CN109491245B - Disturbance compensation control method of CSTR system - Google Patents

Disturbance compensation control method of CSTR system Download PDF

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CN109491245B
CN109491245B CN201811277244.9A CN201811277244A CN109491245B CN 109491245 B CN109491245 B CN 109491245B CN 201811277244 A CN201811277244 A CN 201811277244A CN 109491245 B CN109491245 B CN 109491245B
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disturbance
cstr
input
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cstr system
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CN109491245A (en
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丁世宏
梅珂琪
李鸿一
马莉
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Yangzhong Guangshan Kechuang Service Co.,Ltd.
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Jiangsu University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • 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 disturbance compensation control method of a CSTR system, belonging to the technical field of automatic control. The method utilizes a dynamic input and output model in a CSTR system mathematical model to construct an auxiliary system based on the theory of a disturbance observer, and further designs a novel disturbance observer. In the CSTR control system, the output physical quantity is the temperature of the reactor and the temperature of the cooling sleeve, and the intermediate variable chemical reaction concentration in the mathematical model expression of the CSTR system is eliminated according to the mathematical model expression of the CSTR system, so that a second order differential expression between the temperature of the reactor and the reaction input concentration is obtained. By using the second order differential equation, an auxiliary system with the same structure as the auxiliary system is constructed, and the output is z1The input is h, and h is x2And z1K times the error. In the novel disturbance observer, the estimated values of the CSTR system disturbance are h and u1Q times the difference between the two, where the q value is the system coefficient. The invention is easy to realize, has stronger anti-load capacity, improves the system performance and realizes better control effect.

