A high-speed water pump engine speed control method

Abstract

The present invention discloses a method for controlling the speed of a high-speed water pump engine, belonging to the technical field of PID control optimization. The specific steps are as follows: Step 1, construct a speed control system for the high-speed water pump engine; Step 2, improve the whale migration optimization algorithm, including: D1, use a hybrid sine-cosine mapping strategy to generate the initial population of the algorithm; D2, use an adaptive convergence step size strategy that combines crossover and mutation to improve the mathematical model for updating the individual positions of the whale migration optimization algorithm; Step 3, use the improved whale migration optimization algorithm to optimize the parameters of the PID controller module in the speed control system of the high-speed water pump engine; Step 4, apply the optimal control parameters obtained in Step 3 to the PID controller module in the speed control system of the high-speed water pump engine; By optimizing the PID controller module in the speed control system of the high-speed water pump engine with the improved whale migration optimization algorithm, the adaptability and robustness of the entire control system are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of PID control optimization, and particularly relates to a method for controlling the speed of a high-speed water pump engine. Background Art

[0002] The speed control technology of high-speed water pump engines is widely used in fields such as petrochemical, electric power, fire protection, and aerospace. The speed control technology of high-speed water pump engines can accurately adjust the rotational speed of the water pump according to system requirements, ensuring the stable operation of the water pump under different loads and working conditions. By changing the rotational speed of the motor, the flow rate and pressure can be directly controlled, thereby meeting various operation requirements. By precisely controlling the rotational speed, the high-speed water pump engine can optimize the operation efficiency under different working loads, avoid overload and unnecessary energy waste, reduce the system operation cost and equipment wear. The PID controller plays a core role in the speed control system of the water pump. The PID controller calculates the error between the target rotational speed and the actual rotational speed, and adjusts the motor input signal (such as voltage, current or frequency), thereby precisely controlling the rotational speed of the water pump.

[0003] The PID controller (Proportional-Integral-Derivative controller) is a feedback control technology widely used in industrial automation and process control. It processes the error signal (i.e., the difference between the set value and the actual value) in real time, and adjusts the control quantity to make the system output as close as possible to the target value. The PID controller consists of three parts: proportional (P) control, integral (I) control, and derivative (D) control. The PID controller has the advantages of simple structure, easy implementation, and strong real-time performance, and is suitable for many systems that require precise adjustment. However, its performance strongly depends on the adjustment of parameters and cannot adapt to system parameter changes. Therefore, further optimization or improvement may be required in complex or dynamically changing environments.

[0004] The Whale Migration Optimization Algorithm (WMA) is a bio-inspired optimization algorithm based on the migration behavior of humpback whale groups. This algorithm simulates the process of global and local search by humpback whale groups through collective cooperation, leader individual guidance, and following strategies during migration. Compared with traditional optimization methods, WMA effectively balances the trade-off between exploration and exploitation by introducing a leader-follower mechanism, thereby avoiding falling into local optimal solutions and accelerating the convergence speed of the algorithm. WMA performs well in a variety of standard optimization problems and has higher accuracy and faster convergence speed than other common optimization algorithms such as Particle Swarm Optimization (PSO) and Whale Optimization Algorithm (WOA). Summary of the Invention

[0005] The object of the invention is to improve the initial population of the whale migration optimization algorithm and the mathematical model for updating the individual positions. The improved whale migration optimization algorithm has a faster convergence speed and better optimization accuracy during the optimization process, can reach near the optimal solution under fewer iterations, and has stronger adaptability. The improved whale migration optimization algorithm is used for parameter tuning of the PID controller in the speed control system of a high-speed water pump engine, solving the problem of poor system adaptability caused by fixed parameters. By finding the optimal PID control parameters through the improved whale migration optimization algorithm, the control accuracy of the speed control system of the high-speed water pump engine is improved, enabling the water pump to quickly reach the target speed and better adapt to environmental disturbances and maintain a stable state in a high-speed environment, reducing the impact of steady-state error on control performance.

[0006] To achieve the above object, the present invention adopts the following technical solutions.

[0007] A method for controlling the speed of a high-speed water pump engine, the specific steps are as follows.

[0008] Step 1: Construct a speed control system for a high-speed water pump engine, the control system includes: an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module.

