A feedforward adaptive PID control optimization method

Abstract

The invention discloses a feedforward adaptive PID control optimization method, which belongs to the technical field of PID control optimization. The method comprises the following specific steps: step 1, constructing a feedforward adaptive PID control model; step 2, improving an arctic puffin optimization algorithm, wherein the improvement strategy comprises the following steps: D1, adopting a Circle chaos mapping strategy integrating Latin hypercube to generate an initial population; D2, using an adaptive nonlinear search adjustment strategy to improve a mathematical model of a diving predation stage; D3, using a bidirectional elite perturbation strategy to improve a mathematical model of a collection and foraging stage; step 3, using an improved arctic puffin optimization algorithm to adjust parameters of a PID controller module in a feedforward adaptive PID control model, and obtaining optimal Kp, Ki and Kd parameters through optimization; and step 4, inputting the obtained optimal Kp, Ki and Kd parameters into the feedforward adaptive PID control model to optimize the control effect.

Description

Technical Field

[0001] The invention belongs to the technical field of PID control optimization, and in particular relates to a feedforward adaptive PID control optimization method. Background Art

[0002] Feedforward control is a control method that directly adjusts the control signal by measuring external disturbances or setting inputs in advance. Unlike feedback control, feedforward control does not rely on the system's output feedback, but predicts the system response based on known disturbances or reference signals, and makes adjustments in advance to reduce hysteresis errors. It can effectively improve the dynamic performance and response speed of the system. Combining feedforward control with PID control can make full use of the advantages of both to achieve more accurate control effects. Feedforward control adjusts the control amount in advance based on known disturbances or reference signals, thereby quickly responding to changes in the system's input and reducing system lag, while PID control performs fine dynamic adjustments based on feedback errors to ensure the steady-state accuracy and robustness of the system.

[0003] PID controller is an algorithm widely used in the field of industrial control. It can help the control system reach and stably maintain the set target value. PID stands for three control parameters: proportional, integral and derivative. They work together to adjust the output of the system. To achieve the ideal control effect, it is usually necessary to adjust the three parameters of the PID controller, that is, adjust the values ​​of proportional gain, integral gain and derivative gain to achieve the best control performance. Traditional PID controllers have poor adaptability to nonlinear systems and large time-delay systems, and difficulty in parameter tuning. Automatically tuning PID parameters through intelligent optimization algorithms can overcome the difficulties of manual tuning and increase the adaptability of PID controllers.

[0004] The Arctic Puffin Optimization (APO) algorithm is a meta-heuristic optimization algorithm based on the survival and predation behavior of the Arctic Puffin. It consists of aerial flight (exploration) and underwater foraging (exploitation) stages. In the exploration stage, the Levy flight and speed factor mechanisms are introduced to enhance the algorithm's ability to jump out of the local optimum and improve the algorithm's convergence speed. In the development stage, strategies such as collaborative and adaptive change factors are adopted to ensure that the algorithm can effectively utilize the current optimal solution and guide the search direction. In addition, the dynamic transition between the exploration and development stages is achieved through the behavior conversion factor, which effectively balances the global search and local development. Although the Arctic Puffin Optimization Algorithm has good advancement and applicability, it also has many defects, such as low accuracy and poor adaptability in some complex optimization scenarios. Summary of the invention

[0005] The purpose of the present invention is to propose a feedforward adaptive PID control optimization method, combine feedforward control with PID control, enhance the dynamic performance of the system by adding a feedforward compensation signal, improve the optimization algorithm of the Arctic Puffin, increase the optimization convergence speed of the algorithm, increase the adaptability and optimization accuracy of the algorithm, and use the improved Arctic Puffin optimization algorithm to optimize the three parameters Kp, Ki, and Kd of the PID controller, improve the adaptability and robustness of the PID controller, and reduce the overshoot of the PID controller and the complexity of manual debugging parameters.

[0006] In order to achieve the above object, the present invention adopts the following technical solution.

[0007] A feedforward adaptive PID control optimization method, the specific steps are as follows.

[0008] S1. Construct a feedforward adaptive PID control model, wherein the control model includes: an error calculation module, a feedforward control module, a PID controller module, an improved Arctic puffin optimization algorithm module, and a controlled object module.

[0009] S2. Improve the Arctic Puffin optimization algorithm. The specific improvement strategies are as follows:

[0010] S21, using the Circle chaos mapping strategy fused with Latin hypercube to generate the initial population of the algorithm;

[0011] S22. Improve the mathematical model of the diving predation phase of the Arctic puffin optimization algorithm using an adaptive nonlinear search adjustment strategy. The strategy uses an adaptive factor ,With the increase of the number of iterations, the value of the adaptive factor keeps changing to adjust the change of the population position, and the nonlinear perturbation is performed through the hyperbolic tangent function to update the population position;

[0012] S23. Use a two-way elite perturbation strategy to improve the mathematical model of the collection and foraging phase of the Arctic puffin optimization algorithm, and move the optimal position in the population As an elite position guide, through the size of the random factor, the population is selected for positive adjustment or reverse adjustment to update the position of the population.