Description

Disturbance compensation control method of CSTR system
Technical Field
The invention discloses a disturbance compensation control method of a CSTR system, belonging to the technical field of automatic control.
Background
Continuous Stirred Tank Reactors (CSTRs) are a common process industry device and conventional PID control has not been satisfactory due to the diversity and complexity of chemical reactions within the reactor. Many control methods have been developed that have been used in CSTR control systems, such as predictive control, fuzzy control, and adaptive control, among others. However, these control methods are often affected by external disturbances, resulting in poor dynamic and steady-state performance of the system.
It is worth proposing that in an actual control system, in order to weaken the influence of external disturbance of the system, it is often a more common method to introduce an observer for disturbance compensation. The invention aims to adopt a novel disturbance observation technology to carry out disturbance observation on the CSTR system and carry out disturbance compensation on the CSTR system, thereby achieving the purpose of weakening disturbance. It should be noted that the conventional state observer generally requires a state quantity as a condition to obtain an observed quantity. The disturbance observer provided by the invention only needs input quantity, and is simple in design and easy to realize.
Disclosure of Invention
The invention aims to provide a disturbance compensation control method of a CSTR system of a novel disturbance observer based on an input-output model. The method estimates the disturbance in the CSTR by constructing a novel disturbance observer only needing to output information, and then feeds the obtained disturbance estimator forward to a control input end to compensate the disturbance estimator, thereby weakening the influence of the disturbance on the stability of the CSTR system.
The implementation of a disturbance compensation control method of a CSTR system comprises the following steps:
step one, establishing a mathematical model of a CSTR system, and establishing an input and output model of disturbance and reactor temperature;
secondly, constructing an auxiliary system of the input-output model based on the input-output model in the first step, and determining the input and the output of the auxiliary system;
thirdly, determining an observed value of the disturbance based on the input-output system in the first step and the auxiliary system in the second step;
and step four, feeding the disturbance observation value obtained in the step three forward to the input end of the CSTR system and compensating the disturbance observation value, thereby weakening the influence of disturbance on the CSTR system.
In order to achieve the purpose, the invention adopts the following technical scheme:
further, the mathematical model for establishing the CSTR system is:
Figure BDA0001847267210000021
wherein x is1Is the chemical reaction concentration, x2Is the reactor temperature, x3Is the cooling jacket temperature u1Is the initial reaction concentration, u2Is the initial reactor temperature u3Is the initial cooling jacket temperature at which,
Figure BDA0001847267210000022
is a kinetic constant, qcAnd delta1Are all system coefficients, d (t) is the external perturbation.
Go toStep (2), the formula (1) can be used to obtain the formula2And x3To represent x1：
Figure BDA0001847267210000023
Further, the derivation by equation (2) can yield:
Figure BDA0001847267210000024
further, the compound is obtained by the formula (1):
Figure BDA0001847267210000025
further, substituting equation (3) into equation (4) can yield:
Figure BDA0001847267210000026
further, the input-output mathematical relationship between the disturbance in the CSTR system and the reactor temperature is obtained by the formula (5):
Figure BDA0001847267210000027
to estimate the disturbance d (t), the following disturbance observations are constructed:
Figure BDA0001847267210000028
wherein h ═ K (x)2-z1) And dynamic z1The following constraint equations are satisfied:
Figure BDA0001847267210000031
and (8) establishing an auxiliary system in the second step. Wherein z is1Is the disturbance observed by the novel disturbance observer; in this auxiliary system, the input is h and the output is z1(ii) a The control input is h ═ K (x)2-z1)。
Through the formula (7) and the deduction, the disturbance observation of the CSTR system can be realized.
Further, since the actual disturbance is related to the control input u1Are acted upon together in the CSTR system so that this disturbance observation is fed directly back to the CSTR system control input u1And a closed-loop control is formed, actual disturbance is compensated, and therefore the influence of the disturbance on the stability of the CSTR system is weakened, and the schematic block diagram is shown in FIG. 2.
The invention has the beneficial effects that:
(1) the traditional state observer is mature in theory and simple in algorithm, but has certain conservation in control precision, the novel disturbance observer is convenient to regulate in precision, and the observation performance of the novel disturbance observer can be regulated only by regulating the gain K.
(2) The novel disturbance observer is wide in application range, state variables are not needed like the existing state observer, the novel disturbance observer is constructed based on a single-input single-output system, only output quantity is needed, and other state variables are not needed.
(3) Compared with the existing method, the method of the invention is greatly simplified and optimized, is easy to realize, has stronger anti-load capacity, improves the system performance and realizes better control effect.
Drawings
FIG. 1 is a schematic diagram of a CSTR system;
FIG. 2 is a block diagram of a CSTR system design;
FIG. 3 is a CSTR system simulation setup diagram;
FIG. 4 is a diagram of a novel observer application of the system of the present invention;
FIG. 5 is a CSTR system perturbation perspective diagram;
FIG. 6 is an observed error of a CSTR system disturbance;
FIG. 7 is a state diagram of a CSTR system with no disturbance compensation;
FIG. 8 is a state diagram of a CSTR system with disturbance compensation;
FIG. 9 is a block diagram of a CSTR system disturbance observation.
Detailed Description
The present invention will be further explained with reference to the accompanying drawings, specific parameters of a CSTR system and simulation waveforms.
To more clearly illustrate the technical solution of the present invention, the embodiments of the present invention will be specifically described with reference to a specific set of parameters of the CSTR and its simulation results in MATLAB software. It should be apparent that the following description is only for one specific CSTR system, and that it will be apparent to those skilled in the art that if the method is used to perform disturbance observation, the analysis operations should be performed for the parameters of the CSTR system for the specific application.
A schematic diagram of a CSTR system used in the simulation experiment is shown in FIG. 1. The parameters of the CSTR system are set to q 1 and q respectivelyc＝0.28,δ1＝10,u1＝1,u2＝0,u3Is-1. In this simulation experiment, the initial state of the CSTR system was selected to be x, respectively1(0)＝0.58,x2(0)＝2.67,x3(0) 0.12 and assuming that the perturbation d (t) is given the form:
Figure BDA0001847267210000041
based on the above system, the disturbance observation method of the CSTR system according to the present invention is explained below by specific implementation:
step one, according to the specific parameters of the CSTR system, the mathematical model of the adopted CSTR system is established as follows:
Figure BDA0001847267210000042
FIG. 3 is a CSTR system diagram constructed in a simulation experiment under the CSTR system parameters.
Secondly, establishing an auxiliary system of a novel disturbance observer applied to the specific CSTR system;
further, formula (8) is arranged as:
Figure BDA0001847267210000043
by using equation (9), an auxiliary system of the disturbance observer can be constructed.
Step three, determining the observed value of disturbance
Further, formula (7) is arranged as:
Figure BDA0001847267210000044
wherein h ═ K (x)2-z1) And dynamic z1Produced by equation (9). FIG. 9 is a block diagram of disturbance observations of the CSTR system.
FIG. 4 is a schematic block diagram of the novel disturbance observer constructed in a simulation experiment under the CSTR system parameters.
Step four, verifying the observation effect of the novel disturbance observer and the influence of the observation effect on the stability of the CSTR system through simulation comparison
Further, the larger the gain K value of the novel disturbance observer is, the higher the disturbance observation precision is, the closer the estimated disturbance is to the real disturbance, but the larger the buffeting caused by the disturbance observer is, the value range of K selected by the invention is 50-90, the preferred gain K value is 69, and the buffeting can be overcome while the observation disturbance precision is improved. Suppose the following form of perturbation is given:
Figure BDA0001847267210000051
the observed waveform is shown in fig. 5. To further verify whether the observed perturbation is close to the actual perturbation, an observed error map of the perturbation is given, as shown in fig. 6.
Further, after disturbance is observed and disturbance compensation is introduced, it can be seen from a comparison between fig. 7 and fig. 8 that the stability of the CSTR system with disturbance compensation is significantly improved.
The present invention is not limited to the above-described embodiments, and any obvious modifications, substitutions or alterations can be made by those skilled in the art without departing from the spirit of the present invention.

