CN106896721B - A kind of binary distillation column centerized fusion method - Google Patents

A kind of binary distillation column centerized fusion method Download PDF

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CN106896721B
CN106896721B CN201710163840.3A CN201710163840A CN106896721B CN 106896721 B CN106896721 B CN 106896721B CN 201710163840 A CN201710163840 A CN 201710163840A CN 106896721 B CN106896721 B CN 106896721B
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靳其兵
杜星瀚
蒋北艳
周星
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Beijing University of Chemical Technology
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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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 variable, the model of binary distillation column is established.The binary distillation column model of acquisition is sought and analyzes the frequency domain characteristic of its inversion model to determine the filter parameter in centralized PID controller, the adjustment parameter of PID controller is determined further according to desired dynamic property and robustness.Control signal is adjusted using calculated centralized PID controller, so that the purity of two-component fractionation column overhead and tower bottom light component and heavy constituent reaches requirement.This method thinking is simple, it is easy to accomplish, it can be to there are the binary distillation columns of coupling to implement effective control.

Description

A kind of binary distillation column centerized fusion method
Technical field
The invention belongs to the automation fields of petrochemical industry rectifying column, especially binary distillation column centerized fusion method And system.
Background technique
Rectifying is the mass transport process being most widely used in petrochemical industry, and the purification of about 90% product is to pass through with recycling Rectifying is completed.The mechanism of rectifying separation is mainly separated using the volatility difference of different component in mixture.Mixture After rectifying column, the product produced from tower top or tower bottom meets certain purity requirement.Binary distillation column is mainly used to separate Mixture containing two kinds of components.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 proposes higher requirement 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 controls, but it does not carry out the coupling between variable The criterion for effectively compensating, and matching is worked as often according to static Relative increasing rate (RGA) to tower progress both ends It is necessary to process progress comprehensive analysis when component controls.Decoupling control is one and eliminates the good method that couples between variable, but existing Decoupling control in, though static decoupling is easy to accomplish, equally face ignore process dynamics information the problem of, and ideal decoupling or Process is difficult to seek again after its decouplers of dynamic decoupling methods such as simple decoupling or decoupling, 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, controls it well Binary distillation column processed is a good problem to study.
Summary 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:
The numerical value of each input and each output of S1, measurement binary distillation column, and the value pick-up that measurement is obtained is electricity Signal；
S2, the electric signal that S1 step obtains is stored, after storage time t, electric signal is sent to system and is distinguished Know module；
S3, the transmission function that each control channel is recognized using linear least squares method algorithm, establish the biography of binary distillation column Delivery function matrix model；
S4, the transfer function model obtained according to S3 step are calculated the frequency characteristic of normalization inversion model, then lead to Cross analysis inversion model frequency characteristic design filter.
The filter that S5, the transfer function model obtained according to S3 step and S4 step obtain, according to given robustness And dynamic performance requirements, PID controller parameter is calculated, and determine final centralized PID controller；
S6, input is adjusted using the centralized PID controller obtained by S5 step.
The storage time t is to reach new steady to output from being added step signal moment for recognizing each channel Period until state value.
The detailed process of S3 are as follows: according to the output Y of the amplitude h of the step signal, sampling period Ts and acquisition target (k), the parameter in the transmission function in each channel is calculated according to the following formula
θ=(PT·P)-1PTZ
Wherein P and Z is the coefficient matrix being made of h, Ts, Y (k) respectively, and θ is for identifying the transmission function of each branch Parameter.
The specific steps of S4 are as follows:
The steady-state gain inverse matrix K of S401, finding process.
S402, it is found out respectively and the minimum time lag τ in 1 corresponding all channels of output according to process transfer function matrix1 With with output 2 corresponding all channels in minimum time lag τ2.。
S403, τ will be reduced with the time lag part in 1 corresponding all channels of output1, with 2 corresponding all channels of output Time lag part reduces τ2Afterwards, the model G for designing filter is obtained0。
S404, selected maximum frequency ωmax, in frequency range [0, ωmax] on draw normalized inversion model each ElementFrequency characteristic (Nyquist figure).Maximum frequency ωmaxMeet all elements of normalization inversion model Frequency characteristic all in the right half plane of complex plane.The frequency characteristic of normalized inversion model element is found out as the following formula
Wherein, j is imaginary unit, and ω is frequency, and K is the steady-state gain inverse matrix of process,For inversion model frequency Rate feature matrix,To normalize inversion model frequency characteristic matrix, subscript i and k respectively represent the i-th row and k column of matrix Element.
