary distillation column Delivery function matrix model；

S4, the transfer function model obtained according to S3 steps, are calculated the frequency characteristic of normalization inversion model, Ran Houtong Cross analysis inversion model frequency characteristic design wave filter.

The wave filter that S5, the transfer function model obtained according to S3 steps and S4 steps are obtained, according to given robustness And dynamic performance requirements, PID controller parameter is calculated, and determine final centralized PID controller；

S6, adjust input using the centralized PID controller that is obtained by S5 steps.

The storage time t is from the step signal moment for recognizing each passage is added, to be reached to output new steady Time period untill state value.

The detailed process of S3 is：The output Y of amplitude h, sampling period Ts and acquisition target according to the step signal K (), is calculated the parameter in the transmission function of each passage according to the following formula

θ=(P^T·P)^-1P^TZ

Wherein P and Z are respectively the coefficient matrixes being made up of h, Ts, Y (k), and θ is the transmission function for identifying each branch road Parameter.

S4's concretely comprises the following steps：

S401, the steady-state gain inverse matrix K for asking for process.

S402, according to process transfer function matrix obtain respectively and export 1 corresponding all passages in minimum time lag τ₁ And with output 2 corresponding all passages in minimum time lag τ_2.。

S403, will with output 1 corresponding all passages time lag part reduce τ₁, with 2 corresponding all passages of output Time lag part reduces τ₂Afterwards, the model G for designing wave filter is obtained₀。

S404, selected peak frequency ω_max, in frequency range [0, ω_max] on draw normalized inversion model each ElementFrequency characteristic (Nyquist figures).Peak frequency ω_maxMeet all elements of normalization inversion model Frequency characteristic all in the RHP of complex plane.The frequency characteristic of normalized inversion model element is obtained as the following formula

Wherein, j is imaginary unit, and ω is frequency, and K is the steady-state gain inverse matrix of process,It is inversion model frequency Feature matrix,It is normalization inversion model frequency characteristic matrix, subscript i and k represent the i-th row and the k row of matrix respectively Element.

S405, the frequency characteristic to the element of normalization inversion model are analyzed to determine controller parameter by column γ_kValue, subscript k represents parameter γ_kThe kth column element of correspondence normalization inversion model, parameter γ_kSelection standard be selection one Individual smaller value causes the frequency characteristic through the kth row all elements of the normalization inversion model after overcompensation all in stable region Domain, the kth column element for normalizing inversion model is compensated according to the following formula

Wherein, j is imaginary unit, and ω is frequency, γ_kIt is corresponding controller parameter,It is normalization inversion model Frequency characteristic matrix,It is the normalization inversion model frequency characteristic matrix after compensation, subscript i and k represent matrix respectively The element of the i-th row and kth row,

S406, using the normalization inversion model after the compensation for obtaining, taken on the frequency characteristic of each of which element N number of Point, the corresponding frequency of these points is respectively ω₁, ω₂... ω_N, wherein, ω₁=0.The method of compound curve fitting is recycled to obtain To the transmission function of corresponding wave filter

Wherein, Q_ik(s) be by compensating after normalization inversion model the i-th row kth column element fitting obtain wave filter, A_ikAnd B_ikIt is the corresponding parameter value of wave filter, K_ikIt is the i-th row kth column element of the steady-state gain inverse matrix of process, s is general to draw Laplacian operater, parameter is asked for according to following compound curve approximating method：

Wherein, Q_ik(jω_m) it is the i-th row kth column element, take ω in frequency on frequency characteristic_mWhen corresponding plural number, | Q_ik(jω_m) | it is to ask for the plural modulus value, Re (Q_ik(jω_m)) it is to ask for the real, Im (Q_ik(jω_m)) it is to ask for The plural imaginary part, N is the number of the Frequency point chosen, and a, b, c, d are intermediate variable.

The detailed process of S5 is

The value of S501, given robustness index Ms, controller regulation parameter λ₁And λ₂Ask for according to the following formula

S502, the sub- PID controller parameter of calculating

Wherein, K_pIt is proportional gain, K_IIt is storage gain, K_dIt is the differential gain, T_fIt is filter time constant, these ginsengs Several specific acquiring methods is as follows：

The centralized PID controller that can obtain final band filter is：

Wherein, C is total centralized PID controller, C₁And C₂It is the above-mentioned sub- PID controller asked for, Q_ikTo ask before The wave filter for taking.

