CN115755589B - Optimization method of fuzzy control system in reaction kettle based on genetic algorithm - Google Patents
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Abstract
The application discloses an optimization method of a fuzzy control system in a reaction kettle based on a genetic algorithm, which comprises the following steps: acquiring an initial value of a PID control system to obtain optimal PID control parameters after genetic optimization; inputting the optimal PID control parameters as initial values to a fuzzy PID control system, and determining optimal membership functions and fuzzy rules of fuzzy PID control; optimizing membership functions and fuzzy rule parameters in the fuzzy PID controller by adopting a genetic algorithm to obtain an optimal chromosome gene; and implanting the optimal chromosome genes into a fuzzy PID controller to finish optimization. The membership function and the fuzzy rule selection in the fuzzy controller are optimized through the genetic algorithm, and the adaptation degree of the PID control parameter increment output by the fuzzy controller and the current system is effectively improved. The application provides a control method for the high-precision temperature control system, so that the temperature control system has better robustness, response speed and interference resistance.
Description
Technical Field
The application belongs to the technical field of automatic temperature control, and particularly relates to an optimization method of a fuzzy control system based on a genetic algorithm in a reaction kettle.
Background
The reaction kettle is widely applied to the fields of chemical production, production and manufacturing, medicine, environmental protection and the like, along with the rapid development of scientific technology, the requirements on the rapidity and the stability of a temperature control system of the reaction kettle are higher, the reaction kettle has wide application in industrial detection, the temperature sensor is checked and needs to be detected in a constant temperature system of the reaction kettle, the temperature control effect of the reaction kettle can directly influence the quality of products, and in order to improve the temperature control effect of the reaction kettle and improve the quality of the products, the temperature control method of the reaction kettle needs to be optimized.
The temperature control system has the characteristics of nonlinearity, hysteresis, time variability and the like, disturbance factors are more, the control parameter setting method is complex, the traditional PID temperature control is a fixed control parameter, the PID control parameter is often obtained through experience, when the target temperature changes, the same parameter cannot control a controlled object to be stabilized at different temperature gradients, in addition, the temperature control system can be influenced by a temperature control environment, the temperature control precision and the temperature control speed of the control system can be seriously influenced, and for a system requiring high precision in temperature control, the traditional PID fixed parameter control cannot meet the requirement of the control system.
The fuzzy PID control has better self-adaptive capacity, is widely applied to temperature control systems, and plays an important role in improving the rapidity of the temperature control systems of the reaction kettles. The fuzzy rules are usually formed into a plurality of fuzzy rules according to expert experience, the intelligent control targets can be met by adaptively adjusting control parameters through simple, flexible and quick parameter setting, membership functions and fuzzy rules are often obtained through expert experience, objective consistency assessment is not available, selection of PID initial values, determination of fuzzy membership functions and fuzzy rules are complicated, how to find membership functions and fuzzy rules adapting to a current system is extremely important, the genetic algorithm is an intelligent method for high-efficiency global search optimization, the genetic algorithm is used for offline optimization of fuzzy PID initial values, after the initial values are assigned to the system, the membership functions and fuzzy rules are optimized online by adopting an improved genetic algorithm, and simulation research proves that the method is effective and can be widely applied to the setting system of the temperature control PID parameters of the reaction kettle in practical engineering.
Disclosure of Invention
The application provides an optimization method of a fuzzy control system in a reaction kettle based on a genetic algorithm, which mainly aims to solve the problem that membership functions and fuzzy rules are difficult to confirm in a fuzzy PID temperature control system through the genetic algorithm, so that the increment of the fuzzy PID controller on output PID control is more reasonable, the control performance of the fuzzy PID is further improved, and the temperature control system has better robustness, response speed and anti-interference performance.
