CN107861387A - A kind of internal thermally coupled air separation column control device based on concentration curve optimized algorithm - Google Patents
A kind of internal thermally coupled air separation column control device based on concentration curve optimized algorithm Download PDFInfo
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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
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The invention discloses a kind of internal thermally coupled air separation column control device based on concentration curve optimized algorithm, including intelligence instrument, controller and the DCS system being directly connected to internal thermally coupled air separation column.The DCS system includes host computer, control station, storage device, fieldbus and data-interface.Control parameter after optimization is passed to control station by the host computer to realize the real-time optimization of control parameter, including concentration curve describing module, setting value modular converter, control parameter real-time optimization module by fieldbus.The control station, by the data-interface being connected with fieldbus, is adjusted according to obtained control parameter to controller.The controller realizes the direct control adjustment to internal thermally coupled air separation column.The present invention can handle the strong nonlinearity feature of internal thermally coupled air separation column well, have efficient on-line operation speed and outstanding energy-saving effect, and with extraordinary servo tracking control effect, interference suppressioning effect.
Description
Technical field
The present invention relates to the field of non-linear control of industrial energy saving control, especially, it is related to internal thermal coupled air separation process
Real-time optimal control device design.
Background technology
Air separation unit is that air is separated, and obtains the device of high-purity industrial gasses such as oxygen, nitrogen, argon, and it is extensive
Applied to the various industrial circles such as oil, chemical industry, metallurgy, electronics, the energy, Aero-Space, food and drink, health care.Gained
To the application in a national national economy of oxygen, nitrogen and argon product it is quite varied.Since " the stone twice of the seventies in last century
Since oily crisis ", energy crisis is deepened, and consumingly requires effective utilization of many field energy.In energy consumption very big air point
From in industry, energy cost account for the 75% of air products price.Then situation as occurring, on the one hand, due to modern work
The development of industry, some large scale industry projects such as steel and iron industry, chemical industry, oil exploitation etc. are required for being carried by large-scale space division device
It is also increasing for air product, demand.On the other hand, energy consumption cost becomes increasing also with energy crisis.Therefore
In view of this situation, the energy efficiency for improving air separation technology seems very urgent.
For internal thermal coupled spatial division technology than conventional spatial division technology energy-conservation more than 40%, energy-saving effect is notable.However, due to interior
Portion's thermal coupling air separation process has the complicated Nonlinear Dynamics such as close coupling, strong ill, strong asymmetry, strong inverse response special
Property, the control strategy design of the tower seems particularly difficult.Traditional PID, internal model control scheme etc. can not meet to require,
Among the process control of internal thermally coupled air separation column, these schemes have been difficult to make air separation process stable.And it is based on linear Identification
The control program of model can only operate near steady operation point, somewhat increases interference magnitude, or setting value Spline smoothing, is
System control quality is then decreased obviously.The nonlinear characteristic of internal thermally coupled air separation column is accurately held, using real-time optimization skill
Art, realize control requirement and the power conservation requirement of internal thermally coupled air separation column simultaneously on this basis, be the production for improving the process
The premise of Control platform, has become a crucial air separation energy saving technology, and tool is of great significance.
The content of the invention
In order to overcome at present at present internal thermally coupled air separation column control device suppress interference performance it is poor, control effect is poor,
Accurate set point tracking, the deficiency that energy-saving effect is not good enough are difficult to, it is an object of the invention to provide one kind to suppress interference energy
Power is good, control effect is good, can realize setting value tracking accurately and rapidly while ensure the internal thermal coupled sky of energy-saving effect
Divide the non-linear controller of tower.
