A water flow rate control method for a hydraulic actuator system

Abstract

The present invention proposes a water flow rate control method for a hydraulic actuator system, belonging to the field of water flow rate control, including: S1, collecting the water flow rate and pressure change data of the hydraulic actuator system, and establishing a data-driven water flow rate control model; S2, constructing an improved eagle-fish optimization algorithm, and using the improved eagle-fish optimization algorithm to online adjust the proportional, integral, and differential parameters of the positional PID control algorithm; S3, the positional PID control algorithm is used for the water flow rate controller of the hydraulic actuator system to adjust the output signal of the water flow rate controller; the output signal is input into the water flow rate control model to obtain the water flow rate of the real-time hydraulic actuator system; S4, calculating the difference between the target water flow rate and the real-time water flow rate, inputting the difference into the water flow rate controller, and using the positional PID control algorithm to adjust the water flow rate of the real-time hydraulic actuator system until the difference is lower than the target threshold, so as to realize the optimization of water flow rate control. Improve the control accuracy and response speed of the system.

Description

Technical Field

[0001] This application relates to the field of water flow rate control, and specifically relates to a water flow rate control method for a hydraulic execution system. Background Art

[0002] In various hydraulic execution systems, such as liquid transportation pipe networks, water pressure regulation equipment, pump-valve linkage systems, and fire water systems, water flow rate control, as a core link, directly affects the stability and response performance of system operation. To achieve precise control of the flow rate, the traditional proportional-integral-differential (PID) control algorithm is generally used to adjust the hydraulic system at present; the traditional PID controller adjusts the opening of the water pump or valve by generating a control signal based on the proportion, cumulative amount, and change rate of the error through real-time feedback adjustment of the flow rate error; it is difficult for the proportional, integral, and differential parameters of the traditional PID controller to achieve rapid adjustment for different hydraulic systems or dynamic load environments, and it relies on empirical settings and cannot meet the response requirements under complex working conditions; the response speed is limited and overshoot and oscillation are likely to occur: when facing system disturbances or setpoint changes, the control response often lags, which easily leads to large fluctuations in water pressure or water speed and a long stabilization time.

[0003] The HawkFish Optimization Algorithm (HFOA) is a swarm intelligence optimization algorithm inspired by the unique biological habits of hawkfish (fish with sex-changing behavior) in nature; when dealing with complex problems, especially water flow rate control problems with high control requirements, the standard HawkFish Optimization Algorithm is prone to premature convergence and getting stuck at local extreme points; as the number of iterations increases, the individual positions may tend to be the same, resulting in a significant reduction in population diversity, thus affecting the global search performance of the algorithm; after introducing the optimization algorithm, the computational complexity is higher than that of the traditional single PID algorithm, which poses higher requirements for the real-time processing ability of the water flow rate control system in practical applications. Summary of the Invention

[0004] Aiming at the problems existing in the above background art, this application proposes a self-regulating feedback control method for water flow rate control in a hydraulic execution system, aiming to use the traditional positional PID control algorithm and intelligent optimization algorithm to improve the control accuracy and control speed of the water flow rate controller of the hydraulic execution system by optimizing the water flow rate controller of the hydraulic execution system. The control accuracy is achieved by controlling the overshoot, and the control speed is achieved by adjusting the response time. The water flow rate control optimization method for the hydraulic execution system proposed in this application significantly improves the control accuracy and response speed of the system by combining the traditional PID control and intelligent optimization algorithm; this method is applicable to a variety of water application scenarios and can effectively improve the efficiency of the hydraulic execution system, providing a new solution for intelligent hydraulic application optimization.

[0005] The present invention proposes a water flow rate control method for a hydraulic actuator system, which optimizes the water flow rate controller of the hydraulic actuator system. The specific steps are as follows:

[0006] S1. Collect the water flow rate and pressure change data of the hydraulic actuator system, and establish a data-driven water flow rate control model;

[0007] S2. Construct an improved eagle-fish optimization algorithm, and use the improved eagle-fish optimization algorithm to online adjust the proportional, integral, and differential parameters of the positional PID control algorithm; the improved eagle-fish optimization algorithm improves the eagle-fish individual movement rule and learning coefficient of the standard eagle-fish optimization algorithm; specifically: S21. Regard the distribution state of the eagle-fish population in the search space as a spatial distribution field with a topological structure, and define a topological folding strategy to adaptively change the learning coefficient; S22. Introduce a probabilistic jump-type movement strategy, and use the historical difference trend of the surrogate individual fitness as the trigger condition for the jump to improve the eagle-fish individual movement rule;

[0008] S3. The positional PID control algorithm is used for the water flow rate controller of the hydraulic actuator system to adjust the output signal of the water flow rate controller; the output signal is input into the water flow rate control model to obtain the water flow rate of the real-time hydraulic actuator system;

[0009] S4. Calculate the difference between the target water flow rate and the real-time water flow rate, input the difference into the water flow rate controller, and use the positional PID control algorithm to adjust the water flow rate of the real-time hydraulic actuator system until the difference is lower than the target threshold, so as to realize the optimization of the water flow rate control.