[0009] Step 2: Improve the whale migration optimization algorithm, including two improvements:

[0010] D1: Use a hybrid sine-cosine mapping strategy to generate the initial population of the algorithm. This strategy uses Tent mapping to generate the mapping value xn, and selects sine or cosine mapping to generate the positions of the initial population of the algorithm according to the distribution of xn;

[0011] D2: Use an adaptive convergence step size strategy that combines crossover and mutation to improve the mathematical model in the stage where experienced whales or leaders in the whale migration optimization algorithm discover and search new areas. This strategy randomly selects four individuals in the population for crossover and mutation, and determines the size of the convergence step according to the fitness value of the current individual. When the individual fitness value is far from the optimal fitness value, the step size is increased to accelerate the movement towards the optimal area, and conversely, the step size is decreased for local exploitation.

[0012] Step 3: Use the improved whale migration optimization algorithm to optimize the parameters of the PID controller module in the speed control system of the high-speed water pump engine, and obtain a set of optimal control parameter values of Kp, Ki, and Kd through algorithm optimization.

[0013] Step 4: Apply the optimal control parameters obtained in Step 3 to the PID controller module in the speed control system of the high-speed water pump engine to optimize the speed control of the system.

[0014] Furthermore, in the first step, for the constructed high-speed water pump engine speed control system, the relationship between each module is as follows: The error calculation module calculates the real-time speed error e(t) by calculating the target speed and the actual speed obtained by the rotational speed feedback module, inputs the real-time error e(t) into the PID controller module, and tunes the parameters of the PID controller module through an improved whale migration optimization algorithm. The control quantity u(t) obtained through tuning is output to the high-speed water pump engine control module for speed control. The mathematical model of the high-speed water pump engine control module is shown in Equation (1):

[0015] (1);

[0016] In Equation (1), represents the rotational speed, J represents the moment of inertia of the motor, u(t) represents the control quantity output by the PID controller, B represents the damping coefficient of the motor, k represents a constant related to the system resistance, Q represents the flow rate of the water pump, represents the back electromotive force constant of the motor;

[0017] (2);

[0018] In Equation (2), Kp represents the proportional gain, Ki represents the integral gain, Kd represents the derivative gain, and e(t) represents the real-time error.

[0019] Furthermore, in D1, the initial population of the algorithm is generated using a hybrid sine-cosine mapping strategy. The specific mathematical model is as follows:

[0020] (3);

[0021] In Equation (3), w represents the position of the initial population, lb represents the lower limit of the search space, ub represents the upper limit of the search space, represents the Tent mapping value, and its calculation formula is shown in Equation (4). μ represents the mapping control coefficient with a value of 0.8;

[0022] (4);

[0023] In Equation (4), represents the updated Tent mapping value.

[0024] Furthermore, the hybrid sine-cosine mapping strategy performs complementary mapping between the sine mapping and the cosine mapping, which can prevent the generated individuals from concentrating in a certain area, enhance the search range of the initial population, and use the Tent mapping value for adjustment, which can enhance the diversity of the initial population. The initial population generated through this strategy is not easily skewed, which is helpful for the global search in the early stage of the algorithm.

[0025] Further, in D2, an adaptive convergence step size strategy integrating crossover and mutation is used to improve the mathematical model in the stage where experienced whales or leaders in the whale migration optimization algorithm discover and search for new areas. The improved specific mathematical model is as follows:

[0026] (5);

[0027] In Equation (5), w(iter + 1) represents the updated individual position, w(iter) represents the current individual position, iter represents the current iteration number, λ() represents the adaptive step size function, and its calculation formula is shown in Equation (6). f represents the fitness value of the current individual, represents the optimal fitness value, rand represents a random number between [0, 1], represents the position of the optimal individual, F represents the mutation factor with a value of 0.5, 、 、 、 represent the positions of four randomly selected individuals;

[0028] (6);

[0029] In Equation (6), λ0 represents the base step size coefficient, f represents the fitness value of the current individual, represents the optimal fitness value, represents the average fitness value in the population, and ε represents a very small constant to prevent the denominator of the formula from being zero.

[0030] Furthermore, crossover and mutation generate a mutation vector by randomly selecting individuals, effectively enhancing the global search ability of the algorithm and avoiding falling into local optima. The adaptive step size dynamically adjusts the step size according to the difference between the fitness values of the individual and the optimal individual, enabling individuals with poor fitness values to quickly approach the optimal region, while individuals with good fitness values perform fine exploitation with small step sizes, thus achieving an efficient balance between global exploration and local exploitation and improving the convergence speed and accuracy of the algorithm.