The technical solution adopted for the present invention to solve the technical problems is：
A kind of internal thermally coupled air separation column control device based on concentration curve optimized algorithm, including with internal thermal coupled sky
Intelligence instrument, controller and the DCS system for dividing tower to be directly connected to.The DCS system include host computer, control station, storage device,
Fieldbus and data-interface, storage device, control station and host computer are connected by fieldbus with data-interface.The intelligence
Energy instrument measures relevant parameter by detector unit, pressure detecting element, flow detecting element, and connects with data-interface
Connect.The host computer realizing the real-time optimization of control parameter, including concentration curve describing module, setting value modular converter,
Control parameter real-time optimization module, and the control parameter after optimization is passed into control station by fieldbus.The control station
According to obtained control parameter by the data-interface being connected with fieldbus, controller is adjusted.The controller is real
The now direct control adjustment to internal thermally coupled air separation column.The host computer includes：
1) concentration curve describing module, examined by the detector unit collecting temperature information in intelligence instrument and pressure
Element collection pressure data is surveyed, the data collected are entered horizontal electrical signal by data-interface and changed, and will be examined by fieldbus
Survey signal and be transported to the module, it is as follows to be inferred to the static described function of each column plate concentration profile：
Wherein,For liquid phase i components (oxygen, nitrogen or argon gas) prediction concentrations of t sampling instant jth block column plates,
Si,h (t)、Si,l (t)The respectively sign position of t sampling instants internal thermally coupled air separation column high-pressure tower, lower pressure column concentration curve,
Xi,h_minRepresent the Cmin value of high-pressure tower i concentration of component curves, Xi,h_maxRepresent the maximum of high-pressure tower i concentration of component curves
Concentration value, γi,hRepresent that high-pressure tower i concentration of component curve characterizes the slope of opening position, Xi,l_minRepresent lower pressure column i concentration of component
The Cmin value of curve, Xi,l_maxRepresent the Cmax value of lower pressure column i concentration of component curves, γi,lRepresent lower pressure column i groups
Concentration curve is divided to characterize the slope of opening position, N is total number of plates.
2) setting value modular converter, the concentration curve parameter obtained according to concentration curve describing module, concentration is set
Value is converted to sign position setting value, and conversion formula is as follows：
Wherein,The respectively setting value of the vapour phase light component concentration of tower top and the Oxygen in Liquid component of bottom of towe is dense
The setting value of degree,Respectively high-pressure tower and lower pressure column concentration curve characterize the setting value of position, ki,jFor jth block
The vapor liquid equilibrium coefficient of column plate i components, it can be calculated by Peng-Robinson state equations, final calculation formula is such as
Under：
The fugacity coefficient of gas-liquid two-phase wherein on every layer of column plateIt can be calculated by following formula：
Mixture a and b mixing rule is：
Wherein P is pressure, and T is temperature, and v is molal volume, and R is gas constant, takes 8.3145, xiFor i groups in mixture
Divide the concentration of (oxygen, nitrogen or argon gas),For i1The concentration of component,For i2Concentration of component, aiIt is the gravitation ginseng of i components
Number,It is i1And i2Gravitational parameter between two kinds of components, a are the weighted sums of all components intermolecular attraction parameter, biIt is i components
Van der waals volumes, b is the weighted sum of all components Van der waals volumes, and A serves as reasons the coefficient that (9) formula defines, and B (10) formulas of serving as reasons are fixed
The coefficient of justice, Z is compressibility factor.
3) control parameter real-time optimization module, the module include following three parts：
3.1) model is established, the current time information obtained according to concentration curve describing module and setting value modular converter,
The model of internal thermally coupled air separation column is formed, is made up of below equation：
yi,j(t)=ki,jxi,j(t) (14)
Qj(t)=UovAΔTj(t) (15)
Wherein, yi,j(t) it is the gas phase i concentration of component of t sampling instant jth block column plates, xi,j(t) it is t sampling instant jth blocks
The liquid phase i concentration of component of column plate, zi,j(t) it is the i concentration of component of t sampling instant jth blocks column plate charging, Qj(t) when being sampled for t
Carve the heat output of jth block column plate, UovA is heat transfer coefficient, Δ Tj(t) temperature difference between t sampling instant jth group column plates, λ are latent for vaporization
Heat, Lj(t) it is the liquid phase flow of t sampling instant jth block column plates, Fj(t) it is the feed rate of t sampling instants, Vj(t) sampled for t
The gas phase flow rate of moment jth block column plate, Uj(t) flow, G are produced for the liquid phase of t sampling instant jth block column platesj(t) when being sampled for t
Carve the gas phase extraction flow of jth block column plate, qj(t) it is the hot situation of charging of t sampling instants；Pressure P effect is included in gas-liquid
Coefficient of balance ki,jIn, relation is derived as described in 2), Si,h、Si,lRespectively internal thermally coupled air separation column high-pressure tower and lower pressure column
The sign position of concentration curve, qF(t+1)、Ph(t+1) be respectively t+1 sampling instants the hot situation of charging and high-pressure tower pressure,
It is also the control parameter of control device subsequent time simultaneously.
