PID (Proportion Integration Differentiation) control method for Taylor space external fixed bracket based on improved South goose algorithm

Abstract

The invention discloses a Taylor space external fixation support PID control method based on an improved South goose algorithm, and belongs to the technical field of PID control, and the method specifically comprises the steps: 1, building a Taylor space external fixation support control model based on a PID controller; step 2, improving a South goose algorithm, including introducing boundary excitation and a chaotic elite strategy to initialize a population so as to give consideration to global and boundary exploration; an elitist retention and worst reset mechanism is adopted to ensure excellent solution inheritance and diversity; the global search efficiency is improved by utilizing a golden proportion reverse exploration method; multi-directional Levy flight is introduced to enhance the local optimal jumping capability; step 3, optimizing PID controller parameters by using an improved South goose algorithm to obtain optimal Kp, Ki and Kd; 4, simulating a PID (Proportion Integration Differentiation) controller of the control model by adopting MATLAB (Matrix Laboratory) and Simulink; the improved Swane algorithm can improve the adaptive control capability of the system, and enhance the stability and control precision.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of PID control optimization, and particularly relates to a Taylor space external support PID control method based on an improved snow goose algorithm. BACKGROUND

[0002] Taylor space external support is an external fixation device widely used in orthopedics, especially in complex trauma and limb reconstruction surgery. It can achieve multi-axis accurate positioning and gradual traction of fractured bones through multiple adjustable connecting rods and spherical joint modules, thereby promoting bone healing and restoring physiological axis. Due to factors such as patient activity, muscle contraction and external disturbance, the support system often faces challenges such as decreased positioning accuracy, uneven stress distribution and soft tissue traction discomfort during clinical use. Traditional manual or fixed parameter PID control often has difficulty in timely and stable compensation for these dynamic changes, thereby affecting the rehabilitation effect.

[0003] Therefore, a Taylor space external support PID control system based on an improved snow goose algorithm is developed. With the help of advanced improved snow goose optimization algorithm, the system can monitor and adjust the position and angle of the support in real time. Using PID control technology, the system can automatically adjust the control parameters of the support according to the different stages of bone healing, changes in external force caused by patient activity and other complex conditions, thereby accurately controlling the position and angle of the support and ensuring the fracture site heals in the best mechanical environment, helping patients recover quickly and effectively.

[0004] PID control is a classical feedback regulation technology widely used in industrial automation. It collects the error between system output and set target in real time, and generates control quantity through three parallel action channels: proportional P, integral I and derivative D. The proportional element linearly amplifies the current error and quickly responds to large deviations; the integral element corrects the error accumulation to eliminate steady-state deviation; and the derivative element predicts the error change rate to suppress system overshoot and oscillation. With its simple structure, strong adjustability, good stability and low dependence on model, PID controller has been successfully applied in process control, motor drive, robot and other fields. However, in the face of complex disturbance environment of Taylor space external support and other multivariable coupled systems, traditional fixed parameter PID often has difficulty in balancing fast response and robust stability. Therefore, it is necessary to design an adaptive PID control strategy to achieve high-precision, high-response and high-stability control of Taylor space external support.

[0005] The Snow Goose Algorithm (SGA) is a novel metaheuristic algorithm inspired by the behavioral characteristics of snow geese during their long-distance migrations in autumn and winter. The algorithm simulates typical V-shaped and linear formations during migration and dynamically adjusts the formation configuration based on varying flight conditions, achieving collaborative guidance between the algorithm's exploration and development phases. The algorithm divides the flock into three functional components: the leader, the middle layer, and the trailing. The leader plays a central role in the formation, creating a favorable aerodynamic environment to reduce overall air resistance and enhance the flock's endurance. Young or weaker geese occupy the middle layer, leveraging their layout advantages to gain protection and reduce wind resistance, thereby conserving energy. The trailing individuals collaborate to maintain formation stability. Based on these collaborative characteristics, the algorithm constructs corresponding velocity update rules and position adjustment mechanisms for the V-shaped exploration mode and the linear development mode, respectively. By dynamically adapting the two modes, the algorithm achieves an efficient balance between global exploration capability and local development accuracy. This algorithm demonstrates significant application potential in solving various constrained optimization problems in diverse fields, including engineering design and scientific research. Summary of the Invention

[0006] The purpose of the present invention is to propose a Taylor space external fixed bracket PID control method based on the improved Snow Goose algorithm. This method effectively solves the core defects of the original Snow Goose algorithm, such as slow convergence speed, poor stability of the iterative process, and easy to fall into local optimal solutions. The bracket displacement control accuracy reaches 0.1mm, the response time is shortened to within 0.5 seconds, the anti-interference ability is improved by 60%, and the safety and efficiency of complex skeletal orthopedic treatment are significantly improved.

[0007] To achieve the above object, the present invention adopts the following technical solutions: A Taylor space external fixed support PID control method based on an improved Snow Goose algorithm is characterized in that the three parameters Kp, Ki, and Kd of the PID controller are optimized using the improved Snow Goose algorithm. The specific steps are as follows.

[0008] Step 1: Establish a Taylor space external fixed support control model based on PID controller.

[0009] Step 2: Improve the snow goose optimization algorithm, including introducing boundary excitation and chaotic elite strategy to initialize the population, introducing elite retention strategy, improving the update of the population center position and the position of the disadvantaged group and introducing the worst reset strategy, regularly eliminating individuals with poor performance, using the golden ratio reverse exploration method to improve group guidance, and using enhanced multi-directional adaptive Lévy flight to improve random Brownian motion behavior.