[0013] S3. Use the improved Arctic Puffin optimization algorithm to adjust the parameters of the PID controller module in the feedforward adaptive PID control model, and obtain the optimal Kp, Ki, and Kd parameters through optimization.

[0014] S4. Input the obtained optimal Kp, Ki, and Kd parameters into the feedforward adaptive PID control model to optimize the control effect.

[0015] Preferably, in said S1, the execution process of the constructed feedforward adaptive PID control model is: firstly, the real-time output value and the target value are input into the error calculation module to obtain the real-time error e(t), the real-time error e(t) is input into the PID controller module, and the PID parameters are optimized by the improved Arctic Puffin optimization algorithm, the PID controller outputs the control quantity u(t) through the optimized parameters, the control quantity u(t) is added to the feedforward increment F output by the feedforward control module, and is input into the controlled object module for control, wherein the calculation formula of the control quantity u(t) is shown in formula (1);

[0016] (1);

[0017] In formula (1), Kp represents proportional gain, Ki represents integral gain, Kd represents differential gain, and e(t) represents real-time error.

[0018] Preferably, in S1, the feedforward control module includes a feedforward path transfer function, a feedforward gain and a low-pass filter, wherein the feedforward path transfer function Set as the second-order transfer function in the controlled plant model The double differential in the feedforward path transfer function produces high-frequency effects, which are then filtered through a low-pass filter. To solve the high-frequency effect caused by differentiation, the cutoff frequency of the low-pass filter is set to 2000, and the calculation formula for the feedforward increment is:

[0019] (2);

[0020] In formula (2), F represents the feedforward increment, represents the second-order transfer function, represents the feedforward gain, s represents the function variable, Represents a low pass filter .

[0021] Preferably, in S21, the Circle chaos mapping strategy integrating Latin hypercube is adopted to generate the initial population of the algorithm, two initial populations are generated by combining Latin hypercube sampling and Circle chaos mapping, the two initialization populations are merged, and N individuals are randomly selected as the initialization population of the algorithm. The specific mathematical model is:

[0022] (3);

[0023] In formula (3), represents the initial population generated by Latin hypercube sampling, lb represents the lower limit of the search space, ub represents the upper limit of the search space, lhsdesign() represents the Latin hypercube matrix function, N represents the number of populations, and dim represents the problem dimension;

[0024] (4);

[0025] In formula (4), represents the initial population generated by Circle chaotic mapping, lb represents the lower limit of the search space, ub represents the upper limit of the search space, p represents a random number between [0, 1], c represents a constant control parameter with a value range of [0, 1], k represents the chaos control parameter, mod() represents the modulo operation, which is modulo 1 in formula (4), and the value range after modulo 1 is [0, 1].

[0026] Preferably, the Circle chaotic mapping strategy integrated with Latin hypercube makes full use of the uniform distribution characteristics of Latin hypercube sampling and the randomness of chaotic mapping to generate a more diverse and evenly distributed population. It can converge quickly in the early stage of the algorithm and reach the vicinity of the optimal solution with fewer iterations, which is beneficial to the optimization speed of the algorithm and more accurate optimization with the remaining number of iterations.

[0027] Preferably, in S22, an adaptive nonlinear search adjustment strategy is used to improve the mathematical model of the diving predation phase of the Arctic puffin optimization algorithm, and the adaptive factor As the number of iterations increases, nonlinear changes are made. The population position updated in the aerial search phase of the algorithm is adjusted by changing the adaptive factor. The improved mathematical model of the diving predation phase is:

[0028] (5);

[0029] In formula (5), Z(iter+1) represents the updated population position in the diving predation phase, iter represents the current iteration number, and Y(iter+1) represents the updated population position in the aerial search phase. represents the adaptive factor, and the calculation formula is shown in formula (6), max_iter represents the maximum number of iterations, tanh() represents the hyperbolic tangent function, λ represents the nonlinear change parameter value of 0.5, and rand represents a random number between [0, 1];

[0030] (6);

[0031] In formula (6), Represents the adaptive factor, max_iter represents the maximum number of iterations, iter represents the current number of iterations, and cosh() represents the hyperbolic cosine function.

[0032] Preferably, the value of the adaptive factor is larger in the early stage of the algorithm, which can increase the global search capability of the algorithm. As the number of iterations increases, the value of the adaptive factor decreases nonlinearly, which can increase the local search capability of the algorithm in the later stage of the algorithm, thereby improving the adaptability of the algorithm at different stages and balancing the entire optimization process of the algorithm. The hyperbolic tangent function tanh() used in the improved mathematical model is a smooth nonlinear function that can avoid the generation of some extreme values.

