CN117970782B - Fuzzy PID control method based on fish scale evolution GSOM improvement - Google Patents
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Abstract
The invention belongs to the technical field of fuzzy PID control, and particularly relates to a fuzzy PID control method based on fish scale evolution GSOM improvement, which comprises the steps of establishing a fish scale regulating system, introducing a differential evolution algorithm into the fish scale regulating system, and optimizing and upgrading the fuzzy PID control system through the fish scale regulating system; introducing GSOM modules into the fish scale regulating system, and dynamically updating the weight in the fuzzy PID control system; setting a fuzzy rule base in the fuzzy PID control system, and dynamically optimizing the fuzzy rule base and a parameter adjusting mechanism in the fuzzy PID control system to finish the improvement of the fuzzy PID control system. According to the invention, a fish scale adjusting system, a differential evolution theory and dynamic adjustment of GSOM modules are introduced, so that a fuzzy PID control method based on fish scale evolution GSOM improvement is obtained, and the stability, control precision and feedback output effect of the traditional fuzzy PID control are effectively improved.
Description
Technical Field
The invention belongs to the technical field of fuzzy PID control, and particularly relates to a fuzzy PID control method based on fish scale evolution GSOM improvement.
Background
Fuzzy PID control is a technique that combines fuzzy logic and classical PID control. The fuzzy logic concept is introduced on the basis of the traditional PID control so as to process nonlinear systems, environments with large changes and fuzzy input-output relations. The fuzzy PID control mainly comprises three parts of data blurring processing, reasoning according to a fuzzy design rule and data blurring by deblurring. The fuzzy PID control involves applications in robot control in a number of aspects, such as motion control, multi-machine collaboration, path planning, visual tracking, etc. In order to meet the requirements of industrial intelligent development, improved methods of fuzzy PID control are continuously emerging. Common improvement methods include adaptive fuzzy PID control, fuzzy PID control based on genetic algorithm, fuzzy PID neural network control, etc.
(1) And (5) self-adaptive fuzzy PID control. The self-adaptive fuzzy PID control realizes the on-line adjustment of the parameters of a controller (fuzzy PID control system) by introducing a self-adaptive mechanism so as to adapt to the change of the working state of the system. However, the method introduces higher computational load, so that the response speed of the controller is slower, and meanwhile, the rapid adjustment capability on the system parameter change is insufficient, so that the robustness is affected.
(2) Fuzzy PID control based on genetic algorithm. And optimizing the fuzzy rules and parameters of the fuzzy PID controller by utilizing a genetic algorithm so as to realize a better control effect. Through the evolution process of the genetic algorithm, the optimized solution in the parameter space can be effectively searched, so that the controller is more suitable for different systems and control requirements. But the searching process may have drawbacks such as local optimal solution, and the like, resulting in insufficient stability of the controller.
(3) And (5) fuzzy PID neural network control. And combining the fuzzy logic with the neural network to construct the fuzzy PID neural network controller. The neural network can learn the dynamic characteristics and nonlinear relations of the system, so that the performance and the robustness of the controller are improved. This approach can be applied to complex nonlinear systems and can achieve better control and generalization capability. It requires a lot of data and computational resources during the training process resulting in a long training time. Meanwhile, the neural network structure and parameter setting have great influence on the stability and robustness of the controller.
In summary, several common fuzzy PID control methods have shortcomings in system stability, computational complexity, parameter adjustment, adaptability to environmental changes, and saturation. Therefore, it is important to explore a new fuzzy PID control method to effectively solve these drawbacks, to achieve efficient control over complex systems, and to improve the stability, robustness, and adaptability of the controller.
Disclosure of Invention
According to the defects in the prior art, the invention provides the fuzzy PID control method based on the improvement of the fish scale evolution GSOM, which can realize the efficient control of a complex system and improve the stability, the robustness and the adaptability of PID control.
In order to achieve the above purpose, the invention provides a fuzzy PID control method based on fish scale evolution GSOM improvement, which comprises the following steps:
s1, establishing a fish scale regulating system, introducing a differential evolution algorithm into the fish scale regulating system, and optimizing and upgrading a fuzzy PID control system through the fish scale regulating system, wherein the method comprises the following steps of:
s11, calculating the fitness of each individual in the population by using a differential evolution algorithm, and initializing the population for the fish scale regulation system;
s12, calculating scene parameter differences, and evaluating the current working state of the fish scale regulating system to determine whether the population is gathered or dispersed, so as to regulate the control effect of the fuzzy PID control system;
s13, establishing a scale adjustment control characteristic theorem, and updating the population state based on the scale adjustment control characteristic theorem;
s2, introducing GSOM a module into the fish scale regulating system, wherein the GSOM module is of a self-organizing neural network structure, and dynamically updating the weight in the fuzzy PID control system;
S3, setting a fuzzy rule base in the fuzzy PID control system, and dynamically optimizing the fuzzy rule base and a parameter adjusting mechanism in the fuzzy PID control system to finish the improvement of the fuzzy PID control system. The fuzzy PID control system is used for fuzzy PID control, and the improved fuzzy PID control method is obtained.
The invention discloses a fish scale regulating system, which is a regulating system based on a fish scale arrangement mode. It aims to optimize the performance of the fuzzy PID control system. The design inspiration of the system comes from the behavior characteristics of fish in different water temperature environments. Wherein, fish scales gather at lower water temperature, and the heat dissipation surface area is reduced to keep the body temperature. And the scales are dispersed at a higher water temperature, so that the heat dissipation surface area is increased to dissipate heat. The fish scale regulation system is used for simulating the behavior characteristics so as to cope with different working environments and task demands. The introduction of differential evolution theory makes the system further optimized and upgraded.
