A taylor space outer support frame PID control method based on improved snow goose algorithm

Abstract

The application discloses a Taylor space external fixed support PID control method based on an improved snow goose algorithm, and belongs to the technical field of PID control, and the specific steps comprise the following steps. Step one, a Taylor space external fixed support control model based on a PID controller is established. Step two, the snow goose algorithm is improved, including introducing boundary excitation and a chaos elite strategy to initialize a population so as to take into account global and boundary exploration; an elite reservation and worst resetting mechanism is adopted to ensure the inheritance of excellent solutions and diversity; a golden ratio reverse exploration method is used to improve the global search efficiency; a multi-directional Lévy flight is introduced to enhance the ability to jump out of a local optimum; step three, the improved snow goose algorithm is used to optimize the parameters of the PID controller, and optimal Kp, Ki and Kd are obtained; step four, MATLAB and Simulink are used to simulate the PID controller of the control model. The improved snow goose algorithm can improve the adaptive control capability of the system, and enhance the stability and control precision.

Description

Technical Field

[0001] This invention belongs to the field of PID control optimization technology, and in particular relates to a PID control method for Taylor space external fixed supports based on an improved Xueyan algorithm. Background Technology

[0002] Taylor Space External Fixation is a widely used external fixation device in orthopedics, especially in complex trauma and limb reconstruction surgeries. Through multiple adjustable links and ball joint modules, it enables precise multi-axis alignment and progressive traction of fractures, thereby promoting bone healing and restoring the physiological axis. However, due to factors such as patient activity, muscle contraction, and external disturbances, the fixation system often faces challenges in clinical use, including decreased positioning accuracy, uneven stress distribution, and discomfort from soft tissue traction. Traditional manual or fixed-parameter PID control often struggles to compensate for these dynamic changes in a timely and stable manner, thus affecting rehabilitation outcomes.

[0003] Based on this, a Taylor space external fixation scaffold PID control system based on an improved Xueyan algorithm was developed. This system utilizes an advanced, improved Xueyan optimization algorithm to monitor and adjust the position and angle of the scaffold in real time. Using PID control technology, the system can automatically adjust the scaffold's control parameters according to complex conditions such as different stages of bone healing and changes in external forces generated by physical activity. This precisely controls the scaffold's position and angle, ensuring that the fracture site heals in the optimal mechanical environment and helping patients recover quickly and effectively.

[0004] PID control is a classic feedback regulation technique widely used in industrial automation. It acquires the error between the system output and the set target in real time, and generates the control quantity through three parallel action channels: proportional (P), integral (I), and derivative (D). The proportional element linearly amplifies the current error, responding quickly to large deviations; the integral element corrects for accumulated errors, thus eliminating steady-state deviations; and the derivative element predicts the rate of change of the error, suppressing system overshoot and oscillations. Due to its simple structure, high adjustability, good stability, and low model dependence, PID controllers have been successfully applied in process control, motor drives, and robotics. However, in the complex disturbance environment of multivariable coupled systems such as Taylor space externally fixed supports, traditional fixed-parameter PID controllers often struggle to balance fast response and robust stability. Therefore, there is an urgent need to design an adaptive PID control strategy to achieve high-precision, high-response, and high-stability control of Taylor space externally fixed supports.

[0005] The Snow Goose Algorithm is a novel metaheuristic algorithm inspired by the behavioral characteristics of snow geese migrating in flocks during the autumn and winter seasons. This algorithm simulates typical V-formation and straight-line formations during migration and dynamically adjusts the formation based on different flight conditions, providing coordinated guidance for both the exploration and development phases. The algorithm divides the population into three functional parts: the leader, the middle layer, and the follower. The leader plays a core leading role in the formation, creating a favorable aerodynamic environment to reduce overall air resistance and enhance the group's endurance. Younger or weaker snow geese occupy the middle layer, utilizing the layout advantage for protection and reducing wind resistance to conserve energy. The follower individuals collaboratively maintain formation stability. Based on these group cooperative characteristics, the algorithm constructs corresponding speed update rules and position adjustment mechanisms for the V-formation exploration mode and the straight-line development mode, achieving an efficient balance between global exploration capability and local development accuracy through dynamic adaptation between the two modes. This algorithm demonstrates significant application potential in solving various constrained optimization problems in engineering design, scientific research, and other fields. Summary of the Invention

[0006] The purpose of this invention is to propose a Taylor space external fixation scaffold PID control method based on an improved Xueyan algorithm. This method effectively solves the core defects of the original Xueyan algorithm, such as slow convergence speed, poor stability of the iteration process, and easy getting trapped in local optima. It enables the scaffold displacement control accuracy to reach the 0.1mm level, shortens the response time to within 0.5 seconds, and improves the anti-interference ability by 60%, significantly improving the safety and efficiency of complex bone orthopedic treatment.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A Taylor space external fixed support PID control method based on an improved Xueyan algorithm is characterized by optimizing the three parameters Kp, Ki, and Kd of the PID controller using the improved Xueyan algorithm. The specific steps are as follows.

[0009] Step 1: Establish a Taylor space external fixed support control model based on a PID controller.