[0033] Preferably, in S23, a bidirectional elite perturbation strategy is used to improve the mathematical model of the collection and foraging phase of the Arctic Puffin optimization algorithm, which introduces Weibull distribution to generate random perturbations and uses the optimal position The update of the population is guided. When the random factor R>=0.5, the update is executed towards the optimal position. When the current random factor R<0.5, the update is executed in the direction away from the optimal position. The improved mathematical model of the collection and foraging stage is:

[0034] (7);

[0035] In formula (7), Indicates the updated population position during the foraging phase, iter indicates the current iteration number, d indicates the factor approaching the optimal position, which is 0.1, β indicates the amplitude factor of the disturbance term, which is 0.05, y indicates the shape parameter of the Weibull distribution, which is 1.5, f indicates the scale coefficient of the Weibull distribution, σ indicates the amplitude factor of the reverse disturbance term, which is 0.1, represents the reverse update factor, with a value of 0.2, wblrnd() represents the Weibull distribution function, and R represents the random factor. represents the optimal position in the population, Indicates the population position at the current iteration number.

[0036] Preferably, the bidirectional elite perturbation strategy combines the guiding idea in the optimization algorithm with the Weibull distribution perturbation mechanism, which improves the randomness and flexibility of the population update while ensuring the trend of the population update. When making positive adjustments, the individual position update not only moves closer to the optimal position, but also adds the positive perturbation generated by the Weibull distribution. The updated individual can quickly converge to the optimal position while maintaining a certain diversity. When making reverse adjustments, the individual updates the position away from the optimal solution, expands the exploration space, and can quickly jump out and continue to seek the best solution when the algorithm falls into a local optimal solution.

[0037] Preferably, in S3, the parameters of the PID controller module in the feedforward adaptive PID control model are adjusted using an improved Arctic Puffin optimization algorithm, and the specific steps are as follows:

[0038] S31, initialize the parameters of the improved Arctic puffin optimization algorithm, including the population size N, the problem dimension dim, the lower limit lb of the search space, the upper limit ub of the search space, and the maximum number of iterations max_iter, and generate the initial population of the algorithm by integrating the Circle chaos mapping strategy of Latin hypercube. The specific mathematical model is shown in formula (3) and formula (4);

[0039] S32, setting the objective function of the algorithm optimization, using the absolute error integral function as the objective function, as shown in formula (8), calculating the fitness value of the individuals in the initial population through the objective function, and selecting the individual with the best fitness value as the optimal individual;

[0040] (8);

[0041] In formula (8), J represents the objective function, T represents the total time of system operation, and e(t) represents the real-time error;

[0042] S33, updating the position of the population by improving the mathematical model of the Arctic Puffin optimization algorithm, calculating and updating the fitness value of the individual, and updating the optimal position in the population;

[0043] S34. Determine whether the current number of iterations has reached the maximum number of iterations. If not, continue to execute S33 to update the position. If reached, convert the optimal position in the population into the three parameters Kp, Ki, and Kd of the PID controller as the optimal solution output.

[0044] Preferably, in S33, the position of the population is updated by improving the mathematical model of the Arctic Puffin optimization algorithm, and the specific steps are:

[0045] Step 1. Calculate the behavior conversion factor B. If the value of B is greater than 0.5, execute the exploration phase of the Arctic Puffin Optimization Algorithm. Otherwise, execute the development phase. The calculation formula of the conversion factor B is:

[0046] (9);

[0047] In formula (9), iter represents the current number of iterations, max_iter represents the maximum number of iterations, and rand represents a random number between [0, 1];

[0048] Step 2: When the conversion factor B is greater than 0.5, the algorithm executes the exploration phase. The exploration phase is divided into the aerial search phase and the diving predation phase. First, the aerial search phase is entered to update the position. The mathematical model of the aerial search phase is shown in formula (10). Then, the diving predation phase is entered to update the position. The mathematical model of the diving predation phase is improved using an adaptive nonlinear search adjustment strategy. The improved mathematical model is shown in formula (5). Finally, the new positions obtained in the aerial search phase and the diving predation phase are merged, and the fitness value of the merged individual is calculated. The position with the smallest fitness value is selected as the updated position of the population.

[0049] (10);

[0050] In formula (10), Y(iter+1) represents the updated position in the aerial search phase, represents the population position at the current iteration number, L(dim) represents the random number generated by Levy flight, and dim represents the problem dimension. represents a random position in the selected population, and Rn represents a random number from a standard normal distribution;

[0051] Step 3, when the conversion factor B is less than or equal to 0.5, the algorithm executes the development phase. The development phase is divided into the collection and foraging phase, the enhanced search phase and the predator avoidance phase. First, the collection and foraging phase is entered to update the position. The collection and foraging phase is improved using a two-way elite perturbation strategy. The improved mathematical model is shown in formula (7). Then, the enhanced search phase is entered to update the position. The mathematical model of the enhanced search phase is shown in formula (11). Finally, the predator avoidance phase is entered to update the position. The mathematical model of the predator avoidance phase is shown in formula (12). The updated positions obtained in the three phases are merged, and the fitness value of the merged individual is calculated. The position with the best fitness value is selected as the final updated position.