In order to achieve the above object, the present application provides the following solutions:
an optimization method of a fuzzy control system based on a genetic algorithm in a reaction kettle comprises the following steps:
acquiring an initial value of a PID control system to obtain optimal PID control parameters after genetic optimization;
inputting the optimal PID control parameters as initial values to a fuzzy PID control system, and determining optimal membership functions and fuzzy rules of fuzzy PID control;
Optimizing membership functions and fuzzy rule parameters in the fuzzy PID controller by adopting a genetic algorithm to obtain an optimal chromosome gene;
and implanting the optimal chromosome gene into a fuzzy PID controller to finish optimization.
Preferably, the method for obtaining the initial value of the PID control system comprises the following steps: and adopting a genetic algorithm, adopting binary coding to PID parameters to form a chromosome of 15 genes, determining fitness function, selection operator and operation parameters, acquiring optimal dyeing individuals after multi-generation inheritance, and obtaining PID control parameters through decoding.
Preferably, the ITAE index is used as one index of the fitness function, the selection operator adopts a tournament selection strategy, and the operation parameters include: algebra, crossover rate, mutation rate.
Preferably, the method for determining the optimal membership function and the fuzzy rule of the fuzzy PID control comprises the following steps: integer coding is carried out on the membership function and the fuzzy rule, and a chromosome of 177 genes is formed by coding; secondly, selecting offspring chromosomes from the parent chromosome population according to the fitness value; and thirdly, forming a next generation chromosome population by crossing mutation of the offspring chromosome genes, and finally ending the cycle according to the optimization algebra and the selection index of the system.
Preferably, the crossover rate and the mutation rate are adjusted according to the genetic algebra, and the adjustment formula is as follows:
in the formula, pc is the crossover rate, pm is the mutation rate, gen is the current algebra, and Maxgen is the algebra.
Preferably, the fuzzy language includes: positive Big (PB), median (PM), positive Small (PS), zero (Z), negative Small (NS), negative Median (NM), negative Big (NB).
Preferably, the membership functions include a Z-shaped membership function, an S-shaped membership function, and a triangular membership function.
Preferably, the first 30 genes of 177 basic chromosomes are coded by membership functions, and the last 147 genes are coded by fuzzy rules.
The beneficial effects of the application are as follows:
The simulation result shows that the fuzzy PID controller is optimized through the genetic algorithm, has better dynamic and static performance indexes in the reaction kettle control system, can obviously show better control effect, has smaller disturbance amplitude output by the system and can quickly recover and stabilize in shorter time after disturbance is added in the system, the anti-interference capability is obviously better than that of the traditional PID fixed value control, and the genetic algorithm selects the membership function and the fuzzy rule which are most suitable for the system through global search, so that the fuzzy PID control system is a method for effectively solving the problem that the membership function and the fuzzy rule table in the fuzzy PID control system are difficult to determine.
Drawings
In order to more clearly illustrate the technical solutions of the present application, the drawings that are needed in the embodiments are briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of an optimization method of a fuzzy control system in a reaction kettle based on a genetic algorithm in an embodiment of the application;
FIG. 2 is a schematic diagram of the overall structure of a temperature control system according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a simulation model of a fuzzy PID controller according to an embodiment of the application;
FIG. 4 is a schematic diagram of an off-line genetic algorithm optimized PID dyeing individual code according to an embodiment of the application;
FIG. 5 is a schematic diagram of an online genetic algorithm optimized fuzzy PID dyeing individual code according to an embodiment of the application;
FIG. 6 is a diagram of a membership function code abscissa diagram according to an embodiment of the present application;
FIG. 7 is a schematic diagram of a process for optimizing an fitness function genetic algorithm according to an embodiment of the present application;
FIG. 8 is a schematic diagram of a step response curve of a control system according to an embodiment of the present application after adding a disturbance;
FIG. 9 is a schematic diagram of a step response curve of a control system varying an input signal according to an embodiment of the present application;
FIG. 10 is a membership function diagram of an input variable e after genetic algorithm optimization according to an embodiment of the present application;
FIG. 11 is a membership function diagram of an input variable ec after genetic algorithm optimization according to an embodiment of the present application;
FIG. 12 is a graph showing membership functions of the output variable ΔKp after optimization of the genetic algorithm according to an embodiment of the present application;
FIG. 13 is a graph showing membership functions of the output variable ΔKi after genetic algorithm optimization according to an embodiment of the present application;
FIG. 14 is a graph showing the membership function of the output variable ΔKd after optimization of the genetic algorithm according to the embodiment of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
In order that the above-recited objects, features and advantages of the present application will become more readily apparent, a more particular description of the application will be rendered by reference to the appended drawings and appended detailed description.