[0010] Step 2: Improve the Snow Goose optimization algorithm, including introducing boundary excitation and chaotic elite strategy to initialize the population, introducing an elite retention strategy, improving the updating of the population center position and the position of the weak group and introducing a worst-case reset strategy, periodically eliminating poorly performing individuals, using the golden ratio backward exploration method to improve population guidance, and using enhanced multi-directional adaptive Lévy flight to improve random Brownian motion behavior.

[0011] There are four improvements to the algorithm described in step two, as detailed below.

[0012] Firstly, based on the fundamental ideas of global search and boundary exploration, a boundary excitation and chaotic elite initialization population strategy is introduced. The initial population is constructed into two core components: a chaotic group and a boundary group. The chaotic group comprises 4 / 5 of the total population, and the boundary group comprises 1 / 5. The relevant formulas for the specific initialization process of these two types of individuals are as follows:

[0013] ;

[0014] ;

[0015] In the formula, The position vector of individual i initialized for the chaotic group. Let i be a random variable of individual i, and let i follow a uniform distribution. This increases the coverage of the global space. , Let the upper and lower bound vectors of the search space be defined to ensure that the position is within a certain range. The position vector of individual i initialized for the boundary group. By selecting a probability threshold for the boundary, the ability to explore the boundary region of the solution space is enhanced.

[0016] Secondly, based on the survival-of-the-fittest mechanism in biological evolution theory, an elite retention strategy is introduced. By improving the updates of the population center position and the position of weaker groups, other individuals are guided to concentrate in better areas, thereby improving the convergence speed and stability of the algorithm. At the same time, a worst-case reset strategy is introduced to periodically eliminate poorly performing individuals and regenerate new individuals, effectively avoiding the defect of the population getting trapped in local optima due to premature convergence. The relevant formula is:

[0017] ;

[0018] ;

[0019] ;

[0020] In the formula, This is the center position vector of the population, used for grouping updates (exploration phase). For the fitness of individual i, Let be the position vector of individual i. For the size of the population, The size of the elite pool, Let j be the position vector of the elite individual. The leading factor is a random number in the range [-2, 2], representing the dominant individual's tendency to move towards the global optimal solution. This represents the optimal position vector for the current population. is the cohesion factor, a random number with a value in the range [-1.5, 1.5], representing the factors that attract individuals to cluster towards the weighted center of the group. Let i be the velocity vector of individual i. This is the elite guidance coefficient, which regulates the intensity of guidance that elite individuals exert on current individuals. Let be the position vector of an elite individual randomly selected from the elite pool. Let i be the position vector of individual i among the w worst individuals. , Let these be the upper and lower bound vectors of the search space. To reset the conditional probability, It is a perturbation random factor used to increase the diversity of solutions.

[0021] Thirdly, the golden ratio reverse exploration method is adopted to improve the group guidance. The golden ratio is introduced as the basic weight parameter, and a dynamic proportional coefficient adjustment model is constructed by integrating random perturbation factors to optimize the search direction. This effectively improves the algorithm's global exploration efficiency and solution space traversal capability. The relevant formula is as follows:

[0022] ;

[0023] In the formula, Let be the position vector of individual i. Using the golden ratio (0.618) as a baseline scaling factor, we balance local and minor global shifts. To introduce randomness as a perturbation factor, the step size for each dimension is slightly different. This is the optimal position vector for the current population.

[0024] Fourthly, an enhanced multi-directional adaptive Lévy flight strategy is adopted to improve the behavior of random Brownian motion. By introducing a multi-directional perturbation mechanism, the search range limitation of the traditional Gaussian distribution is overcome, enhancing the algorithm's global exploration breadth of the solution space and improving the population's ability to escape from local optima and global optimization accuracy. The relevant formula is as follows:

[0025] ;

[0026] ;

[0027] In the formula, The step size is the standard. The Lévy index is randomly sampled from [1,2), and the heavy-tailed distribution is dynamically adjusted to achieve a balance between local fine-tuning and global jumps. , Given two independent random numbers, which follow a uniform distribution. , used to generate the random intensity of S and the superposition direction perturbation. Let be the position vector of individual i. , , These are independent Gaussian random direction vectors, ensuring directional diversity. To enhance spatial coverage against random noise.

[0028] Step 3: The improved Xueyan optimization algorithm is used to optimize the PID controller parameters. The optimized proportional coefficient Kp, integral coefficient Ki, and derivative coefficient Kd are obtained through iterative calculation. These parameters are then configured in the PID controller to achieve rapid and accurate control of the Taylor space external fixation support control system.

[0029] Step 4: Simulate the PID controller of the Taylor space external fixation support control model using MATLAB and Simulink to verify the adaptive control of the Taylor space external fixation support system.

