CN113244647A - Rectifying tower VOFFLC temperature control method and system based on matrix decoupling - Google Patents
Rectifying tower VOFFLC temperature control method and system based on matrix decoupling Download PDFInfo
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Abstract
The invention discloses a rectifying tower VOFFLC temperature control system based on matrix decoupling, which comprises: the VOFFLC controller is used for respectively receiving the two errors and the first-order derivatives of the two errors, carrying out fractional order fuzzy control processing on the first-order derivatives, obtaining corresponding control parameters in a self-adaptive mode according to a fractional order fuzzy control rule, and carrying out FOPID control on the control parameters; the two errors are respectively: the error between the actual temperature of the tower top and the set temperature and the error between the actual temperature of the tower bottom and the set temperature; the matrix decoupling module is used for performing matrix decoupling on the control parameters subjected to FOPID control to respectively obtain control parameters of the tower top reflux quantity and the reboiler heating steam quantity and control the tower top reflux quantity and the reboiler heating steam quantity.
Description
Technical Field
The invention relates to the technical field of rectifying tower control, in particular to a rectifying tower temperature control method.
Background
Rectification is a mass transfer process widely used in many production processes such as oil refining, chemical engineering and the like. In the rectification process, through repeated vaporization and condensation, each component in the mixture material is separated to reach the specified purity respectively. The control of the rectification column directly affects the quality, yield and energy consumption of the product, so the problem of automatic control of the rectification column has been highly regarded by people for a long time. In the dynamic control process of the rectifying tower, because more controlled variables are involved, more control variables can be selected, and meanwhile, strong coupling correlation exists between the control variables and the control variables. In addition, because the number of control channels of the rectifying tower is large, the response speed is low, the internal working process is complex, the coupling among all variables is strong, and the requirement on the control quality of the tower is high, the internal working mechanism and the working process of the rectifying tower must be known and mastered firstly when the specific scheme is designed, and the specific control requirement is combined, so that the reasonable and effective control quality can be obtained. When a temperature control system of the rectifying tower is built by adopting the traditional PID control, when the structure and the parameters of a controlled object have certain uncertainty, the structure and the parameters cannot be accurately modeled, and the parameters cannot be adjusted in real time. In addition, the same control parameters are adopted under different working conditions, and a good control effect is difficult to obtain.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a rectifying tower VOFFLC temperature control method and system based on matrix decoupling, solves the problems that the traditional PID control cannot implement parameter adjustment and is poor in control effect, and realizes high-quality control.
The purpose of the invention is realized as follows: a rectifying tower VOFFLC temperature control method based on matrix decoupling comprises
1) Acquiring the actual temperature of the tower top and the actual temperature of the tower bottom, and calculating errors and first-order derivatives of the errors according to the actual temperature of the tower top and the actual temperature of the tower bottom and respective set values;
2) respectively sending the two errors and the first derivative of the two errors to a VOFFLC controller for fractional order fuzzy control processing, and obtaining a corresponding control parameter K ═ K (K) in a self-adaptive manner according to a fractional order fuzzy control rulep,Ki,Kdλ, μ), by said control parameter K ═ K (K)p,Ki,KdLambda, mu) and then carrying out FOPID control;
3) and performing matrix decoupling on the control parameters subjected to FOPID control to respectively obtain control parameters of the tower top reflux amount and the reboiler heating steam amount.
Preferably, in the step 2), an integral link in the design process of the transfer function module in the FOPID controller adopts a filter to approximate, specifically: approximating a calculus operator in a controller, comprising the steps of:
2-1) determining the range [ omega ] of the approximate frequency bandb,ωh]And an approximate order N;
2-2) calculating zero pole ω 'from the following formula'k,ωkAnd a gain K;
wherein alpha is more than 0 and less than 1, and N belongs to Z;
2-3) finally obtaining an expression form of an integer order rational transfer function of a fractional order Laplace operator s alpha according to the following formula;
2-4) after the approximation from the fractional order transfer function to the integer order transfer function is realized, a fractional order transfer function module is designed by adopting a simulink module packaging technology.
This allows for higher accuracy.
Preferably, the integrator is further reconstructed by the following formula in the design process of the transfer function module:
in the formula: λ and μ are the integration and differentiation orders, respectively.