Claims (3)

1. A disturbance compensation control method of a CSTR system is characterized by comprising the following steps:
step 1, establishing a mathematical model of a CSTR system, and establishing an input and output model of disturbance and CSTR reactor temperature;
step 2, constructing an auxiliary system of the input-output model based on the input-output model in the step 1, and determining the input and output of the auxiliary system;
step 3, determining an observed value of the disturbance based on the input-output model in the step 1 and the auxiliary system in the step 2;
step 4, feeding the disturbance observation value obtained in the step 3 forward to a CSTR system to compensate the actual disturbance, and weakening the influence of the disturbance on the CSTR system;
in step 1, the mathematical model expression of the CSTR system is established as follows:
Figure FDA0003062298440000011
wherein x is1Is the chemical reaction concentration, x2Is the reactor temperature, x3Is the cooling jacket temperature u1Is the initial reaction concentration, u2Is the initial reactor temperature u3Is the initial cooling jacket temperature at which,
Figure FDA0003062298440000012
is a kinetic constant, qcAnd delta1All are system coefficients, d (t) is external disturbance;
in step 1, a method for establishing an input and output model of disturbance and reactor temperature comprises the following steps:
step 1.1, the mathematical model expression of the CSTR system is used for obtaining:
Figure FDA0003062298440000013
step 1.2. from the formula of step 1.1:
Figure FDA0003062298440000014
step 1.3. the formula of step 1.1 is then repeated to obtain:
Figure FDA0003062298440000015
step 1.4. substituting the formula of step 1.2 into the formula of step 1.3 can obtain:
Figure FDA0003062298440000021
step 1.5, the input and output mathematical relation between the disturbance in the CSTR system and the temperature of the reactor obtained by the formula of the step 1.4 is as follows:
Figure FDA0003062298440000022
wherein x is2Is the reactor temperature, x3Is the temperature of the cooling jacket or jackets and,
Figure FDA0003062298440000023
is a kinetic constant, u1Is the initial reaction concentration, u2Is a reaction at the beginningTemperature of the vessel, d (t) is perturbation, q and delta1Are all system coefficients;
in step 2, the model expression of the auxiliary system for constructing the input and output model is as follows:
Figure FDA0003062298440000024
in step 2, the input of the auxiliary system is set as h, and the output is set as z1；
In step 3, the observed value of the determined disturbance is
Figure FDA0003062298440000025
Wherein h ═ K (x)2-z1) Dynamic z1And satisfying a constraint equation expressed by an input and output model auxiliary system, and K represents a gain.
2. The disturbance compensation control method of a CSTR system according to claim 1, wherein the K value ranges from 50 to 90.
3. The disturbance compensation control method of the CSTR system according to claim 1, wherein the step 4 is implemented by: observing the disturbance
Figure FDA0003062298440000026
Feedback to CSTR System control input u1And the end forms a closed loop to compensate the actual disturbance of the CSTR system.
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