[0010] Preferably, the hydraulic actuator system reflects AI intelligent control by automatically controlling the water flow. The hydraulic actuator system includes a data acquisition unit, a data-driven water flow rate control model unit, a PID controller unit, and an execution unit; the input data includes the water flow rate and pressure change data; based on the real-time collected water flow rate and pressure change data, a water flow rate control model is established; the real-time water flow rate data and the target water flow rate data are input into the data acquisition unit, and the water flow rate difference is output. The water flow rate difference is input into the PID controller unit, and the water flow rate difference is processed by the online adjusted positional PID control algorithm to output a control signal First, it acts on the water pump of the hydraulic actuator system to adjust the water pressure in real time; when the water pressure changes, according to the mapping relationship between the real-time water flow rate and the water pressure, through the water flow rate control model, the water flow rate changes accordingly, and finally the accurate regulation of the actual water flow rate is realized.

[0011] Preferably, the pressure control of the hydraulic actuator system is a dynamic process, and the present invention uses a typical second-order inertia link model to represent it. The second-order inertia link model is a time-domain model, and the input is a control signal , the output is the real-time water pressure of the hydraulic execution system; the real-time water pressure is converted into the real-time water flow rate through the water flow rate control model, and the water flow rate control model is:

[0012] ;

[0013] In the formula, is the water flow rate at the moment, and are model parameters, which are determined by online data identification, is the real-time water pressure at the moment, is the water flow rate at the moment.

[0014] Preferably, when the standard eaglefish optimization algorithm is used to adjust the parameters of the positional PID control algorithm, it is difficult to accurately capture the actual state of the agent individual in the search space, resulting in poor group exploration and development capabilities and being prone to falling into local optima; when using the improved eaglefish optimization algorithm to online adjust the parameters of the positional PID control algorithm, the eaglefish individual of the improved eaglefish optimization algorithm is used as the agent individual, and the position of the agent individual is updated through the eaglefish individual movement rule and the eaglefish learning rule. Among them, the position of the agent individual is mapped to the proportional, integral, and differential parameters of the positional PID control algorithm of the water flow rate controller of the hydraulic execution system, and the position of the mapped agent individual is a three-dimensional value, which is represented by a mathematical model as: \left ( {{K}^{n}_{p},{K}^{n}_{i},{K}^{n}_{d}} \right )=\left [ {{X}^{1}_{n},{X}^{2}_{n},{X}^{3}_{n}} \right ] ; Among them, , and are the proportional parameter, integral coefficient, and differential parameter corresponding to the position value of the nth agent individual; , and are the position values of the 1st, 2nd, and 3rd dimensions of the nth agent individual.

[0015] Preferably, the present invention breaks through the simple distance representation method in the existing standard eaglefish optimization algorithm and proposes a topological folding strategy. Specifically, this method regards the distribution state of the eaglefish population in the search space as a spatial distribution field with a topological structure, defines a topological folding strategy, and the topological folding strategy reflects the geometric characteristics and distribution density of the population position distribution. Through the topological folding strategy, the improved eaglefish optimization algorithm can keenly capture the subtle changes in the group state and drive the learning coefficient to adaptively change; the mathematical model is:

[0016] S211. Define the distribution of the eagle-fish population in the search space at the t-th iteration as the topological folding strategy , and the mathematical model is: ;

[0017] ;

[0018] In the formula, is the topological folding strategy at the t-th iteration, N is the maximum scale of the agent individuals, and n≠j; The Euclidean distance between the agent individuals in the population at the t-th iteration;

[0019] S212. Introduce the topological folding strategy and propose an adaptive regulation mathematical model for the learning coefficient:

[0020] ;

[0021] In the formula, is the minimum value of the learning coefficient, is the maximum value of the learning coefficient, μ is the sensitivity adjustment factor. The sensitivity adjustment factor starts from the fitness ranking ratio. The change trend of the relative ranking of the optimal agent individual in the population essentially reflects the search state of the group, and thus automatically feeds back to the sensitivity adjustment factor. The mathematical model is:

[0022] ;

[0023] Among them, is the sensitivity adjustment factor at the t-th iteration, is the ranking of the current optimal agent individual in the population.

[0024] Preferably, the sin term reflects the folding state of the topological space. The distance ratio is combined with the sine function, so that the topological folding strategy can reflect both the distance and the non-linear topological characteristics. The topological folding strategy reflects the tightness of the agent individual group and the complexity of the topological structure. When the value is large, the topological structure of the population is complex, indicating that the distribution of agent individuals is dispersed, that is, the distribution of solutions is dispersed. When the value is small, the topological structure is simple, indicating that the positions of agent individuals are concentrated, that is, there is a risk that the existence of solutions falls into local optima; arctan() is a non-linear smooth mapping function, which can naturally realize the adaptive regulation of the learning coefficient with the change of topological potential energy; when the population changes violently, the learning coefficient is adaptively increased to enhance the global exploration or fast focusing ability; when the population tends to be stable, the learning coefficient is automatically reduced to strengthen the local fine search.

[0025] Preferably, in the individual movement rule of the eagle fish in the present invention, on the basis of the conventional progressive update of the movement of the eagle fish individuals, a probabilistic jump-type movement strategy is innovatively introduced. When the eagle fish is trapped in a local search area for a long time, a jump is triggered with a certain probability (the trigger jump value), and a cross-space jump-type movement is implemented to effectively avoid the algorithm from premature convergence and falling into the local optimum; the strategy no longer uses the simple regulation of traditional distance or fitness, but uses the historical differential trend of the fitness of the proxy individuals as the trigger condition for the jump.