3.2) optimization problem is standardized, and for standardization, partial expression is designated as into following form：
Wherein Si(t) it is t sampling instant system mode vectors,For leading for t sampling instant system mode vectors
Number, h (t) are constraint equation, and u (t) represents the control parameter to be optimized, qF(t)、Ph(t) be respectively t sampling instants charging
Hot situation and high-pressure tower pressure,For default value,Respectively high-pressure tower and lower pressure column concentration curve characterize position
Setting value, φ (t) is the function of characterization control error and energy consumption.So converted for the real-time optimization can of control parameter
For following optimization problems：
Wherein, J represents object function, while ensures control effect and energy-saving effect, TpRepresent prediction time domain, TcRepresent control
Time domain processed, and Tc≤Tp。
3.3) optimization problem Real-time solution, first will control time domain TcIt is divided into the time segments such as m, variable u is every for control
It is steady state value in the period of individual decile.Gradient information can obtain with the following method：
Construct Hamiltonian H (t)：
H (t)=φ (t)+vTh(t) (24)
Wherein v is Lagrange multiplier, can be obtained,
And then obtain the expression formula of gradient formula：
Given initial control variable u0(t), initial step length α0, iteration cut-off condition ε and primary iteration count k=0,
The real-time optimization to control parameter is completed by following steps：
3.3.1) calculate
3.3.2) if k=0, the 3rd step is jumped to；Otherwise, by ukObject function J is substituted into, if | Jk-Jk+1|≤ε, stop changing
In generation, simultaneously exports ukIf | Jk-Jk+1| ＞ ε, then calculateWherein sk-1=uk-uk-1, yk-1=gk-gk-1；
3.3.3) calculate uk+1=uk+αk·(-gk)；
3.3.4) increase iteration count k=k+1, and return to the 1st step and carry out next iteration.
Wherein subscript k represents iteration count, can real-time optimal control parameter by above step
As a kind of preferable scheme：Described host computer is additionally operable to set the vapour phase nitrogen concentration of component and lower pressure column of high pressure
Oxygen in Liquid concentration of component setting valueAnd the control variable u that setting is initial0(t), initial step length α0, iteration
The control parameter for lower a period of time that cut-off condition ε, display current time concentration measurement and real-time optimization go out, and by after optimization
Control parameter control station is passed to by fieldbus, control station is adjusted by data-interface to controller again, so as to
Complete the control action of control device.Information above is also passed to storage dress by described host computer by fieldbus simultaneously
Put, facilitate operating personnel to consult historical record, improve production Control platform.
The present invention technical concept be：Concentration curve characteristic in internal thermal coupled air separation process is accurately described,
The non-linear dynamic characteristic of internal thermally coupled air separation column is held in success exactly, is joined by application real-time optimization algorithm optimal control
Number, overcoming existing control device to suppress, interference performance is poor, control effect is poor, is difficult to accurate set point tracking, energy-conservation effect
The deficiency that fruit is not good enough, so as to design, the suppression interference performance of internal thermal coupled air separation process is good, control effect is good, Ke Yishi
Now setting value accurately and rapidly tracks while ensures the non-linear controller of energy-saving effect.