GSOM modules are prior art. The conventional SOM model has many disadvantages, in particular, limitations in the number of network elements and the configuration thereof need to be predetermined. For this reason, researchers have proposed various solutions for dynamically determining the shape of the network and the number of cells during training, typically GSOM (Growing Self-Organizing network). The basic idea of the algorithm is to take a simplex in n-dimensional space, such as a line segment in one-dimensional space, a triangle in two-dimensional space and a tetrahedron in three-dimensional space as basic building modules, and progressively and dynamically generate an SOM network along with continuous training.
Initializing populations is one of the key steps in establishing a scale regulation system. In the step S11, the initializing of the population (namely, the fish scale population) comprises the following steps:
S111, defining a parameter space of a fuzzy PID control system, wherein the parameter space comprises a proportional coefficient K p, an integral coefficient K i and a differential coefficient K d, the ranges of K p、Ki and K d are set as [ a, b ], and the precision is p; setting the range and the precision of parameters according to the specific application scene of the parameter space;
s112, initializing individuals, representing by means of an individual set F, F is the initial starting point of the population,/>Is an individual (namely, a fish scale individual);
S113, for each individual in F, generating K p、Ki and K d corresponding to each individual, wherein the K p、Ki and the K d are represented by a set H: K p、Ki and K d corresponding to each individual meet the range requirements [ a, b ] and the precision requirement p;
s114, calculating the fitness of each individual by using a differential evolution algorithm, wherein the calculation indexes of the fitness are as follows:
（1）；
Wherein Fit is the total fitness function of the population; m is the total number of individuals; out target_k and out actual_k are the target output and the actual output of the kth individual in the fuzzy PID control scenario, k=1, 2, … …, m;
The error function here is constant based on the error between the actual output of the fuzzy PID control system and the target output. And calculating the fitness, namely setting the current performance of the fuzzy PID control system according to the current parameters, and evaluating the control effect. The adaptation calculation method commonly used in the known differential evolution algorithm is based on an error function. Therefore, in the context of fuzzy PID control, the control effect is evaluated using an error function.
S115, the fitness of each individual is the absolute value of the difference between the actual output and the target output of the individual in the fuzzy PID control scene, and for the kth individual, the fitness is that; The smaller the calculated fitness value is, the better the control effect of the fuzzy PID control system is, and the higher the fitness of an individual is, so that the probability of the individual to become a father of the next generation is higher;
S116, forming an initial population by the individuals with calculated fitness, taking the initial population as a starting point of a differential evolution algorithm, wherein each individual in the population represents a PID control strategy and is expressed as an individual parameter vector K pk、Kik and K dk are the proportional, integral and differential coefficients, respectively, of the kth individual, and the initialization process of the population is expressed as/>Rand () is a random function.
The scene parameters refer to important parameter factors in the actual application scene of the invention. The process of calculating scene parameter differences is a very critical step in the scale adjustment system. In the step S12, the step of adjusting the control effect of the fuzzy PID control system is as follows:
S121, representing actual scene parameters by phi, representing reference values of phi as vectors, defining reference scene parameters as phi ref and current scene parameters as phi current, wherein Phi ref is a matrix vector of 1 row and m columns,/>Actual scene parameters corresponding to each individual;
S122, calculate the difference between Φ current and Φ ref, i.e The difference determines the aggregation or dispersion state of the population in the fish scale regulating system so as to realize dynamic regulation of scene change;
S123, adjusting the output of a fuzzy PID control system through scene parameters, wherein the output of the fuzzy PID control system is expressed as:
（2）；
Wherein u (t) is the output of the fuzzy PID control system at the time t; e (t_k) represents the deviation of the kth individual from the current moment, i.e. the error between the desired value and the actual value, e (t_k) corresponds to the fitness function, i.e ；An integral term representing the deviation, representing the cumulative amount of the deviation over time; /(I)A derivative term representing the deviation, representing the rate of change of the deviation over time; /(I)As the difference between the current scene parameter Φ current_k and the reference scene parameter Φ ref_k of the kth individual, Φ ref_k is the kth vector in Φ ref;
The scene parameter difference in the fish scale regulating system is mainly aimed at regulating the output in the fuzzy PID control system. And (3) through the formula (2), the control effect of the fuzzy PID control system is finely adjusted through scene differences and fitness functions of each individual.
In the step S13, the method for establishing the scale regulation control characteristic theorem and updating the population state comprises the following steps:
Defining an important current parameter gamma current, an ideal adjusting parameter gamma goal and a parameter threshold gamma threv of the fuzzy PID control system, and a scale aggregation coefficient sigma gather and a scale dispersion coefficient sigma disperse of the scale adjusting system;
When (when) When the fish scales gather, the fish scale regulating system reduces the variation amplitude of Γ current and Γ goal so as to maintain the stability of the fuzzy PID control system, and update parameters:；
When (when) When the fish scales are dispersed, the fish scale regulating system increases the variation amplitude of Γ current and Γ goal, accelerates the speed of the fuzzy PID control system adapting to environmental change, and updates the parameter/>；
When (when)When the fish scales are kept in a stable state, the current gamma current and gamma goal are maintained, and the balance state of the fuzzy PID control system is kept;
Wherein, sigma gather and sigma disperse are feedback results of dynamic adjustment of the fish scale system by a differential evolution algorithm, and the adjustment mode is as follows:
（3）；
（4）；
wherein, sigma gold and sigma dold are respectively the scale aggregation coefficient and the scale dispersion coefficient before adjustment; p 1 and p 2 are respectively a scaling factor and a convergence factor in a differential evolution algorithm, and are used for controlling the step length of adjustment, p 1 and p 2 are constants, and the values are in the range of [0,1 ];
When Γ goal deviates from Γ current, the adjustment amplitude of sigma gold and sigma dold becomes large, so that the convergence speed of the fuzzy PID control system is increased; as Γ goal approaches Γ current, the adjustment amplitude of σ gold and σ dold decreases, maintaining the stability of the fuzzy PID control system. The aggregation and dispersion coefficients in the fish scale regulating system are dynamically adjusted through differential evolution, so that the fish scale regulating system can be better adapted to different working environments and task requirements, and the control effect of the fuzzy PID control system is improved.