[0026] The mathematical model is:

[0027] ;

[0028] Wherein, is the position of the nth proxy individual at the (t + 1)-th iteration, is the position of the nth proxy individual at the t-th iteration, is the step size of the nth proxy individual, is the j-th dimension value of the direction vector of the nth proxy individual, is the centroid position of the current population, is the position of the current global optimal proxy individual; is the trigger jump value at the t-th iteration, rand is a random number uniformly distributed within 0 to 1, is the pseudo-pulse jump sensitivity parameter, which controls the change degree of the jump probability. The mathematical model is:

[0029] ;

[0030] In the formula, is the position of the nth proxy individual at the (t + 1)-th iteration, is the maximum number of iterations, randn(0,1) is a random number of the standard normal distribution;

[0031] Wherein, the trigger jump factor is used to judge that the eagle fish is trapped in the local search area for a long time. The mathematical model of the trigger jump factor is:

[0032] ;

[0033] In the formula, and are the fitness values of the i-th proxy individual at two consecutive iteration times.

[0034] Preferably, the improved eagle fish optimization algorithm is used to online adjust the proportional, integral, and differential parameters of the position-type PID control algorithm. During the adjustment process, the improved eagle fish optimization algorithm is guided by the fitness function to optimize the parameters, and the global optimal solution is found, that is, the position of the proxy individual corresponding to the minimum value of the fitness function. The specific steps are as follows:

[0035] S31. Initialize the positions of the population agents of the improved eagle-fish optimization algorithm , where the position of each agent is a D-dimensional vector; set the maximum number of iterations and the maximum population size ;

[0036] S32. Divide the eagle-fish individuals into male and female agents, define the availability of food resources in the environment as d(t), and design a gender transition mechanism model;

[0037] S33. Calculate the fitness value of each agent in the current iteration. The fitness value is the fitness function value of each agent's position. Denote the position of the agent corresponding to the current minimum fitness value as ;

[0038] S34. Calculate the triggering transition value in the t-th iteration, and update the positions of the agents by the mathematical model of the eagle-fish individual movement rule through the triggering transition value;

[0039] S35. Dynamically divide the subpopulations using the Euclidean distance matrix, perform dynamic clustering, and determine the positions of the subgroup leaders, where the positions of the subgroup leaders are the best agent positions in the subgroups;

[0040] S36. Adaptive regulate the learning coefficient through the topological folding strategy to construct the eagle-fish learning rule, and update the positions of the agents using the eagle-fish learning rule;

[0041] S37. The agents adjust the search range according to their genders, set a threshold. If the fitness value of an agent exceeds the threshold, the agent changes its gender and updates its position according to the dynamic vision rule;

[0042] S38. Limit the positions of the agents within the range [lb, ub], increment the current iteration count by one, and determine whether the current iteration count satisfies t + 1 = Tmax; if it satisfies, exit the optimization process, output the current global optimal agent position, and parse it into the proportional, integral, and differential parameter values of the position-type PID control algorithm, otherwise return to execute S33.

[0043] Preferably, the specific process of the gender transition mechanism is as follows: When the improved eagle-fish optimization algorithm is started, initialize the initial population of all eagle-fish individuals as agents of a single gender. Use the average fitness value of the current population as the threshold. If the fitness value of an agent exceeds the threshold, select a part of the female individuals from the current agent population for gender transition. After completing the gender transition, the improved eagle-fish optimization algorithm re-updates the gender ratio in the eagle-fish population and records the current male-to-female ratio for subsequent iterations.

[0044] Preferably, after the position of the agent individual is updated by the improved eagle-fish optimization algorithm, the position of the agent individual is less than the lower bound lb or greater than the upper bound ub. If the position of the agent individual is greater than the upper bound ub, the position of this individual is directly set to the upper bound value ub; if the position of the agent individual is less than the lower bound lb, the position of this individual is directly set to the lower bound value lb; if the position of the agent individual is between the upper and lower bounds, it remains unchanged.

[0045] Preferably, in S35, the eagle-fish learning rule is designed based on the position of the best agent individual in the subgroup and the adaptively regulated learning coefficient. The mathematical model is:

[0046] ;

[0047] In the formula, is the j-th dimensional value of the position of the n-th agent individual at the (t + 1)-th iteration, is the j-th dimensional value of the position of the n-th agent individual at the t-th iteration, is the adaptively regulated learning coefficient, is the j-th dimensional value of the position of the best agent individual at the t-th iteration.