In the use process of the practical FOPID controller, because the integral link is approximated by a filter, and the steady-state error can not be completely eliminated when the lambda is less than 1, the integrator is reconstructed by adopting the method to eliminate the steady-state error.
A rectifying column VOFFLC temperature control system based on matrix decoupling comprises:
the VOFFLC controller is used for respectively receiving the two errors and the first derivatives of the two errors, carrying out fractional order fuzzy control processing on the first derivatives, and obtaining a corresponding control parameter K ═ K (K) in a self-adaptive manner according to a fractional order fuzzy control rulep,Ki,Kdλ, μ), by said control parameter K ═ K (K)p,Ki,KdLambda, mu) and then carrying out FOPID control; the two errors are respectively: the error between the actual temperature of the tower top and the set temperature and the error between the actual temperature of the tower bottom and the set temperature;
and the matrix decoupling module is used for performing matrix decoupling on the control parameters subjected to FOPID control to respectively obtain control parameters of the tower top reflux amount and the reboiler heating steam amount and control the tower top reflux amount and the reboiler heating steam amount.
Compared with the prior art, the invention has the beneficial effects that: the invention adopts a mode that a VOFFLC system is matched with a matrix for decoupling, and two control parameters are added compared with the traditional PID system, thereby improving the description capability of the system and having high-quality control performance indexes; meanwhile, compared with the existing FLC system, the system has stronger domain fault tolerance and achieves accurate control; compared with the traditional PID control system, the system has no requirement on the initial value of the control parameter, and can realize the self-adaptation of the control parameter; from the view of anti-interference experimental data, the anti-interference test device also has stronger anti-interference capability; the control performance index of the rectifying tower MIMO temperature control method is designed to be optimal by adopting a matrix decoupling VOFFLC system, and the rectifying tower MIMO temperature control method has stronger anti-interference capability and self-adaptive level; the design of the rectifying tower MIMO temperature control system by adopting the matrix decoupling VOFFLC system is a promising work and provides important values for theoretical research and engineering application.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic view of the control of a rectifying column in the present invention.
Fig. 2 is a schematic diagram of a matrix-structured VOFFLC control system according to the present invention.
Fig. 3 is a schematic diagram of the structure of the VOFFLC controller according to the present invention.
FIG. 4 is a diagram of a matrix decoupling tower bottom PID control simulation result in the prior art.
FIG. 5 is a diagram of a matrix decoupling tower bottom PID control simulation result in the prior art.
FIG. 6 is a graph of the matrix decoupling tower bottom VOFFLC control simulation result in the present invention.
Fig. 7 is a diagram showing the simulation result of matrix decoupling tower top VOFFLC control in the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
FIG. 1 is a schematic diagram of a rectifying tower structure controlled by the present invention, wherein the tower bottom temperature is used as the indirect quality index of the tower bottom product, and the tower top temperature is used as the indirect quality index of the tower top product. The temperature at the top of the tower is controlled through the reflux quantity, so that the components of the product at the top of the tower are ensured; the tower bottom reboiler is used for heating steam quantity to control the tower bottom temperature, so that the product components at the tower bottom are ensured.
A rectifying tower VOFFLC temperature control method based on matrix decoupling comprises
1) Acquiring the actual temperature of the tower top and the actual temperature of the tower bottom, and calculating errors and first-order derivatives of the errors according to the actual temperature of the tower top and the actual temperature of the tower bottom and respective set values;
when the temperature is collected, the temperature sensors are arranged at the top and the bottom of the tower to collect the respective temperatures;
2) respectively sending the two errors and the first derivative of the two errors to a VOFFLC controller for fractional order fuzzy control processing, and obtaining a corresponding control parameter K ═ K (K) in a self-adaptive manner according to a fractional order fuzzy control rulep,Ki,Kdλ, μ), by said control parameter K ═ K (K)p,Ki,KdLambda, mu) and then carrying out FOPID control; an integral link in the design process of a transfer function module in the FOPID controller adopts filter approximation operation, and the method specifically comprises the following steps: adopting an Oustaloup method to approximate a calculus operator in a controller, comprising the following steps:
2-1) determining the range [ omega ] of the approximate frequency bandb,ωh]And an approximate order N;
2-2) calculating zero pole ω 'from the following formula'k,ωkAnd a gain K;
wherein alpha is more than 0 and less than 1, and N belongs to Z;
2-3) finally obtaining an expression form of an integer order rational transfer function of a fractional order Laplace operator s alpha according to the following formula;
2-4) after the approximation from the fractional order transfer function to the integer order transfer function is realized, designing a fractional order transfer function module by adopting a simulink module packaging technology;
the transfer function module design process also needs to reconstruct an integrator through the following formula:
in the formula: λ and μ are the integration order and the differentiation order, respectively;
3) and performing matrix decoupling on the control parameters subjected to FOPID control to respectively obtain control parameters of the tower top reflux amount and the reboiler heating steam amount.