The method for acquiring the related parameters comprises the following steps: the simulated PID parameters are parameters of an object to be controlled in an actual application scene. The important current parameters Γ current, ideal tuning parameters Γ goal, etc. as in the present invention all fall within this category. The method for acquiring the parameters is different according to application scenes. As for the control of the robot arm, the torque therein is an important parameter. The magnitude of the torque may be constantly changing over time on the test system screen. Therefore, the tester only needs to record the different parameter changes at different moments according to the screen information. Some analog PID parameters can be obtained by external devices, such as a temperature sensor. The acquisition of the parameters with respect to the analog PID is thus different from application scenario to application scenario.
The scale aggregation coefficient σ gather and the scale dispersion coefficient σ disperse are important regulation coefficients in a scale regulation system. A fish scale regulating system belongs to a meta heuristic system. Inspired by the scale change effect of fish scales on water temperature change. The fish scales correspond to the fuzzy PID control method of the invention, and the water temperature change corresponds to the parameters to be controlled. The fish scale aggregation coefficient sigma gather and the fish scale dispersion coefficient sigma disperse are descriptions of aggregation and dispersion effects of fish scales. Therefore, the method is a description of the protection effect of the fuzzy PID control method, namely the coping strategy of the control method on the control parameters. Therefore, the sizes of the scale aggregation coefficient sigma gather and the scale dispersion coefficient sigma disperse need to be reasonably adjusted according to actual application scenes.
The application of the scale regulation control characteristic theorem is the key of the scale regulation system to adjust the output saturation degree of the fuzzy PID control system. The method can effectively prevent the oversaturation and undersaturation of the fuzzy PID control system and maintain the stable operation of the fuzzy PID control system.
In the step S2, a method for introducing GSOM modules into the fish scale regulating system and dynamically updating weights in the fuzzy PID control system comprises the following steps:
s21, in the self-organizing neural network structure, each neuron is regarded as a root node of the network, the connection weight among the neurons is regarded as the intensity of branches, and the connection weight among the neurons is expressed as:
（5）；
wherein W is the total weight; the neuron equivalent is an individual in the fish scale regulation system, i.e. the neuron equivalent is ; For each individual F d,d=1,2,……,m,Φcurrent_d in F, the current scene parameter of F d; phi ref_d is the reference scene parameter of f d; η is the learning rate and is used for controlling the step length of the weight update;
S22, mapping the f d to a GSOM module for competition learning, wherein each f d corresponds to one phi ref_d and weight W (d);
Setting N Input variables in a fuzzy PID control system, wherein the N Input variables are respectively expressed as input= { Input 1,input2,……,inputN }; the fuzzy rules are nl=m, and are respectively expressed as nl= { NL 1,nl2,……,nlM }, and the weight of each fuzzy rule is expressed as W (d) of each individual;
The GSOM module dynamically updates weights in the fuzzy PID control system, expressed as:
（6）；
In the method, in the process of the invention, The weight of the ith input variable at the time t+1 is represented; The weight of the ith input variable at the time t is represented; η (t) is the learning rate at time t; /(I) A parameter threshold value at the time t; /(I)The weight of the jth fuzzy rule at the time t is represented;
In the formula (6), the learning rate eta (t) controls the step length of weight updating, so that the step length is gradually reduced in the training process, and the stability of the formula (6) is ensured; difference weight Representing the topological relation between the jth fuzzy rule and the ith input variable, wherein the neuron is updated only when the input variable is related to the current fuzzy rule weight; The desired weight change threshold limit is represented such that the weight of the current fuzzy rule gradually trends toward the weight corresponding to the input variable, enabling dynamic adjustment and optimization of the weight.
In the step S3, the step of dynamically optimizing the fuzzy rule base in the fuzzy PID control system is as follows:
s31, setting a fuzzy rule base in the fuzzy PID control system, and initializing the fuzzy rule base into ; The general rule of the fuzzy rule base (the general rule is a conventional operation, and generally relates to the problem about the fuzzy rule base, and the used rules are the same) is defined as u=u k if e=e i and ec=ec j, where e represents the deviation, e i represents the membership of the deviation, e c represents the error rate, ec j represents the membership of the error rate, u represents the output of the fuzzy PID control system, and u k represents the membership of the output; setting an evaluation function/>E t represents the steady state error at time t;
S32, parameterizing membership functions in the fuzzy PID control system, updating the parameters through a scale regulation control characteristic theorem, and expressing the parameterized membership functions as ; Wherein individual f k represents/>C is the mathematical expectation and σ is the standard deviation;
When meeting the requirements Time,/>The update rule of (2) becomes:
（7）；
If not, the update rule becomes:
（8）；
In the method, in the process of the invention, For/>Is an optimization objective of (1);
The updating rules in the fuzzy rule base can better regulate the response attribute of the fuzzy rule base when the control input under different conditions is faced, improve the feedback output effect of fuzzification and fuzzy reasoning, and further need to improve the fuzzy rule base through the differential evolution thought thereof, and select and keep the rules with higher fitness.
S33, improving a fuzzy rule base by utilizing a differential evolution algorithm, and knowing individual parameter vectorsThe mutation operation is regulated and controlled by a fish scale regulating system, wherein the mutation operation mode of K pk is as follows:
（9）；
Wherein R rand1 and R rand2 are randomly selected rule bases (the rule bases are the number of rules used for describing and processing fuzzification in a fuzzy rule base; by adding the rule bases, the flexibility of the system can be increased, and the control input under different conditions can be better adapted); as a variation factor,/> And/>The scaling factors of the kth individual before and after updating are respectively;
the mutation operations of K ik and K dk were performed in the same manner;
s34, the cross mutation operation in the fuzzy rule base is expressed as follows:
（10）；
Wherein K child1 is the crossover parameter of K pk; CR is the probability of crossover variation;
Both K child2 and K child3 were cross mutated in the same way; k child2 and K child3 are crossover parameters of K ik and K dk, respectively; the rule base cross mutation principle is to reserve the rule with higher fitness and discard the rule with lower fitness.