[0048] Compared with the existing method, the beneficial effects and innovations of the present invention are as follows: The present invention breaks through the simple distance-based representation method in the standard eagle-fish optimization algorithm, and innovatively proposes a method for adaptively regulating the learning coefficient based on the topological folding strategy. The topological folding strategy keenly captures the geometric characteristics of the population position distribution, drives the dynamic change of the learning coefficient, enables the algorithm to quickly respond to small changes in the optimization environment, more effectively avoids the algorithm falling into local optimum, and thus optimizes to obtain the proportional, integral, and differential parameter values of the best position-type PID control algorithm; at the same time, the probabilistic jump-type movement strategy is innovatively introduced, and the historical differential trend of the agent individual fitness is used as the basis for jump triggering. When the agent individual is trapped in the local search area for a long time, the algorithm performs cross-region jumps with a certain probability, enhancing the global search ability of the algorithm and effectively preventing premature convergence; by combining the traditional position-type PID control with the improved eagle-fish optimization algorithm, the improved eagle-fish optimization algorithm can optimize the PID controller parameters in real time, enabling the control system to maintain good self-adaptability and stability in different types of water application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a schematic flowchart of the water flow velocity control optimization method for the hydraulic execution system.

[0050] Figure 2 is a schematic diagram of the improved eagle-fish optimization algorithm for online adjusting the parameters of the position-type PID control algorithm.

[0051] Figure 3 It is a comparison chart of the fitness value changes during the optimization processes of the existing algorithm and the algorithm of the present invention.

[0052] Figure 4 It is a result chart of the online adjustment of the parameters of the position - type PID control algorithm by the algorithm of the present invention.

[0053] Figure 5 It is a comparison chart of the control effects of the method of the present invention and the existing method on optimizing the water flow rate controller of the hydraulic actuator system. Specific embodiments

[0054] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. Without conflict, to make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0055] The present invention is implemented based on intelligent optimization algorithms and PID control technologies to realize a water flow rate control method for a hydraulic actuator system, and optimize the water flow rate controller of the hydraulic actuator system. The specific steps are as Figure 1 shown.

[0056] S1. Collect the water flow rate and pressure change data of the hydraulic actuator system, and establish a data - driven water flow rate control model.

[0057] Specifically, the water flow rate and pressure change data are collected in real - time at a sampling interval of 0.5 seconds, and a data sample \(\left [ {P\left ( {τ} \right ),v\left ( {τ} \right )} \right ]\) is obtained in each sampling period , and the data sample set is: ; By constructing the collected water flow rate and pressure change data of the hydraulic actuator system in excel, it is found that there is a linear proportional relationship between the real - time water flow rate and the real - time water pressure. Therefore, the present invention uses the real - time data acquisition and online least - squares fitting method to determine the parameters. The specific implementation model is:

[0058] ;

[0059] In the formula, \(T\) is the maximum running time, set to 20, and minimizing can obtain the optimal model parameters and .

[0060] Specifically, the real-time water pressure is converted into real-time water flow velocity through a water flow velocity control model, and the water flow velocity control model is:

[0061] ;

[0062] In the formula, is the water flow velocity at the th moment, and are model parameters determined through online data identification, is the real-time water pressure at the th moment, is the water flow velocity at the th moment.

[0063] Specifically, complete the model sub-file and the code in MATLAB;

[0064] P = randn(1, T); % Initial water pressure data

[0065] v = randn(1, T); % Initial water flow velocity data

[0066] % Initialize the historical water flow velocity and remove the initial state

[0067] v_prev = [0, v(1:end - 1)]; % Data of the previous moment of the current moment's water flow velocity

[0068] % Define the objective function J(a, b)

[0069] J = @(a, b)sum((v(2:end) - a * P(2:end) - b * v_prev(2:end)).^2);

[0070] % Use fminsearch to minimize J(a, b) and obtain the optimal parameters a and b

[0071] initial_guess = [0, 0]; % Initial a and b

[0072] options = optimset('Display', 'off'); % Turn off the output

[0073] optimal_params = fminsearch(@(params)J(params(1), params(2)), initial_guess, options);

[0074] % Output the optimal parameters a and b

[0075] a_optimal = optimal_params(1);

[0076] b_optimal = optimal_params(2);

[0077] % Fit the water flow velocity according to the optimal parameters

[0078] v_fitted = a_optimal * P(2:end) + b_optimal * v_prev(2:end).

[0079] S2. Construct an improved eagle-fish optimization algorithm, and use the improved eagle-fish optimization algorithm to online adjust the proportional, integral, and differential parameters of the positional PID control algorithm; the improved eagle-fish optimization algorithm is improved by the eagle-fish individual movement rule and learning coefficient of the standard eagle-fish optimization algorithm; specifically: S21. Regard the distribution state of the eagle-fish population in the search space as a spatial distribution field with a topological structure, and define a topological folding strategy to adaptively change the learning coefficient; S22. Introduce a probabilistic transition movement strategy, and use the historical differential trend of the surrogate individual fitness as the trigger condition for the transition to improve the eagle-fish individual movement rule.