FIG. 1 is a schematic flow chart of an optimization method of a fuzzy control system in a reaction kettle based on a genetic algorithm according to an embodiment of the application; comprising the following steps: acquiring an initial value of a PID control system to obtain optimal PID control parameters after genetic optimization; inputting the optimal PID control parameters as initial values to a fuzzy PID control system, and determining optimal membership functions and fuzzy rules of fuzzy PID control; optimizing membership functions and fuzzy rule parameters in the fuzzy PID controller by adopting a genetic algorithm to obtain an optimal chromosome gene; and implanting the optimal chromosome gene into a fuzzy PID controller for optimization verification.
As shown in fig. 2, the temperature control system firstly adopts a genetic algorithm to acquire an initial PID value offline, and gives a global optimal PID initial value to an online control system, the online genetic algorithm is to search an optimal membership function and a fuzzy rule for the fuzzy PID control system, the membership function and the fuzzy rule directly affect the increment size of the PID, the membership function and the fuzzy rule are continuously adjusted through the genetic algorithm, and a global optimal membership function and a fuzzy rule table can be obtained after multiple generations of inheritance, wherein a transfer function is used as a controlled system, and the transfer function is as follows:
where s is a complex variable, 1 is an open loop gain of the control system, 40.89 is a time constant of the control system, and 6.055 is a delay time constant of the system.
As shown in FIG. 3, a simulation model of the control system is built by Simulink for algorithm verification, and one oscilloscope is used for observing a plurality of data simultaneously, so that the transformation of each parameter of the system is convenient to observe.
As shown in FIG. 4, the initial value of the traditional PID control system is obtained offline by adopting a genetic algorithm, the optimal PID control parameter is taken as the initial value of the fuzzy PID control parameter, the PID parameter is binary coded to form a chromosome of 15-bit genes, and an fitness function, a selection operator and an operation parameter are determined, wherein an ITAE index is taken as one index of the fitness function, the adjustment time and the overshoot are added as the objective function of the evaluation system on the premise of taking the ITAE index as the basis, the inverse weighting of the objective function is taken as the fitness function, and the direction of genetic algorithm optimization is the direction of the increase of the fitness value. The selection operator adopts a tournament selection strategy, two dyeing individuals are randomly selected from the parent population each time, one dyeing individual with higher fitness is selected to enter the offspring population by comparing the fitness of the two dyeing individuals, and the better individual is continuously selected by the circulation operation until the population number reaches the same chromosome number as the parent population. In addition, if all the genes of the father generation participate in the cross mutation of the post-selection operator, the gene with the highest quality possibly can be destroyed along with the genetic cross mutation, so that the optimal fitness of the offspring dyeing individuals is not higher than that of the father generation, the evolution does not develop towards the higher fitness value, and the genetic algebra is increased, therefore, when the offspring is selected, the optimal 5 offspring dyeing individuals of the father generation are reserved to be directly copied to the offspring, and the chromosome cross and mutation are not carried out. Wherein the operating parameters include: the genetic algebra, the crossover rate and the mutation rate are adjusted according to the genetic algebra, the convergence speed can be accelerated by the larger crossover rate and the smaller mutation rate, the later stage is evolved, the smaller crossover rate and the larger mutation rate can prevent sinking into local optimum, and the adjustment formula is expressed as follows:
