CN109992887B - Anti-interference control method and system for binary distillation tower - Google Patents
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Abstract
The invention discloses an anti-interference control method and system for a binary distillation tower, and belongs to the field of automatic control of a multivariable time-lag system. Firstly, the transfer function model of the existing binary distillation tower is decomposed about time lag to obtain a residual matrix and a pure time lag matrix. And solving and analyzing the frequency characteristic of the residual matrix inverse model, and obtaining a simplified inverse model through compensation and approximation. Then, H is obtained∞A sub-optimal filter and determining adjustable parameters of the filter according to the desired robustness. Finally, an improved anti-interference control system structure is obtained based on the method. Compared with the prior art, the method has the advantages of simple thought, convenience for understanding and application of control engineers, capability of more effectively realizing interference estimation and inhibition and capability of obtaining better anti-interference effect aiming at the binary distillation tower.
Description
Technical Field
The invention belongs to the field of automatic control of multivariable time-lag systems, and particularly relates to an anti-interference control method and system for a binary distillation tower.
Background
Distillation is the typical unit operation that was first implemented industrially to separate a liquid homogeneous mixture. The basic principle of distillation is that a vapor-liquid two-phase system is formed by heating, and the purposes of component separation and purification are achieved by utilizing the difference of the volatility of each component in the mixture. The distillation technology is widely applied to the fields of oil refining, chemical engineering, light industry and the like, and the separation efficiency greatly influences the product quality and the energy consumption of the device. In industrial production, two-component distillation is the basis of multi-component distillation, and a binary distillation column for realizing two-component distillation is the focus of the research of the invention. In practical distillation column systems, disturbances tend to be widespread and often have a detrimental effect on control system performance. For example, changes in vapor pressure, feed temperature, and composition can all affect the quality of the product in the distillation column to varying degrees. In view of this, how to design an effective disturbance rejection control method and system for a binary distillation column is a problem to be studied.
Disclosure of Invention
In view of the above, the main object of the present invention is to provide an anti-interference control method for a binary distillation column, comprising the following steps:
s1, decomposing the existing transfer function model of the binary distillation tower about time lag to obtain a residual matrix and a pure time lag matrix;
s2, solving and analyzing the frequency characteristics of the residual matrix inverse model, and obtaining a simplified inverse model through compensation and approximation;
s3, design H∞The suboptimal filter determines the adjustable parameters of the filter according to the given robustness requirement;
s4, obtaining an improved anti-interference control system structure based on the steps and the method.
The target object of the invention is a binary distillation tower, and the transfer function matrix of the binary distillation tower is as follows:
wherein,
h 1,2, l 1,2 is Gm(s) element of the h-th row and l-th column, khlTo proportional gain, ThlIn order to be a first-order time constant of inertia,
for pure lag term, tauhlIs the pure lag time, s is the laplace operator; based on the existing transfer function model of the binary distillation column, G is performed according to the following formulam(s) decomposition with respect to time lag
Wherein G ism0(s) is the residual matrix after skew extraction, Gm0,hl(s) is a matrix Gm0Row h and column l elements of(s), E(s) being a time-lag diagonal matrix, τ1,τ2Are each Gm(s) minimum time lag in column 1, column 2, s is the Laplace operator.
The specific process of S2 is as follows:
s201, obtaining a steady-state gain inverse matrix of the process object
S202, according to the residual matrix Gm0(S) and the steady state gain inverse obtained in step S201Matrix array
The frequency characteristics of the normalized inverse model element at frequency ω are found as follows
Wherein j is an imaginary unit, ω is a frequency,
in order to be the inverse model frequency characteristic matrix,
to normalize the inverse model frequency characteristic matrix, the indices m, n represent the m-th row and n-th column of the matrix, respectively.
Given frequency range [ omega ]0,ωr]，ω0,ωrRespectively minimum and maximum frequencies considered, usually taken as ω 00. Selecting a plurality of frequency points omega in the frequency range0,ω1,…,ωrRespectively calculating normalized inverse model elements at the frequency points
To obtain the frequency characteristic of
I.e. the Nyquist curve.