Beneficial effects of the present invention are mainly manifested in：1. nonlinear Control scheme is established on high precision nonlinear model basis
On, interference effect can be suppressed in time；2. control program has preferably handled coupled problem, setting can be rapidly and accurately tracked
Value changes.3. by real-time optimization algorithm, while it ensure that the energy-saving effect of internal thermally coupled air separation column.
Brief description of the drawings
Fig. 1 is the structure chart of the non-linear controller of internal thermally coupled air separation column proposed by the invention.
Fig. 2 is the schematic diagram of host computer implementation method.
Embodiment
The present invention is illustrated below according to accompanying drawing.
Referring to Figures 1 and 2, a kind of internal thermally coupled air separation column control device based on concentration curve optimized algorithm, including
Intelligence instrument 2, controller 8 and the DCS system being directly connected to internal thermally coupled air separation column 1.The DCS system includes host computer
6th, control station 5, storage device 4, fieldbus 7 and data-interface 3, storage device 4, control station 5 and host computer 6 pass through live total
Line 7 is connected with data-interface 3.The intelligence instrument 2 passes through detector unit, pressure detecting element, flow detecting element
Relevant parameter is measured, and is connected with data-interface 3.The host computer 6 is realizing the real-time optimization of control parameter, including concentration
Curve describing module 9, setting value modular converter 10, control parameter real-time optimization module 11, and the control parameter after optimization is led to
Cross fieldbus 7 and pass to control station 5.The control station 5 passes through the number that is connected with fieldbus 7 according to obtained control parameter
According to interface 3, controller 8 is adjusted.The controller 8 realizes the direct control adjustment to internal thermally coupled air separation column 1.Institute
Stating host computer 6 includes：
Concentration curve describing module 9, examined by the detector unit collecting temperature information in intelligence instrument 2 and pressure
Element collection pressure data is surveyed, the data collected are entered horizontal electrical signal by data-interface 3 and changed, and will by fieldbus 7
Detection signal is transported to the module, as follows to be inferred to the static described function of each column plate concentration profile：
1) wherein,For liquid phase i components (oxygen, nitrogen or argon gas) prediction concentrations of t sampling instant jth block column plates, Si,h
(t)、Si,l(t) it is respectively t sampling instant internal thermally coupled air separation columns high-pressure tower, the sign position of lower pressure column concentration curve,
Xi,h_minRepresent the Cmin value of high-pressure tower i concentration of component curves, Xi,h_maxRepresent the maximum of high-pressure tower i concentration of component curves
Concentration value, γ i,H represents that high-pressure tower i concentration of component curve characterizes the slope of opening position, Xi,l_minRepresent lower pressure column i concentration of component
The Cmin value of curve, Xi,l_maxRepresent the Cmax value of lower pressure column i concentration of component curves, γ i,L represents lower pressure column i groups
Concentration curve is divided to characterize the slope of opening position, N is total number of plates.
Setting value modular converter 10, the concentration curve parameter obtained according to concentration curve describing module 9, concentration is set
Value is converted to sign position setting value, and conversion formula is as follows：
Wherein,The respectively setting value of the vapour phase light component concentration of tower top and the Oxygen in Liquid component of bottom of towe is dense
The setting value of degree,Respectively high-pressure tower and lower pressure column concentration curve characterize the setting value of position, ki,jFor jth block
The vapor liquid equilibrium coefficient of column plate i components, it can be calculated by Peng-Robinson state equations, final calculation formula is such as
Under：
The fugacity coefficient of gas-liquid two-phase wherein on every layer of column plateIt can be calculated by following formula：
Mixture a and b mixing rule is：
Wherein P is pressure, and T is temperature, and v is molal volume, and R is gas constant, takes 8.3145, xiFor i groups in mixture
Divide the concentration of (oxygen, nitrogen or argon gas),For i1The concentration of component,For i2Concentration of component, aiIt is the gravitation ginseng of i components
Number,It is i1And i2Gravitational parameter between two kinds of components, a are the weighted sums of all components intermolecular attraction parameter, biIt is i components
Van der waals volumes, b is the weighted sum of all components Van der waals volumes, and A serves as reasons the coefficient that (9) formula defines, and B (10) formulas of serving as reasons are fixed
The coefficient of justice, Z is compressibility factor.