S405, the frequency characteristic of the element of normalization inversion model is analyzed by column to determine controller parameter γkValue, subscript k expression parameter γkThe kth column element of corresponding normalization inversion model, parameter γkSelection criteria be selection one A smaller value makes by the frequency characteristic of the kth column all elements of compensated normalization inversion model all in stable region Domain, the kth column element for normalizing inversion model compensate according to the following formula
Wherein, j is imaginary unit, and ω is frequency, γkFor corresponding controller parameter,To normalize inversion model Frequency characteristic matrix,For compensated normalization inversion model frequency characteristic matrix, subscript i and k respectively represent matrix The element of i-th row and kth column,
S406, using obtained compensated normalization inversion model, taken on the frequency characteristic of each of which element N number of Point, the corresponding frequency of these points is respectively ω1, ω2... ωN, wherein ω1=0.The method for recycling compound curve fitting obtains To the transmission function of corresponding filter
Wherein, QikIt (s) is the filter obtained by the i-th row kth column element fitting of compensated normalization inversion model, AikAnd BikFor the corresponding parameter value of filter, KikFor the i-th row kth column element of the steady-state gain inverse matrix of process, s is that drawing is general Laplacian operater, parameter are sought according to following compound curve approximating method:
Wherein, Qik(jωm) it is the i-th row kth column element, ω is taken in frequency on frequency characteristicmWhen corresponding plural number, | Qik(jωm) | it is the modulus value for seeking the plural number, Re (Qik(jωm)) it is to seek the real, Im (Qik(jωm)) it is to ask The imaginary part of the plural number is taken, N is the number for 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 adjustment parameter λ1And λ2Seek according to the following formula
S502, sub- PID controller parameter is calculated
Wherein, KpFor proportional gain, KIFor integral gain, KdFor the differential gain, TfFor filter time constant, these ginsengs Several specific acquiring methods is as follows:
The centralized PID controller of final band filter can be obtained are as follows:
Wherein, C is total centralized PID controller, C1And C2For the above-mentioned sub- PID controller sought, QikTo ask before The filter taken.
Second aspect, the present invention provide a kind of binary distillation column centralized control system, including sequentially connected measurement becomes It send device and data store and output unit, data storage is also linked in sequence later with output unit and has System Discrimination unit, parameter Analytical unit and controller unit, wherein
Measuring transducer, for acquiring input signal and output signal；
The data that measuring transducer transmission comes are stored, and exported to system by data storage and output unit Identification unit；
System Discrimination unit identifies the transmission function in each channel using identification algorithm, constitutes transfer function matrix；
Parameter analysis unit analyzes the transfer function matrix of process, designs centralized filter, and utilize and determine Robustness index calculates PID controller parameter；
Controller unit constitutes centralized PID controller using obtained filter parameter and PID controller parameter, from And export control signal.
According to the controller that this method designs, the influence that coupling exports system can be effectively reduced, so that The effective product quality for promoting tower top and tower bottom extraction.And controller architecture is simple, it is easy to accomplish, controller parameter can be straight It obtains and takes, avoid the process rule of thumb adjusted.
Detailed description of the invention
Fig. 1 is the flow chart of binary distillation column of embodiment of the present invention centerized fusion method.
Fig. 2 is the structure chart of binary distillation column of embodiment of the present invention centralized control system.
Fig. 3 is that the embodiment of the present invention normalizes frequency characteristic of each element of inversion model in regulation frequency range.
Fig. 4 is the judgement of stability schematic diagram for each element that the embodiment of the present invention normalizes inversion model.
Fig. 5 is frequency characteristic of each element of the compensated normalization inversion model of the embodiment of the present invention in regulation frequency range Curve.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
By taking group is divided into the binary distillation column of methanol and water as an example, the input (control variable) which chooses is returning for tower top The steam flow of flow and tower bottom, output (controlled variable) are selected as the molar fraction of tower top methanol component and rubbing for tower bottom methanol That score.It is coupled between the input of process and output there are stronger, control target is the methanol in tower top and the product of tower bottom 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, include following Step:
Step 1, the input end measuring overhead reflux magnitude from process, tower bottom steam flow value are measured from the output of process end Flow value and molar fraction pick-up are electric signal by the Methanol Molar score of tower top and tower bottom；
Electric signal in step 2, storing step 1 passes electric signal after meeting quantity required for recognizing each channel It send to System Discrimination module；
Step 3, the transmission function that each channel is identified according to the linear least squares method algorithm of setting, and the transmitting picked out Function forms transfer function matrix；
Transfer function matrix that is recognized, obtaining are as follows:
Wherein, y1And y2The molar fraction of methanol respectively in tower top and tower bottom product, R and S are respectively overhead reflux amount Steam flow is heated with tower bottom.