The parameter adjustment mechanism in the fuzzy PID control system is a key to improve the control performance. However, this increases the complexity of system modeling and tuning because fuzzy PID requires the determination of fuzzy sets, membership functions, and fuzzy rules. Thus, parameter tuning of the fuzzy PID control system is more complex than conventional PID control. The performance instability in parameter adjustment is particularly problematic when dealing with complex dynamic systems and rapidly changing environments. In order to overcome the defects, the invention optimizes a parameter adjustment mechanism from the established fish scale evolution GSOM to finish the further upgrading of the fuzzy PID.
In the step S3, the step of the parameter adjusting mechanism in the dynamic optimization fuzzy PID control system is as follows:
s35, defining a multi-objective function of the fuzzy PID control system as follows:
（11）；
In the method, in the process of the invention, Is a parametric objective function with respect to Φ current and Γ current; mu 1 and mu 2 are both weighting coefficients; e d is the error at the current time; /(I)Is the error change rate at the current moment;
S36, iteratively updating parameters phi current and gamma current according to GSOM modules, wherein a set value of parameter initialization is phi current=r1,Γcurrent=r2;
Definition condition 1 is:
（12）；
Condition 2 is:
（13）；
Wherein Xn d represents the parameter error of the d-th individual;
When the parameters of the update iteration respectively meet the condition 1 or the condition 2, the adopted parameter adjustment mechanism is as follows:
（14）；
Wherein V d is the parameter update factor of the d-th individual; para is a parameter involved in regulation; Representation/> To update；/>Indicating that no update has occurred;
updating iterative parameters to select individuals with higher fitness as the population of the next generation fish scale regulating system, thereby finishing the improvement of the fuzzy PID control system.
The algorithm according to the present invention may be executed by an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the algorithm being implemented by the processor executing software.
The invention has the beneficial effects that:
According to the invention, by introducing a fish scale regulating system, a differential evolution theory and dynamic regulation of GSOM modules, an improved fuzzy PID control method based on fish scale evolution GSOM is obtained, the stability, control precision and feedback output effect of traditional fuzzy PID control are effectively improved, and the efficient control of a complex system can be realized, which is specifically expressed in:
(1) In the aspect of stability, the invention can reach a stable state more quickly, the stability effect is more obvious along with the time increase, and compared with the traditional fuzzy PID control, the stability is effectively improved;
(2) In the aspect of control precision, compared with the traditional simulated annealing PID and genetic algorithm PID, the invention has better performance, and realizes effective improvement of control precision by dynamically optimizing a fuzzy rule base and a parameter adjustment mechanism in fuzzy PID control;
(3) Simulation experiments prove that the invention has more excellent performance in the aspect of feedback output effect, obtains more excellent feedback output effect in a short time, and improves the response speed and accuracy of the control process.
In conclusion, the method is superior to the traditional fuzzy PID control method, particularly has the obvious advantages in the aspects of better adapting to dynamic change environment and having stronger robustness, and provides an effective solution for improving the stability and the precision of a fuzzy PID control system.
Drawings
FIG. 1 is a flow schematic of the present invention;
FIG. 2 is a graph of stability versus experiment during the verification process of the present invention; fig. 2 (a) is a graph of stability versus experiment for the first simulation test; fig. 2 (b) is a graph of stability versus experiment for the second simulation test;
FIG. 3 is a graph of stability effects of a robust simulation experiment during verification of the present invention, where (a) in FIG. 3 is a graph of stability effects of the fuzzy PID control method of the present invention under a changed input environment, and the number of iterations is 143; FIG. 3 (b) is a graph of the stability effect of the fuzzy PID control method of the present invention under varying input conditions, with an iteration number of 119; FIG. 3 (c) is a graph of the stability effect of the fuzzy PID control method of the present invention under varying input conditions, with an iteration number of 128; fig. 3 (d) is a graph of stability effects of the conventional fuzzy PID control method under a changed input environment, and the number of iterations is 201; FIG. 3 (e) is a graph of the stability effect of the conventional fuzzy PID control method under a changed input environment, with the iteration number being 172; FIG. 3 (f) is a graph of the stability effect of the conventional fuzzy PID control method under a changed input environment, with a number of iterations of 195;
FIG. 4 is a graph of control accuracy versus experiment during verification of the present invention; FIG. 4 (a) is a graph showing the control accuracy of the simulated annealing PID over time; fig. 4 (b) is a graph of control accuracy of the genetic algorithm PID over time; FIG. 4 (c) is a graph of control accuracy over time for the improved PID of the invention;
FIG. 5 is a graph showing the comparison of feedback output effects in the verification process of the present invention.
Detailed Description
Embodiments of the invention are further described below with reference to the accompanying drawings:
as shown in fig. 1, a fuzzy PID control method based on fish scale evolution GSOM improvement comprises the following steps:
s1, establishing a fish scale regulating system, introducing a differential evolution algorithm into the fish scale regulating system, and optimizing and upgrading a fuzzy PID control system through the fish scale regulating system, wherein the method comprises the following steps of:
s11, calculating the fitness of each individual in the population by using a differential evolution algorithm, and initializing the population for the fish scale regulation system;
s12, calculating scene parameter differences, and evaluating the current working state of the fish scale regulating system to determine whether the population is gathered or dispersed, so as to regulate the control effect of the fuzzy PID control system;
s13, establishing a scale adjustment control characteristic theorem, and updating the population state based on the scale adjustment control characteristic theorem;
s2, introducing GSOM a module into the fish scale regulating system, wherein the GSOM module is of a self-organizing neural network structure, and dynamically updating the weight in the fuzzy PID control system;
s3, setting a fuzzy rule base in the fuzzy PID control system, and dynamically optimizing the fuzzy rule base and a parameter adjusting mechanism in the fuzzy PID control system to finish the improvement of the fuzzy PID control system.