[0052] (11);

[0053] In formula (11), IS(iter) represents the updated position in the enhanced search phase, Indicates the updated population position during the foraging phase, rand indicates a random number between [0, 1], max_iter indicates the maximum number of iterations, and iter indicates the current number of iterations;

[0054] (12);

[0055] In formula (12), AP(iter) represents the updated population position in the predator avoidance phase, rand represents a random number between [0, 1], represents the population position at the current iteration number, and represents two positions in the randomly selected population, L(dim) represents the random number generated by Levy flight, and dim represents the problem dimension;

[0056] Step 4: Compare the fitness value of the updated position with the fitness value of the optimal position in the population, and take the position with the smallest fitness as the optimal position in the population.

[0057] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are as follows.

[0058] The present invention proposes a feedforward adaptive PID control optimization method, applies feedforward control technology to a PID controller, improves the response performance of the PID controller, and uses three updating strategies to improve the initial population mathematical model and the mathematical model of the updated population position of an Arctic puffin optimization algorithm, thereby accelerating the optimization speed of the algorithm and improving the adaptability of the algorithm. When the algorithm falls into a local optimal situation, it can quickly jump out of the local optimal situation and continue to optimize, thereby improving the optimization accuracy of the algorithm. The improved Arctic puffin optimization algorithm is used to automatically adjust the parameters of the PID controller, thereby enhancing the robustness and adaptability of the PID controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a flow chart of a feedforward adaptive PID control optimization method.

[0060] Figure 2 This is the feedforward adaptive PID control model diagram.

[0061] Figure 3 This is a response comparison curve of the ordinary PID controller and the feedforward PID controller.

[0062] Figure 4 Comparison chart of fitness values ​​of the improved Arctic Puffin Optimization Algorithm and the standard Arctic Puffin Optimization Algorithm during the optimization process.

[0063] Figure 5 Parameter change diagram of the optimized feedforward adaptive PID controller for the standard Arctic Puffin optimization algorithm.

[0064] Figure 6 Parameter variation diagram of feedforward adaptive PID controller for improving Arctic Puffin optimization algorithm.

[0065] Figure 7 Comparison curve of the response of feedforward adaptive PID controller optimized by standard Arctic Puffin optimization algorithm and improved Arctic Puffin optimization algorithm. DETAILED DESCRIPTION

[0066] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention; it is obvious that the described embodiments are only 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 ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0067] See also Figure 1-Figure 7 , the present invention provides a technical solution.

[0068] The present invention provides a technical solution: a feedforward adaptive PID control optimization method, the specific steps are as follows Figure 1 shown.

[0069] S1, build a feedforward adaptive PID control model, such as Figure 2 As shown, the control model includes: an error calculation module, a feedforward control module, a PID controller module, an improved Arctic puffin optimization algorithm module, and a controlled object module.

[0070] Furthermore, in said S1, the execution process of the constructed feedforward adaptive PID control model is as follows: first, the real-time output value and the target value are input into the error calculation module to obtain the real-time error e(t), the real-time error e(t) is input into the PID controller module, and the PID parameters are optimized by the improved Arctic Puffin optimization algorithm, the PID controller outputs the control quantity u(t) through the optimized parameters, the control quantity u(t) is added to the feedforward increment F output by the feedforward control module, and is input into the controlled object module for control, wherein the calculation formula of the control quantity u(t) is shown in formula (1);

[0071] (1);

[0072] In formula (1), Kp represents proportional gain, Ki represents integral gain, Kd represents differential gain, and e(t) represents real-time error.

[0073] Furthermore, in S1, the feedforward control module includes a feedforward path transfer function, a feedforward gain and a low-pass filter, and the feedforward path transfer function Set as the second-order transfer function in the controlled plant model The double differential in the feedforward path transfer function produces high-frequency effects, which are then filtered through a low-pass filter. To solve the high-frequency effect caused by differentiation, the cutoff frequency of the low-pass filter is set to 2000, and the calculation formula for the feedforward increment is:

[0074] (2);

[0075] In formula (2), F represents the feedforward increment, represents the second-order transfer function, represents the feedforward gain, s represents the function variable, Represents a low pass filter .

[0076] S2. Improve the Arctic Puffin optimization algorithm. The specific improvement strategies are as follows:

[0077] S21, using the Circle chaos mapping strategy fused with Latin hypercube to generate the initial population of the algorithm;

[0078] S22. Improve the mathematical model of the diving predation phase of the Arctic puffin optimization algorithm using an adaptive nonlinear search adjustment strategy. The strategy uses an adaptive factor ,With the increase of the number of iterations, the value of the adaptive factor keeps changing to adjust the change of the population position, and the nonlinear perturbation is performed through the hyperbolic tangent function to update the population position;

[0079] S23. Use a two-way elite perturbation strategy to improve the mathematical model of the collection and foraging phase of the Arctic puffin optimization algorithm, and move the optimal position in the population to As an elite position guide, through the size of the random factor, the population is selected for positive adjustment or reverse adjustment to update the position of the population.