As shown in fig. 2-3, a rectification column voffllc temperature control system based on matrix decoupling includes:
the VOFFLC controller is used for respectively receiving the two errors and the first derivatives of the two errors, carrying out fractional order fuzzy control processing on the first derivatives, and obtaining a corresponding control parameter K ═ K (K) in a self-adaptive manner according to a fractional order fuzzy control rulep,Ki,Kdλ, μ), by said control parameter K ═ K (K)p,Ki,KdLambda, mu) and then carrying out FOPID control; the two errors are respectively: the error between the actual temperature of the tower top and the set temperature and the error between the actual temperature of the tower bottom and the set temperature;
and the matrix decoupling module is used for performing matrix decoupling on the control parameters subjected to FOPID control to respectively obtain control parameters of the tower top reflux amount and the reboiler heating steam amount and control the tower top reflux amount and the reboiler heating steam amount.
In order to meet the requirement of real-time adjustment of a complex rectifying tower temperature multi-input multi-output (MIMO) system, the invention adopts matrix decoupling and integrates variable order fractional order fuzzy PID control (VOFFLC) of fuzzy control (FLC) and fractional order PID control (FOPID) related theories: compared with an FLC system, the two parameters of lambda and mu are increased, and the description capacity of the system is improved; the stability and robustness of the fractional order system are improved, and the problems of uncertainty and external disturbance are solved; meanwhile, as a self-adaptive system, the VOFFLC can continuously test the error (e) and the error derivative (ec) in the running process, and on-line adjusts all five controller parameters according to a fuzzy control rule so as to enhance the system.
The design scheme of the control system is as follows:
the VOFFLC controller adopted by the invention completes the control task, allows all five parameters of the FOPID controller to change along with the system structure as the change of VOFFLC output, the fuzzy rule of the controller parameters can do a large number of simulation experiments, observes the influence of the order lambda and mu on the closed loop response of the control system, summarizes a meaningful table of fuzzy inference rules, and the adjusting method of the order lambda and mu increment summarized by the experiments is shown in the table (1-5).
TABLE 1 Δ K for VOFFLC controllerpFuzzy rule table
TABLE 2 Δ K for VOFFLC controlleriFuzzy rule table
TABLE 3 Δ K for VOFFLC controllerdFuzzy rule table
Table 4 a lambda fuzzy rule table for VOFFLC controller
TABLE 5 Δ μ fuzzy rule Table for VOFFLC controller
Fuzzy rules and PID parameters of controllers at the top and the bottom of the rectifying tower are specified as follows:
[kpt,pit,kdt]is a tower top PID parameter; [ t ] of1,t2,t3]The domain coverage coefficient of the tower top fuzzy rule e, ec and u is as follows: e is equal to t1*[-6 6]；ec∈t2*[-6 6]；u∈t3*[-6 6]；
[kpd,pid,kdd]Is a tower bottom PID parameter; [ d1,d2,d3]The domain coverage coefficient of the tower bottom fuzzy rule e, ec and u is as follows: e is as large as d1*[-6 6]；ec∈d2*[-6 6]；u∈d3*[-6 6]；
The temperature control system of the rectifying tower is a bivariate control model, and the mathematical model of the coupling system adopted by the invention is as follows:
according to the diagonal matrix decoupling, calculating a relative gain matrix as follows:
the relative gain matrix shows that the input and output pairing selection of the control system is correct; stronger mutual coupling exists between channels, and the system is subjected to decoupling analysis.