3) control parameter real-time optimization module 11, the module include following three parts：
3.1) model is established, and the current time obtained according to concentration curve describing module 9 and setting value modular converter 10 believes
Breath, forms the model of internal thermally coupled air separation column, is made up of below equation：
yi,j(t)=ki,jxi,j(t) (14)
Qj(t)=UovAΔTj(t) (15)
Wherein, yi,j(t) it is the gas phase i concentration of component of t sampling instant jth block column plates, xi,j(t) it is t sampling instant jth blocks
The liquid phase i concentration of component of column plate, zi,j(t) it is the i concentration of component of t sampling instant jth blocks column plate charging, Qj(t) when being sampled for t
Carve the heat output of jth block column plate, UovA is heat transfer coefficient, Lj(t) it is the liquid phase flow rate of t sampling instant jth block column plates, λ is vaporization
Latent heat, Fj(t) it is the feed rate of t sampling instants, Vj(t) it is the gas phase flow rate of t sampling instant jth block column plates, Uj(t) adopted for t
The liquid phase extraction flow of sample moment jth block column plate, Gj(t) flow, q are produced for the gas phase of t sampling instant jth block column platesj(t) it is t
The hot situation of charging of sampling instant；Pressure P effect is included in vapor liquid equilibrium coefficient ki,jIn, relation is derived as described in 2),
Si,h、Si,lThe respectively sign position of internal thermally coupled air separation column high-pressure tower and lower pressure column concentration curve, qF(t+1)、Ph(t+1)
The hot situation of charging and high-pressure tower pressure of respectively t+1 sampling instants, while be also the control ginseng of control device subsequent time
Number.
3.2) optimization problem is standardized, and for standardization, partial expression is designated as into following form：
Wherein Si(t) it is t sampling instant system mode vectors,For leading for t sampling instant system mode vectors
Number, h (t) are constraint equation, and u (t) represents the control parameter to be optimized, qF(t)、Ph(t) be respectively t sampling instants charging
Hot situation and high-pressure tower pressure,For default value,Respectively high-pressure tower and lower pressure column concentration curve characterize position
Setting value, φ (t) is the function of characterization control error and energy consumption.So converted for the real-time optimization can of control parameter
For following optimization problems：
Wherein, J represents object function, while ensures control effect and energy-saving effect, TpRepresent prediction time domain, TcRepresent control
Time domain processed, and Tc≤Tp。
3.3) optimization problem Real-time solution, first will control time domain TcIt is divided into the time segments such as m, variable u is every for control
It is steady state value in the period of individual decile.Gradient information can obtain with the following method：
Construct Hamiltonian H (t)：
H (t)=φ (t)+vTh(t) (24)
Wherein v is Lagrange multiplier, can be obtained：
And then obtain the expression formula of gradient formula：
Given initial control variable u0(t), initial step length α0, iteration cut-off condition ε and primary iteration count k=0,
The real-time optimization to control parameter is completed by following steps：
3.3.1) calculate
3.3.2) if k=0, the 3rd step is jumped to；Otherwise, by ukObject function J is substituted into, if | Jk-Jk+1|≤ε, stop changing
In generation, simultaneously exports ukIf | Jk-Jk+1| ＞ ε, then calculateWherein sk-1=uk-uk-1, yk-1=gk-gk-1；
3.3.3) calculate uk+1=uk+αk·(-gk)；
3.3.4) increase iteration count k=k+1, and return to the 1st step and carry out next iteration.