In S11, the initializing step of the population is as follows:
S111, defining a parameter space of a fuzzy PID control system, wherein the parameter space comprises a proportional coefficient K p, an integral coefficient K i and a differential coefficient K d, the ranges of K p、Ki and K d are set as [ a, b ], and the precision is p;
s112, initializing individuals, representing by means of an individual set F, F is the initial starting point of the population,/>Is an individual therein;
S113, for each individual in F, generating K p、Ki and K d corresponding to each individual, wherein the K p、Ki and the K d are represented by a set H: K p、Ki and K d corresponding to each individual meet the range requirements [ a, b ] and the precision requirement p;
s114, calculating the fitness of each individual by using a differential evolution algorithm, wherein the calculation indexes of the fitness are as follows:
（1）；
Wherein Fit is the total fitness function of the population; m is the total number of individuals; out target_k and out actual_k are the target output and the actual output of the kth individual in the fuzzy PID control scenario, k=1, 2, … …, m;
s115, the fitness of each individual is the absolute value of the difference between the actual output and the target output of the individual in the fuzzy PID control scene, and for the kth individual, the fitness is that ；
S116, the individuals with calculated fitness form an initial population, each individual in the population represents a PID control strategy and is expressed as an individual parameter vectorK pk、Kik and K dk are the proportional, integral and differential coefficients, respectively, of the kth individual, and the initialization process of the population is expressed asRand () is a random function.
In S12, the step of adjusting the control effect of the fuzzy PID control system is:
S121, representing actual scene parameters by phi, representing reference values of phi as vectors, defining reference scene parameters as phi ref and current scene parameters as phi current, wherein Phi ref is a matrix vector of 1 row and m columns,/>Actual scene parameters corresponding to each individual;
S122, calculate the difference between Φ current and Φ ref, i.e The difference determines the aggregation or dispersion state of the population in the fish scale regulating system so as to realize dynamic regulation of scene change;
S123, adjusting the output of a fuzzy PID control system through scene parameters, wherein the output of the fuzzy PID control system is expressed as:
（2）；
Wherein u (t) is the output of the fuzzy PID control system at the time t; e (t_k) represents the deviation of the kth individual from the current moment, i.e. the error between the desired value and the actual value, e (t_k) corresponds to the fitness function, i.e ；An integral term representing the deviation, representing the cumulative amount of the deviation over time; /(I)A derivative term representing the deviation, representing the rate of change of the deviation over time; /(I)As the difference between the current scene parameter Φ current_k and the reference scene parameter Φ ref_k of the kth individual, Φ ref_k is the kth vector in Φ ref;
And (3) through the formula (2), the control effect of the fuzzy PID control system is finely adjusted through scene differences and fitness functions of each individual.
In S13, the method for establishing the scale regulation control characteristic theorem and updating the population state comprises the following steps:
Defining an important current parameter gamma current, an ideal adjusting parameter gamma goal and a parameter threshold gamma threv of the fuzzy PID control system, and a scale aggregation coefficient sigma gather and a scale dispersion coefficient sigma disperse of the scale adjusting system;
When (when) When the fish scales gather, the fish scale regulating system reduces the variation amplitude of Γ current and Γ goal so as to maintain the stability of the fuzzy PID control system, and update parameters:；
When (when) When the fish scales are dispersed, the fish scale regulating system increases the variation amplitude of Γ current and Γ goal, accelerates the speed of the fuzzy PID control system adapting to environmental change, and updates the parameter/>；
When (when)When the fish scales are kept in a stable state, the current gamma current and gamma goal are maintained, and the balance state of the fuzzy PID control system is kept;
Wherein, sigma gather and sigma disperse are feedback results of dynamic adjustment of the fish scale system by a differential evolution algorithm, and the adjustment mode is as follows:
（3）；
（4）；
wherein, sigma gold and sigma dold are respectively the scale aggregation coefficient and the scale dispersion coefficient before adjustment; p 1 and p 2 are respectively a scaling factor and a convergence factor in a differential evolution algorithm, and are used for controlling the step length of adjustment, p 1 and p 2 are constants, and the values are in the range of [0,1 ];
When Γ goal deviates from Γ current, the adjustment amplitude of sigma gold and sigma dold becomes large, so that the convergence speed of the fuzzy PID control system is increased; as Γ goal approaches Γ current, the adjustment amplitude of σ gold and σ dold decreases, maintaining the stability of the fuzzy PID control system.
In S2, the method for introducing GSOM modules into the fish scale regulating system and dynamically updating the weight in the fuzzy PID control system comprises the following steps:
s21, in the self-organizing neural network structure, each neuron is regarded as a root node of the network, the connection weight among the neurons is regarded as the intensity of branches, and the connection weight among the neurons is expressed as:
（5）；/>
wherein W is the total weight; the neuron equivalent is an individual in the fish scale regulation system, i.e. the neuron equivalent is ; For each individual F d,d=1,2,……,m,Φcurrent_d in F, the current scene parameter of F d; phi ref_d is the reference scene parameter of f d; η is the learning rate and is used for controlling the step length of the weight update;
S22, mapping the f d to a GSOM module for competition learning, wherein each f d corresponds to one phi ref_d and weight W (d);
Setting N Input variables in a fuzzy PID control system, wherein the N Input variables are respectively expressed as input= { Input 1,input2,……,inputN }; the fuzzy rules are nl=m, and are respectively expressed as nl= { NL 1,nl2,……,nlM }, and the weight of each fuzzy rule is expressed as W (d) of each individual;
The GSOM module dynamically updates weights in the fuzzy PID control system, expressed as:
（6）；
In the method, in the process of the invention, The weight of the ith input variable at the time t+1 is represented; The weight of the ith input variable at the time t is represented; η (t) is the learning rate at time t; /(I) A parameter threshold value at the time t; /(I)The weight of the jth fuzzy rule at the time t is represented;
In the formula (6), the learning rate eta (t) controls the step length of weight updating, so that the step length is gradually reduced in the training process, and the stability of the formula (6) is ensured; difference weight Representing the topological relation between the jth fuzzy rule and the ith input variable, wherein the neuron is updated only when the input variable is related to the current fuzzy rule weight; The desired weight change threshold limit is represented such that the weight of the current fuzzy rule gradually trends toward the weight corresponding to the input variable, enabling dynamic adjustment and optimization of the weight.