[0080] Furthermore, in S21, the Circle chaos mapping strategy integrating Latin hypercube is adopted to generate the initial population of the algorithm. Two initial populations are generated by combining Latin hypercube sampling and Circle chaos mapping. The two initialization populations are merged, and N individuals are randomly selected as the initialization population of the algorithm. In the early stage of the algorithm, fast convergence can be performed, and the optimal solution can be reached in a smaller number of iterations, which is beneficial to the optimization speed of the algorithm, and more accurate optimization can be performed in the remaining number of iterations. The specific mathematical model is:

[0081] (3);

[0082] In formula (3), represents the initial population generated by Latin hypercube sampling, lb represents the lower limit of the search space, ub represents the upper limit of the search space, lhsdesign() represents the Latin hypercube matrix function, N represents the number of populations, and dim represents the problem dimension;

[0083] (4);

[0084] In formula (4), represents the initial population generated by Circle chaotic mapping, lb represents the lower limit of the search space, ub represents the upper limit of the search space, p represents a random number between [0, 1], c represents a constant control parameter with a value range of [0, 1], k represents the chaos control parameter, mod() represents the modulo operation, which is modulo 1 in formula (4), and the value range after modulo 1 is [0, 1].

[0085] Further, in said S22, an adaptive nonlinear search adjustment strategy is used to improve the mathematical model of the diving predation phase of the Arctic puffin optimization algorithm, and the adaptive factor As the number of iterations increases, nonlinear changes are made. The population position updated in the aerial search phase of the algorithm is adjusted by changing the adaptive factor. The improved mathematical model of the diving predation phase is:

[0086] (5);

[0087] In formula (5), Z(iter+1) represents the updated population position in the diving predation phase, iter represents the current iteration number, and Y(iter+1) represents the updated population position in the aerial search phase. represents the adaptive factor, and the calculation formula is shown in formula (6), max_iter represents the maximum number of iterations, tanh() represents the hyperbolic tangent function, λ represents the nonlinear change parameter value of 0.5, and rand represents a random number between [0, 1];

[0088] (6);

[0089] In formula (6), Represents the adaptive factor, max_iter represents the maximum number of iterations, iter represents the current number of iterations, and cosh() represents the hyperbolic cosine function.

[0090] Furthermore, in S23, a two-way elite perturbation strategy is used to improve the mathematical model of the collection and foraging phase of the Arctic Puffin optimization algorithm. The strategy introduces Weibull distribution to generate random perturbations and uses the optimal position The update of the population is guided. When the random factor R>=0.5, the update is executed towards the optimal position. When the current random factor R<0.5, the update is executed in the direction away from the optimal position. The improved mathematical model of the collection and foraging stage is:

[0091] (7);

[0092] In formula (7), Indicates the updated population position during the foraging phase, iter indicates the current iteration number, d indicates the factor approaching the optimal position, which is 0.1, β indicates the amplitude factor of the disturbance term, which is 0.05, y indicates the shape parameter of the Weibull distribution, which is 1.5, f indicates the scale coefficient of the Weibull distribution, σ indicates the amplitude factor of the reverse disturbance term, which is 0.1, represents the reverse update factor, with a value of 0.2, wblrnd() represents the Weibull distribution function, and R represents the random factor. represents the optimal position in the population, Indicates the population position at the current iteration number.

[0093] S3. Use the improved Arctic Puffin optimization algorithm to adjust the parameters of the PID controller module in the feedforward adaptive PID control model, and obtain the best Kp, Ki, and Kd parameters through optimization. The specific steps are as follows:

[0094] S31, initialize the parameters of the improved Arctic puffin optimization algorithm, including the population size N, the problem dimension dim, the lower limit lb of the search space, the upper limit ub of the search space, and the maximum number of iterations max_iter, and generate the initial population of the algorithm by integrating the Circle chaos mapping strategy of Latin hypercube. The specific mathematical model is shown in formula (3) and formula (4);

[0095] S32, setting the objective function of the algorithm optimization, using the absolute error integral function as the objective function, as shown in formula (8), calculating the fitness value of the individuals in the initial population through the objective function, and selecting the individual with the best fitness value as the optimal individual;

[0096] (8);

[0097] In formula (8), J represents the objective function, T represents the total time of system operation, and e(t) represents the real-time error;

[0098] S33, updating the position of the population by improving the mathematical model of the Arctic Puffin optimization algorithm, calculating and updating the fitness value of the individual, and updating the optimal position in the population;

[0099] S34. Determine whether the current number of iterations has reached the maximum number of iterations. If not, continue to execute S33 to update the position. If reached, convert the optimal position in the population into the three parameters Kp, Ki, and Kd of the PID controller as the optimal solution output.

