CN115755589A - Optimization method based on genetic algorithm in reaction kettle fuzzy control system - Google Patents
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Abstract
The application discloses an optimization method based on a genetic algorithm in a fuzzy control system of a reaction kettle, which comprises the following steps: acquiring an initial value of a PID control system to obtain an optimal PID control parameter after genetic optimization; inputting the optimal PID control parameter as an initial value into a fuzzy PID control system, and determining a fuzzy PID control optimal membership function and a fuzzy rule; optimizing a membership function 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 complete optimization. According to the method and the system, the membership function and the fuzzy rule in the fuzzy controller are optimized through a 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 method 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 of a reaction kettle based on a genetic algorithm.
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 verification of a temperature sensor 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 product quality, and the temperature control method of the reaction kettle needs to be optimized in order to improve the temperature control effect of the reaction kettle and improve the product quality.
The temperature control system has the characteristics of nonlinearity, hysteresis, time-varying property and the like, disturbance factors are multiple, a 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 for temperature control, the traditional PID fixed parameter control cannot meet the requirements of the control system.
The fuzzy PID control has better self-adaptive capacity, is widely applied to a temperature control system, and has an important function of improving the rapidity of the temperature control system of the reaction kettle. The fuzzy rules usually form a plurality of fuzzy rules according to expert experiences, and control parameters can be adaptively adjusted through concise, flexible and quick parameter setting to meet an intelligent control target, but a membership function and the fuzzy rules are usually obtained through the expert experiences and have no objective consistency evaluation, the selection of a PID initial value and the determination of the fuzzy membership function and the fuzzy rules are tedious, and it is very important how to find the membership function and the fuzzy rules which are suitable for a current system, the genetic algorithm is an efficient and globally search optimal intelligent method, the method optimizes the fuzzy PID initial value offline through the genetic algorithm, and after the initial value is assigned to the system, the membership function and the fuzzy rules are optimized online through the improved genetic algorithm, and the method effectiveness is proved through simulation research, so that the method can be widely applied to a setting system for controlling the PID parameters through the reaction kettle temperature in practical engineering.
Disclosure of Invention
The application provides an optimization method based on a genetic algorithm in a fuzzy control system of a reaction kettle, and mainly aims to solve the problem that membership functions and fuzzy rules in the fuzzy PID temperature control system are difficult to confirm through the genetic algorithm, so that the fuzzy PID controller is more reasonable in output PID control increment, 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 purpose, the present application provides the following solutions:
an optimization method based on a genetic algorithm in a fuzzy control system of a reaction kettle comprises the following steps:
acquiring an initial value of a PID control system to obtain an optimal PID control parameter after genetic optimization;
inputting the optimal PID control parameter as an initial value to a fuzzy PID control system, and determining a fuzzy PID control optimal membership function and a fuzzy rule;
optimizing a membership function and fuzzy rule parameters in a 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 complete optimization.
Preferably, the method for acquiring the initial value of the PID control system includes: and (3) adopting a genetic algorithm, carrying out binary coding on the PID parameters to form a chromosome of the 15-bit gene, determining a fitness function, selecting an operator and operating parameters, obtaining an optimal dyeing individual after multi-generation heredity, and decoding to obtain PID control parameters.
Preferably, an ITAE index is used as one index in the fitness function, the selection operator uses a tournament selection strategy, and the operation parameters include: genetic algebra, cross rate, mutation rate.
Preferably, the method for determining the fuzzy PID control optimal membership function and the fuzzy rule comprises the following steps: carrying out integer coding on the membership function and the fuzzy rule to form a chromosome of 177 genes; secondly, selecting offspring chromosomes from the parent chromosome population according to the fitness value; and thirdly, forming a next generation chromosome population by the aid of cross variation of the chromosome genes of the filial generations, and finally, finishing circulation according to the optimized generation number and the selection index of the system.
Preferably, the cross rate and the mutation rate are adjusted according to a genetic algebra, and the adjustment formula is as follows:
in the formula, pc is the cross rate, pm is the mutation rate, gen is the current genetic algebra, and Maxgen is the genetic algebra.
Preferably, the fuzzy language includes: positive Big (PB), positive Middle (PM), positive Small (PS), zero (Z), negative Small (NS), negative Middle (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, in the 177 basic chromosomes, the first 30 genes are coded by membership function, and the last 147 genes are coded by fuzzy rule.