S3, the step of dynamically optimizing a fuzzy rule base in the fuzzy PID control system is as follows:
s31, setting a fuzzy rule base in the fuzzy PID control system, and initializing the fuzzy rule base into ; The general rule of the fuzzy rule base is defined as u=u k if e=e i and ec=ec j, where e represents the deviation, e i represents the membership of the deviation, e c represents the rate of error change, ec j represents the membership of the rate of error change, u represents the output of the fuzzy PID control system, u k represents the membership of the output; setting an evaluation function/>E t represents the steady state error at time t;
S32, parameterizing membership functions in the fuzzy PID control system, updating the parameters through a scale regulation control characteristic theorem, and expressing the parameterized membership functions as ; Wherein individual f k represents/>C is the mathematical expectation and σ is the standard deviation;
When meeting the requirements Time,/>The update rule of (2) becomes:
（7）；
If not, the update rule becomes:
（8）；
In the method, in the process of the invention, For/>Is an optimization objective of (1);
s33, improving a fuzzy rule base by utilizing a differential evolution algorithm, and knowing individual parameter vectors The mutation operation is regulated and controlled by a fish scale regulating system, wherein the mutation operation mode of K pk is as follows:
（9）；
Wherein R rand1 and R rand2 are randomly selected rule bases; as a variation factor,/> AndThe scaling factors of the kth individual before and after updating are respectively;
the mutation operations of K ik and K dk were performed in the same manner;
s34, the cross mutation operation in the fuzzy rule base is expressed as follows:
（10）；
Wherein K child1 is the crossover parameter of K pk; CR is the probability of crossover variation;
both K child2 and K child3 were cross mutated in the same way; k child2 and K child3 are crossover parameters of K ik and K dk, respectively.
In S3, the steps of the parameter adjusting mechanism in the dynamic optimization fuzzy PID control system are as follows:
s35, defining a multi-objective function of the fuzzy PID control system as follows:
（11）；
In the method, in the process of the invention, Is a parametric objective function with respect to Φ current and Γ current; mu 1 and mu 2 are both weighting coefficients; e d is the error at the current time; /(I)Is the error change rate at the current moment;
S36, iteratively updating parameters phi current and gamma current according to GSOM modules, wherein a set value of parameter initialization is phi current=r1,Γcurrent=r2;
Definition condition 1 is:
（12）；
Condition 2 is:
（13）；
Wherein Xn d represents the parameter error of the d-th individual;
When the parameters of the update iteration respectively meet the condition 1 or the condition 2, the adopted parameter adjustment mechanism is as follows:
（14）；
Wherein V d is the parameter update factor of the d-th individual; para is a parameter involved in regulation; Representation/> To update；/>Indicating that no update has occurred;
updating iterative parameters to select individuals with higher fitness as the population of the next generation fish scale regulating system, thereby finishing the improvement of the fuzzy PID control system.
The effectiveness of the fuzzy PID control method is verified through experimental simulation, and the comparison indexes are stability, robustness, control precision and feedback output effect respectively. The simulation experiment is now analyzed.
Stability comparison experiments are shown in figure 2. In fig. 2, the conventional PID parameter tuning curve does not reach a good steady state within a set time. And the output curve after GSOM dynamic adjustments by the PID control method of the present invention approaches steady state after 8 seconds. The stabilizing effect becomes more pronounced with increasing time. The simulation process shows that the fuzzy PID control method has higher stability in the parameter adjusting curve.
In fig. 2, the dotted line of the PID control method of the present invention coincides with the solid line of the fitted curve, and the same line is formed, that is, the solid line after the coincidence. The stable section in fig. 2 is one up-down section. The interval is different according to the application scene. Such as torque for the robotic arm, this upper and lower interval is typically 0-1602rpm. When the curve is stable within the upper and lower sections, the curve becomes almost a horizontal straight line, and the stability adjustment is completed by the method represented by the curve.
In fig. 2, two simulation tests were performed to avoid the occurrence of accidents when testing the validity and feasibility of the PID control method of the present invention.
The robustness simulation experiment is shown in fig. 3. Robustness is embodied in this experiment as a stability analysis under different varying environments. Fig. 3 (a), fig. 3 (b) and fig. 3 (c) show the stability effect of the fuzzy PID control method of the present invention under the changed input environment, and the iteration times are 143, 119 and 128, respectively. Fig. 3 (d), fig. 3 (e) and fig. 3 (f) show the stability effect of the conventional fuzzy PID control method under the changed input environment, and the iteration times are 201, 172 and 195, respectively. Through a comparison experiment, the fuzzy PID control method is verified to have fewer iteration times, easier to enter a stable state and stronger robustness in a dynamic change environment.
In fig. 3, the parameter optimization curves: the model performance curves were evaluated in PID control. Convergence threshold: criteria for determining whether the optimization algorithm has converged to an optimal solution or near an optimal solution. Optimal parameters: parameter values or combinations of parameters that enable the model to achieve optimal performance. Steady state curve: the parameter optimization curve reaches the curve at the stable moment. In the robust simulation experiment, the convergence threshold and the optimal parameters are nearly equal.
The control accuracy comparison experiment is shown in fig. 4. The control accuracy is embodied as supersaturation and undersaturation phenomena in the experiment. The reasons such as membership function and system dynamic change in the fuzzy PID control can cause oversaturation and undersaturation, and the accuracy is reduced. Two traditional control methods, namely simulated annealing PID and genetic algorithm PID, are compared in terms of control accuracy. As can be seen from fig. 4, there are different deviations between the state outputs of the simulated annealing PID and the genetic algorithm PID and the optimization targets, thereby causing undersaturation and oversaturation phenomena to occur. The fuzzy PID control method has higher consistency between the state output and the optimization target. Wherein the critical curve plays a major critical limiting role in the state output.