[0030] Furthermore, in step one, the Taylor space external fixed support control model of the PID controller mainly includes the following modules: position difference calculation module, improved Xueyan algorithm module, position PID control module, load compensation calculation module, position adjustment module, speed detection module, and support pressure detection module. Specifically, the position difference calculation module calculates the deviation between the target position and the actual position; the improved Xueyan algorithm module iteratively obtains optimal PID parameters Kp, Ki, and Kd and inputs them into the position PID control module; the position PID control module adjusts the output position control signal to the load compensation calculation module based on the position error value from the position difference calculation module; the load compensation calculation module combines the position control signal from the position PID control module with the load change deviation, adjusts the position signal, and outputs it to the position adjustment module; the position adjustment module adjusts the final position output based on the position signal from the load compensation calculation module to ensure precise system position control; the speed detection module detects the actual motor speed and provides feedback on the support movement speed change information to optimize the position control effect; the support pressure detection module detects the support pressure and provides feedback on key information about the support status to assist in precise position adjustment.

[0031] Furthermore, in step three, the specific steps for optimizing the PID controller through the improved Xueyan optimization algorithm are as follows:

[0032] S1. Initialize the parameters of the improved Xueyan optimization algorithm, including the basic idea of ​​global search and boundary exploration, introducing boundary excitation and chaotic elite strategy to initialize the population position, population velocity, population size N, upper bound ub and lower bound lb of the search space, solution space dimension dim and maximum number of iterations T. The relevant formulas of boundary excitation and chaotic elite are shown in equation (1) and equation (2).

[0033] S2. Select an optimization objective function to calculate the fitness value. The objective function formula is:

[0034] ;

[0035] In the formula, Let be the objective function. As the expected value, This is the current value.

[0036] S3. Calculate the current fitness value of each individual in the snow goose population, determine the solution corresponding to the minimum fitness value as the initial global optimal solution, and select the top k individuals with the best fitness performance as elite individuals and include them in the elite pool.

[0037] S4. During the speed update phase of snow geese, the significant impact of key factors such as air resistance and energy consumption on the flight dynamics of snow geese in the real migration environment is simulated: that is, the energy level of snow geese increases with the group's cooperative gain in the early stage of migration, while the energy gradually decreases due to continuous consumption as they approach the target area. Based on this behavioral characteristic, a dynamic speed update mechanism is constructed, and the speed update formula is:

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula, As a velocity weighting factor, it quantifies the correlation between the velocities of the current and previous generations of the population. Its value variation simulates the dynamic characteristics of collective energy first increasing and then decreasing during population flight. This represents the current iteration number. The maximum number of iterations, For individual i, the inherent energy This represents the optimal position vector for the current population. Let be the position vector of individual i. The air resistance experienced by an individual i during flight. Let the random number be between (0, 1), and let random perturbation characterize the differences in resistance experienced by individuals. Let i be the velocity vector of individual i. Air resistance factors are formed by the combined effects of the drag coefficient, cross-sectional area, and the flight angle of the snow goose. The quality of an individual in the population.

[0043] S5. Utilize the simulated cooperative flight behavior of snow geese (their unique V-formation and straight-line formations) to update the population's location, including two methods, as detailed below.

[0044] Method 1: V-formation, if the angle between the snow geese during flight (formation phase factor) Less than the threshold Then, a simulated snow goose V-formation (exploration phase) is used to update positions. At this time, a stratified position update strategy is implemented based on individual fitness performance. For individuals with excellent fitness performance in the population, the position update strategy is implemented accordingly. For individuals, position updates are performed using formula (14). For individuals with poor fitness in the population (including weak, sick, or immobile individuals, i.e., those with the lowest fitness), the position updates are performed using formula (14). The position is updated using formula (4), and finally, for the remaining individuals in the population, the position is updated using formula (15). The above stratification strategy can dynamically adjust the position update rules according to the individual fitness level, adapt to the differences in individual ability and state within the population, and take into account both optimization efficiency and diversity protection. Formulas (14) and (15) are shown below:

[0045] ;

[0046] ;

[0047] ;

[0048] In the formula, This is the navigation factor, a random number in the range [-2, 2], used to guide individuals toward the global optimal solution. The cohesion factor is a random number with a value in the range [-1.5, 1.5], used to drive individuals to cluster towards the population weighting center. This is a repulsion factor, a random number with a value in the range [-1, 1], used to avoid and repel the weakest or most distant individual in the population, thereby enhancing population diversity. Let be the population center location vector. This is the position vector of the worst-performing individual in the population, used to implement the obstacle avoidance mechanism. , These are the upper and lower bounds of the search space; the other parameters and functions have the same meaning as S4.

[0049] Method 2: Straight-line formation, if the angle between the snow geese during flight (formation phase factor) Exceeding the threshold Then, the simulated snow goose linear formation (development stage) is used to update the position. This method focuses more on improving the escape ability of the local optimal solution area. This stage adopts a dual-strategy dynamic selection mechanism. If the strategy selection factor r>0.5, the golden ratio reverse exploration method mentioned in step 2 is used to improve the group guidance for position update. The update formula is shown in equation (6). The simulated snow geese follow experienced and strong individuals to search for the optimal target area. If the strategy selection factor r<=0.5, the enhanced multi-directional adaptive Lévy flight mentioned in step 2 is used to improve the random Brownian motion behavior for position update. The update formula is shown in equation (8).

[0050] S6. Based on the inspiration of biological evolution, simulate the survival of the fittest, introduce the worst reset strategy mentioned in step 2 to update the position of snow geese in the population, eliminate the w individuals with the worst fitness, and simultaneously inject newly generated individuals to enhance the diversity of the solution space, avoid the population from falling into local optima due to premature convergence, and explore and develop the dynamic balance algorithm. The specific reset formula is shown in equation (5).