In the formula, pc is the crossover rate, pm is the mutation rate, gen is the current algebra, and Maxgen is the algebra. Obtaining an optimal dyeing individual after multiple generations of inheritance, obtaining PID control parameters through decoding, and recording the optimal PID control parameters after genetic optimization; the off-line genetic algorithm adopts binary coding, PID parameters are obtained through calculation according to a critical proportion method, the estimated parameter range [0,20] is 10 < -4 >, the parameter range is required to be divided into intervals of 20 x 104 equal length, so that one parameter coding bit number at least needs 15 bits, and three parameter codes need 45 bit binary numbers to be represented. Confirming a fuzzy set of input and output variables in a fuzzy PID control system, determining a basic domain and a quantitative domain of the input and output variables, determining a quantization factor through the basic domain and the quantitative domain, and then determining a membership function basic form of a fuzzy subset in the fuzzy PID control;
decoding by an offline genetic algorithm, converting each chromosome binary number into a decimal number, and obtaining PID parameters after conversion, wherein the conversion formula is expressed as follows:
Where s i is a binary number of each bit, l is a gene coding length, a is a minimum value of a parameter range, b is a maximum value of the parameter range, x' is a decimal number of a chromosome, and x is a calculated parameter value.
As shown in fig. 5, a genetic algorithm is adopted to optimize membership function and fuzzy rule parameters in the fuzzy PID controller on line, the fitness function and the operation parameters are the same as those in the second step, and first, integer coding is carried out on the membership function and the fuzzy rule, so that a chromosome of 177 genes is formed by coding; 177 basic chromosomes, the first 30 genes are coded by membership functions, and the last 147 genes are coded by fuzzy rules. Secondly, selecting offspring chromosomes from the parent chromosome population according to the fitness value; thirdly, forming a next generation chromosome population by crossing mutation of the offspring chromosome genes, and finally ending the cycle according to the optimization algebra and the selection index of the system; and (3) coding the abscissa of the membership function, wherein the NB subset adopts a Z-shaped membership function, the PB subset adopts an S-shaped membership function, and the NM, NS, Z, PS, PM subset adopts a triangular membership function.
The triangle membership function adopted by the fuzzy subset NM, NS, PS, PM is respectively a Z-shaped membership function adopted by the NB, a B and a PB, wherein the triangle membership function adopted by the fuzzy subset NM, NS, PS, PM is B, C, D, E, the Z-shaped membership function adopted by the NB is A, the S-shaped membership function adopted by the PB is B. The fuzzy rule codes, the fuzzy controller has 7 fuzzy subsets, 49 rules and 3 outputs, the code length of the fuzzy rules is 49x3 = 147, the 49 fuzzy rules to be optimized are coded by integers, the fuzzy set { NB, NM, NS, ZO, PS, PM, PB } is correspondingly coded by integers {1,2,3,4,5,6,7}, the gene variation range of the population is set as an integer with delta kp, delta ki and delta kd as [1,7], and the membership value of the fuzzy subset can be correspondingly obtained.
As shown in fig. 6, a common fuzzy language: positive Big (PB), median (PM), positive Small (PS), zero (Z), negative Small (NS), negative Median (NM), negative Big (NB), fuzzy set { NB, NM, NS, ZO, PS, PM, PB }.
And decoding the membership function, and converting the integer codes corresponding to the first 30 genes of the chromosome genes into the coordinate positions in the corresponding input-output basic domains [ -3,3 ]. Taking e membership function as an example, the conversion formula is expressed as follows:
Wherein, x1, x2, x3, x4, x5 and x6 are gene coding values corresponding to the membership function of error e, A, B, C, D, E, F is that the abscissa position A, B, C point in the basic domain of the fuzzy subset NB, NM, NS, PS, PM, PB is at the left side of the coordinate axis, and the calculated result takes a negative value. And decoding fuzzy rules, namely sequentially arranging the last 147 genes in the dyeing individual into a matrix of 49 rows and 3 columns, wherein each row of genes corresponds to one fuzzy rule, and adding the fuzzy rule to the FIS structure through a addrule () function in Matlab.