In fig. 4, the optimization objective is the criteria to be met. I.e. the upper limit boundary. The state output is the real-time state output of the method. The critical curve is the boundary of the lower limit. The optimization objective and the critical curve thus actually correspond to a range. When the state output exceeds the optimization goal: supersaturation; when the state output is equal to the optimization objective: an optimal state; when the state output is less than the optimization goal: undersaturation.
The comparison experiment of the feedback output effect is shown in fig. 5, the simulated annealing PID and the genetic algorithm PID are respectively compared, and the time offset is increased on the basis of the feedback output. The fuzzy PID control method has better feedback output effect in a short time no matter before or after the offset.
In fig. 4 and 5, the improved PID is the fuzzy PID control method of the present invention.
In fig. 5, the fast responsiveness of the output effect is compared. The basis for the determination is the time period used when the process variable changes fastest (fastest change, i.e., fastest change when approaching a horizontal line). Compared with the genetic algorithm PID and the simulated annealing PID, the fuzzy PID control method of the invention has the advantages of least time consumption and earliest rapid change of the process variable.
The time offset represents a given offset, i.e. the time to start the comparison is not from 0, but rather waits for a period of time to be compared, the simulated offset being 0.1s. Therefore, after the time offset is added, the fuzzy PID control method still has better effect, and the quick response of the feedback output effect is shown.
Claims (1)
1. A fuzzy PID control method based on fish scale evolution GSOM improvement is characterized by comprising the following steps:
s1, establishing a fish scale regulating system, introducing a differential evolution algorithm into the fish scale regulating system, and optimizing and upgrading a fuzzy PID control system through the fish scale regulating system, wherein the method comprises the following steps of:
s11, calculating the fitness of each individual in the population by using a differential evolution algorithm, and initializing the population for the fish scale regulation system;
s12, calculating scene parameter differences, and evaluating the current working state of the fish scale regulating system to determine whether the population is gathered or dispersed, so as to regulate the control effect of the fuzzy PID control system;
s13, establishing a scale adjustment control characteristic theorem, and updating the population state based on the scale adjustment control characteristic theorem;
s2, introducing GSOM a module into the fish scale regulating system, wherein the GSOM module is of a self-organizing neural network structure, and dynamically updating the weight in the fuzzy PID control system;
S3, setting a fuzzy rule base in the fuzzy PID control system, and dynamically optimizing the fuzzy rule base and a parameter adjustment mechanism in the fuzzy PID control system to finish the improvement of the fuzzy PID control system;
In the step S11, the initializing of the population includes:
S111, defining a parameter space of a fuzzy PID control system, wherein the parameter space comprises a proportional coefficient K p, an integral coefficient K i and a differential coefficient K d, the ranges of K p、Ki and K d are set as [ a, b ], and the precision is p;
s112, initializing individuals, representing by means of an individual set F, F is the initial starting point of the population,/>Is an individual therein;
S113, for each individual in F, generating K p、Ki and K d corresponding to each individual, wherein the K p、Ki and the K d are represented by a set H: K p、Ki and K d corresponding to each individual meet the range requirements [ a, b ] and the precision requirement p;
s114, calculating the fitness of each individual by using a differential evolution algorithm, wherein the calculation indexes of the fitness are as follows:
（1）；
Wherein Fit is the total fitness function of the population; m is the total number of individuals; out target_k and out actual_k are the target output and the actual output of the kth individual in the fuzzy PID control scenario, k=1, 2, … …, m;
s115, the fitness of each individual is the absolute value of the difference between the actual output and the target output of the individual in the fuzzy PID control scene, and for the kth individual, the fitness is that ；
S116, the individuals with calculated fitness form an initial population, each individual in the population represents a PID control strategy and is expressed as an individual parameter vectorK pk、Kik and K dk are the proportional, integral and differential coefficients, respectively, of the kth individual, and the initialization process of the population is expressed asThe rand () is a random function;
In the step S12, the step of adjusting the control effect of the fuzzy PID control system is as follows:
S121, representing actual scene parameters by phi, representing reference values of phi as vectors, defining reference scene parameters as phi ref and current scene parameters as phi current, wherein Phi ref is a matrix vector of 1 row and m columns,/>Actual scene parameters corresponding to each individual;
S122, calculate the difference between Φ current and Φ ref, i.e The difference determines the aggregation or dispersion state of the population in the fish scale regulating system so as to realize dynamic regulation of scene change;
S123, adjusting the output of a fuzzy PID control system through scene parameters, wherein the output of the fuzzy PID control system is expressed as:
（2）；
Wherein u (t) is the output of the fuzzy PID control system at the time t; e (t_k) represents the deviation of the kth individual from the current moment, i.e. the error between the desired value and the actual value, e (t_k) corresponds to the fitness function, i.e ；An integral term representing the deviation, representing the cumulative amount of the deviation over time; /(I)A derivative term representing the deviation, representing the rate of change of the deviation over time; /(I)As the difference between the current scene parameter Φ current_k and the reference scene parameter Φ ref_k of the kth individual, Φ ref_k is the kth vector in Φ ref;
The control effect of the fuzzy PID control system is finely adjusted through scene difference and fitness function of each individual through the formula (2);
in the step S13, the method for establishing the scale regulation control characteristic theorem and updating the population state comprises the following steps:
Defining an important current parameter gamma current, an ideal adjusting parameter gamma goal and a parameter threshold gamma threv of the fuzzy PID control system, and a scale aggregation coefficient sigma gather and a scale dispersion coefficient sigma disperse of the scale adjusting system;
When (when) When the fish scales gather, the fish scale regulating system reduces the variation amplitude of Γ current and Γ goal so as to maintain the stability of the fuzzy PID control system, and update parameters:；