[0080] Specifically, construct a mathematical model of the standard eagle-fish optimization algorithm, regard the distribution state of the eagle-fish population in the search space as a spatial distribution field with a topological structure, and define a topological folding strategy. The topological folding strategy reflects the geometric characteristics and distribution density of the population position distribution. Through the topological folding strategy, the improved eagle-fish optimization algorithm can keenly capture the subtle changes in the group state and drive the learning coefficient to adaptively change with the underlying geometric characteristics; the implementation mathematical model is:

[0081] S211. Define the distribution of the eagle-fish population in the search space at the t-th iteration as the topological folding strategy The mathematical model is:

[0082] ;

[0083] In the formula, is the topological folding strategy at the t-th iteration, N is the maximum scale of the surrogate individual, n ≠ j; it is set to 30 in the program; The Euclidean distance between the surrogate individuals of the population at the t-th iteration;

[0084] S212. Introduce the topological folding strategy and propose an adaptive regulation mathematical model for the learning coefficient:

[0085] ;

[0086] In the formula, ​is the minimum value of the learning coefficient, which is set to 0 in implementation; is the maximum value of the learning coefficient, which is set to 2 in implementation; μ is the sensitivity adjustment factor. Starting from the fitness ranking ratio, the change trend of the relative ranking of the population's optimal agent individual essentially reflects the search state of the group, and thus automatically feeds back to the sensitivity adjustment factor. The mathematical model is:

[0087] ;

[0088] where, is the sensitivity adjustment factor at the t-th iteration, is the ranking of the current optimal agent individual in the population.

[0089] Specifically, in the movement rule of the eagle-fish individual, on the basis of the conventional progressive update of the movement of the eagle-fish individual, a probabilistic jump-type movement strategy is innovatively introduced. When the eagle-fish is trapped in the local search area for a long time, a jump is triggered with a certain probability, and a cross-space jump movement is implemented to effectively avoid the algorithm from premature convergence to the local optimum; the strategy no longer uses the traditional simple regulation of distance or fitness, but uses the historical differential trend of the agent individual's fitness as the trigger condition for the jump; the implementation mathematical model is:

[0090] ;

[0091] where, is the position of the n-th agent individual at the (t + 1)-th iteration, is the position of the n-th agent individual at the t-th iteration, is the step size of the n-th agent individual, is the j-th dimensional value of the direction vector of the n-th agent individual, is the centroid position of the current population, is the position of the current global optimal agent individual; is the trigger jump value at the t-th iteration, rand is a random number uniformly distributed between 0 and 1, is the pseudo-pulse jump sensitivity parameter, which controls the degree of change of the jump probability. The mathematical model is:

[0092] ;

[0093] In the formula, is the position of the n-th agent individual at the (t + 1)-th iteration, is the maximum number of iterations, which is set to 20, randn(0,1) is a random number with a standard normal distribution;

[0094] where, the trigger jump factor is used to judge whether the eagle-fish is trapped in the local search area for a long time. The mathematical model of the trigger jump factor is:

[0095] ;

[0096] In the formula, and are the fitness values of the i-th agent individual at two consecutive iteration times.

[0097] Specifically, establish a relationship between the improved eagle-fish optimization algorithm and the position PID algorithm of the hydraulic execution system. The eagle-fish individuals of the improved eagle-fish optimization algorithm are used as agent individuals, and the positions of the agent individuals are updated through the eagle-fish individual movement rule and the eagle-fish learning rule. Among them, the position of the agent individual is mapped to the proportional, integral, and differential parameters of the position-type PID control algorithm of the water flow velocity controller of the hydraulic execution system. The position of the mapped agent individual is a three-dimensional value, which is represented by a mathematical model as: \(\left ( {{K}^{n}_{p},{K}^{n}_{i},{K}^{n}_{d}} \right )=\left [ {{X}^{1}_{n},{X}^{2}_{n},{X}^{3}_{n}} \right ]\) ; where , and are the proportional parameter, integral coefficient, and differential parameter corresponding to the position value of the n-th agent individual; , and are the position values of the 1st, 2nd, and 3rd dimensions of the n-th agent individual. The MATLAB code is:

[0098] [HFOA_score,HFOA_pos,HFOA _ curve , HFOA_PID]=HFOA(N,T,lb,ub,D,f);

[0099] [WHFOA_score,WHFOA_pos,WHFOA _ curve,WHFOA_PID]=WHFOA(N,T,lb,ub,D,f);

[0100] Among them, the HFOA and WHFOA functions are the sub-file codes of the standard eagle-fish optimization algorithm and the improved eagle-fish optimization algorithm respectively. The results obtained by running will be assigned to WHFOA_score, WHFOA_pos, and WHFOA _ curve, WHFOA_PID, all of which are three-dimensional variables. Among them, WHFOA_score is the position value, WHFOA_pos is the optimal control parameter value, WHFOA _ curve is the fitness value, and WHFOA_PID is the control parameter value of each iteration.

[0101] S3. The positional PID control algorithm is used for the water flow rate controller of the hydraulic actuator system to adjust the output signal of the water flow rate controller; the output signal is input into the water flow rate control model to obtain the water flow rate of the real-time hydraulic actuator system.