[0100] Furthermore, in S33, the position of the population is updated by improving the mathematical model of the Arctic Puffin optimization algorithm, and the specific steps are as follows:

[0101] Step 1. Calculate the behavior conversion factor B. If the value of B is greater than 0.5, execute the exploration phase of the Arctic Puffin Optimization Algorithm. Otherwise, execute the development phase. The calculation formula of the conversion factor B is:

[0102] (9);

[0103] In formula (9), iter represents the current number of iterations, max_iter represents the maximum number of iterations, and rand represents a random number between [0, 1];

[0104] Step 2: When the conversion factor B is greater than 0.5, the algorithm executes the exploration phase. The exploration phase is divided into the aerial search phase and the diving predation phase. First, the aerial search phase is entered to update the position. The mathematical model of the aerial search phase is shown in formula (10). Then, the diving predation phase is entered to update the position. The mathematical model of the diving predation phase is improved using an adaptive nonlinear search adjustment strategy. The improved mathematical model is shown in formula (5). Finally, the new positions obtained in the aerial search phase and the diving predation phase are merged, and the fitness value of the merged individual is calculated. The position with the best fitness value is selected as the final updated position.

[0105] (10);

[0106] In formula (10), Y(iter+1) represents the updated position in the aerial search phase, represents the population position at the current iteration number, L(dim) represents the random number generated by Levy flight, and dim represents the problem dimension. represents a random position in the selected population, and Rn represents a random number from a standard normal distribution;

[0107] Step 3, when the conversion factor B is less than or equal to 0.5, the algorithm executes the development phase. The development phase is divided into the collection and foraging phase, the enhanced search phase and the predator avoidance phase. First, the collection and foraging phase is entered to update the position. The collection and foraging phase is improved using a two-way elite perturbation strategy. The improved mathematical model is shown in formula (7). Then, the enhanced search phase is entered to update the position. The mathematical model of the enhanced search phase is shown in formula (11). Finally, the predator avoidance phase is entered to update the position. The mathematical model of the predator avoidance phase is shown in formula (12). The updated positions obtained in the three phases are merged, and the fitness value of the merged individual is calculated. The position with the best fitness value is selected as the final updated position.

[0108] (11);

[0109] In formula (11), IS(iter) represents the updated position in the enhanced search phase, Indicates the updated population position during the foraging phase, rand indicates a random number between [0, 1], max_iter indicates the maximum number of iterations, and iter indicates the current number of iterations;

[0110] (12);

[0111] In formula (12), AP(iter) represents the updated population position in the predator avoidance phase, rand represents a random number between [0, 1], represents the population position at the current iteration number, and represents two positions in the randomly selected population, L(dim) represents the random number generated by Levy flight, and dim represents the problem dimension;

[0112] Step 4: Compare the fitness value of the updated position with the fitness value of the optimal position in the population, and take the position with the smallest fitness as the optimal position in the population.

[0113] S4. Input the obtained optimal Kp, Ki, and Kd parameters into the feedforward adaptive PID control model to optimize the control effect.

[0114] In order to verify that the feedforward adaptive PID control optimization method proposed in the present invention has better performance than other methods, the present invention conducts experiments through Matlab and Simulink simulation tools. First, the arctic puffin optimization mathematical model is improved by Matlab, and the feedforward adaptive PID control model diagram is constructed by Simulink. The parameters of the improved arctic puffin optimization algorithm are set, the population size N is 200, the problem dimension dim is 3, the maximum number of iterations is 25, the search space upper limit ub is 20, the lower limit lb is 0.01, and the second-order transfer of the controlled object module in the feedforward adaptive PID control model is set to , set the parameters of the ordinary PID controller and the parameters of the feedforward adaptive PID controller to the same value, and perform simulation to obtain Figure 3 , Figure 3 This is a response comparison curve diagram of an ordinary PID controller and a feedforward PID controller. The target value is set to 1 unit. It can be seen from the figure that compared with the ordinary PID controller, the response curve of the feedforward PID controller has a lower overshoot, better stability, and faster response speed.

[0115] Figure 4This is a fitness value comparison diagram of the optimization process of the improved Arctic Puffin Optimization Algorithm and the standard Arctic Puffin Optimization Algorithm. From the figure, we can see that according to the principle that the smaller the fitness value, the better the algorithm performance, the improved Arctic Puffin Optimization Algorithm reaches the optimal solution in a shorter number of iterations, and has better optimization performance. Figure 5 and Figure 6 They are the parameter change diagrams of the feedforward adaptive PID controller optimized by the standard Arctic Puffin optimization algorithm and the improved Arctic Puffin optimization algorithm. From the diagram, we can see the changing trend of the parameters during the optimization process. Figure 7 This is a response comparison curve of the feedforward adaptive PID controller optimized by the standard Arctic Puffin optimization algorithm and the improved Arctic Puffin optimization algorithm. The target value is set to 1 unit. It can be seen from the figure that the response curves of the PID controllers optimized by the standard Arctic Puffin optimization algorithm and the improved Arctic Puffin optimization algorithm have good stability and adaptability, but the response curve of the PID controller optimized by the improved Arctic Puffin optimization algorithm has lower overshoot and faster response time, indicating that the parameter control effect obtained by the improved Arctic Puffin optimization algorithm is better.