Wherein subscript k represents iteration count, can real-time optimal control parameter by above step
Described host computer 6 is additionally operable to set the vapour phase nitrogen concentration of component of high pressure and the Oxygen in Liquid concentration of component of lower pressure column
Setting valueAnd the control variable u that setting is initial0(t), initial step length α0, iteration cut-off condition ε, display is current
The control parameter for lower a period of time that moment concentration measurement and real-time optimization go out, and the control parameter after optimization is passed through into scene
Bus 7 passes to control station 5, and control station 5 is adjusted by data-interface 3 to controller 8 again, so as to complete control device
Control action.Information above is also passed to storage device 4 by described host computer 6 by fieldbus 7 simultaneously, facilitates operator
Member consults historical record, improves production Control platform.
Above-described embodiment is used for illustrating the present invention, rather than limits the invention, the present invention spirit and
In scope of the claims, to any modifications and changes of the invention made, protection scope of the present invention is both fallen within.
Claims (1)
1. a kind of internal thermally coupled air separation column control device based on concentration curve optimized algorithm, including with internal thermal coupled space division
Intelligence instrument, controller and the DCS system that tower is directly connected to.The DCS system includes host computer, control station, storage device, existing
Field bus and data-interface, storage device, control station and host computer are connected by fieldbus with data-interface.The intelligence
Instrument is measured relevant parameter, and is connected with data-interface by detector unit, pressure detecting element, flow detecting element.
The host computer is realizing the real-time optimization of control parameter, including concentration curve describing module, setting value modular converter, control
Parameter real-time optimization module, and the control parameter after optimization is passed into control station by fieldbus.The control station according to
Obtained control parameter is adjusted by the data-interface being connected with fieldbus to controller.The controller realization pair
The direct control adjustment of internal thermally coupled air separation column.The host computer includes：
1) concentration curve static state describing module, examined by the detector unit collecting temperature information in intelligence instrument and pressure
Element collection pressure data is surveyed, the data collected are entered horizontal electrical signal by data-interface and changed, and will be examined by fieldbus
Survey signal and be transported to the module, it is as follows to be inferred to the static described function of each column plate concentration profile：
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Wherein,For liquid phase i components (oxygen, nitrogen or argon gas) prediction concentrations of t sampling instant jth block column plates, Si,h
(t)、Si,l(t) it is respectively t sampling instant internal thermally coupled air separation columns high-pressure tower, the sign position of lower pressure column concentration curve,
Xi,h_minRepresent the Cmin value of high-pressure tower i concentration of component curves, Xi,h_maxRepresent the maximum of high-pressure tower i concentration of component curves
Concentration value, γi,hRepresent that high-pressure tower i concentration of component curve characterizes the slope of opening position, Xi,l_minRepresent lower pressure column i concentration of component
The Cmin value of curve, Xi,l_maxRepresent the Cmax value of lower pressure column i concentration of component curves, γi,lRepresent lower pressure column i groups
Concentration curve is divided to characterize the slope of opening position, N is total number of plates.
2) setting value modular converter, the concentration curve parameter obtained according to concentration curve describing module, concentration set point is turned
Sign position setting value is changed to, conversion formula is as follows：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mn>1</mn>
</mrow>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>X</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>h</mi>
<mo>_</mo>
<mi>min</mi>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>X</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>h</mi>
<mo>_</mo>
<mi>max</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>X</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>h</mi>
<mo>_</mo>
<mi>min</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>&gamma;</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>h</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<msup>
