CN106040676B - A kind of rectifying column pipeline auto-flushing method - Google Patents
A kind of rectifying column pipeline auto-flushing method Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B08—CLEANING
- B08B—CLEANING IN GENERAL; PREVENTION OF FOULING IN GENERAL
- B08B9/00—Cleaning hollow articles by methods or apparatus specially adapted thereto
- B08B9/02—Cleaning pipes or tubes or systems of pipes or tubes
- B08B9/027—Cleaning the internal surfaces; Removal of blockages
- B08B9/032—Cleaning the internal surfaces; Removal of blockages by the mechanical action of a moving fluid, e.g. by flushing
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B08—CLEANING
- B08B—CLEANING IN GENERAL; PREVENTION OF FOULING IN GENERAL
- B08B9/00—Cleaning hollow articles by methods or apparatus specially adapted thereto
- B08B9/02—Cleaning pipes or tubes or systems of pipes or tubes
- B08B9/027—Cleaning the internal surfaces; Removal of blockages
- B08B9/032—Cleaning the internal surfaces; Removal of blockages by the mechanical action of a moving fluid, e.g. by flushing
- B08B9/0321—Cleaning the internal surfaces; Removal of blockages by the mechanical action of a moving fluid, e.g. by flushing using pressurised, pulsating or purging fluid
- B08B9/0325—Control mechanisms therefor
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D9/00—Level control, e.g. controlling quantity of material stored in vessel
- G05D9/12—Level control, e.g. controlling quantity of material stored in vessel characterised by the use of electric means
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B08—CLEANING
- B08B—CLEANING IN GENERAL; PREVENTION OF FOULING IN GENERAL
- B08B2209/00—Details of machines or methods for cleaning hollow articles
- B08B2209/02—Details of apparatuses or methods for cleaning pipes or tubes
- B08B2209/027—Details of apparatuses or methods for cleaning pipes or tubes for cleaning the internal surfaces
- B08B2209/032—Details of apparatuses or methods for cleaning pipes or tubes for cleaning the internal surfaces by the mechanical action of a moving fluid
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Abstract
The present invention relates to a kind of rectifying column pipeline auto-flushing method, belong to chemical oil refining's production flow line technical field.This method carries out kinematic function compensation on the basis of traditional liquid level-flow serials control, to bottom of towe liquid level variable, that is, takes the main interference volume of liquid level --- and the variable quantity of tower inlet amount is as feed-forward signal.Feed variation amount is preset according to technological requirement, using stabilizer bottom liquid level as target, using the method for kinematic function compensation, effective dynamic control is carried out to bottom of towe liquid level, bottom of towe liquid level remains to stable operation in the case of technique adjustment inlet amount.This method can realize the steady control to rectifying tower bottom liquid level, greatly reduce influence of the inlet amount change to the normal production of rectifying column, while reduce influence of the model mismatch to kinematic function compensating action, increase filtration module, the robustness of strengthening system.
Description
Technical Field
The invention relates to an automatic flushing method for a rectifying tower pipeline, and belongs to the technical field of chemical oil refining production pipelines.
Background
In the chemical oil refining production, the rectifying tower is a key rectifying operation device, and whether the rectifying tower runs stably or not is related to the purity of a target product. Wherein, the liquid level at the bottom of the tower is directly related to the material balance and the energy balance of the whole rectifying tower, when the liquid level of the tower is too high, the full kettle can be caused, and when the liquid level is too low, the empty kettle can be caused. In order to maintain proper production of the column equipment, the bottom liquid level needs to be controlled within a certain safe operating range.
The tower feeding pipeline of some rectifying towers is easy to block the subsequent process pipeline because the feeding raw materials contain heavy oil components, and the generally adopted method is to manually and periodically carry out the operations of increasing, maintaining and decreasing the tower feeding to flush the downstream pipeline, but the tower bottom liquid level can be greatly fluctuated. However, the liquid level at the bottom of the tower is usually adjusted by the discharge amount at the bottom of the tower, and a liquid level-flow cascade control scheme is adopted, so that the problem of time lag exists in the adjusting mode, and the liquid level at the bottom of the tower is not adjusted timely enough, which is a main reason for large fluctuation of the liquid level. For some tower plants where the level of control is high, large fluctuations in the liquid level at the bottom of the tower must be taken into account.