Step 4, the process model obtained using identification, analysis design centralized filter.
(1) Steady-state process gain inverse matrix K can be found out first
(2) minimum time lag relevant to 1 (molar fraction of methanol in the product of overhead extraction) of output is 1, with output 1 (molar fraction of methanol in the product of tower bottom extraction) relevant minimum time lag is 3, i.e. τ1=1, τ2=3.
(3) τ will be reduced with the time lag part in 1 corresponding all channels of output1, with output 2 corresponding all channels when Stagnant part reduces τ2, obtain the model G for designing filter0。
(4) maximum frequency ω is chosenmax=10-2, then [0, ωmax] on, according to G0Draw the every of normalization inversion model The frequency characteristic of a element, as shown in Figure 3.
(5) stability of analytical element is so that it is determined that controller parameter γk, the stability of element judged according to Fig. 4. In Fig. 4, the right half plane of complex plane is divided by real axis and the dotted line (straight line for the plural number composition that real part perseverance is 1) perpendicular to real axis 4 regions, if the frequency characteristic of normalization inversion model element in region II or region III, element be it is stable, such as For fruit in region I or region IV, element is unstable, therefore to compensate to normalization inversion model, so that compensated normalization The frequency characteristic of all elements of inversion model is all in region II or region III.Filter will utilize compensated normalizing in this way Change inversion model to seek.It is to use up when designing controller since unnecessary dynamic will certainly be introduced after introducing compensator Possible this partial dynamic of counteracting, so compensator parameter γkIt will appear in the controller, become controller parameter.Parameter γk Selection criteria be selection one smaller value so that by it is compensated normalization inversion model kth column all elements frequency Characteristic curve is all in stability region, since the same compensator will compensate the element of former normalization one permutation of inversion model, 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 γ1It will be selected to be the smaller value that two elements of inversion model first row are stable simultaneously after capable of making compensation, γ2It will choosing It is selected as the smaller value that two elements of inversion model secondary series are stable simultaneously after capable of making to compensate.It in this example, is computed, optional γ1=2, γ2=10.It can thus be concluded that the frequency characteristic of element is as shown in figure 5, as shown in Figure 5 after compensation, and after compensated, all members The frequency characteristic of element is all in stability region.Therefore filtering will be fitted using the frequency characteristic of compensated element Device.
(6) 100 points are taken on the frequency characteristic of each compensated element one by one, these put corresponding frequency minute It Wei not ω1,ω2,……ω100, ω1=0.By taking the element of the first row first row as an example, the filter parameter sought are as follows:
According to this method, entire electric-wave filter matrix can be found out are as follows:
The 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 with the minimum time lag τ relevant to each output of acquisition1=1, τ2= 3, the another set parameter of determining controller can be found out:
(2) parameter lambda found out is utilized1And λ2, and the γ obtained by step 41And γ2, can determine final PID ginseng Number, bringing formula into can obtain:
Thus final centralized PID controller is obtained are as follows:
Step 6 utilizes the overhead reflux amount of the PID controller regulating system found out and the heating quantity of steam of tower bottom.
The present embodiment is binary distillation column centralized control system, and structure is as shown in Figure 2.
The present embodiment is other than comprising a binary distillation column, further includes: measuring transducer, for measuring overhead reflux Amount, tower bottom heat the Methanol Molar score of quantity of steam and tower top and tower bottom extraction, and are electric signal by the above parameter pick-up；
Data storage and output unit, future, the signal of measurement transmitter stored, and recognized each channel until meeting Required data volume, then output a signal to System Discrimination unit；
System Discrimination unit, for picking out the transmission function of each branch by calculating；
Parameter analysis unit analyzes the transfer function matrix of process, designs centralized filter, and utilize and give Determine robustness index and calculates PID controller parameter；
Controller unit constitutes centralized PID controller using obtained filter parameter and PID controller parameter, from And export control signal.
Above-described embodiment is only the displaying to spirit of that invention, and the present invention is not limited to the present embodiment.