Claims

1. A feedforward adaptive PID control optimization method, characterized in that: The mathematical model of the Arctic Puffin optimization algorithm is improved, and the improved Arctic Puffin optimization algorithm is used to optimize the parameters of the feedforward adaptive PID controller. The specific steps are as follows: S1, constructing a feedforward adaptive PID control model, the control model comprising: an error calculation module, a feedforward control module, a PID controller module, an improved Arctic puffin optimization algorithm module, and a controlled object module; S2. Improve the Arctic Puffin optimization algorithm. The specific improvement strategies are as follows: S21, using the Circle chaos mapping strategy fused with Latin hypercube to generate the initial population of the algorithm; S22. Improve the mathematical model of the diving predation phase of the Arctic puffin optimization algorithm using an adaptive nonlinear search adjustment strategy. The strategy uses an adaptive factor ,With the increase of the number of iterations, the value of the adaptive factor keeps changing to adjust the change of the population position, and the nonlinear perturbation is performed through the hyperbolic tangent function to update the population position; S23. Use a two-way elite perturbation strategy to improve the mathematical model of the collection and foraging phase of the Arctic puffin optimization algorithm, and move the optimal position in the population As an elite position guide, through the size of the random factor, choose the positive adjustment or negative adjustment of the population to update the position of the population; S3, using the improved Arctic Puffin optimization algorithm to adjust the parameters of the PID controller module in the feedforward adaptive PID control model, and obtaining the best Kp, Ki, Kd parameters through optimization; S4. Input the obtained optimal Kp, Ki, and Kd parameters into the feedforward adaptive PID control model to optimize the control effect.

2. A feedforward adaptive PID control optimization method according to claim 1, characterized in that: In S1, the execution process of the constructed feedforward adaptive PID control model is as follows: first, the real-time output value and the target value are input into the error calculation module to obtain the real-time error e(t), the real-time error e(t) is input into the PID controller module, and the PID parameters are optimized by the improved Arctic Puffin optimization algorithm. The PID controller outputs the control quantity u(t) through the optimized parameters, and the control quantity u(t) is added to the feedforward increment F output by the feedforward control module, and is input into the controlled object module for control, wherein the calculation formula of the control quantity u(t) is shown in Formula (1); (1)； In formula (1), Kp represents proportional gain, Ki represents integral gain, Kd represents differential gain, and e(t) represents real-time error.

3. A feedforward adaptive PID control optimization method according to claim 2, characterized in that: In S1, the feedforward control module includes a feedforward path transfer function, a feedforward gain and a low-pass filter. Set as the second-order transfer function in the controlled plant model The double differential in the feedforward path transfer function produces high-frequency effects, which are then filtered through a low-pass filter. To solve the high-frequency effect caused by differentiation, the cutoff frequency of the low-pass filter is set to 2000, and the calculation formula for the feedforward increment is: (2)； In formula (2), F represents the feedforward increment, represents the second-order transfer function, represents the feedforward gain, s represents the function variable, Represents a low pass filter .

4. A feedforward adaptive PID control optimization method according to claim 3, characterized in that: In S21, the Circle chaos mapping strategy integrating Latin hypercube is adopted to generate the initial population of the algorithm. Two initial populations are generated by combining Latin hypercube sampling and Circle chaos mapping. The two initialization populations are merged, and N individuals are randomly selected as the initialization population of the algorithm. The specific mathematical model is: (3)； In formula (3), represents the initial population generated by Latin hypercube sampling, lb represents the lower limit of the search space, ub represents the upper limit of the search space, lhsdesign() represents the Latin hypercube matrix function, N represents the number of populations, and dim represents the problem dimension; (4)； In formula (4), represents the initial population generated by Circle chaotic mapping, lb represents the lower limit of the search space, ub represents the upper limit of the search space, p represents a random number between [0, 1], c represents a constant control parameter with a value range of [0, 1], k represents the chaos control parameter, mod() represents the modulo operation, which is modulo 1 in formula (4), and the value range after modulo 1 is [0, 1].

5. A feedforward adaptive PID control optimization method according to claim 4, characterized in that: In S22, an adaptive nonlinear search adjustment strategy is used to improve the mathematical model of the diving predation stage of the Arctic puffin optimization algorithm, and the adaptive factor As the number of iterations increases, nonlinear changes are made. The population position updated in the aerial search phase of the algorithm is adjusted by changing the adaptive factor. The improved mathematical model of the diving predation phase is: (5)； In formula (5), Z(iter+1) represents the updated population position in the diving predation phase, iter represents the current iteration number, and Y(iter+1) represents the updated population position in the aerial search phase. represents the adaptive factor, and the calculation formula is shown in formula (6), max_iter represents the maximum number of iterations, tanh() represents the hyperbolic tangent function, λ represents the nonlinear change parameter value of 0.5, and rand represents a random number between [0, 1]; (6)； In formula (6), Represents the adaptive factor, max_iter represents the maximum number of iterations, iter represents the current number of iterations, and cosh() represents the hyperbolic cosine function.