[0051] S7. Update fitness and merge elite solutions. Recalculate the objective function value for all individuals after the current iteration update, obtain new fitness, merge the current population with the historical best solutions retained in the elite pool, filter and update the elite pool, and provide a guiding benchmark for continuous optimization in subsequent iterations.

[0052] S8. Determine whether the maximum number of iterations for the population has been reached. If it has, stop the iteration and analyze the optimal solution into proportional coefficient Kp, integral coefficient Ki, and derivative coefficient Kd. Input these into the PID controller to complete parameter optimization and tuning. Otherwise, return to S4 to continue iterating and finding the optimal solution.

[0053] Furthermore, in step four, the transfer function formula for the selected controlled object is:

[0054] ;

[0055] In the formula, For transfer functions, It is a function variable.

[0056] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0057] This invention proposes a PID control method for Taylor space externally fixed supports based on an improved Snow Goose algorithm. Building upon the original Snow Goose algorithm, it introduces boundary excitation and chaotic elite methods, elite retention methods, worst-case reset methods, golden ratio inverse exploration methods, and an improved Lévy flight mechanism, significantly enhancing the algorithm's global optimization capability and local search accuracy. Compared to the original algorithm's premature convergence and insufficient search efficiency, the improved algorithm exhibits stronger robustness and adaptability in complex environments such as high-dimensionality, strong coupling, and dynamic disturbances. It can effectively escape local optima, accelerate convergence speed, and improve solution accuracy and stability. Applying this algorithm to PID parameter optimization allows for dynamic adjustment of Kp, Ki, and Kd coefficients based on support motion feedback, enabling the control system to maintain good response characteristics and stable control performance under complex loads and uncertain environments. It is suitable for the control of precision actuators such as Taylor space externally fixed supports and has significant engineering practical value. Attached Figure Description

[0058] Figure 1 To improve the Xueyan algorithm, the PID controller model diagram of the Taylor space external fixation system is optimized.

[0059] Figure 2 Block diagram of Taylor space external fixation system.

[0060] Figure 3 The flowchart for optimizing the PID control of the Taylor space external fixation system based on the improved Xueyan algorithm is presented.

[0061] Figure 4 A comparison chart showing the optimization of Kp parameters for PID using the improved Xueyan optimization algorithm and the basic Xueyan optimization algorithm.

[0062] Figure 5 A comparison chart showing the optimization of Ki parameters for PID using the improved Xueyan optimization algorithm and the basic Xueyan optimization algorithm.

[0063] Figure 6 A comparison chart showing the optimization of the Kd parameter of PID using the improved Xueyan optimization algorithm and the basic Xueyan optimization algorithm.

[0064] Figure 7 A curve comparing the optimal individual fitness values ​​of the improved Snow Goose optimization algorithm and the basic Snow Goose optimization algorithm.

[0065] Figure 8 A comparison curve showing the control performance of the improved Xueyan optimization algorithm and the basic Xueyan optimization algorithm for PID control. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them; all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0067] Please see Figures 1-8 The present invention provides a technical solution:

[0068] A PID control method for Taylor space external fixation support based on an improved Snow Goose algorithm is proposed. The improved Snow Goose optimization algorithm is used to achieve rapid optimization and determine the PID control parameters of the Taylor space external fixation support system, thereby improving the system's reliability, stability, response speed and control accuracy. The specific steps are as follows.

[0069] Step 1: As Figure 2 As shown, a Taylor space external fixed support control model based on a PID controller is established.

[0070] Step 2: Improve the Snow Goose optimization algorithm, including introducing boundary excitation and chaotic elite strategy to initialize the population, introducing an elite retention strategy, improving the updating of the population center position and the position of the weak group and introducing a worst-case reset strategy, periodically eliminating poorly performing individuals, using the golden ratio backward exploration method to improve population guidance, and using enhanced multi-directional adaptive Lévy flight to improve random Brownian motion behavior.

[0071] There are four improvements to the algorithm described in step two, as detailed below.

[0072] Firstly, based on the fundamental ideas of global search and boundary exploration, a boundary excitation and chaotic elite initialization population strategy is introduced. The initial population is constructed into two core components: a chaotic group and a boundary group. The chaotic group comprises 4 / 5 of the total population, and the boundary group comprises 1 / 5. The relevant formulas for the specific initialization process of these two types of individuals are as follows:

[0073] ;

[0074] ;

[0075] In the formula, The position vector of individual i initialized for the chaotic group. Let i be a random variable of individual i, and let i follow a uniform distribution. This increases the coverage of the global space. , Let the upper and lower bound vectors of the search space be defined to ensure that the position is within a certain range. The position vector of individual i initialized for the boundary group. By selecting a probability threshold for the boundary, the ability to explore the boundary region of the solution space is enhanced.