As shown in FIG. 7, as the number of genetic algebra increases, the fitness value of the optimally stained individuals of the population increases, and the final optimal fitness is 0.750083.
As shown in fig. 8, the PID optimal initial value kp=2.4039, ki=0.0352 and kd= 13.5048 obtained through the offline genetic algorithm, through the given system unit step input, the GA-Fuzzy-PID, GA-PID and control effect are compared, and the rapidity and stability of the GA-Fuzzy-PID are obviously superior to those of the Fuzzy-PID and GA-PID, and the adjustment time is 36.8s, 44.3s and 75.8s respectively. When the system runs to 250s, 50% of interference of input signals is added, the overshoot is 8.5%, 9.6% and 12% respectively, the system recovery stability time is 75.7s, 88.2s and 126.9s respectively, and the anti-interference performance is obviously superior to that of Fuzzy-PID and GA-PID.
As shown in FIG. 9, when the system is running stably and then is running to 250s, the step input signal is changed, and the system adjustment time is respectively 30.4s, 39.3s and 58.9s, so that the GA-Fuzzy-PID has better rapidity and basically no overshoot.
As shown in table 1, the optimal fuzzy rule table after genetic algorithm optimization is shown.
TABLE 1
As shown in fig. 10, a membership function diagram of the optimal input variable e after genetic algorithm optimization is shown.
As shown in fig. 11, a membership function diagram of the optimal input variable ec after genetic algorithm optimization is shown.
As shown in fig. 12, a membership function diagram of the optimal output variable Δkp after genetic algorithm optimization is shown.
As shown in fig. 13, a membership function diagram of the optimal output variable Δki after genetic algorithm optimization is shown.
As shown in fig. 14, a membership function diagram of the optimal output variable Δkd after genetic algorithm optimization is shown.
The above embodiments are merely illustrative of the preferred embodiments of the present application, and the scope of the present application is not limited thereto, but various modifications and improvements made by those skilled in the art to which the present application pertains are made without departing from the spirit of the present application, and all modifications and improvements fall within the scope of the present application as defined in the appended claims.
Claims (4)
1. The optimization method of the fuzzy control system of the reaction kettle based on the genetic algorithm is characterized by comprising the following steps:
acquiring an initial value of a PID control system to obtain optimal PID control parameters after genetic optimization;
inputting the optimal PID control parameters as initial values to a fuzzy PID control system, and determining optimal membership functions and fuzzy rules of fuzzy PID control;
Optimizing membership functions and fuzzy rule parameters in the fuzzy PID controller by adopting a genetic algorithm to obtain an optimal chromosome gene;
implanting the optimal chromosome gene into a fuzzy PID controller to finish optimization;
The method for acquiring the initial value of the PID control system comprises the following steps: adopting a genetic algorithm, adopting binary coding to PID parameters to form a chromosome of 15 genes, determining fitness function, selection operator and operation parameters, acquiring optimal dyeing individuals after multi-generation inheritance, and obtaining PID control parameters through decoding;
adopting ITAE index as one index in the fitness function, adding adjusting time and overshoot as objective function, adopting reciprocal weighting of the objective function as fitness function, adopting tournament selection strategy by the selection operator, selecting two chromosomes from parent population randomly each time, selecting one chromosome with higher fitness to enter offspring population by comparing fitness of two chromosomes, continuously selecting better individuals by cyclic operation until population number reaches the same chromosome number as parent, and keeping parent optimal 5 chromosomes to copy directly to offspring when selecting to enter offspring, without chromosome crossing and mutation; the operating parameters include: algebra, crossover rate, mutation rate;