[0031] Further, in Step 3, the improved whale migration optimization algorithm is used to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system. The specific steps are as follows:

[0032] S1. Initialize the parameters of the improved whale migration optimization algorithm, including the population size N, problem dimension dim, maximum number of iterations max_iter, upper bound ub of the search space, and lower bound lb. Use the hybrid sine-cosine mapping strategy with the initial parameters of the algorithm to generate the initial population position of the algorithm. The specific mathematical model is shown in Equation (3);

[0033] S2. By introducing the improved whale migration optimization algorithm into the PID controller parameter tuning process, establish the correspondence between the individual position vector w(iter) of the algorithm and the PID parameters: Among them, the first, second, and third dimensions of the vector represent the proportional coefficient Kp, the integral coefficient Ki, and the differential coefficient Kd respectively. During the iterative process of the algorithm, continuously adjust the position of the individual in the solution space, thereby continuously updating the corresponding PID parameter values, and gradually approach the optimal solution of the system performance index with the optimization of the algorithm. Finally, obtain a set of PID controller parameters with the optimal response performance;

[0034] S3. Set the fitness value function of the improved whale migration optimization algorithm, calculate the fitness values of the individuals in the initial population of the algorithm through the fitness value function, and sort them according to the size of the fitness values. The specific fitness value function is;

[0035] (7);

[0036] In formula (7), J represents the fitness value, e(t) represents the real-time error value, T represents the running time of the system, and t represents the real-time running time of the system;

[0037] S4. Update the positions of the individuals in the population through the mathematical model of the improved whale migration optimization algorithm, judge whether the fitness value of the updated individual is better than that of the individual before the update, retain the excellent individuals, and update the fitness value ranking in the population. The specific mathematical model is:

[0038] S41. The algorithm enters the movement stage of the whales with insufficient experience for position update. First, calculate the average position of the NL individuals with the top fitness values in the population. NL is the number of leaders, taking 1 / 3 of the population size. The specific update formula for this stage is:

[0039] (8);

[0040] In formula (8), w(iter + 1) represents the updated individual position, w(iter) represents the current individual position, w(iter - 1) represents the individual position at the previous iteration number, iter represents the current iteration number, rand represents a random number between [0, 1], represents the position of the optimal individual, represents the average position of the leaders;

[0041] S42. The algorithm enters the stage where the whales with rich experience or leaders discover and search for new areas for position update. The specific update formula for this stage is shown in formula (5);

[0042] S5. Determine whether the current iteration count has reached the maximum iteration count. If not, return to execute S4 for optimization. If so, complete the algorithm optimization and output the optimal solution.

[0043] By adopting the above technical solution, the beneficial effects of the present invention are as follows: Through the improvement of the whale migration optimization algorithm, the adaptability and performance of the algorithm are improved, which can better adapt to the controlled environment of the high-speed water pump engine speed control, can more accurately adjust the control parameters of the PID controller, improve the response speed and steady-state performance of the system, effectively enhance the control accuracy and stability, and thus achieve efficient and stable control of the high-speed water pump engine speed. Description of the Drawings

[0044] Figure 1 It is a flowchart of a high-speed water pump engine speed control method.

[0045] Figure 2 It is a model diagram for constructing a high-speed water pump engine speed control system.

[0046] Figure 3 It is a comparison diagram of the change of fitness value during the optimization process between the improved whale migration optimization algorithm and the standard whale migration optimization algorithm.

[0047] Figure 4 It is a comparison diagram of the response of the improved whale migration optimization algorithm and the standard whale migration optimization algorithm to optimize the system PID controller. Detailed Embodiments

[0048] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0049] The present invention provides a technical solution: a high-speed water pump engine speed control method, which specifically includes the following steps, as Figure 1 shown.

[0050] Step 1. Construct a high-speed water pump engine speed control system, and the control system includes: an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module.

[0051] Step 2. Improve the whale migration optimization algorithm, including two improvements:

[0052] D1. Generate the initial population of the algorithm using a hybrid sine-cosine mapping strategy. This strategy uses the Tent mapping to generate the mapping value xn, and selects the sine or cosine mapping to generate the positions of the initial population of the algorithm based on the distribution of xn.