[0076] Secondly, based on the survival-of-the-fittest mechanism in biological evolution theory, an elite retention strategy is introduced. By improving the updates of the population center position and the position of weaker groups, other individuals are guided to concentrate in better areas, thereby improving the convergence speed and stability of the algorithm. At the same time, a worst-case reset strategy is introduced to periodically eliminate poorly performing individuals and regenerate new individuals, effectively avoiding the defect of the population getting trapped in local optima due to premature convergence. The relevant formula is:

[0077] ;

[0078] ;

[0079] ;

[0080] In the formula, This is the center position vector of the population, used for grouping updates (exploration phase). For the fitness of individual i, Let be the position vector of individual i. For the size of the population, The size of the elite pool, Let j be the position vector of the elite individual. The leading factor is a random number in the range [-2, 2], representing the dominant individual's tendency to move towards the global optimal solution. This represents the optimal position vector for the current population. is the cohesion factor, a random number with a value in the range [-1.5, 1.5], representing the factors that attract individuals to cluster towards the weighted center of the group. Let i be the velocity vector of individual i. This is the elite guidance coefficient, which regulates the intensity of guidance that elite individuals exert on current individuals. Let be the position vector of an elite individual randomly selected from the elite pool. Let i be the position vector of individual i among the w worst individuals. , Let these be the upper and lower bound vectors of the search space. To reset the conditional probability, It is a perturbation random factor used to increase the diversity of solutions.

[0081] Thirdly, the golden ratio reverse exploration method is adopted to improve the group guidance. The golden ratio is introduced as the basic weight parameter, and a dynamic proportional coefficient adjustment model is constructed by integrating random perturbation factors to optimize the search direction. This effectively improves the algorithm's global exploration efficiency and solution space traversal capability. The relevant formula is as follows:

[0082] ;

[0083] In the formula, Let be the position vector of individual i. Using the golden ratio (0.618) as a baseline scaling factor, we balance local and minor global shifts. To introduce randomness as a perturbation factor, the step size for each dimension is slightly different. This is the optimal position vector for the current population.

[0084] Fourthly, an enhanced multi-directional adaptive Lévy flight strategy is adopted to improve the behavior of random Brownian motion. By introducing a multi-directional perturbation mechanism, the search range limitation of the traditional Gaussian distribution is overcome, enhancing the algorithm's global exploration breadth of the solution space and improving the population's ability to escape from local optima and global optimization accuracy. The relevant formula is as follows:

[0085] ;

[0086] ;

[0087] In the formula, The step size is the standard. The Lévy index is randomly sampled from [1,2), and the heavy-tailed distribution is dynamically adjusted to achieve a balance between local fine-tuning and global jumps. , Given two independent random numbers, which follow a uniform distribution. , used to generate the random intensity of S and the superposition direction perturbation. Let be the position vector of individual i. , , These are independent Gaussian random direction vectors, ensuring directional diversity. To enhance spatial coverage against random noise.

[0088] Step 3: The improved Xueyan optimization algorithm is used to optimize the PID controller parameters. The optimized proportional coefficient Kp, integral coefficient Ki, and derivative coefficient Kd are obtained through iterative calculation. These parameters are then configured in the PID controller to achieve rapid and accurate control of the Taylor space external fixation support control system.

[0089] Step 4: Simulate the PID controller of the Taylor space external fixation support control model using MATLAB and Simulink to verify the adaptive control of the Taylor space external fixation support system.

[0090] Furthermore, in step one, the Taylor space external fixed support control model of the PID controller mainly includes the following modules: position difference calculation module, improved Xueyan algorithm module, position PID control module, load compensation calculation module, position adjustment module, speed detection module, and support pressure detection module. Specifically, the position difference calculation module calculates the deviation between the target position and the actual position; the improved Xueyan algorithm module iteratively obtains optimal PID parameters Kp, Ki, and Kd and inputs them into the position PID control module; the position PID control module adjusts the output position control signal to the load compensation calculation module based on the position error value from the position difference calculation module; the load compensation calculation module combines the position control signal from the position PID control module with the load change deviation, adjusts the position signal, and outputs it to the position adjustment module; the position adjustment module adjusts the final position output based on the position signal from the load compensation calculation module to ensure precise system position control; the speed detection module detects the actual motor speed and provides feedback on the support movement speed change information to optimize the position control effect; the support pressure detection module detects the support pressure and provides feedback on key information about the support status to assist in precise position adjustment.

[0091] Furthermore, such as Figure 3 As shown, in step three, the specific steps for optimizing the PID controller using the improved Xueyan optimization algorithm are as follows:

[0092] S1. Initialize the parameters of the improved Xueyan optimization algorithm, including the basic idea of ​​global search and boundary exploration, introducing boundary excitation and chaotic elite strategy to initialize the population position, population velocity, population size N, upper bound ub and lower bound lb of the search space, solution space dimension dim and maximum number of iterations T. The relevant formulas of boundary excitation and chaotic elite are shown in equation (1) and equation (2).

[0093] S2. Select an optimization objective function to calculate the fitness value. The objective function formula is:

[0094] ;

[0095] In the formula, Let be the objective function. As the expected value, This is the current value.

[0096] S3. Calculate the current fitness value of each individual in the snow goose population, determine the solution corresponding to the minimum fitness value as the initial global optimal solution, and select the top k individuals with the best fitness performance as elite individuals and include them in the elite pool.