<mi>S</mi>
<mo>*</mo>
</msup>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>h</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>y</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mn>1</mn>
</mrow>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>k</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>x</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mn>1</mn>
</mrow>
<mo>*</mo>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<msub>
<mi>O</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>n</mi>
</mrow>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>X</mi>
<mrow>
<msub>
<mi>O</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>l</mi>
<mo>_</mo>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>X</mi>
<mrow>
<msub>
<mi>O</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>l</mi>
<mo>_</mo>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>X</mi>
<mrow>
<msub>
<mi>O</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>l</mi>
<mo>_</mo>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>&gamma;</mi>
<mrow>
<msub>
<mi>O</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>l</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<msub>
<msup>
<mi>S</mi>
<mo>*</mo>
</msup>
<mrow>
<msub>
<mi>O</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mi>l</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,The respectively Oxygen in Liquid concentration of component of the setting value of the vapour phase light component concentration of tower top and bottom of towe
Setting value,Respectively high-pressure tower and lower pressure column concentration curve characterize the setting value of position, ki,jFor jth block column plate i
The vapor liquid equilibrium coefficient of component, it can be calculated by Peng-Robinson state equations, final calculation formula is as follows：
<mrow>
<msub>
<mi>k</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>&phi;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mi>L</mi>
</msubsup>
<msubsup>
<mi>&phi;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mi>V</mi>
</msubsup>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
The fugacity coefficient of gas-liquid two-phase wherein on every layer of column plateIt can be calculated by following formula：
<mrow>
<msub>
<mi>ln&phi;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<mi>b</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mi>Z</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mi>Z</mi>
<mo>-</mo>
<mi>B</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mfrac>
<mi>A</mi>
<mrow>
<mn>2</mn>
<msqrt>
<mn>2</mn>
</msqrt>
<mi>B</mi>
</mrow>
</mfrac>
<mo>&times;</mo>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>&Sigma;</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
</mrow>
<mi>a</mi>
</mfrac>
<mo>-</mo>
<mfrac>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<mi>b</mi>
</mfrac>
<mo>&rsqb;</mo>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>Z</mi>
<mo>+</mo>
<mn>2.414</mn>
<mi>B</mi>
</mrow>
<mrow>
<mi>Z</mi>
<mo>-</mo>
<mn>0.414</mn>
<mi>B</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Mixture a and b mixing rule is：
<mrow>
<mi>a</mi>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<msub>
<mi>i</mi>
<mn>1</mn>
</msub>
</munder>
<munder>
<mo>&Sigma;</mo>
<msub>
<mi>i</mi>
<mn>2</mn>
</msub>
</munder>
<msub>
<mi>x</mi>
<msub>
<mi>i</mi>
<mn>1</mn>
</msub>
</msub>
<msub>
<mi>x</mi>
<msub>
<mi>i</mi>
<mn>2</mn>
</msub>
</msub>
<msub>
<mi>a</mi>
<mrow>
<msub>
<mi>i</mi>
<mn>1</mn>
</msub>
<msub>
<mi>i</mi>
<mn>2</mn>
</msub>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>b</mi>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mi>i</mi>
</munder>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>A</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>a</mi>
<mi>P</mi>
</mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>B</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>b</mi>
<mi>P</mi>
</mrow>
<mrow>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>Z</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>P</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein P is pressure, and T is temperature, and v is molal volume, and R is gas constant, takes 8.3145, xiFor i components (oxygen in mixture
Gas, nitrogen or argon gas) concentration,For i1The concentration of component,For i2Concentration of component, aiIt is the gravitational parameter of i components,
It is i1And i2Gravitational parameter between two kinds of components, a are the weighted sums of all components intermolecular attraction parameter, biIt is the model moral of i components
Magnificent volume, b are the weighted sum of all components Van der waals volumes, and A serves as reasons the coefficient that (9) formula defines, and what B served as reasons that (10) formula defines is
Number, Z is compressibility factor.