At present, the manual quantity increasing, maintaining and reducing are mostly adopted in the method for flushing the rectifying tower pipeline, and the effect of flushing the downstream pipeline is achieved.
The manual washing method adopted in the prior art easily causes the large-amplitude fluctuation of the liquid level at the bottom of the tower, the liquid level at the bottom of the tower is usually adjusted by the discharge amount at the bottom of the tower, and a liquid level-flow cascade control scheme is adopted, so that the adjustment mode has the problem of time lag, the liquid level at the bottom of the tower is not timely adjusted, the main reason for the large-amplitude fluctuation of the liquid level at the bottom of the tower is caused, and the large-amplitude fluctuation of the liquid level at the bottom of the tower must be emphasized for certain tower.
Disclosure of Invention
The object of the present invention is to propose a novel method for flushing a pipeline which ensures stable operation of a rectifying column. The method is based on the traditional liquid level-flow cascade control, dynamic function compensation is carried out on the liquid level variable of the tower bottom, namely, the main liquid level interference quantity, namely the variable quantity of the tower feeding quantity is adopted as a feedforward signal. The feeding variable quantity is preset according to the process requirements, the tower bottom liquid level is stabilized as a target, a dynamic function compensation method is adopted, the tower bottom liquid level is effectively and dynamically controlled, and the tower bottom liquid level can still stably run under the condition that the feeding quantity is adjusted through the process.
In order to achieve the purpose, the technical scheme adopted by the invention is an automatic flushing method for a rectifying tower pipeline, so that the flushing of a downstream pipeline of a rectifying tower is realized, the set value of the feeding amount of the rectifying tower is adjusted according to the process requirement, dynamic function compensation is added on the basis of the conventional liquid level-flow cascade control, the stable control of the liquid level at the bottom of the rectifying tower is realized, and the influence of the feeding amount change on the normal production of the rectifying tower is reduced or eliminated.
As shown in figure 1, the flow chart of the rectifying tower of the method is shown, the feeding amount of the rectifying tower is FIC1001, the given value FIC001.SV is adjusted according to the process requirement, and the liquid level LIC001 at the bottom of the tower and the discharging amount FIC002 realize cascade control. On the basis, the dynamic function compensation is carried out on the cascade control of the liquid level at the bottom of the tower according to the adjustment change of the feeding quantity, and the block diagram of a control loop is shown as figure 2.
The liquid level at the bottom of the rectifying tower is mainly disturbed into the change of the feeding amount, and when the feeding amount changes according to the preset value, the interference on the liquid level at the bottom of the tower is great. In the original control scheme, the controller does an adjusting action only after the liquid level is detected to change, so that the original liquid level-flow cascade control scheme has lag in adjustment and is not ideal in control effect. To this end, the feed quantity variation Δ PV is increased as a dynamic function to compensate the signal. When the feeding amount changes, the system detects the change of the feeding amount in each scanning period, the feeding variable quantity is sent to a compensation operation module for operation processing, the compensation operation is output to the output end of a liquid level controller after being filtered and is used as the increment of a set value FIC002.SV of a discharging flow controller, dynamic function compensation is carried out on the cascade control of the liquid level-flow at the bottom of the rectifying tower, thus, before the liquid level at the bottom of the rectifying tower is influenced by the change of the feeding amount, the liquid level at the bottom of the rectifying tower is changed according to the rule of a function f (t) according to the feeding amount, the discharging amount is subjected to dynamic function compensation adjustment, and the effect of stabilizing the.
The dynamic function compensation scheme is as follows: by detecting the variation of the feeding amount and according to the dynamic balance principle of the liquid level variation at the bottom of the tower, the discharging variation delta PV corresponding to the feeding variation delta PV(s) is calculated1(s) the relationship is as follows:
wherein, Δ PV1(s) Ralsberg transform for variation in discharge, Δ PV(s) Ralsberg transform for variation in feed, GP(s) is the transfer function of the main object liquid level, GPD(s) is the interference channel transfer function.