The method for determining the optimal membership function and the fuzzy rule of the fuzzy PID control comprises the following steps: integer coding is carried out on the membership function and the fuzzy rule, and a chromosome of 177 genes is formed by coding; secondly, selecting offspring chromosomes from the parent chromosome population according to the fitness value; thirdly, forming a next generation chromosome population by crossing mutation of the offspring chromosome genes, and finally ending the cycle according to the optimization algebra and the selection index of the system;
the fuzzy languages include: positive large PB, median PM, positive small PS, zero Z, negative small NS, negative median NM, negative large NB;
the conversion formula for membership function decoding is as follows:
Wherein x 1、x2、x3、x4、x5、x6 is a gene coding value corresponding to an error e membership function, A, B, C, D, E, F is the abscissa position in the basic domain of the fuzzy subset NB, NM, NS, PS, PM, PB, A, B, C points are on the left side of the coordinate axis, and the calculation result takes a negative value;
And decoding fuzzy rules, namely sequentially arranging the last 147 genes in the dyeing individual into a matrix of 49 rows and 3 columns, wherein each row of genes corresponds to one fuzzy rule, and adding the fuzzy rule to the FIS structure through a addrule () function in Matlab.
2. The optimization method of the fuzzy control system based on the genetic algorithm in the reaction kettle according to claim 1, wherein the crossover rate and the mutation rate are adjusted according to the genetic algebra, and an adjustment formula is as follows:
in the formula, pc is the crossover rate, pm is the mutation rate, gen is the current algebra, and Maxgen is the algebra.
3. The optimization method based on a fuzzy control system of a reaction kettle according to claim 1, wherein the membership functions comprise a Z-shaped membership function, an S-shaped membership function and a triangle membership function.
4. The optimization method based on the genetic algorithm in the fuzzy control system of the reaction kettle according to claim 1, wherein the first 30 genes are membership function codes and the last 147 genes are fuzzy rule codes of one 177 basic chromosomes.
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| CN103116276A (en) * | 2013-03-04 | 2013-05-22 | 广西大学 | Piezoelectric ceramic objective driver control method |
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| CN103792959A (en) * | 2012-10-30 | 2014-05-14 | 重庆科技学院 | Genetic algorithm optimized fuzzy PID flow control method in variable-rate spraying system |
| CN103984234A (en) * | 2014-05-15 | 2014-08-13 | 张万军 | Electro hydraulic servo system self-correction fuzzy PID control method |
| CN105867112B (en) * | 2016-04-15 | 2019-02-12 | 浙江大学 | A kind of intelligent vehicle and its control method of the control algolithm based on parameter automatic optimization |
| CN105807607B (en) * | 2016-05-11 | 2018-09-25 | 杭州电子科技大学 | A kind of genetic algorithm optimization predictive fuzzy PID coking furnace temprature control methods |
| CN107779593A (en) * | 2016-08-25 | 2018-03-09 | 郭琳 | A kind of scheelite temperature of reaction kettle control system |
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| CN107894716A (en) * | 2017-11-28 | 2018-04-10 | 昆山艾派科技有限公司 | Temprature control method |
| CN110609478B (en) * | 2019-10-21 | 2023-03-03 | 常州大学 | Air pressure self-adaptive online PID (proportion integration differentiation) setting method based on improved genetic algorithm |
| CN114002946B (en) * | 2021-12-31 | 2022-05-03 | 浙江中控技术股份有限公司 | Self-adaptive PID parameter setting method, system, electronic equipment and storage medium |
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| CN103116276A (en) * | 2013-03-04 | 2013-05-22 | 广西大学 | Piezoelectric ceramic objective driver control method |
| CN112947627A (en) * | 2021-02-24 | 2021-06-11 | 金陵科技学院 | Temperature control method based on DDPG-fuzzy PID |
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