Second aspect, the present invention provides a kind of binary distillation column Centralized Control System, including the measurement being sequentially connected becomes Device and data storage and output unit are sent, being also linked in sequence after data storage and output unit has System Discrimination unit, parameter Analytic unit and controller unit, wherein

Measuring transducer, for gathering input signal and output signal；

Data storage and output unit, the data that measuring transducer transmission comes are stored, and export to system Identification unit；

System Discrimination unit, the transmission function of each passage is identified using identification algorithm, constitutes transfer function matrix；

Parameter analysis unit, the transfer function matrix to process is analyzed, and designs centralized wave filter, and using fixed Robustness index calculates PID controller parameter；

Controller unit, centralized PID controller is constituted using the filter parameter and PID controller parameter for obtaining, from And output control signal.

According to the controller that this method is designed, coupling can be effectively reduced for the influence that system is exported, so that Effective lifting tower top and the product quality of bottom of towe extraction.And controller architecture is simple, it is easy to accomplish, controller parameter can be straight Obtain and take, it is to avoid the process rule of thumb adjusted.

Brief description of the drawings

Fig. 1 is the flow chart of embodiment of the present invention binary distillation column centerized fusion method.

Fig. 2 is the structure chart of embodiment of the present invention binary distillation column Centralized Control System.

Fig. 3 is frequency characteristic of each element of embodiment of the present invention normalization inversion model in regulation frequency range.

Fig. 4 is the judgement of stability schematic diagram of each element of embodiment of the present invention normalization inversion model.

Fig. 5 is frequency characteristic of each element of the normalization inversion model after embodiment of the present invention compensation in regulation frequency range Curve.

Specific embodiment

The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.

So that component is for the binary distillation column of first alcohol and water as an example, the input (control variables) that the process is chosen is returned for tower top The steam flow of flow and bottom of towe, output (controlled variable) selection is the molar fraction of tower top methyl alcohol component and rubbing for bottom of towe methyl alcohol That fraction.There is stronger coupling between the input and output of process, control targe is the methyl alcohol in the product of tower top and bottom of towe Molar fraction be intended to reach the requirement of setting.Binary distillation column centerized fusion embodiment of the method is as shown in figure 1, including following Step：

Step 1, the input end measuring overhead reflux value from process, tower bottom steam flow value, from the measurement of the output of process end The Methanol Molar fraction of tower top and bottom of towe, is electric signal by flow value and molar fraction pick-up；

Electric signal in step 2, storing step 1, until after the quantity required for meeting each passage of identification, electric signal being passed Deliver to System Discrimination module；

Step 3, the transmission function that each passage is recognized according to the linear least squares method algorithm of setting, and the transmission for picking out Function constitutes transfer function matrix；

Recognized, the transfer function matrix for obtaining is：

Wherein, y₁And y₂The molar fraction of the methyl alcohol respectively in tower top and tower bottom product, R and S are respectively overhead reflux amount Steam flow is heated with bottom of towe.

Step 4, the process model obtained using identification, the centralized wave filter of analysis design.

(1) Steady-state process gain inverse matrix K can be obtained first

(2) the minimum time lag related to 1 (molar fraction of methyl alcohol in the product of overhead extraction) of output is 1, with output 1 (molar fraction of methyl alcohol in the product of bottom of towe extraction) related minimum time lag is 3, i.e. τ₁=1, τ₂=3.

(3) the time lag part with 1 corresponding all passages of output is reduced into τ₁, with output 2 corresponding all passages when Stagnant part reduces τ₂, obtain the model G for designing wave filter₀。

(4) peak frequency ω is chosen_max=10^-2, then [0, ω_max] on, according to G₀Draw the every of normalization inversion model The frequency characteristic of individual element, as shown in Figure 3.

(5) stability of analytical element is so that it is determined that controller parameter γ_k, the stability of element judged according to Fig. 4. In Fig. 4, be divided into for the RHP of complex plane by real axis and the dotted line (straight line that the permanent plural number for 1 of real part is constituted) perpendicular to real axis 4 regions, if the frequency characteristic of normalization inversion model element is in region II or region III, element be it is stable, such as Fruit is in region I or region IV, and element is unstable, therefore normalization inversion model is compensated so that the normalization after compensation The frequency characteristic of all elements of inversion model is all in region II or region III.So wave filter is by using the normalizing after compensation Change inversion model to ask for.Unnecessary dynamic will certainly be introduced after due to introducing compensator, therefore is to use up when controller is designed Possible this partial dynamic of counteracting, so compensator parameter γ_kOccur in the controller, as controller parameter.Parameter γ_k Selection standard be selection one smaller value so that through after overcompensation normalization inversion model kth row all elements frequency Characteristic curve all in stability region, the element of the former normalization permutation of inversion model one will be compensated due to same compensator, for example, containing There is parameter γ₁Compensator will act on two elements of first row, contain parameter γ₂Compensator will act on secondary series Two elements, therefore γ₁Will be selected to be can make two smaller values of element Simultaneous Stabilization of inversion model first row, γ after compensation₂Will choosing It is selected as that two smaller values of element Simultaneous Stabilization of inversion model secondary series after compensation can be made.In this example, it is computed, optional γ₁=2, γ₂=10.It can thus be concluded that after compensation the frequency characteristic of element as shown in figure 5, as shown in Figure 5, it is compensated after, all of unit The frequency characteristic of element is all in stability region.Therefore filtering will be fitted using the frequency characteristic of the element after compensation Device.