Input-output relationship by the secondary loop:
wherein G isC1(s) is the secondary loop flow controller transfer function, GP1(s) is the transfer function of the secondary loop flow object, and Δ SV(s) is the Laplace transformation of the discharge flow set value variation.
And further deducing the set value variable quantity delta SV(s) of the discharge flow, as shown in the formula (3):
the obtained dynamic function compensation operation module is as follows:
wherein,is a transfer function of the variation of the bottom discharge flow calculated theoretically.
The object model to be identified by the dynamic function compensation operation module obtained from the above equation (4) includes: secondary circuit flow object GP1(s) main circuit level object GP(s) and interference channel object GPD(s)。
In practical application, model errors, namely model mismatch, inevitably exist in mathematical model identification of an object, in order to reduce the influence of the model mismatch on the compensation effect of a dynamic function and enhance the robustness of a system, a first-order filtering module is added behind a compensation operation module:
where α is the adjustable filter constant, Gf(s) is the filter module transfer function. The final compensation operation module is obtained as follows:
wherein G isFCAnd(s) is a transfer function of the change of the bottom discharge flow rate of the actual output, namely the transfer function of the feedforward controller.
Compared with the prior art, the invention has the following beneficial effects.
(1) On the basis of the original method for flushing the pipeline of the rectifying tower, dynamic function compensation is added to the scheme for controlling the liquid level-flow cascade at the bottom of the tower, and when the feeding amount changes according to a preset function, the dynamic function compensation control is carried out on the liquid level-flow cascade at the bottom of the tower, so that the stable control on the liquid level at the bottom of the rectifying tower is realized, and the influence of the change of the feeding amount on the normal production of the rectifying tower is greatly reduced.
(2) In the scheme of the invention, in order to reduce the influence of the model mismatch on the dynamic function compensation effect, a filtering module is added, and the robustness of the system is enhanced.
Drawings
FIG. 1 is a flow chart of the control of the liquid level at the bottom of a rectifying tower.
FIG. 2 is a block diagram of a rectifying tower bottom liquid level control loop.
In the figure:
GC(s) transfer function of liquid level controller
GP(s) transfer function of main loop level object
GC1(s) transfer function of secondary loop flow controller
GP1(s) transfer function of secondary loop flow object
GFC(s) transfer function of feedforward controller
GPD(s) interference channel transfer function
SV(s) Ralsh transformation of set value of liquid level
L(s) Ralsh transform of liquid level output
Delta PV(s) Rad's transformation of the interference
Delta SV(s) Ralski transformation of feed forward compensation
Detailed Description
In order to verify the effectiveness of the scheme, simulation verification of the scheme is performed in the Yanghe CS3000 system in combination with an industrial actual production case.
In the ethylene industrial production, in order to prevent the discharge pipeline of the light fuel oil stripping tower in the quenching section from being blocked by the downstream heavy oil, a means of periodically increasing, maintaining and decreasing the feeding quantity of the light fuel oil tower is generally adopted to flush the downstream pipeline, but the liquid level at the bottom of the light fuel oil tower is greatly fluctuated, the liquid level at the bottom of the light fuel oil tower is generally regulated by adopting a liquid level-flow cascade control scheme through controlling the discharge quantity, and the regulation speed is often too slow due to the hysteresis problem of a liquid level object. Aiming at the problem, the dynamic function compensation control scheme is adopted for control.
Before implementation of the solution, as shown in fig. 2, the object models required for the dynamic function compensation solution are identified.
The secondary loop flow controller parameters are: the proportional coefficient P is 100, the integral time I is 10 and the differential time D is 0, thus obtaining the productFilter parameter α being 2, i.e.The feedforward controller obtained according to the formula (6) is:
and (3) carrying out simulation according to the provided model parameters and controller parameters, comparing the original control scheme with the scheme of the invention, increasing the feeding flow from 40t/h to 50t/h, changing according to a ramp function at the rate of 900t/h, keeping for 2 minutes after the feeding flow is increased to 50t/h, and then reducing the flow at the rate of 900 t/h.