[0053] D2. Use an adaptive convergence step size strategy that combines crossover and mutation to improve the mathematical model in the stage where experienced whales or leaders in the whale migration optimization algorithm discover and search for new areas. This strategy randomly selects four individuals in the population for crossover and mutation, and determines the size of the convergence step based on the fitness value of the current individual. When the individual fitness value is far from the optimal fitness value, the step size is increased to accelerate the movement towards the optimal area; conversely, the step size is decreased for local exploitation.

[0054] Step 3. Use the improved whale migration optimization algorithm to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, and obtain a set of optimal control parameter values of Kp, Ki, and Kd through algorithm optimization.

[0055] Step 4. Apply the optimal control parameters obtained in Step 3 to the PID controller module in the high-speed water pump engine speed control system to optimize the speed control of the system.

[0056] Furthermore, in Step 1, for the constructed high-speed water pump engine speed control system, the relationship between each module is as follows: The error calculation module calculates the real-time speed error e(t) by calculating the target speed and the actual speed obtained by the speed feedback module, inputs the real-time error e(t) into the PID controller module, and uses the improved whale migration optimization algorithm to tune the parameters of the PID controller module. The control quantity u(t) obtained by the tuning is output to the high-speed water pump engine control module for speed control. The mathematical model of the high-speed water pump engine control module is shown in Equation (1):

[0057] (1);

[0058] In Equation (1), represents the rotational speed, J represents the moment of inertia of the motor, u(t) represents the control quantity output by the PID controller, B represents the damping coefficient of the motor, k represents a constant related to the system resistance, Q represents the flow rate of the water pump, represents the back electromotive force constant of the motor;

[0059] (2);

[0060] In Equation (2), Kp represents the proportional gain, Ki represents the integral gain, Kd represents the derivative gain, and e(t) represents the real-time error.

[0061] Further, in D1, an initial population of the algorithm is generated using a hybrid sine-cosine mapping strategy. The specific mathematical model is as follows:

[0062] (3);

[0063] In Equation (3), w represents the initial population position, lb represents the lower bound of the search space, and ub represents the upper bound of the search space. represents the Tent mapping value, and its calculation formula is shown in Equation (4). μ represents the mapping control coefficient with a value of 0.8.

[0064] (4);

[0065] In Equation (4), represents the updated Tent mapping value.

[0066] Further, in D2, a self-adaptive convergence step size strategy integrating crossover and mutation is used to improve the mathematical model in the stage of experienced whales or leaders discovering and searching new areas in the whale migration optimization algorithm. The improved specific mathematical model is as follows:

[0067] (5);

[0068] In Equation (5), w(iter + 1) represents the updated individual position, w(iter) represents the current individual position, iter represents the current iteration number, λ() represents the self-adaptive step size function, and its calculation formula is shown in Equation (6). f represents the fitness value of the current individual. represents the optimal fitness value, rand represents a random number between [0, 1]. represents the position of the optimal individual, F represents the mutation factor with a value of 0.5. 、 、 、 represent the positions of four randomly selected individuals.

[0069] (6);

[0070] In Equation (6), λ0 represents the basic step size coefficient, f represents the fitness value of the current individual. represents the optimal fitness value. represents the average fitness value in the population, and ε represents a very small constant to prevent the denominator of the formula from being zero.

[0071] Further, in Step 3, the improved whale migration optimization algorithm is used to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system. The specific steps are as follows:

[0072] S1. Initialize the parameters of the improved whale migration optimization algorithm, including the population size N, the problem dimension dim, the maximum number of iterations max_iter, the upper bound ub and the lower bound lb of the search space. Generate the initial population positions of the algorithm using the hybrid sine-cosine mapping strategy with the initial parameters of the algorithm. The specific mathematical model is shown in Equation (3);

[0073] S2. By introducing the improved whale migration optimization algorithm into the PID controller parameter tuning process, establish the correspondence between the individual position vector w(iter) of the algorithm and the PID parameters: Among them, the first, second, and third dimensions of the vector represent the proportional coefficient Kp, the integral coefficient Ki, and the derivative coefficient Kd respectively. During the iterative process of the algorithm, continuously adjust the position of the individual in the solution space, thereby continuously updating the corresponding PID parameter values, and gradually approaching the optimal solution of the system performance index with the optimization of the algorithm. Finally, obtain a set of PID controller parameters with the optimal response performance;