(6) 100 points are taken on the frequency characteristic of element one by one after each compensation, these corresponding frequencies minute of point Wei not ω₁,ω₂,……ω₁₀₀, ω₁=0.By taking the element of the first row first row as an example, the filter parameter asked for is：

According to this method, can obtain whole electric-wave filter matrix is：

The wave filter of step 5, the process transfer function matrix based on acquisition and design, determines PID controller parameter.

(1) robustness index Ms=1.6 is given, by the minimum time lag τ related to each output to obtain₁=1, τ₂= 3, the another set parameter for determining controller can be obtained：

(2) using the parameter lambda obtained₁And λ₂, and the γ obtained by step 4₁And γ₂, it may be determined that final PID ginsengs Number, bringing formula into can obtain：

Thus obtaining final centralized PID controller is：

The heating quantity of steam of step 6, the overhead reflux amount using the PID controller regulating system obtained and bottom of towe.

The present embodiment is binary distillation column Centralized Control System, and its structure is as shown in Figure 2.

The present embodiment also includes in addition to comprising a binary distillation column：Measuring transducer, for measuring overhead reflux Amount, bottom of towe heating quantity of steam and tower top and the Methanol Molar fraction of bottom of towe extraction, and be electric signal by above parameter pick-up；

Data storage and output unit, the signal of transmitter of testing oneself in the future are stored, until meeting each passage of identification Required data volume, then output a signal to System Discrimination unit；

System Discrimination unit, for by calculating, picking out the transmission function of each branch road；

Parameter analysis unit, the transfer function matrix to process is analyzed, and designs centralized wave filter, and utilization is given Determine robustness index and calculate PID controller parameter；

Controller unit, centralized PID controller is constituted using the filter parameter and PID controller parameter for obtaining, from And output control signal.

Above-described embodiment is only the displaying to spirit of the present invention, and the present invention is not limited to the present embodiment.

Claims (6)

1. a kind of binary distillation column centerized fusion method, it is characterised in that comprise the following steps：

S1, each input of measurement binary distillation column and the numerical value of each output, and will measure the value pick-up for obtaining is electric signal；

S2, the electric signal that S1 steps are obtained is stored, by after storage time t, electric signal being sent into System Discrimination mould Block；

S3, the transmission function that each control passage is recognized using linear least squares method algorithm, set up the transmission letter of binary distillation column Matrix number model；

S4, the transfer function model obtained according to S3 steps, are calculated the frequency characteristic of normalization inversion model, then by dividing Analysis inversion model frequency characteristic design wave filter,

The frequency characteristic of the normalization inversion model is obtained as the following formula

${\stackrel{\‾}{G}}_{ik}\left(j\mathrm{\ω}\right)=\frac{{\left(G_0^{-1}\right(j\mathrm{\ω}\left)\right)}_{ik}}{K_{ik}}$

Wherein, j is imaginary unit, and ω is frequency, and K is the steady-state gain inverse matrix of process,It is inversion model frequency characteristic Matrix,It is normalization inversion model frequency characteristic matrix, subscript i and k represent the unit of the i-th row and the kth row of matrix respectively Element.

The wave filter that S5, the transfer function model obtained according to S3 steps and S4 steps are obtained, according to given robustness and dynamic State performance requirement, calculates PID controller parameter, and determine final centralized PID controller；

S6, adjust input using the centralized PID controller that is obtained by S5 steps.

2. binary distillation column centerized fusion method according to claim 1, it is characterised in that the storage time t is From the step signal moment for recognizing each passage is added, the time period new steady-state value is reached to output.