[0102] Specifically, as Figure 2 shown, the improved eagle-fish optimization algorithm is used to online adjust the proportional, integral, and derivative parameters of the positional PID control algorithm. During the adjustment process, the improved eagle-fish optimization algorithm is guided by the fitness function to optimize the parameters and find the global optimal solution, that is, the position of the proxy individual corresponding to the minimum value of the fitness function. The specific steps are as follows:

[0103] S31. Initialize the position of the proxy individual of the population of the improved eagle-fish optimization algorithm , and each proxy individual position is a D-dimensional vector; set the maximum number of iterations and the maximum population size ;

[0104] S32. Divide the eagle-fish individuals into male and female proxy individuals, define the availability of food resources in the environment as d(t), and design a gender transformation mechanism model;

[0105] S33. Calculate the fitness value of each proxy individual in the current iteration. The fitness value is the fitness function value of each proxy individual position, and record the position of the proxy individual corresponding to the current minimum fitness value as ;

[0106] S34. Calculate the trigger transition value of the t-th iteration, and update the proxy individual position by executing the mathematical model of the eagle-fish individual movement rule through the trigger transition value;

[0107] S35. Dynamically divide the sub-populations using the Euclidean distance matrix, perform dynamic clustering, and determine the position of the sub-population leader, where the position of the sub-population leader is the best proxy individual position in the sub-population;

[0108] S36. Adaptive regulate the learning coefficient through the topological folding strategy to construct the eagle-fish learning rule, and update the proxy individual position using the eagle-fish learning rule;

[0109] S37. The proxy individual adjusts the search range according to gender, sets a threshold. If the fitness value of the proxy individual exceeds the threshold, the proxy individual changes gender and updates the proxy individual position according to the dynamic vision rule;

[0110] S38. Limit the position of the agent individual within the range of [lb, ub], increment the current iteration count by one, and determine whether the current iteration count satisfies t + 1 = Tmax. If it is satisfied, exit the optimization process, output the current global optimal agent individual position, and parse it into the proportional, integral, and differential parameter values of the positional PID control algorithm; otherwise, return to execute S33.

[0111] More specifically, design the fitness function according to the implementation mathematical model;

[0112] ;

[0113] In the formula, is the fitness function, is the total running time, set to 20; is the control signal, is the control signal at the previous moment, is the difference in water flow velocity, calculate the difference between the actually measured real water flow velocity and the target water flow velocity: , where the target water flow velocity is determined according to the set water pressure, the initial value of the set water pressure is set to 8, and the final value is set to 4 to verify the mobility and stability of the method of the present invention after the change of the target water flow velocity.

[0114] More specifically, the mathematical model executed by S35 is:

[0115] S351. Calculate the distance matrix of two agent individuals:

[0116] ;

[0117] S352. Divide the agent individual population into k clusters C1, C2,..., Ck based on the distance matrix, and the mathematical model is:

[0118] , where p = 1, 2,..., k;

[0119] S353. The cluster center position is the current optimal individual position, and the mathematical model is:

[0120] ;

[0121] In the formula, is the cluster center position at the t-th iteration, is the fitness value of the position of the n-th agent individual.

[0122] More specifically, S37 updates the position of the agent individual according to the dynamic vision rule, and the specific implementation model is:

[0123] ;

[0124] In the formula, is the position of the nth agent individual at the (t + 1)th iteration, is the position of the nth agent individual at the tth iteration, and step is the step size, which is set to 0.5 in implementation.

[0125] S4. Calculate the difference between the target water flow rate and the real-time water flow rate. The difference is input into the water flow rate controller, and the position-type PID control algorithm is used to adjust the water flow rate of the real-time hydraulic execution system until the difference is lower than the target threshold, so as to realize the optimization of water flow rate control.

[0126] Specifically, the optimized best proportional, integral, and differential parameter values are used in the position-type PID control algorithm. The mathematical model of the position-type PID control algorithm is:

[0127] ;

[0128] Among them, is the proportional parameter, is the integral parameter, is the differential parameter, is the water flow rate difference, is the water flow rate difference at the previous moment.

[0129] Furthermore, during the implementation process, the control signal and the real-time water pressure are represented by a typical second-order inertia link model. The second-order inertia link model is a time-domain model, with the input being the control signal , and the output being the real-time water pressure of the hydraulic execution system; the mathematical model is:

[0130] ;

[0131] Among them, is the second-order inertia time constant, which reflects the lag inertia characteristic of the water pressure response process, is the damping ratio, which reflects the oscillation situation in the water pressure response process, is the static gain coefficient of the system, which represents the proportional relationship between the control input signal and the water pressure output; the code is completed in MATLAB:

[0132] % Time vector

[0133] time = 0:dt:T;

[0134] % Initialize variables

[0135] P = zeros(1, length(time)); % Water pressure;

[0136] u = WHFOA_score; % Control signal, WHFOA_score is the control signal output value obtained after mapping;

[0137] e = zeros(1, length(time)); % Error;

[0138] % Initial conditions

[0139] P(1) = 0; % Initial water pressure;

[0140] e(1) = 10; % Assume the initial error is 10;

[0141] u(1) = 0; % Initial control signal is 0;

[0142] % State variables of the second-order inertia model

[0143] P_dot = 0; % Rate of change of water pressure;

[0144] P_ddot = 0; % Acceleration of water pressure

[0145] % PID control and water flow rate calculation

[0146] for t = 2:length(time)

[0147] e(t) = 10 - v(t-1); % The target water flow rate is 10;

[0148] u(t) = Kp * e(t) + Ki * sum(e(1:t)) * dt + Kd * (e(t) - e(t-1)) / dt;

[0149] % Second-order inertia link model

[0150] P_ddot = K * u(t) - 2 * xi * beta * P_dot - beta^2 * P(t); % Acceleration of water pressure;

[0151] P_dot = P_dot + P_ddot * dt; % Update the rate of change of water pressure;

[0152] P(t) = P(t-1) + P_dot * dt; % Update the water pressure.