The beneficial effect of this application does:
simulation results show that the fuzzy PID controller optimized through the genetic algorithm has better dynamic and static performance indexes in the reaction kettle control system, better control effect can be obviously seen, after disturbance is added in the system, the system output disturbance amplitude is smaller, the system can be quickly recovered and stabilized in a shorter time, the anti-interference capability is obviously superior to that of the traditional PID fixed value control, the genetic algorithm selects the membership function and the fuzzy rule which are most suitable for the system through global search, and the method 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 required to be used 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 it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without inventive labor.
FIG. 1 is a schematic flow chart of an optimization method based on a genetic algorithm in a fuzzy control system of a reaction kettle according to an embodiment of the present application;
FIG. 2 is a schematic diagram of an 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 the offline genetic algorithm optimized PID staining individual code of the embodiment of the application;
FIG. 5 is a schematic diagram of an online genetic algorithm optimized fuzzy PID dyed individual code according to an embodiment of the present application;
FIG. 6 is a schematic diagram of a membership function encoded abscissa in accordance with an embodiment of the present application;
FIG. 7 is a diagram illustrating a fitness function genetic algorithm optimization process 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 and a step response curve after adding interference;
FIG. 9 is a schematic diagram of a step response curve of a control system for varying an input signal according to an embodiment of the present application;
FIG. 10 is a diagram illustrating a membership function of an input variable e after genetic algorithm optimization according to an embodiment of the present application;
FIG. 11 is a schematic diagram of a membership function of an input variable ec after genetic algorithm optimization according to an embodiment of the present application;
FIG. 12 is a diagram illustrating a membership function of an output variable Δ Kp after genetic algorithm optimization according to an embodiment of the present application;
FIG. 13 is a schematic diagram of a membership function of an output variable Δ Ki after genetic algorithm optimization according to an embodiment of the present application;
FIG. 14 is a diagram illustrating a membership function of an output variable Δ Kd after genetic algorithm optimization according to an embodiment of the present application.
Detailed Description
The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only some embodiments of the present application, and not all embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort belong to the protection scope of the present application.
In order to make the aforementioned objects, features and advantages of the present application more comprehensible, the present application is described in further detail with reference to the accompanying drawings and the detailed description.
Fig. 1 is a schematic flow chart of an optimization method based on a genetic algorithm in a fuzzy control system of a reaction kettle according to an embodiment of the present application; the method comprises the following steps: acquiring an initial value of a PID control system to obtain an optimal PID control parameter after genetic optimization; inputting the optimal PID control parameter as an initial value into a fuzzy PID control system, and determining a fuzzy PID control optimal membership function and a fuzzy rule; optimizing a membership function 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 and verification.
As shown in fig. 2, the temperature control system firstly adopts the genetic algorithm to obtain the initial PID value offline, and then gives the global optimal PID value to the online control system, the online genetic algorithm searches the fuzzy PID control system for the optimal membership function and fuzzy rule, the membership function and fuzzy rule directly affect the increment of PID, the membership function and fuzzy rule are continuously adjusted by the genetic algorithm, and after a plurality of generations of inheritance, the global optimal membership function and fuzzy rule table can be obtained, wherein the transfer function is used as the controlled system, and the transfer function is:
where s is a complex variable, 1 is the open loop gain of the control system, 40.89 is the time constant of the control system, and 6.055 is the 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 simultaneously observing a plurality of data, so that the parameter transformation of the system can be conveniently observed.