3. binary distillation column centerized fusion method according to claim 1, it is characterised in that the specific steps of the S3 For：Output Y (k) of amplitude h, sampling period Ts and acquisition target according to the step signal, is calculated according to the following formula Parameter in the transmission function of each passage

$\begin{array}{cc}P=\left[\begin{array}{ccc}Y\left(1\right)-Y\left(0\right)& -Tsh& h\\ Y\left(2\right)-Y\left(0\right)& -2Tsh& h\\ .& .& .\\ .& .& .\\ .& .& .\\ Y\left(n\right)-Y\left(0\right)& -nTsh& h\end{array}\right]& \mathrm{\θ}=\left[\begin{array}{c}{\mathrm{\θ}}_1\\ {\mathrm{\θ}}_2\\ {\mathrm{\θ}}_3\end{array}\right]\end{array}$

$Z=\left[\begin{array}{c}-Ts\underset{i=0}{\overset{1}{\Σ}}Y\left(i\right)\\ -Ts\underset{i=0}{\overset{2}{\Σ}}Y\left(i\right)\\ .\\ .\\ .\\ -Ts\underset{i=0}{\overset{n}{\Σ}}Y\left(i\right)\end{array}\right]$

θ=(P^T·P)^-1P^TZ

Wherein P and Z are respectively the coefficient matrixes being made up of h, Ts, Y (k), and θ is the ginseng for identifying the transmission function of each branch road Number.

4. binary distillation column centerized fusion method according to claim 1, it is characterised in that the detailed process of S4 is：

S401, the steady-state gain inverse matrix K for asking for process,

S402, according to process transfer function matrix obtain respectively and export 1 corresponding all passages in minimum time lag τ₁And with it is defeated The minimum time lag τ gone out in 2 corresponding all passages_2.,

S403, will with output 1 corresponding all passages time lag part reduce τ₁, the time lag portion with 2 corresponding all passages of output Divide and reduce τ₂Afterwards, the model G for designing wave filter is obtained₀,

S404, selected peak frequency ω_max, in frequency range [0, ω_max] on draw each element of normalized inversion modelFrequency characteristic, i.e. Nyquist figure, peak frequency ω_maxMeet all elements of normalization inversion model Frequency characteristic all in the RHP of complex plane, obtain as the following formula by the frequency characteristic of normalized inversion model element

${\stackrel{\‾}{G}}_{ik}\left(j\mathrm{\ω}\right)=\frac{{\left(G_0^{-1}\right(j\mathrm{\ω}\left)\right)}_{ik}}{K_{ik}}$

Wherein, j is imaginary unit, and ω is frequency, and K is the steady-state gain inverse matrix of process,It is inversion model frequency characteristic Matrix,It is normalization inversion model frequency characteristic matrix, subscript i and k represent the unit of the i-th row and the kth row of matrix respectively Element,

S405, the frequency characteristic to the element of normalization inversion model are analyzed to determine controller parameter γ by column_k's Value, subscript k represents parameter γ_kThe kth column element of correspondence normalization inversion model, parameter γ_kSelection standard be selection one it is smaller Value so that through the frequency characteristic of the kth row all elements for normalizing inversion model after overcompensation all in stability region, normalizing The kth column element for changing inversion model is compensated according to the following formula

${\widetilde{\stackrel{\‾}{G}}}_{ik}\left(j\mathrm{\ω}\right)={\stackrel{\‾}{G}}_{ik}\left(j\mathrm{\ω}\right)\frac{1}{1+{\mathrm{j\ω\γ}}_k}$

Wherein, j is imaginary unit, and ω is frequency, γ_kIt is corresponding controller parameter,For normalization inversion model frequency is special Property matrix,Be the normalization inversion model frequency characteristic matrix after compensation, subscript i and k represent respectively matrix the i-th row and The element of kth row,

S406, using the normalization inversion model after the compensation for obtaining, N number of point is taken on the frequency characteristic of each of which element, The corresponding frequency of these points is respectively ω₁, ω₂... ω_N, wherein, ω₁=0.The method of compound curve fitting is recycled to obtain right The transmission function of the wave filter answered

$Q_{ik}\left(s\right)=K_{ik}\·\frac{A_{ik}s+1}{B_{ik}s+1}$

Wherein, Q_ik(s) be by compensating after normalization inversion model the i-th row kth column element fitting obtain wave filter, A_ikWith B_ikIt is the corresponding parameter value of wave filter, K_ikIt is the i-th row kth column element of the steady-state gain inverse matrix of process, s is Laplce Operator, parameter is asked for according to following compound curve approximating method：