When (when) When the fish scales are dispersed, the fish scale regulating system increases the variation amplitude of Γ current and Γ goal, accelerates the speed of the fuzzy PID control system adapting to environmental change, and updates parameters；
When (when)When the fish scales are kept in a stable state, the current gamma current and gamma goal are maintained, and the balance state of the fuzzy PID control system is kept;
Wherein, sigma gather and sigma disperse are feedback results of dynamic adjustment of the fish scale system by a differential evolution algorithm, and the adjustment mode is as follows:
（3）；
（4）；
wherein, sigma gold and sigma dold are respectively the scale aggregation coefficient and the scale dispersion coefficient before adjustment; p 1 and p 2 are respectively a scaling factor and a convergence factor in a differential evolution algorithm, and are used for controlling the step length of adjustment, p 1 and p 2 are constants, and the values are in the range of [0,1 ];
When Γ goal deviates from Γ current, the adjustment amplitude of sigma gold and sigma dold becomes large, so that the convergence speed of the fuzzy PID control system is increased; when Γ goal approaches Γ current, the adjustment amplitude of sigma gold and sigma dold is reduced, and the stability of the fuzzy PID control system is maintained;
In the step S2, a method for introducing GSOM modules into the fish scale regulating system and dynamically updating weights in the fuzzy PID control system comprises the following steps:
s21, in the self-organizing neural network structure, each neuron is regarded as a root node of the network, the connection weight among the neurons is regarded as the intensity of branches, and the connection weight among the neurons is expressed as:
（5）；
wherein W is the total weight; the neuron equivalent is an individual in the fish scale regulation system, i.e. the neuron equivalent is ; For each individual F d,d=1,2,……,m,Φcurrent_d in F, the current scene parameter of F d; phi ref_d is the reference scene parameter of f d; η is the learning rate and is used for controlling the step length of the weight update;
S22, mapping the f d to a GSOM module for competition learning, wherein each f d corresponds to one phi ref_d and weight W (d);
Setting N Input variables in a fuzzy PID control system, wherein the N Input variables are respectively expressed as input= { Input 1,input2,……,inputN }; the fuzzy rules are nl=m, and are respectively expressed as nl= { NL 1,nl2,……,nlM }, and the weight of each fuzzy rule is expressed as W (d) of each individual;
The GSOM module dynamically updates weights in the fuzzy PID control system, expressed as:
（6）；
In the method, in the process of the invention, The weight of the ith input variable at the time t+1 is represented; /(I)The weight of the ith input variable at the time t is represented; η (t) is the learning rate at time t; /(I)A parameter threshold value at the time t; /(I)The weight of the jth fuzzy rule at the time t is represented;
In the formula (6), the learning rate eta (t) controls the step length of weight updating, so that the step length is gradually reduced in the training process, and the stability of the formula (6) is ensured; difference weight Representing the topological relation between the jth fuzzy rule and the ith input variable, wherein the neuron is updated only when the input variable is related to the current fuzzy rule weight; Representing a desired weight change threshold limit such that the weight of the current fuzzy rule gradually tends to the weight corresponding to the input variable, thereby realizing dynamic adjustment and optimization of the weight;
in the step S3, the step of dynamically optimizing the fuzzy rule base in the fuzzy PID control system is as follows:
s31, setting a fuzzy rule base in the fuzzy PID control system, and initializing the fuzzy rule base into ; The general rule of the fuzzy rule base is defined as u=u k if e=e i and ec=ec j, where e represents the deviation, e i represents the membership of the deviation, e c represents the rate of error change, ec j represents the membership of the rate of error change, u represents the output of the fuzzy PID control system, u k represents the membership of the output; setting an evaluation function/>E t represents the steady state error at time t;
S32, parameterizing membership functions in the fuzzy PID control system, updating the parameters through a scale regulation control characteristic theorem, and expressing the parameterized membership functions as ; Wherein individual f k represents/>C is the mathematical expectation and σ is the standard deviation;
When meeting the requirements Time,/>The update rule of (2) becomes:
（7）；
If not, the update rule becomes:
（8）；
In the method, in the process of the invention, For/>Is an optimization objective of (1);
s33, improving a fuzzy rule base by utilizing a differential evolution algorithm, and knowing individual parameter vectors The mutation operation is regulated and controlled by a fish scale regulating system, wherein the mutation operation mode of K pk is as follows:
（9）；
Wherein R rand1 and R rand2 are randomly selected rule bases; as a variation factor,/> And/>The scaling factors of the kth individual before and after updating are respectively;
the mutation operations of K ik and K dk were performed in the same manner;
s34, the cross mutation operation in the fuzzy rule base is expressed as follows:
（10）；
Wherein K child1 is the crossover parameter of K pk; CR is the probability of crossover variation;
Both K child2 and K child3 were cross mutated in the same way; k child2 and K child3 are crossover parameters of K ik and K dk, respectively;
In the step S3, the step of the parameter adjusting mechanism in the dynamic optimization fuzzy PID control system is as follows:
s35, defining a multi-objective function of the fuzzy PID control system as follows:
（11）；
In the method, in the process of the invention, Is a parametric objective function with respect to Φ current and Γ current; mu 1 and mu 2 are both weighting coefficients; e d is the error at the current time; /(I)Is the error change rate at the current moment;
S36, iteratively updating parameters phi current and gamma current according to GSOM modules, wherein a set value of parameter initialization is phi current=r1,Γcurrent=r2;
Definition condition 1 is:
（12）；
Condition 2 is:
（13）；
Wherein Xn d represents the parameter error of the d-th individual;
When the parameters of the update iteration respectively meet the condition 1 or the condition 2, the adopted parameter adjustment mechanism is as follows:
（14）；
Wherein V d is the parameter update factor of the d-th individual; para is a parameter involved in regulation; Representation/> To update；/>Indicating that no update has occurred;
updating iterative parameters to select individuals with higher fitness as the population of the next generation fish scale regulating system, thereby finishing the improvement of the fuzzy PID control system.
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