6. A feedforward adaptive PID control optimization method according to claim 5, characterized in that: In S23, a bidirectional elite perturbation strategy is used to improve the mathematical model of the collection and foraging phase of the Arctic Puffin optimization algorithm. The strategy introduces Weibull distribution to generate random perturbations and uses the optimal position The update of the population is guided. When the random factor R>=0.5, the update is executed towards the optimal position. When the current random factor R<0.5, the update is executed in the direction away from the optimal position. The improved mathematical model of the collection and foraging stage is: (7)； In formula (7), Indicates the updated population position during the foraging phase, iter indicates the current iteration number, d indicates the factor approaching the optimal position, which is 0.1, β indicates the amplitude factor of the disturbance term, which is 0.05, y indicates the shape parameter of the Weibull distribution, which is 1.5, f indicates the scale coefficient of the Weibull distribution, σ indicates the amplitude factor of the reverse disturbance term, which is 0.1, represents the reverse update factor, with a value of 0.2, wblrnd() represents the Weibull distribution function, and R represents the random factor. represents the optimal position in the population, Indicates the population position at the current iteration number.

7. A feedforward adaptive PID control optimization method according to claim 6, characterized in that: In S3, the parameters of the PID controller module in the feedforward adaptive PID control model are adjusted using the improved Arctic Puffin optimization algorithm, and the specific steps are as follows: S31, initialize the parameters of the improved Arctic puffin optimization algorithm, including the population size N, the problem dimension dim, the lower limit lb of the search space, the upper limit ub of the search space, and the maximum number of iterations max_iter, and generate the initial population of the algorithm by integrating the Circle chaos mapping strategy of Latin hypercube. The specific mathematical model is shown in formula (3) and formula (4); S32, setting the objective function of the algorithm optimization, using the absolute error integral function as the objective function, as shown in formula (8), calculating the fitness value of the individuals in the initial population through the objective function, and selecting the individual with the best fitness value as the optimal individual; (8)； In formula (8), J represents the objective function, T represents the total time of system operation, and e(t) represents the real-time error; S33, updating the position of the population by improving the mathematical model of the Arctic Puffin optimization algorithm, calculating and updating the fitness value of the individual, and updating the optimal position in the population; S34. Determine whether the current number of iterations has reached the maximum number of iterations. If not, continue to execute S33 to update the position. If reached, convert the optimal position in the population into the three parameters Kp, Ki, and Kd of the PID controller as the optimal solution output.

8. A feedforward adaptive PID control optimization method according to claim 7, characterized in that: In S33, the position of the population is updated by improving the mathematical model of the Arctic Puffin optimization algorithm, and the specific steps are as follows: Step 1. Calculate the behavior conversion factor B. If the value of B is greater than 0.5, execute the exploration phase of the Arctic Puffin Optimization Algorithm. Otherwise, execute the development phase. The calculation formula of the conversion factor B is: (9)； In formula (9), iter represents the current number of iterations, max_iter represents the maximum number of iterations, and rand represents a random number between [0, 1]; Step 2: When the conversion factor B is greater than 0.5, the algorithm executes the exploration phase. The exploration phase is divided into the aerial search phase and the diving predation phase. First, the aerial search phase is entered to update the position. The mathematical model of the aerial search phase is shown in formula (10). Then, the diving predation phase is entered to update the position. The mathematical model of the diving predation phase is improved using an adaptive nonlinear search adjustment strategy. The improved mathematical model is shown in formula (5). Finally, the new positions obtained in the aerial search phase and the diving predation phase are merged, and the fitness value of the merged individual is calculated. The position with the smallest fitness value is selected as the updated position of the population. (10)； In formula (10), Y(iter+1) represents the updated position in the aerial search phase, represents the population position at the current iteration number, L(dim) represents the random number generated by Levy flight, and dim represents the problem dimension. represents a random position in the selected population, and Rn represents a random number from a standard normal distribution; Step 3, when the conversion factor B is less than or equal to 0.5, the algorithm executes the development phase. The development phase is divided into the collection and foraging phase, the enhanced search phase and the predator avoidance phase. First, the collection and foraging phase is entered to update the position. The collection and foraging phase is improved using a two-way elite perturbation strategy. The improved mathematical model is shown in formula (7). Then, the enhanced search phase is entered to update the position. The mathematical model of the enhanced search phase is shown in formula (11). Finally, the predator avoidance phase is entered to update the position. The mathematical model of the predator avoidance phase is shown in formula (12). The updated positions obtained in the three phases are merged, and the fitness value of the merged individual is calculated. The position with the best fitness value is selected as the final updated position. (11)； In formula (11), IS(iter) represents the updated position in the enhanced search phase, Indicates the updated population position during the foraging phase, rand indicates a random number between [0, 1], max_iter indicates the maximum number of iterations, and iter indicates the current number of iterations; (12)； In formula (12), AP(iter) represents the updated population position in the predator avoidance phase, rand represents a random number between [0, 1], represents the population position at the current iteration number, and represents two positions in the randomly selected population, L(dim) represents the random number generated by Levy flight, and dim represents the problem dimension; Step 4: Compare the fitness value of the updated position with the fitness value of the optimal position in the population, and take the position with the smallest fitness as the optimal position in the population.

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