Claims (4)

1. a kind of binary distillation column centerized fusion method, which comprises the following steps:
The numerical value of each input and each output of S1, measurement binary distillation column, and the value pick-up that measurement is obtained is electric signal；
S2, the electric signal that S1 step obtains is stored, after storage time t, electric signal is sent to System Discrimination mould Block；
S3, the transmission function that each control channel is recognized using linear least squares method algorithm, establish the transmitting letter of binary distillation column Matrix number model；
The frequency characteristic of normalization inversion model is calculated in S4, the transfer function model obtained according to S3 step, then by dividing It analyses inversion model frequency characteristic and designs filter,
The frequency characteristic of the normalization inversion model is found out as the following formula
Wherein, j is imaginary unit, and ω is frequency, and K is the steady-state gain inverse matrix of process,For inversion model frequency characteristic Matrix,To normalize inversion model frequency characteristic matrix, subscript i and k respectively represent the i-th row of matrix and the member of kth column Element；
The detailed process of the S4 are as follows:
The steady-state gain inverse matrix K of S401, finding process,
S402, it is found out respectively and the minimum time lag τ in 1 corresponding all channels of output according to process transfer function matrix1With with it is defeated Minimum time lag τ in 2 corresponding all channels out2.,
S403, τ will be reduced with the time lag part in 1 corresponding all channels of output1, with the time lag portion in 2 corresponding all channels of output Divide and reduces τ2Afterwards, the model G for designing filter is obtained0,
S404, selected maximum frequency ωmax, in frequency range [0, ωmax] on draw each element of normalized inversion modelFrequency characteristic, i.e. Nyquist figure, maximum frequency ωmaxMeet all elements of normalization inversion model All in the right half plane of complex plane, the frequency characteristic of normalized inversion model element is found out frequency characteristic as the following formula
Wherein, j is imaginary unit, and ω is frequency, and K is the steady-state gain inverse matrix of process,For inversion model frequency characteristic Matrix,To normalize inversion model frequency characteristic matrix, subscript i and k respectively represent the i-th row of matrix and the member of kth column Element,
S405, the frequency characteristic of the element of normalization inversion model is analyzed by column to determine controller parameter γk's Value, subscript k expression parameter γkThe kth column element of corresponding normalization inversion model, parameter γkSelection criteria be selection it is one smaller Value, so that by the frequency characteristic of the compensated kth column all elements for normalizing inversion model all in stability region, normalizing The kth column element for changing inversion model compensates according to the following formula
Wherein, j is imaginary unit, and ω is frequency, γkFor corresponding controller parameter,It is special for normalization inversion model frequency Property matrix,For compensated normalization inversion model frequency characteristic matrix, subscript i and k respectively represent matrix the i-th row and The element of kth column,
S406, using obtained compensated normalization inversion model, 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... ωN, wherein ω1=0, the method for recycling compound curve fitting obtains pair The transmission function for the filter answered
Wherein, QikIt (s) is the filter obtained by the i-th row kth column element fitting of compensated normalization inversion model, AikWith BikFor the corresponding parameter value of filter, KikFor the i-th row kth column element of the steady-state gain inverse matrix of process, s is Laplce Operator, parameter are sought according to following compound curve approximating method:
Wherein, Qik(jωm) it is the i-th row kth column element, ω is taken in frequency on frequency characteristicmWhen corresponding plural number, | Qik(j ωm) | it is the modulus value for seeking the plural number, Re (Qik(jωm)) it is to seek the real, Im (Qik(jωm)) it is to seek this to answer Several imaginary parts, N are the number for the Frequency point chosen, and a, b, c, d are intermediate variable,
The filter that S5, the transfer function model obtained according to S3 step and S4 step obtain according to given robustness and moves State performance requirement calculates PID controller parameter, and determines final centralized PID controller；
S6, input is adjusted using the centralized PID controller obtained by S5 step.
2. binary distillation column centerized fusion method according to claim 1, which is characterized in that the storage time t is Period from being added the step signal moment for recognizing each channel, until exporting the steady-state value for reaching new.
3. binary distillation column centerized fusion method according to claim 1, which is characterized in that the specific steps of the S3 Are as follows: each channel is calculated in amplitude h, the sampling period Ts of step signal and the output Y (k) of acquisition target according to the following formula Parameter in transmission function
θ=(PT·P)-1PTZ
Wherein P and Z is the coefficient matrix being made of h, Ts, Y (k) respectively, and θ is the ginseng for identifying the transmission function of each branch Number.
4. binary distillation column centerized fusion method according to claim 1, which is characterized in that the detailed process of S5 is The value of S501, given robustness index Ms, controller adjustment parameter λ1And λ2Seek according to the following formula
S502, sub- PID controller parameter is calculated
Wherein, KpFor proportional gain, KIFor integral gain, KdFor the differential gain, TfFor filter time constant, the tool of these parameters Body acquiring method is as follows:
The centralized PID controller of final band filter can be obtained are as follows:
Wherein, C is total centralized PID controller, C1And C2For the above-mentioned sub- PID controller sought, QikFor the filter sought before Wave device.
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