[0097] S4. During the speed update phase of snow geese, the significant impact of key factors such as air resistance and energy consumption on the flight dynamics of snow geese in the real migration environment is simulated: that is, the energy level of snow geese increases with the group's cooperative gain in the early stage of migration, while the energy gradually decreases due to continuous consumption as they approach the target area. Based on this behavioral characteristic, a dynamic speed update mechanism is constructed, and the speed update formula is:

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] In the formula, As a velocity weighting factor, it quantifies the correlation between the velocities of the current and previous generations of the population. Its value variation simulates the dynamic characteristics of collective energy first increasing and then decreasing during population flight. This represents the current iteration number. The maximum number of iterations, For individual i, the inherent energy This represents the optimal position vector for the current population. Let be the position vector of individual i. The air resistance experienced by an individual i during flight. Let the random number be between (0, 1), and let random perturbation characterize the differences in resistance experienced by individuals. Let i be the velocity vector of individual i. Air resistance factors are formed by the combined effects of the drag coefficient, cross-sectional area, and the flight angle of the snow goose. The quality of an individual in the population.

[0103] S5. Utilize the simulated cooperative flight behavior of snow geese (their unique V-formation and straight-line formations) to update the population's location, including two methods, as detailed below.

[0104] Method 1: V-formation, if the angle between the snow geese during flight (formation phase factor) Less than the threshold Then, a simulated snow goose V-formation (exploration phase) is used to update positions. At this time, a stratified position update strategy is implemented based on individual fitness performance. For individuals with excellent fitness performance in the population, the position update strategy is implemented accordingly. For individuals, position updates are performed using formula (14). For individuals with poor fitness in the population (including weak, sick, or immobile individuals, i.e., those with the lowest fitness), the position updates are performed using formula (14). The position is updated using formula (4), and finally, for the remaining individuals in the population, the position is updated using formula (15). The above stratification strategy can dynamically adjust the position update rules according to the individual fitness level, adapt to the differences in individual ability and state within the population, and take into account both optimization efficiency and diversity protection. Formulas (14) and (15) are shown below:

[0105] ;

[0106] ;

[0107] ;

[0108] In the formula, This is the navigation factor, a random number in the range [-2, 2], used to guide individuals toward the global optimal solution. The cohesion factor is a random number with a value in the range [-1.5, 1.5], used to drive individuals to cluster towards the population weighting center. This is a repulsion factor, a random number with a value in the range [-1, 1], used to avoid and repel the weakest or most distant individual in the population, thereby enhancing population diversity. Let be the population center location vector. This is the position vector of the worst-performing individual in the population, used to implement the obstacle avoidance mechanism. , These are the upper and lower bounds of the search space; the other parameters and functions have the same meaning as S4.

[0109] Method 2: Straight-line formation, if the angle between the snow geese during flight (formation phase factor) Exceeding the threshold Then, the simulated snow goose linear formation (development stage) is used to update the position. This method focuses more on improving the escape ability of the local optimal solution area. This stage adopts a dual-strategy dynamic selection mechanism. If the strategy selection factor r>0.5, the golden ratio reverse exploration method mentioned in step 2 is used to improve the group guidance for position update. The update formula is shown in equation (6). The simulated snow geese follow experienced and strong individuals to search for the optimal target area. If the strategy selection factor r<=0.5, the enhanced multi-directional adaptive Lévy flight mentioned in step 2 is used to improve the random Brownian motion behavior for position update. The update formula is shown in equation (8).

[0110] S6. Based on the inspiration of biological evolution, simulate the survival of the fittest, introduce the worst reset strategy mentioned in step 2 to update the position of snow geese in the population, eliminate the w individuals with the worst fitness, and simultaneously inject newly generated individuals to enhance the diversity of the solution space, avoid the population from falling into local optima due to premature convergence, and explore and develop the dynamic balance algorithm. The specific reset formula is shown in equation (5).

[0111] S7. Update fitness and merge elite solutions. Recalculate the objective function value for all individuals after the current iteration update, obtain new fitness, merge the current population with the historical best solutions retained in the elite pool, filter and update the elite pool, and provide a guiding benchmark for continuous optimization in subsequent iterations.

[0112] S8. Determine whether the maximum number of iterations for the population has been reached. If it has, stop the iteration and analyze the optimal solution into proportional coefficient Kp, integral coefficient Ki, and derivative coefficient Kd. Input these into the PID controller to complete parameter optimization and tuning. Otherwise, return to S4 to continue iterating and finding the optimal solution.

[0113] Furthermore, such as Figure 1 As shown, in step four, the transfer function formula for the selected controlled object is:

[0114] ;

[0115] In the formula, For transfer functions, It is a function variable.

[0116] analyze Figure 4 , Figure 5 and Figure 6 As can be easily seen from the changes in PID control parameters between the improved and basic Xueyan optimization algorithms, the improved Xueyan optimization algorithm performs better in optimizing Kp, Ki, and Kd parameters. It can quickly converge and stabilize near the optimal parameter values ​​in fewer iterations, effectively shortening the parameter optimization adjustment cycle. At the same time, the parameter change curve of the improved algorithm has smaller fluctuations and a smoother convergence trend, fully demonstrating its stronger stability and more precise parameter adjustment during the optimization process.