As shown in fig. 4, a genetic algorithm is used to obtain an initial value participating in a conventional PID control system in an off-line manner, an optimal PID control parameter is used as an initial value of a fuzzy PID control parameter, the PID parameter is binary-coded to form a chromosome of a 15-bit gene, a fitness function, a selection operator and an operation parameter are determined, wherein an ITAE index is used as one index in the fitness function, an adjustment time and an overshoot are added as an objective function of an evaluation system on the premise of the ITAE index, a reciprocal weight of the objective function is used as the fitness function, and the optimization direction of the genetic algorithm is the direction of increasing the fitness value. The selection operator adopts a tournament selection strategy, randomly selects two dyeing individuals from a parent population each time, selects one dyeing individual with higher fitness to enter an offspring population by comparing the fitness of the two dyeing individuals, and continuously selects a better individual by circulating operation until the population number reaches the same chromosome number as the parent population. In addition, if all genes of the parent participate in cross mutation of the selected operators, the optimality genes can be damaged after genetic cross mutation, so that the optimal fitness of the dyeing individuals of the filial generation is not higher than that of the parent, evolution does not progress towards a higher fitness value, and genetic algebra is increased. Wherein the operating parameters include: the genetic algebra, the cross rate and the mutation rate are adjusted according to the genetic algebra, the convergence rate can be accelerated by the larger cross rate and the smaller mutation rate, the evolution is advanced to the later stage, the smaller cross rate and the larger mutation rate can prevent the local optimization, and the adjustment formula is expressed as follows:
in the formula, pc is the cross rate, pm is the mutation rate, gen is the current genetic algebra, and Maxgen is the genetic algebra. Obtaining an optimal dyeing individual after multi-generation heredity, obtaining a PID control parameter through decoding, and recording the optimal PID control parameter after heredity 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], the PID precision is required to be 10-4, the parameter range needs to be divided into 20-104 equal-length intervals, so that the number of the coded bits of one parameter needs to be at least 15 bits, and the three coded bits of the parameter need to be represented by 45-bit binary numbers. Confirming a fuzzification set of input and output variables in a fuzzy PID control system, confirming a basic discourse domain and a quantitative discourse domain of the input and output variables, confirming a quantization factor through the basic discourse domain and the quantitative discourse domain, and then confirming a membership function basic form of a fuzzy subset in the fuzzy PID control;
decoding by an off-line genetic algorithm, converting binary numbers of each chromosome into decimal numbers, and obtaining PID parameters after conversion, wherein the conversion formula is represented as follows:
in the formula, s i Is the binary number of each digit, l is the gene coding length, a is the minimum value of the parameter range, b is the maximum value of the parameter range, x' is the chromosome decimal number, and x is the calculated parameter value.
As shown in fig. 5, a membership function and fuzzy rule parameters in the fuzzy PID controller are optimized on line by using a genetic algorithm, and the fitness function and the operation parameters are the same as those in the second step, and first, the membership function and the fuzzy rule are integer-coded to form a chromosome of 177 genes; and in one 177 basic chromosomes, the first 30 genes are coded by membership function, and the last 147 genes are coded by fuzzy rule. Secondly, selecting offspring chromosomes from the parent chromosome population according to the fitness value; thirdly, forming a next generation chromosome population by the filial generation chromosome genes through cross variation, and finally ending the circulation according to the optimized generation number and the selection index of the system; and (4) encoding 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 and PM subsets adopt a triangular membership function.
The vertex horizontal coordinates of the triangular functions are B, C, D and E respectively according to the triangular membership functions adopted by the fuzzy subsets NM, NS, PS and PM, the Z-shaped membership function adopted by the NB is A according to the coordinate of the left end point of the NB, the S-shaped membership function adopted by the PB is B according to the coordinate of the right end point of the PB. Fuzzy rule coding, wherein a fuzzy controller has 7 fuzzy subsets, 49 rules and 3 outputs, the coding length of the fuzzy rule is 49x3=147, the 49 fuzzy rules needing to be optimized are coded by integers, the fuzzy set { NB, NM, NS, ZO, PS, PM, PB } is correspondingly coded by the integers {1,2,3,4,5,6,7}, the genetic variation range of the population is set to be an integer with the values of delta kp, delta ki and delta kd being [1,7], and then the membership value of the fuzzy subset can be corresponded.
As shown in fig. 6, the commonly used fuzzy language: positive Big (PB), positive Middle (PM), positive Small (PS), zero (Z), negative Small (NS), negative Middle (NM), negative Big (NB), fuzzy set is { NB, NM, NS, ZO, PS, PM, PB }.
And (4) decoding the membership function, and converting the integer codes corresponding to the first 30 genes of the chromosome genes into coordinate positions in the corresponding input and output basic discourse domain < -3,3 >. Taking the e membership function as an example, the conversion formula is as follows:
in the formula, x1, x2, x3, x4, x5 and x6 are gene coding values corresponding to an error E membership function, A, B, C, D, E and F are fuzzy subsets NB, NM, NS, PS, PM and PB basic theory domain abscissa positions A, B and C are on the left side of the coordinate axis, and the calculation result takes a negative value. And (3) fuzzy rule decoding, wherein the last 147 genes in the dyed individuals are sequentially arranged into a matrix with 49 rows and 3 columns, each row of genes corresponds to one fuzzy rule, and the fuzzy rules are added to the FIS structure through an addrule () function in Matlab.
As shown in fig. 7, with the increase of the genetic algebra, the fitness value of the population individual optimal staining individual is also increased, and the final optimal fitness is 0.750083.