$\left[\begin{array}{c}{A}_{ik}\\ B_{ik}\end{array}\right]={\left[\begin{array}{cc}{a}_{ik}& -b_{ik}\\ b_{ik}& c_{ik}\end{array}\right]}^{-1}\left[\begin{array}{c}{d}_{ik}\\ d_{ik}\end{array}\right]$

$\begin{array}{cc}\left\{\begin{array}{c}{a}_{ik}=\underset{m=0}{\overset{N}{\Σ}}{\mathrm{\ω}}_m^2\\ b_{ik}=\underset{m=0}{\overset{N}{\Σ}}\[{\mathrm{\ω}}_m^2\mathrm{Re}\left(Q_{ik}\right({\mathrm{j\ω}}_m\left)\right)\]\end{array}\right.& \left\{\begin{array}{c}{c}_{ik}=\underset{m=0}{\overset{N}{\Σ}}\[{\mathrm{\ω}}_m^2|Q_{ik}\left({\mathrm{j\ω}}_n\right){|}^2\]\\ d_{ik}=\underset{m=0}{\overset{N}{\Σ}}{\mathrm{\ω}}_m\mathrm{Im}\left(Q_{ik}\right({\mathrm{j\ω}}_m\left)\right)\end{array}\right.\end{array}$

Wherein, Q_ik(jω_m) it is the i-th row kth column element, take ω in frequency on frequency characteristic_mWhen corresponding plural number, | Q_ik(j ω_m) | it is to ask for the plural modulus value, Re (Q_ik(jω_m)) it is to ask for the real, Im (Q_ik(jω_m)) it is to ask for this to answer Several imaginary parts, N is the number of the Frequency point chosen, and a, b, c, d are intermediate variable.

5. binary distillation column centerized fusion method according to claim 1, it is characterised in that the detailed process of S5 is The value of S501, given robustness index Ms, controller regulation parameter λ₁And λ₂Ask for according to the following formula

${\mathrm{\λ}}_i=\frac{0.06991Ms+0.5942}{Ms-1.0260}\×{\mathrm{\τ}}_i,i=1,2$

S502, the sub- PID controller parameter of calculating

$C_1=(K_{P1}+\frac{K_{11}}{s}+K_{d1}s)\frac{1}{T_{f1}s+1}$

$C_2=(K_{P2}+\frac{K_{I2}}{s}+K_{d2}s)\frac{1}{T_{f2}s+1}$

Wherein, K_pIt is proportional gain, K_IIt is storage gain, K_dIt is the differential gain, T_fIt is filter time constant, the tool of these parameters Body acquiring method is as follows：

$\left\{\begin{array}{c}{K}_{Pi}=\frac{{\mathrm{\γ}}_i+{\mathrm{\τ}}_i}{{\mathrm{\λ}}_i+{\mathrm{\τ}}_i}\\ K_{Ii}=\frac{1}{{\mathrm{\λ}}_i+{\mathrm{\τ}}_i}\\ K_{di}=\frac{{\mathrm{\γ}}_i\·{\mathrm{\τ}}_i}{{\mathrm{\λ}}_i+{\mathrm{\τ}}_i}\\ T_{fi}=\frac{{\mathrm{\λ}}_i\·{\mathrm{\τ}}_i}{{\mathrm{\λ}}_i+{\mathrm{\τ}}_i}\end{array}\right.,i=1,2$

The centralized PID controller that can obtain final band filter is：

$C=\left[\begin{array}{cc}{C}_1{Q}_{11}& C_2{Q}_{12}\\ C_1{Q}_{21}& C_2{Q}_{22}\end{array}\right]$

Wherein, C is total centralized PID controller, C₁And C₂It is the above-mentioned sub- PID controller asked for, Q_ikIt is the filter asked for before Ripple device.

6. a kind of binary distillation column Centralized Control System, it is characterised in that including the measuring transducer being sequentially connected and data Also be linked in sequence after storage and output unit, data storage and output unit have System Discrimination unit, parameter analysis unit and Controller unit, wherein

Measuring transducer, for gathering input signal and output signal；

Data storage and output unit, the data that measuring transducer transmission comes are stored, and export to System Discrimination Unit；

System Discrimination unit, the transmission function of each passage is identified using identification algorithm, constitutes transfer function matrix；

Parameter analysis unit, the transfer function matrix to process is analyzed, and designs centralized wave filter, and using given Shandong Rod index calculates PID controller parameter；

Controller unit, constitutes centralized PID controller, so that defeated using the filter parameter and PID controller parameter for obtaining Go out control signal.