[0074] S3. Set the fitness value function of the improved whale migration optimization algorithm, calculate the fitness values of the individuals in the initial population of the algorithm through the fitness value function, and sort them according to the size of the fitness values. The specific fitness value function is;

[0075] (7);

[0076] In Equation (7), J represents the fitness value, e(t) represents the real-time error value, T represents the running time of the system, and t represents the real-time running time of the system;

[0077] S4. Update the individual positions in the population through the mathematical model of the improved whale migration optimization algorithm, judge whether the fitness value of the updated individual is better than that of the individual before the update, retain the excellent individuals, and update the fitness value sorting in the population. The specific mathematical model is:

[0078] S41. The algorithm enters the movement stage of inexperienced whales for position update. First, calculate the average position of the individuals with the top NL fitness values in the population. NL is the number of leaders, taking 1 / 3 of the population size. The specific update formula for this stage is:

[0079] (8);

[0080] In Equation (8), w(iter + 1) represents the updated individual position, w(iter) represents the current individual position, w(iter - 1) represents the individual position at the previous iteration, iter represents the current iteration number, rand represents a random number between [0, 1], represents the position of the optimal individual, Represents the average position of the leader;

[0081] S42. The algorithm enters the stage where experienced whales or leaders discover and search for new areas, and position updates are performed. The specific update formula for this stage is shown in Equation (5);

[0082] S5. Determine whether the current iteration number has reached the maximum iteration number. If not, return to execute S4 for optimization. If so, complete the algorithm optimization and output the optimal solution.

[0083] Furthermore, to verify the advantages of the present invention, experiments are carried out using the simulation software Matlab and Simulink. The standard whale migration optimization algorithm is improved through Matlab, and a simulation model is constructed through Simulink, including an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module. The mathematical model of the high-speed water pump engine control module is Laplace-transformed, and the transformed transfer function is used as the controlled function of the model. According to the actual water pump parameters, it is set as: , s represents the variable in the complex frequency domain. In the main function, the initial parameters of the algorithm are set. The maximum iteration number is set to 30 times, the problem dimension is set to 3, the population size is set to 100, the upper limit of the search space is set to 50, and the lower limit is set to 0.001. The improved whale migration optimization algorithm and the standard whale migration optimization algorithm functions are called in sequence, and the optimization records are retained for visual display, as Figure 3 and Figure 4 shown.

[0084] Furthermore, Figure 3 is a comparison graph of the fitness value changes during the optimization process of the improved whale migration optimization algorithm and the standard whale migration optimization algorithm. It can be seen from the graph that the standard whale migration optimization algorithm falls into the local optimal solution after reaching near the optimal value and cannot jump out for a long time, while the improved whale migration optimization algorithm can jump out of the local optimum and continue to search downward with fewer iteration times, and the fitness value of the finally found individual position is lower, indicating that the improved whale migration optimization algorithm has stronger optimization performance. Figure 4 is a comparison graph of the responses of the improved whale migration optimization algorithm and the standard whale migration optimization algorithm to optimize the system PID controller. The target value is set to 1 unit. It can be seen from the graph that the overshoot of the response curve of the improved whale migration optimization algorithm to optimize the system PID controller is very small, quickly stabilizes after reaching the target value, and the steady-state error during the tuning process is smaller, and the control performance is better.

Claims

1. A speed control method for a high-speed water pump engine, characterized in that, The specific steps are as follows: Step 1: Construct a high-speed water pump engine speed control system, which includes an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module; Step 2: Improve the whale migration optimization algorithm, including two improvements: D1. Use a hybrid sine-cosine mapping strategy to generate the initial population of the algorithm. This strategy uses the Tent mapping to generate the mapping value xn, and selects the sine or cosine mapping to generate the position of the initial population of the algorithm according to the distribution of xn. The specific mathematical model is: (3)； In Equation (3), w represents the initial population position, lb represents the lower bound of the search space, and ub represents the upper bound of the search space. represents the Tent mapping value, and its calculation formula is shown in Equation (4). μ represents the mapping control coefficient with a value of 0.