3) control parameter real-time optimization module, the module include following three parts：
3.1) model is established, the current time information obtained according to concentration curve describing module and setting value modular converter, is formed
The model of internal thermally coupled air separation column, is made up of below equation：
<mrow>
<msub>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>h</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>V</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>F</mi>
<mi>j</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<msub>
<mi>z</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>-</mo>
<msub>
<mi>G</mi>
<mi>j</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<msub>
<mi>y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>-</mo>
<msub>
<mi>U</mi>
<mi>j</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>H</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>l</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>L</mi>
<mi>N</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>F</mi>
<mi>j</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<msub>
<mi>z</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>-</mo>
<msub>
<mi>G</mi>
<mi>j</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<msub>
<mi>y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>-</mo>
<msub>
<mi>U</mi>
<mi>j</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>H</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>N</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
yi,j(t)=ki,jxi,j(t) (14)
Qj(t)=UovAΔTj(t) (15)
<mrow>
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Wherein, yi,j(t) it is the gas phase i concentration of component of t sampling instant jth block column plates, xi,j(t) it is t sampling instant jth block column plates
Liquid phase i concentration of component, zi,j(t) it is the i concentration of component of t sampling instant jth blocks column plate charging, Qj(t) it is t sampling instant jth
The heat output of block column plate, UovA is heat transfer coefficient, Δ Tj(t) temperature difference between t sampling instant jth group column plates, λ are the latent heat of vaporization, Lj
(t) it is the liquid phase flow of t sampling instant jth block column plates, Fj(t) it is the feed rate of t sampling instant jth block column plates, Vj(t) it is t
The gas phase flow rate of sampling instant jth block column plate, Uj(t) flow, G are produced for the liquid phase of t sampling instant jth block column platesj(t) adopted for t
The gas phase extraction flow of sample moment jth block column plate, qj(t) it is the hot situation of charging of t sampling instants；Pressure P effect is included in
Vapor liquid equilibrium coefficient ki,jIn, relation is derived as described in 2), Si,h、Si,lRespectively internal thermally coupled air separation column high-pressure tower and low
Press the sign position of tower concentration curve, qF(t+1)、Ph(t+1) be respectively t+1 sampling instants the hot situation of charging and high-pressure tower
Pressure, while be also the control parameter of control device subsequent time.
3.2) optimization problem standardizes, and for standardization, defines new expression formula and is designated as following form：
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Wherein Si(t) it is t sampling instant system mode vectors,For the derivative of t sampling instant system mode vectors, h
(t) it is constraint equation, u (t) represents the control parameter to be optimized, qF(t)、Ph(t) be respectively t sampling instants the hot shape of charging
Condition and high-pressure tower pressure,For default value,Respectively high-pressure tower and lower pressure column concentration curve characterize setting for position
Definite value, φ (t) are the function of characterization control error and energy consumption.Real-time optimization can so for control parameter be converted into
Lower optimization problems：
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Wherein, J represents object function, while ensures control effect and energy-saving effect, TpRepresent prediction time domain, TcWhen representing control
Domain, and Tc≤Tp。
3.3) optimization problem Real-time solution, first will control time domain TcIt is divided into the time segments such as m, variable u is in each decile for control
Period in be steady state value.Gradient information can obtain with the following method：
Construct Hamiltonian H (t)：
H (t)=φ (t)+vTh(t) (24)
Wherein v is Lagrange multiplier, can be obtained：
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And then obtain gradient formula g (u) expression formula：
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Given initial control variable u0(t), initial step length α0, iteration cut-off condition ε and primary iteration count k=0, pass through
Following steps complete the real-time optimization to control parameter：
3.3.1) calculate
3.3.2) if k=0, the 3rd step is jumped to；Otherwise, by ukObject function J is substituted into, if | Jk-Jk+1|≤ε, stop iteration simultaneously
Export ukIf | Jk-Jk+1| ＞ ε, then calculateWherein sk-1=uk-uk-1, yk-1=gk-gk-1；
3.3.3) calculate uk+1=uk+αk·(-gk)；
3.3.4) increase iteration count k=k+1, and return to the 1st step and carry out next iteration.
Wherein subscript k represents iteration count, can real-time optimal control parameter by above step
3.4) according to above-mentioned internal thermally coupled air separation column control device, it is characterised in that it is high that described host computer is additionally operable to setting
The setting value of the vapour phase nitrogen concentration of component of pressure and the Oxygen in Liquid concentration of component of lower pressure columnAnd the control that setting is initial
Variable u processed0(t), initial step length α0, iteration cut-off condition ε, it is next to show that current time concentration measurement and real-time optimization go out
The control parameter of section time, and the control parameter after optimization is passed into control station by fieldbus, control station passes through number again
Controller is adjusted according to interface, so as to complete the control action of control device.Described host computer is also believed by more than simultaneously
Breath passes to storage device by fieldbus, facilitates operating personnel to consult historical record, improves production Control platform.
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