S203, analyzing the Nyquist curve of each element in the normalized inverse model obtained in the step S202, introducing a compensator and calculating corresponding parameters, wherein the frequency characteristic of the compensated normalized inverse model element is given by the following formula
Where j is an imaginary unit, ω is frequency, γtIs a parameter of the t-th compensator element, Pmn(j ω) is the compensated normalized inverse model frequency characteristic matrix,
to normalize the inverse model frequency characteristic matrix, the indices m, n represent the m-th row and n-th column of the matrix, respectively. Parameter gammatThe selection principle is to ensure that the frequency characteristic curves of all elements in the mth row of the compensated normalized inverse model are located in a stable region, and the transfer function matrix of the compensator is as follows:
s204, based on the compensated normalized inverse model obtained in the step S203, respectively obtaining the frequency point omega of each element0,ω1,…,ωrObtaining an approximate model of each element by using a complex curve fitting technology according to the frequency characteristic, so as to obtain a final simplified inverse model; the approximate model of each element can be expressed as
Wherein,
an approximate model obtained by fitting the mth row and nth column elements based on the compensated normalized inverse model, Amn,BmnFor corresponding fitting parameters, pmnIs a steady state gain inverse matrix in step S201
The mth row and nth column elements of (1), s is a Laplace operator; according to the complex curve fitting technique, the fitting parameters can be obtained as follows
Wherein, ω iskFor a single frequency point, r is the division of the initial frequency point ω0Number of other frequency points than Pmn(jωk) For normalizing the element of the nth column at frequency omega of the mth row of the inverse model after compensationkCorresponding complex value, | Pmn(jωk) I is the modulus of the complex number, Re (P)mn(jωk))，Im(Pmn(jωk) Are the real and imaginary values of the complex number, a, respectivelymn,bmn,cmn,dmnIs an intermediate variable.
The specific process of S3 is as follows:
s301, solving the error of the interference estimation under the framework of an improved interference observer (DOB) based on the time-lag decomposition of the step S1 and the simplified inverse model of the step S2, as shown in FIG. 2, as follows
Wherein e isv(s) interference estimation error of the v-th loop, dv(s) is the interference signal (to be suppressed) of the v-th loop, γtIs the parameter of the t-th compensator element, τ, obtained in step S203lFor G determined in step S1m(s) minimum time lag, Q in column It(s) is the t-th element of the diagonal filter Q(s) to be solved, s being the Laplace operator. Minimizing H of interference estimation error∞Norm to obtain realizable H∞Sub-optimal filter elements, as follows
Wherein Q ist(s) is H∞The t-th element, γ, of the sub-optimal filtertIs the parameter of the t-th compensator element, τ, obtained in step S203lFor G determined in step S1m(s) minimum time lag, λ, in column ItIs a filter element Qt(s) adjustable parameter, s is LappAnd (5) Lass operator.
S302, giving the value of the robustness index Ms and the filter parameter lambda1,λ2Is obtained by the following formula
Wherein, taulFor G determined in step S1m(s) minimum skew in column l. Thus, the final H can be obtained∞The suboptimal filter is as follows:
finally, based on the above steps and methods, the present invention provides an improved implementation of the immunity control system, as shown in fig. 2.
Compared with the prior art, the method has the advantages of simple thought, convenience for understanding and application of control engineers, capability of more effectively realizing interference estimation and inhibition and capability of obtaining better anti-interference effect aiming at the binary distillation tower.
Drawings
FIG. 1 is a flow chart of a binary distillation column disturbance rejection control method according to an embodiment of the present invention.
FIG. 2 is a block diagram of an exemplary binary distillation column immunity control system according to the present invention.
Fig. 3 is a frequency characteristic curve of each element of the normalized inverse model in a given frequency band according to the embodiment of the present invention.
Fig. 4 is a schematic diagram of stability determination of each element of the normalized inverse model according to the embodiment of the present invention. Fig. 5 is a frequency characteristic curve of each element of the compensated normalized inverse model in a given frequency band according to the embodiment of the present invention.