[0153] Furthermore, convert it to the S-domain transfer function Expression for the Siumulink simulation model:

[0154] ;

[0155] Where, is the S-domain parameter of time , set to 0.8, set to 1.5, set to 5; obtain the transfer function of the Simulink simulation model:

[0156] .

[0157] Furthermore, implement the mathematical model in the above embodiment in Matlab and convert it into code form, including: the code of the standard eagle-fish optimization algorithm and the improved eagle-fish optimization algorithm of the present invention, the water flow velocity control model and the code of the positional PID control algorithm, as well as the main function and the fitness function code. Among them, in the main function code, the proportional, integral, and differential parameter mapping of the standard and improved eagle-fish optimization algorithms and the positional PID control algorithm, as well as the mapping with the fitness function value are implemented; map the fitness function to the objective function of the Siumulink simulation model, and input the obtained optimal proportional, integral, and differential parameter values into the PID module of the simulation model. Set the maximum number of iterations and the maximum population size , the problem dimension D = 3; the lower bound lb of the proxy individual position is [0 0.05 0], and the upper bound ub is [20 20 10]; run the main program to obtain as Figures 3 to 5 the result graph.

[0158] Furthermore, as Figure 3 shown in the comparison graph of the fitness value change during the optimization process of the existing algorithm and the algorithm of the present invention, the smaller the fitness value, the higher the accuracy of the solution, and the better the water flow velocity control effect for the hydraulic execution system. It can be clearly seen from the curve trend that the fitness value of the algorithm of the present invention decreases rapidly after the first few iterations and reaches a lower value quickly at the 9th iteration, reflecting the fast convergence characteristic; while for the existing algorithm, that is, the standard eagle-fish optimization algorithm, the convergence speed is significantly slower, with a small decrease in the early stage and remaining basically stable in the later stage, unable to continue to optimize, and the convergence speed is significantly inferior to the algorithm of the present invention; considering the above factors, it can be clearly seen that the overall performance of the algorithm of the present invention is significantly better than that of the existing algorithm; the algorithm of the present invention has a faster convergence speed, higher optimization accuracy, and better stability and robustness; the existing algorithm has obvious deficiencies in all aspects, with limited optimization effect and performance bottlenecks in practical applications.

[0159] Furthermore, after the fitness value of the algorithm of the present invention reaches the minimum value and stabilizes at the 9th iteration, the corresponding as Figure 4 ​As shown, the optimal proportional, integral, and derivative parameter values are obtained in the 9th iteration. The proportional parameter is 0.79642, the integral parameter is 0.26329, and the derivative parameter is 0.53419.

[0160] Furthermore, as Figure 5 shown, in terms of the control overshoot, when the water pressure transitions from 0 to the initial target value of 8, the existing control method has a significant overshoot, exceeding 10, and there is another obvious overshoot during the subsequent process of decreasing from 8 to the target value of 4, showing poor stability; the overshoot of the control method of the present invention is significantly reduced. During the initial rising stage of the water pressure control, it is basically stable at the target value and does not significantly exceed the target water pressure, and there is no obvious overshoot during the subsequent process of decreasing to 4; as can be seen from the curve, the water pressure response of the control method of the present invention is rapid and has high stability, quickly reaching the target set value, showing good response characteristics. Although the existing control method also has a relatively fast initial response speed, it is accompanied by severe overshoot and repeated oscillations, and the overall control speed is affected by the oscillations, resulting in an unstable response.

Claims

1. A water flow rate control method for a hydraulic execution system, characterized in that, Optimize the water flow rate controller of the hydraulic actuator system. The specific steps are as follows: S1. Collect the water flow rate and pressure change data of the hydraulic actuator system, and establish a data-driven water flow rate control model. S2. Construct an improved eagle-fish optimization algorithm, and use the improved eagle-fish optimization algorithm to online adjust the proportional, integral, and differential parameters of the positional PID control algorithm. The improved eagle-fish optimization algorithm is improved by the movement rule and learning coefficient of the eagle-fish individuals in the standard eagle-fish optimization algorithm. Specifically: S21. Regard the distribution state of the eagle-fish population in the search space as a spatial distribution field with a topological structure, and define a topological folding strategy to adaptively change the learning coefficient. S22. Introduce a probabilistic jump-type movement strategy, and use the historical differential trend of the surrogate individual fitness as the trigger condition for the jump to improve the movement rule of the eagle-fish individual. The improved eagle-fish optimization algorithm captures the subtle changes in the group state of the surrogate individuals through the topological folding strategy, and drives the adaptive change of the learning coefficient w with the underlying geometric characteristics. The mathematical model is: S211. Define the distribution of the eagle-fish population X = {X1, X2, X3,..., X N} in the search space as the topological folding strategy U, and the mathematical model is as follows: where \(U(t)\) is the topological folding strategy for the \(t\)-th iteration, \(N\) is the maximum scale of the agent individuals, \(n\neq j\); \(d\) nj (t) is the Euclidean distance between the agent individuals in the population for the \(t\)-th iteration; S212. Introduce a topological folding strategy and propose an adaptive regulation mathematical model of the learning coefficient. where w min is the minimum value of the learning coefficient, w max is the maximum value of the learning coefficient, μ is the sensitivity adjustment factor. The sensitivity adjustment factor starts from the fitness ranking ratio. The change trend of the relative ranking of the population's optimal agent individuals essentially reflects the search state of the group, and thus automatically feeds back to the sensitivity adjustment factor. The mathematical model is as follows: Among them, μ(t) is the sensitivity adjustment factor for the t-th iteration, and Rank best (t) is the ranking of the current optimal surrogate individual in the population; S3. The positional PID control algorithm is used for the water flow rate controller of the hydraulic actuator system to adjust the output signal of the water flow rate controller. The output signal is input into the water flow rate control model to obtain the water flow rate of the real-time hydraulic actuator system. S4. Calculate the difference between the target water flow rate and the real-time water flow rate. The difference is input into the water flow rate controller, and the positional PID control algorithm is used to adjust the water flow rate of the real-time hydraulic actuator system until the difference is lower than the target threshold, so as to realize the optimization of the water flow rate control.