As shown in FIG. 8, optimal initial values kp =2.4039, ki =0.0352 and kd =13.5048 of the PID obtained through an off-line genetic algorithm, and by comparing GA-Fuzzy-PID, GA-PID and control effects given system unit step input, the rapidity and stability of the GA-Fuzzy-PID are obviously superior to those of the Fuzzy-PID and the GA-PID, and the adjusting time is respectively 36.8s, 44.3s and 75.8s. When the system runs to 250s, the interference of 50% input signals is added, the overshoot is respectively 8.5%, 9.6% and 12%, the system recovery stability time is respectively 75.7s, 88.2s and 126.9s, and the anti-interference performance is obviously superior to that of Fuzzy-PID and GA-PID.
As shown in FIG. 9, when the system runs stably and runs to 250s, the step input signal is changed, the system adjusting time is respectively 30.4s, 39.3s and 58.9s, and it can be seen that the GA-Fuzzy-PID has better rapidity and basically has no overshoot.
As shown in table 1, the optimized fuzzy rule table is an optimized fuzzy rule table for genetic algorithm.
TABLE 1
Fig. 10 is a schematic diagram of a membership function of the optimized input variable e after genetic algorithm optimization.
Fig. 11 is a schematic diagram of a membership function of the optimized input variable ec optimized by the genetic algorithm.
As shown in fig. 12, a schematic diagram of a membership function of the optimized output variable Δ kp after genetic algorithm optimization is shown.
Fig. 13 is a schematic diagram of a membership function of the optimized output variable Δ ki after genetic algorithm optimization.
As shown in fig. 14, a schematic diagram of a membership function of the optimized output variable Δ kd after genetic algorithm optimization is shown.
The above-described embodiments are merely illustrative of the preferred embodiments of the present application, and do not limit the scope of the present application, and various modifications and improvements made to the technical solutions of the present application by those skilled in the art without departing from the spirit of the present application should fall within the protection scope defined by the claims of the present application.
Claims (8)
1. A method for optimizing a fuzzy control system of a reaction kettle based on a genetic algorithm is characterized by comprising the following steps:
acquiring an initial value of a PID control system to obtain an optimal PID control parameter after genetic optimization;
inputting the optimal PID control parameter as an initial value to a fuzzy PID control system, and determining a fuzzy PID control optimal membership function and a fuzzy rule;
optimizing a membership function and fuzzy rule parameters in a 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 complete optimization.
2. The optimization method for the fuzzy control system of the reaction kettle based on the genetic algorithm as claimed in claim 1, wherein the method for obtaining the initial value of the PID control system comprises: and (3) adopting a genetic algorithm, carrying out binary coding on the PID parameters to form a chromosome of the 15-bit gene, determining a fitness function, selecting an operator and operating parameters, obtaining an optimal dyeing individual after multi-generation heredity, and decoding to obtain PID control parameters.
3. The method as claimed in claim 2, wherein an ITAE indicator is used as one indicator in the fitness function, the selection operator uses a tournament selection strategy, and the operation parameters include: genetic algebra, cross rate, mutation rate.
4. The optimizing method of the fuzzy control system in the reaction kettle based on the genetic algorithm according to claim 1, wherein the method for determining the fuzzy PID control optimal membership function and the fuzzy rule comprises the following steps: carrying out integer coding on the membership function and the fuzzy rule to form a chromosome of 177 genes; secondly, selecting offspring chromosomes from the parent chromosome population according to the fitness value; and thirdly, forming a next generation chromosome population by the aid of cross variation of the chromosome genes of the filial generations, and finally, finishing circulation according to the optimized generation number and the selection index of the system.
5. The method as claimed in claim 3, wherein the cross 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 variation rate, gen is the current genetic algebra, and Maxgen is the genetic algebra.
6. The method for optimizing the fuzzy control system of the reaction kettle based on the genetic algorithm according to claim 1, wherein the fuzzy language comprises: positive large (PB), positive Middle (PM), positive Small (PS), zero (Z), negative Small (NS), negative Middle (NM), negative large (NB).
7. The genetic algorithm-based optimization method for the fuzzy control system of the reaction kettle according to claim 1, wherein the membership functions comprise Z-shaped membership functions, S-shaped membership functions and triangular membership functions.
8. The genetic algorithm-based optimization method for the fuzzy control system of the reaction kettle according to claim 4, wherein the first 30 genes are coded by the membership function and the last 147 genes are coded by the fuzzy rule in the 177 basic chromosomes.
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| 王平;: "基于差异图和块分类的雷达图像变化检测", 长春师范大学学报, no. 08, 20 August 2020 (2020-08-20) * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN118466173A (en) * | 2024-07-11 | 2024-08-09 | 山东艾盟生物科技有限公司 | Environment temperature control optimization method for canine house |
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| CN115755589B (en) | 2024-07-02 |
| ZA202300287B (en) | 2023-02-22 |
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