Fig. 6 is an output curve of the immunity control system under unit step load disturbance according to the embodiment of the invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Taking the example of a binary distillation column proposed by scholars Luyben and Vinonte, the process has selected inputs as the reflux ratio and steam flow to the reboiler and outputs as the temperatures of the 17 th and 14 th columns. The control targets are as follows: under the influence of the disturbance such as steam pressure change, feed temperature and component change, inaccurate process model identification and the like, the controlled output (the temperature of the tower at the 17 th layer and the 14 th layer) deviates from the set value as little as possible and reaches a new steady state as soon as possible. An embodiment of the disturbance rejection control method of the binary distillation column is shown in fig. 1, and comprises the following steps:
The transfer function model for the binary distillation column considered is:
wherein, y1And y2The temperatures of the 17 th and 14 th column, respectively, and R and S are the reflux ratio and the steam flow to the reboiler, respectively. Gm(s) minimum time lag in the 1 st and 2 nd columns is τ, respectively1＝1,τ 21, so the binary distillation column model can be decomposed into
And 2, based on the frequency characteristics of the residual matrix inverse model, obtaining a simplified inverse model through compensation and approximation.
(1) First, the steady-state gain inverse matrix of the process object is obtained
(2) Selecting omega0＝0,ωr0.2 in the frequency range 0,0.2]Based on the residual matrix Gm0(s) the frequency characteristics of the elements of the normalized inverse model are plotted, as shown in FIG. 3.
(3) Introduction of compensators, based on FIG. 3Showing the frequency characteristic curve of each element, and obtaining the parameter gamma of the compensator by performing stability analysis on the compensated normalized inverse model elementm. Element stability determination referring to fig. 4, in fig. 4, the right half plane of the complex plane is divided into 4 regions, regions II and III are stable regions, and region I, IV is an unstable region. Parameter gammatThe principle of (t ═ 1,2) is to ensure that the frequency response curves of all elements in the m-th row of the compensated normalized inverse model are located in region II or region III. In this case, the derived calculation can give the compensator parameter γ1＝0.7525,γ20.3968, the transfer function matrix for the respective compensator is:
the frequency characteristic curve of each element of the compensated normalized inverse model is shown in fig. 5, and it can be seen that all elements are located in a stable region.
(4) And fitting and approximating each element of the compensated normalized inverse model one by one. Taking the first row and the first column as an example, 50 frequency points ω are selected0,ω1,…,ω49Wherein, ω is0＝0,ω49Frequency points are uniformly selected at an interval of 0.004 and equal to 0.2. Based on the frequency characteristic curve shown in fig. 5, complex values of the corresponding elements of the compensated normalized inverse model at the frequency points are obtained, and then an approximate model is obtained by adopting a complex curve fitting technology as follows:
the simplified inverse models can be obtained by calculating one by one
(1) According to step 1Obtained Gm(s) minimum skew τ in columns 1,21＝1,τ 21, and the compensator parameter γ obtained in step 21＝0.7525,γ2When 0.3968, H can be obtained∞The sub-optimal filter elements are as follows
(2) Given a robustness indicator Ms of 1.35, the filter parameter λ1,λ2Is obtained by the following formula
Thus, the final H can be obtained∞The suboptimal filter is as follows:
and 4, applying each unit obtained based on the steps and the method to the improved disturbance rejection control system shown in fig. 2, and giving an output curve of the system under the unit step load disturbance in fig. 6.
As can be seen from fig. 6, compared with other interference rejection control methods, the method of the present invention has the advantages that the overshoot of the interference response obtained is small, and the interference response can be converged to the set value at the fastest speed, so that a better interference rejection effect is obtained.
The above embodiments are merely illustrative of the spirit of the present invention, and the present invention is not limited to the embodiments.