2. The water flow rate control method for a hydraulic execution system according to claim 1, characterized in that The water flow rate control model is represented by a typical second-order inertia link model. The second-order inertia link model is a time-domain model, the input is the control signal u(τ), and the output is the real-time water pressure of the hydraulic actuator system. The real-time water pressure is converted into the real-time water flow rate through the water flow rate control model. The water flow rate control model is: υ(τ) = a·P(τ) + b·υ(τ - 1); In the formula, u(τ) is the water flow rate at the τ-th moment, a and b are model parameters determined by online data identification, P(τ) is the real-time water pressure at the τ-th moment, and υ(τ - 1) is the water flow rate at the (τ - 1)-th moment.

3. A water flow rate control method for a hydraulic execution system according to claim 2, characterized in that, For the probabilistic jump-type movement strategy, when the surrogate individual is trapped in the local search area for a long time, a jump is triggered by the trigger jump value, and a cross-space jump movement is implemented to effectively avoid the algorithm from premature convergence to the local optimum. The strategy uses the historical differential trend of the surrogate individual fitness as the trigger condition for the jump. The mathematical model is: Among them, X n (t + 1) is the position of the nth agent individual at the (t + 1)-th iteration, X n (t) is the position of the nth agent individual at the t-th iteration, s(n, j) is the step size of the nth agent individual, and d(n, j) is the j-th dimensional value of the direction vector of the nth agent individual. is the centroid position of the current population, X best (t) is the position of the current globally optimal agent individual; P n (t) is the trigger transition value at the t-th iteration, rand is a random number uniformly distributed within 0 to 1, and η(t) is the quasi-pulse transition sensitivity parameter that controls the degree of change of the transition probability. The mathematical model is: where X n (t + 1) is the position of the nth agent individual at the (t + 1)-th iteration, T max is the maximum number of iterations, and randn(0, 1) is a random number from the standard normal distribution; Among them, by triggering the transition factor to determine that the eagle fish is trapped in the local search area for a long time, the mathematical model of the trigger transition factor is as follows: where f n (t) and f n (t - 1) are the fitness values of the i-th agent individual at two consecutive iteration counts.

4. A water flow rate control method for a hydraulic actuator system according to claim 3, characterized in that, Use the improved eagle-fish optimization algorithm to online adjust the proportional, integral, and differential parameters of the positional PID control algorithm. The specific steps are as follows: S31. Initialize the positions of the population agent individuals of the improved eagle-fish optimization algorithm, X = {X1, X2, X3,..., X N}, where the position of each agent individual X i is a D-dimensional vector; Set the maximum number of iterations T max and the maximum population size N; S32. Divide the eagle-fish individuals into male and female surrogate individuals, and define the availability of food resources in the environment as d(t) to design a gender transformation mechanism model. S33. Calculate the fitness value of each agent individual in the current iteration. The fitness value is the fitness function value of the position of each agent individual, and record the position of the agent individual corresponding to the current minimum fitness value as X best (t); S34. Calculate the trigger jump value of the t-th iteration, and update the position of the surrogate individual by executing the movement rule mathematical model of the eagle-fish individual through the trigger jump value. S35. Dynamically divide sub - groups using the Euclidean distance matrix, perform dynamic clustering and determine the positions of subgroup leaders, where the positions of subgroup leaders are the positions of the best surrogate individuals in the subgroups; S36. Adaptive regulate the learning coefficient through the topological folding strategy to construct the eagle - fish learning rule, and use the eagle - fish learning rule to update the positions of surrogate individuals; S37. Surrogate individuals adjust the search range according to gender, set a threshold. If the fitness value of a surrogate individual exceeds the threshold, the surrogate individual changes its gender and updates its position according to the dynamic vision rule; S38. Limit the positions of surrogate individuals within the range of [lb, ub], increment the current iteration count by one, and determine whether the current iteration count satisfies t + 1=Tmax. If it is satisfied, exit the optimization process, output the current global optimal position of the surrogate individual, and parse it into the proportional, integral, and differential parameter values of the positional PID control algorithm. Otherwise, return to execute S33.

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