And then solving a decoupling diagonal matrix as follows:
according to the temperature control experiment, the conditions are as shown in Table 6:
TABLE 6 conditions of the temperature control experiment of the rectifying column
Combining the design work, establishing a rectification tower temperature control simulation system as shown in fig. 2 according to a diagonal decoupling design principle, and performing simulation tests on a combination matrix decoupling PID control (comparative example) and a matrix decoupling VOFFLC control (embodiment); analyzing the performance index data of each control system of the simulation experiment, wherein the index data result of the optimization system is shown in the table 7:
TABLE 7 matrix decoupling optimization PID and VOFFLC control parameter table
The result graph of the simulation test is shown in 4-7, the temperature of the tower top and the tower bottom controlled by the matrix decoupling VOFFLC is obviously superior to the temperature controlled by the matrix decoupling PID, wherein the former has excellent control effect and strong anti-interference; the latter has no control effect and no anti-interference capability; from the experimental results, the matrix decoupling VOFFLC system has two more control parameters than the related PID system, can improve the description capability of the system, and has high-quality control performance indexes; meanwhile, compared with an FLC system, the system has stronger domain fault tolerance and achieves accurate control; compared with the traditional PID control system, the system has no requirement on the initial value of the control parameter, and can realize the self-adaptation of the control parameter; from the view of anti-interference experimental data, the anti-interference device also has stronger anti-interference capability. Namely: the control performance index of the rectifying tower MIMO temperature control system designed by adopting the matrix decoupling VOFFLC system is optimal, and the rectifying tower MIMO temperature control system has stronger anti-interference capability and self-adaptive level. The design of the rectifying tower MIMO temperature control system by adopting the matrix decoupling VOFFLC system is a promising work and provides important values for theoretical research and engineering application.
The above description of the embodiments is only intended to facilitate the understanding of the method of the invention and its core idea. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
Claims (4)
1. A rectifying tower VOFFLC temperature control method based on matrix decoupling is characterized by comprising the following steps:
step 1) acquiring the actual temperature of the tower top and the actual temperature of the tower bottom, and calculating errors and first-order derivatives of the errors according to the actual temperature of the tower top and the actual temperature of the tower bottom and respective set values;
step 2) respectively sending the two errors and the first derivative of the two errors to a VOFFLC controller for fractional order fuzzy control processing, and obtaining a corresponding control parameter K ═ K (K) in a self-adaptive manner according to a fractional order fuzzy control rulep,Ki,Kdλ, μ), by said control parameter K ═ K (K)p,Ki,KdLambda, mu) and then carrying out FOPID control;
and 3) carrying out matrix decoupling on the control parameters subjected to FOPID control to respectively obtain control parameters of the tower top reflux amount and the reboiler heating steam amount.
2. The rectifying tower VOFFLC temperature control method based on matrix decoupling as claimed in claim 1, wherein an integration link in the design process of a transfer function module in the FOPID controller in the step 2) adopts a filter approximation operation, specifically: approximating a calculus operator in a controller, comprising the steps of:
2-1) determining the range [ omega ] of the approximate frequency bandb,ωh]And an approximate order N;
2-2) calculating zero pole ω 'from the following formula'k,ωkAnd a gain K;
wherein alpha is more than 0 and less than 1, and N belongs to Z;
2-3) finally obtaining an expression form of an integer order rational transfer function of a fractional order Laplace operator s alpha according to the following formula;
2-4) after the approximation from the fractional order transfer function to the integer order transfer function is realized, a fractional order transfer function module is designed by adopting a simulink module packaging technology.
3. The rectifying tower VOFFLC temperature control method based on matrix decoupling as claimed in claim 2, wherein the integrator is further reconstructed through the following formula in the design process of the transfer function module:
in the formula: λ and μ are the integration and differentiation orders, respectively.
4. A rectifying column VOFFLC temperature control system based on matrix decoupling is characterized by comprising:
the VOFFLC controller is used for respectively receiving the two errors and the first derivatives of the two errors, carrying out fractional order fuzzy control processing on the first derivatives, and obtaining a corresponding control parameter K ═ K (K) in a self-adaptive manner according to a fractional order fuzzy control rulep,Ki,Kdλ, μ), by said control parameter K ═ K (K)p,Ki,KdLambda, mu) and then carrying out FOPID control; the two errors are respectively: the error between the actual temperature of the tower top and the set temperature and the error between the actual temperature of the tower bottom and the set temperature;
and the matrix decoupling module is used for performing matrix decoupling on the control parameters subjected to FOPID control to respectively obtain control parameters of the tower top reflux amount and the reboiler heating steam amount and control the tower top reflux amount and the reboiler heating steam amount.
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