8. (4)； In formula (4), represents the updated Tent mapping value; D2. Use an adaptive convergence step size strategy that combines crossover and mutation to improve the mathematical model in the stage where experienced whales or leaders in the whale migration optimization algorithm discover and search for new areas. This strategy randomly selects four individuals in the population for crossover and mutation, and determines the size of the convergence step according to the fitness value of the current individual. When the individual fitness value is far from the optimal fitness value, the step size is increased to accelerate the movement towards the optimal area. On the contrary, the step size is decreased for local exploitation. The improved specific mathematical model is: (5)； In Equation (5), w(iter + 1) represents the updated individual position, w(iter) represents the current individual position, iter represents the current iteration number, λ() represents the adaptive step size function, and its calculation formula is shown in Equation (6). f represents the fitness value of the current individual. represents the optimal fitness value, rand represents a random number between [0, 1]. represents the position of the optimal individual, F represents the mutation factor with a value of 0.

5. , , , represent the positions of four randomly selected individuals. (6)； In Equation (6), λ0 represents the basic step size coefficient, f represents the fitness value of the current individual, represents the optimal fitness value, represents the average fitness value in the population, and ε represents a very small constant to prevent the denominator of the formula from being zero; Step 3: Use the improved whale migration optimization algorithm to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, and obtain a set of optimal control parameter values of Kp, Ki, and Kd through algorithm optimization; Step 4: Apply the optimal control parameters obtained in Step 3 to the PID controller module in the high-speed water pump engine speed control system to optimize the speed control of the system.

2. The speed control method of a high-speed water pump engine according to claim 1, wherein In Step 1, for the constructed high-speed water pump engine speed control system, the relationship between each module is as follows: The error calculation module calculates the real-time speed error e(t) by calculating the target speed and the actual speed obtained by the speed feedback module, inputs the real-time error e(t) into the PID controller module, and performs parameter tuning on the PID controller module through the improved whale migration optimization algorithm. The control quantity u(t) obtained through tuning is output to the high-speed water pump engine control module for speed control.

3. A speed control method for a high-speed water pump engine according to claim 2, characterized in that, In Step 3, when using the improved whale migration optimization algorithm to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, the specific steps are as follows: S1. Initialize the parameters of the improved whale migration optimization algorithm, including the population size N, the problem dimension dim, the maximum number of iterations max_iter, the upper limit ub of the search space, and the lower limit lb. Use the hybrid sine-cosine mapping strategy to generate the initial population position of the algorithm through the initial parameters of the algorithm; S2. By introducing the improved whale migration optimization algorithm into the PID controller parameter tuning process, the corresponding relationship between the individual position vector w(iter) of the algorithm and the PID parameters is established: among them, the first, second, and third dimensions of the vector represent the proportional coefficient Kp, the integral coefficient Ki, and the derivative coefficient Kd respectively. During the iteration process of the algorithm, the position of the individual in the solution space is continuously adjusted, so as to continuously update the corresponding PID parameter values. With the optimization of the algorithm, the optimal solution of the system performance index is gradually approximated, and finally a set of PID controller parameters with the best response performance is obtained; S3. Set the fitness value function of the improved whale migration optimization algorithm, calculate the fitness values of the individuals in the initial population of the algorithm through the fitness value function, and sort them according to the size of the fitness values. The specific fitness value function is; (7)； In formula (7), J represents the fitness value, e(t) represents the real-time error value, T represents the running time of the system, and t represents the real-time running time of the system; S4. Update the individual positions in the population through the mathematical model of the improved whale migration optimization algorithm, judge whether the fitness value of the updated individual is better than that of the individual before the update, retain the excellent individuals, and update the fitness value sorting in the population. The specific mathematical model is: S41. The algorithm enters the movement stage of inexperienced whales for position update. The specific update formula for this stage is: (8)； In Equation (8), w(iter + 1) represents the updated individual position, w(iter) represents the current individual position, w(iter - 1) represents the individual position at the previous iteration, iter represents the current iteration number, rand represents a random number between [0, 1], represents the position of the optimal individual, represents the average position of the leaders; S42. The algorithm enters the stage where experienced whales or leaders discover and search for new areas for position update; S5. Judge whether the current iteration number has reached the maximum iteration number. If not, return to execute S4 for optimization. If it has reached, complete the algorithm optimization and output the optimal solution.

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