Claims (2)
1. An anti-interference control method of a binary distillation tower is characterized by comprising the following steps:
s1, decomposing the existing transfer function model of the binary distillation tower about time lag to obtain a residual matrix and a pure time lag matrix;
s2, solving and analyzing the frequency characteristics of the residual matrix inverse model, and obtaining a simplified inverse model through compensation and approximation;
s3, design H∞The suboptimal filter determines the adjustable parameters of the filter according to the given robustness requirement;
the method specifically comprises the following steps: a binary distillation column having a transfer function matrix of:
wherein,
is Gm(s) element of the h-th row and l-th column, khlTo proportional gain, ThlIn order to be a first-order time constant of inertia,
for pure lag term, tauhlIs the pure lag time, s is the laplace operator; g is carried out according to the following formula based on a transfer function model of the binary distillation columnm(s) decomposition with respect to time lag
Wherein G ism0(s) is the residual matrix after skew extraction, Gm0,hl(s) is a matrix Gm0Row h and column l elements of(s), E(s) being a time-lag diagonal matrix, τ1,τ2Are each Gm(s) minimum time lag in columns 1 and 2, s being the laplacian;
the specific process of S2 is as follows:
s201, obtaining a steady-state gain inverse matrix of the process object
S202, according to the residual matrix Gm0(s) and stepThe steady state gain inverse matrix obtained in step S201
The frequency characteristics of the normalized inverse model element at frequency ω are found as follows
Wherein j is an imaginary unit, ω is a frequency,
in order to be the inverse model frequency characteristic matrix,
in order to normalize the inverse model frequency characteristic matrix, subscripts m and n respectively represent the m-th row and the n-th column of the matrix; given frequency range [ omega ]0,ωr]，ω0,ωrTaking ω as the minimum and maximum frequencies considered, respectively00; selecting a plurality of frequency points omega in the frequency range0,ω1,…,ωrRespectively calculating normalized inverse model elements at the frequency points
To obtain the frequency characteristic of
The frequency characteristic curve of (a), i.e., the Nyquist curve;
s203, analyzing the Nyquist curve of each element in the normalized inverse model obtained in the step S202, introducing a compensator and calculating corresponding parameters, wherein the frequency characteristic of the compensated normalized inverse model element is given by the following formula
Wherein j is an imaginary unit,omega is the frequency, gammatIs a parameter of the t-th compensator element, Pmn(j ω) is the compensated normalized inverse model frequency characteristic matrix,
in order to normalize the inverse model frequency characteristic matrix, subscripts m and n respectively represent the m-th row and the n-th column of the matrix;
parameter gammatThe selection principle is to ensure that the frequency characteristic curves of all elements in the mth row of the compensated normalized inverse model are located in a stable region, and the transfer function matrix of the compensator is as follows:
s204, based on the compensated normalized inverse model obtained in the step S203, respectively obtaining the frequency point omega of each element0,ω1,…,ωrObtaining an approximate model of each element by using a complex curve fitting technology according to the frequency characteristic, so as to obtain a final simplified inverse model; the approximate model of each element can be expressed as
Wherein,
an approximate model obtained by fitting the mth row and nth column elements based on the compensated normalized inverse model, Amn,BmnFor corresponding fitting parameters, pmnIs a steady state gain inverse matrix in step S201
The mth row and nth column elements of (1), s is a Laplace operator; according to complex curve fitting techniques, the fitting parameters may be
Is obtained by the following formula
Wherein, ω iskFor a single frequency point, r is the division of the initial frequency point ω0Number of other frequency points than Pmn(jωk) For normalizing the element of the nth column at frequency omega of the mth row of the inverse model after compensationkCorresponding complex value, | Pmn(jωk) I is the modulus of the complex number, Re (P)mn(jωk))，Im(Pmn(jωk) Are the real and imaginary values of the complex number, a, respectivelymn,bmn,cmn,dmnIs an intermediate variable;
the specific process of S3 is as follows:
s301, based on the time lag decomposition of the step S1 and the simplified inverse model of the step S2, under the framework of an improved Disturbance Observer (DOB), the error of the disturbance estimation is obtained as the following formula
Wherein e isv(s) interference estimation error of the v-th loop, dv(s) is the interference signal of the v-th loop, γtIs the parameter of the t-th compensator element, τ, obtained in step S203lFor G determined in step S1m(s) minimum time lag, Q in column It(s) is the t-th element of the diagonal filter q(s) to be solved, s is the laplacian operator;
minimizing H of interference estimation error∞Norm to obtain realizable H∞Sub-optimal filter elements, as follows
Wherein Q ist(s) is H∞Tth of suboptimal filterElement, gammatIs the parameter of the t-th compensator element, τ, obtained in step S203lFor G determined in step S1m(s) minimum time lag, λ, in column ItIs a filter element Qt(s) adjustable parameters, s being a laplacian operator;
s302, giving the value of the robustness index Ms and the filter parameter lambda1,λ2Is obtained by the following formula
Wherein, taulFor G determined in step S1m(s) minimum skew in column l; thus, the final H can be obtained∞The suboptimal filter is as follows:
2. an anti-interference control system for a binary distillation column, characterized by being applied to the anti-interference control method for a binary distillation column according to claim 1.
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