Through example simulation, when the feeding amount is controlled according to the traditional liquid level-flow cascade control scheme, the liquid level fluctuation range is SV +/-6.14% (SV is a set value); the liquid level fluctuation range of the scheme of the invention is SV +/-0.3%. Therefore, after the dynamic function compensation scheme is added on the basis of the original scheme, the influence on the liquid level of the tower is greatly reduced when the lifting and lowering amount operation of the tower feeding is carried out, and the effect is obvious.
Claims (2)
1. An automatic flushing method for a rectifying tower pipeline is characterized by comprising the following steps: the liquid level at the bottom of the rectifying tower is mainly disturbed into the change of the feeding amount, and when the feeding amount changes according to the preset value, the interference on the liquid level at the bottom of the rectifying tower is great; in the original control scheme, the controller does an adjusting action only after the liquid level is detected to change, so that the original liquid level-flow cascade control scheme has lag in adjustment and has an unsatisfactory control effect; for this purpose, the variation Δ PV of the feed quantity is increased as a dynamic function compensation signal; when the feeding amount changes, the system detects the change of the feeding amount in each scanning period, the feeding variable quantity is sent to a compensation operation module for operation processing, the compensation operation is filtered and then output to the output end of a liquid level controller to be used as the increment of a set value FIC002.SV of a discharging flow controller, and dynamic function compensation is carried out on the cascade control of the liquid level-flow at the bottom of the rectifying tower, so that before the liquid level at the bottom of the rectifying tower is influenced by the change of the feeding amount, the liquid level at the bottom of the rectifying tower is changed according to the rule of a function f (t) according to the feeding amount, the discharging amount is subjected to dynamic function compensation adjustment, and the effect of stabilizing;
the dynamic function compensation scheme is as follows: by detecting the variation of the feeding amount and according to the dynamic balance principle of the liquid level variation at the bottom of the tower, the discharging variation delta PV corresponding to the feeding variation delta PV(s) is calculated1(s) the relationship is as follows:
<mrow> <msub> <mi>&Delta;PV</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>&Delta;</mi> <mi>P</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
wherein, Δ PV1(s) Ralsberg transform for variation in discharge, Δ PV(s) Ralsberg transform for variation in feed, GP(s) is the transfer function of the main object liquid level, GPD(s) is an interference channel transfer function;
input-output relationship by the secondary loop:
<mrow> <msub> <mi>&Delta;PV</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>&Delta;</mi> <mi>S</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
wherein G isC1(s) is the secondary loop flow controller transfer function, GP1(s) is a transfer function of a flow object of the secondary loop, and delta SV(s) is Laplace transformation of the variable quantity of a set value of the discharge flow;
and further deducing the set value variable quantity delta SV(s) of the discharge flow, as shown in the formula (3):
<mrow> <mi>&Delta;</mi> <mi>S</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mi>&Delta;PV</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mfrac> <mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>&Delta;</mi> <mi>P</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
the obtained dynamic function compensation operation module is as follows:
<mrow> <msub> <mover> <mi>G</mi> <mo>~</mo> </mover> <mrow> <mi>F</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mfrac> <mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
wherein,a transfer function of the variation of the discharge flow of the tower bottom calculated in theory;
the object model to be identified by the dynamic function compensation operation module obtained from the above equation (4) includes: secondary circuit flow object GP1(s) main circuit level object GP(s) and interference channel object GPD(s)。
2. The automatic flushing method for the rectifying tower pipeline according to claim 1, characterized in that: in practical application, model errors, namely model mismatch, inevitably exist in mathematical model identification of an object, in order to reduce the influence of the model mismatch on the compensation effect of a dynamic function and enhance the robustness of a system, a first-order filtering module is added behind a compensation operation module:
<mrow> <msub> <mi>G</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mi>&alpha;</mi> <mi>s</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
where α is the adjustable filter constant, Gf(s) is the filter module transfer function; the final compensation operation module is obtained as follows:
<mrow> <msub> <mi>G</mi> <mrow> <mi>F</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>G</mi> <mrow> <mi>P</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>G</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mi>G</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
wherein G isFCAnd(s) is a transfer function of the change of the bottom discharge flow rate of the actual output, namely the transfer function of the feedforward controller.
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