[0117] Fitness is a core metric for evaluating the optimization performance of an algorithm, and its value directly reflects how close the algorithm is to the optimal solution. Based on the criterion that a smaller fitness value indicates better algorithm performance, the following analysis... Figure 7 The comparison of fitness changes between the improved and basic Snowgoose optimization algorithms clearly shows that, within the same number of iterations, the fitness value of the improved algorithm is consistently lower than that of the basic version, allowing it to find solutions of higher quality. The basic algorithm is prone to stagnation and getting stuck in local optima during iterations, while the fitness value of the improved algorithm decreases faster, allowing it to quickly escape local optima and continue searching for optimization. It also reaches a stable state earlier, converging to a lower level with fewer iterations, demonstrating superior convergence speed and stability. Therefore, the performance of the improved Snowgoose optimization algorithm is significantly better than that of the basic algorithm.

[0118] Figure 8 A comparison of the effects of the improved Xueyan optimization algorithm and the basic Xueyan optimization algorithm on the PID controller is presented for analysis. Figure 8It can be seen that the PID control system optimized by the improved Xueyan optimization algorithm has a significantly lower overshoot, reducing system fluctuations and losses; it reaches a steady state in a shorter time and responds more quickly; and during dynamic adjustment, the system output can approach the target value with higher efficiency. This indicates that the improved Xueyan optimization algorithm, by optimizing PID parameters, effectively improves the dynamic performance and steady-state accuracy of the system, making the control system more stable, faster in response, and stronger in anti-interference capability.

Claims

1. A PID control method for Taylor space externally fixed supports based on an improved snow goose algorithm, characterized in that, By improving the Xueyan optimization algorithm, the three parameters of the PID controller of the Taylor space external fixation system, namely Kp, Ki, and Kd, are optimized. The specific steps are as follows: Step 1: Establish a Taylor space external fixed support control model based on a PID controller; Step 2: Improve the Snow Goose optimization algorithm, including four improvements, as follows: D1. Based on the ideas of global search and boundary exploration, a boundary excitation and chaotic elite initialization population strategy is adopted. The relevant formula is: In the formula, The position vector of individual i initialized for the chaotic group, R i Let X be a random variable of individual i, following a uniform distribution U(0,1). max X min Let these be the upper and lower bound vectors of the search space. The position vector of individual i is initialized for the boundary group, and τ is the boundary selection probability threshold; D2. Based on the survival of the fittest mechanism in biological evolution theory, we introduce elite retention and worst-case reset strategies, with the relevant formulas as follows: X i =X i +α×(X best -X i )-β×(X c -X i )+V i +δ×(E rd -X i ) (4); In the formula, X c f is the population center location vector. i For the fitness of individual i, X i Let n be the position vector of individual i, n be the population size, k be the size of the elite pool, and E be the position vector of individual i. j Let X be the position vector of elite individual j, α be the navigation factor with a random number value in the range [-2, 2], and X be the position vector of elite individual j. best V represents the optimal position vector for the current population, β is the cohesion factor, and is a random number with a value in the range [-1.5, 1.5]. i Let E be the velocity vector of individual i, δ be the elite guidance coefficient, and E be the velocity vector of individual i. rd Let be the position vector of an elite individual randomly selected from the elite pool. Let p be the position vector of individual i among w worst individuals. r The conditional probability is reset, and χ is the perturbation random factor; D3. Improve group guidance by using the golden ratio reverse exploration method. The relevant formula is: In the formula, ω is the base scaling factor. For disturbance factor; D4. An enhanced multi-directional adaptive Lévy flight strategy is adopted to improve the stochastic Brownian motion behavior. The relevant formula is: In the formula, s is the step size, b is the Lévy exponent, randomly sampled from [1,2), ξ1 and ξ2 are two independent random numbers that follow a uniform distribution U(0,1), d1, d2, and d3 are independent Gaussian random direction vectors, and ρ is random noise to enhance spatial coverage. Step 3: The improved Xueyan optimization algorithm is used to optimize the PID controller parameters. The optimized proportional coefficient Kp, integral coefficient Ki and derivative coefficient Kd are obtained through iterative calculation. The above parameters are then configured in the PID controller to realize the control of the Taylor space external fixed support control system. Step 4: Simulate the PID controller of the Taylor space external fixation support control model using MATLAB and Simulink to verify the adaptive control of the Taylor space external fixation support system.

2. The Taylor space external fixed support PID control method based on the improved Xueyan algorithm according to claim 1, characterized in that, In step one, the Taylor space external fixed support control model of the PID controller mainly includes the following modules: position difference calculation module, improved Xueyan algorithm module, position PID control module, load compensation calculation module, position adjustment module, speed detection module, and support pressure detection module. The position difference calculation module calculates the deviation between the target position and the actual position. The improved Xueyan algorithm module iteratively obtains optimal PID parameters Kp, Ki, and Kd and inputs them into the position PID control module. The position PID control module adjusts the output position control signal to the load compensation calculation module based on the position error value from the position difference calculation module. The load compensation calculation module combines the position control signal from the position PID control module with the load change deviation, adjusts the position signal, and outputs it to the position adjustment module. The position adjustment module adjusts the final position output based on the position signal from the load compensation calculation module to ensure precise system position control. The speed detection module detects the actual motor speed and provides feedback on the support movement speed change information to optimize the position control effect. The support pressure detection module detects the support pressure and provides feedback on key information about the support status to assist in precise position adjustment.

3. The Taylor space external fixed support PID control method based on the improved Xueyan algorithm according to claim 1, characterized in that, Step three includes: S1. Initialize the parameters of the improved Xueyan optimization algorithm, including the basic idea of ​​global search and boundary exploration, introducing boundary excitation and chaotic elite strategies to initialize the population position, population velocity, population size N, upper bound ub and lower bound lb of the search space, solution space dimension dim and maximum number of iterations T. The relevant formulas of boundary excitation and chaotic elite are shown in Equation 1 and Equation 2. S2. Select an optimization objective function to calculate the fitness value. The objective function formula is: In the formula, J is the objective function, and y ref Let y be the expected value. k The current value; S3. Calculate the current fitness value of each individual in the snow goose population, determine the solution corresponding to the minimum fitness value as the initial global optimal solution, and select the top k individuals with the best fitness performance as elite individuals and include them in the elite pool.

4. The Taylor space external fixed support PID control method based on the improved Xueyan algorithm according to claim 3, characterized in that, Step three also includes: S4. During the speed update phase of snow geese, the significant impact of air resistance and energy consumption on the flight dynamics of snow geese in a real migration environment is simulated: that is, the energy level of snow geese increases with the group's cooperative gain in the early stage of migration, while the energy gradually decreases due to continuous consumption as they approach the target area. Based on this behavioral characteristic, a speed dynamic update mechanism is constructed, and the speed update formula is: F i =(X best -X i ) (11); V i =coe×V i +m×(F i -f i )×10 -2 (13); In the formula, coe is the velocity weighting factor, t is the current iteration number, T is the maximum iteration number, and F... i X is the intrinsic energy of individual i. best X is the optimal position vector for the current population. i Let f be the position vector of individual i. i Let V be the air resistance experienced by individual i during flight, ι be a random number between (0, 1), and V be the air resistance experienced by individual i during flight. i Let i be the velocity vector of individual i. Air resistance factor, where m is the mass of an individual in the population.

5. The Taylor space external fixed support PID control method based on the improved Xueyan algorithm according to claim 3, characterized in that, Step three also includes: S5. Update location using simulated snow goose flocking cooperative flight, including two methods, as follows: Method 1: If the angle between the snow geese during flight is less than π, then the simulated snow goose V-formation is used to update the position. For the top 1 / 5 of individuals with excellent fitness in the population, Equation 14 is used to update the position; for the bottom 1 / 5 of individuals with the lowest fitness, Equation 4 is used to update the position; and for the remaining individuals in the population, Equation 15 is used to update the position. Equations 14 and 15 are shown below: X i =X i +α×(X best -X i )+V i (14); X i =X i +α×(X best -X i )+β×(X c -X i )-γ×(X N +X i )+V i (15); X i =min(max(X i ,X min ),X max ) (16); In the formula, α is the navigation factor, taking the value of a random number in the range [-2, 2], β is the cohesion factor, taking the value of a random number in the range [-1.5, 1.5], γ is the repulsion factor, taking the value of a random number in the range [-1, 1], and X... c Let X be the population center location vector. N Let X be the position vector of the worst individual in the population. max X min These are the upper and lower bounds of the search space; the meanings of the other parameters and functions are the same as in S4. Method 2: If the angle between the snow geese and the formation exceeds π, the position is updated using a simulated straight-line formation of snow geese. If the strategy selection factor r > 0.5, the position is updated using the improved group guidance method of the golden ratio reverse exploration method mentioned in step 2. The update formula is shown in Equation 6. If the strategy selection factor r <= 0.5, the position is updated using the enhanced multi-directional adaptive Lévy flight mentioned in step 2. The update formula is shown in Equation 8.

6. The Taylor space external fixed support PID control method based on the improved Xueyan algorithm according to claim 3, characterized in that, Step three also includes: S6. Based on the inspiration of biological evolution, simulate the survival of the fittest, introduce the worst reset strategy mentioned in step 2 to update the position of snow geese in the population, eliminate the w individuals with the worst fitness, and simultaneously inject newly generated individuals to enhance the diversity of the solution space, avoid the population from falling into local optima due to premature convergence, explore and develop the dynamic balance algorithm, and see Equation 5 for the specific reset formula. S7. Update fitness and merge elite solutions. Recalculate the objective function value for all individuals after the current iteration update, obtain new fitness, merge the current population with the historical best solutions retained in the elite pool, filter and update the elite pool, and provide a guiding benchmark for continuous optimization in subsequent iterations. S8. Determine whether the maximum number of iterations for the population has been reached. If it has, stop the iteration and analyze the optimal solution into proportional coefficient Kp, integral coefficient Ki, and derivative coefficient Kd. Input these into the PID controller to complete parameter optimization and tuning. Otherwise, return to S4 to continue iterating and finding the optimal solution.

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