[0010] There are four improvements to the algorithm described in step 2, and the specific improvements are as follows.

[0011] Firstly, based on the basic idea of global search and boundary exploration, the boundary excitation and chaos elite initialization population strategy are introduced. The initial population is constructed as two core components of chaos group and boundary group. Among them, the number of chaos group individuals accounts for 4 / 5 of the total population, and the number of boundary group individuals accounts for 1 / 5 of the total population. The specific initialization process of the two types of individuals is as follows: ; ;

[0012] In the formula, is the position vector of individual i in the chaos group, is a random variable of individual i, which is uniformly distributed , which increases the coverage ability of the global space, , is the upper and lower boundary vectors of the search space, which ensures that the position is within a certain range, is the position vector of individual i in the boundary group, is the boundary selection probability threshold, which enhances the exploration ability of the boundary region of the solution space.

[0013] Secondly, based on the survival of the fittest mechanism in biological evolution theory, the elite preservation strategy is introduced. By improving the population center position and weak group position update, it guides other individuals to concentrate in the better area, thereby improving the convergence speed and stability of the algorithm. At the same time, the worst reset strategy is introduced to periodically eliminate poor performing individuals and generate new individuals, effectively avoiding the defect of the population falling into local optimal solution due to premature convergence. The related formula is as follows: ; ; ;

[0014] In the formula, is the center position vector of the population, which is used for formation update (exploration stage), is the fitness of individual i, is the position vector of individual i, is the size of the population, is the size of the elite pool, is the position vector of elite individual j, is the navigation factor, which is a random number with a value of [-2, 2], indicating that the dominant individual is attracted to the global optimal solution, is the position vector of the current population optimum, is the condensation factor, which is a random number with a value of [-1.5, 1.5], indicating that the individual is attracted to the group weighted center, is the velocity vector of individual i, is the elite guiding coefficient, which controls the guiding strength of the elite individual to the current individual, is the position vector of an elite individual randomly selected from the elite pool, is the position vector of the worst individual i in the worst w individuals, , is the upper bound vector and the lower bound vector of the search space, is the reset condition probability, is the perturbation random factor used to increase the diversity of solutions.

[0015] Thirdly, the golden ratio reverse exploration method is used to improve the group guidance. The golden section ratio is introduced as the basic weight parameter, and a dynamic scaling coefficient adjustment model is constructed by fusing a random perturbation factor to optimize the search direction and effectively improve the global exploration efficiency and solution space traversal ability of the algorithm. The related formula is: ;

[0016] In the formula, is the position vector of individual i, is the golden ratio (0.618), which is used as a reference scaling factor to balance local and small global movement, is the perturbation factor, which introduces randomness to make the step size of each dimension slightly different, is the position vector of the current population optimum.

[0017] Fourthly, the enhanced multi-directional adaptive Lévy flight strategy is used to improve the random Brownian motion behavior. By introducing a multi-directional perturbation mechanism, the search range limitation of traditional Gaussian distribution is broken through, the global exploration breadth of the algorithm in the solution space is enhanced, and the escape ability and global optimization precision of the population from the local optimal solution region are improved. The related formula is: ; ;

[0018] In the formula, is the step size, is the Lévy index, which is randomly sampled from [1, 2) to dynamically adjust the heavy-tailed distribution and achieve a balance between local fine-tuning and global jumping, , are two independent random numbers that follow a uniform distribution , which are used to generate S and the random intensity of the superimposed direction perturbation, is the position vector of individual i, , , is an independent Gaussian random direction vector to ensure direction diversity, is a random noise to enhance spatial coverage.

[0019] Step three: use the improved snow goose optimization algorithm to optimize the PID controller parameters, and obtain the optimized proportional coefficient Kp, integral coefficient Ki and differential coefficient Kd through iterative operation, and configure the above parameters in the PID controller to realize the fast and accurate regulation and control of the Taylor space outer fixed support control system.

[0020] Step four: use MATLAB and Simulink to simulate the PID controller of the Taylor space outer fixed support control model, and verify the adaptive control of the Taylor space outer fixed support system.

[0021] Further, in step one, the Taylor space outer fixed support control model of the PID controller mainly includes the following modules: position difference calculation module, improved snow goose 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 is used to calculate the deviation value of the target position and the actual position. The improved snow goose algorithm module is used to quickly iterate to obtain the optimal PID parameters Kp, Ki and Kd, and input them into the position PID control module. The position PID control module adjusts the output position control signal to the load compensation calculation module according to the position error value of the position difference calculation module. The load compensation calculation module combines the position control signal of the position PID control module and the load change deviation to adjust the position signal and then output it to the position adjustment module. The position adjustment module adjusts the final position output according to the position signal of the load compensation calculation module to ensure accurate control of the system position. The speed detection module is used to detect the actual speed of the motor and feedback the support speed change information to optimize the position control effect. The support pressure detection module is used to detect the support pressure and feedback the key information of the support state to assist accurate position adjustment.

[0022] Further, in step three, the specific steps of optimizing the PID controller by the improved snow goose optimization algorithm are as follows:

[0023] S1, initialize the parameters of the improved snow goose optimization algorithm, including the basic idea of global search and boundary exploration, introduce boundary excitation and chaos elite strategy to initialize the population position, initialize the population speed, population size N, upper bound ub and lower bound lb of the search space, solution space dimension dim and maximum iteration number T, and the related formulas of boundary excitation and chaos elite are shown in formula (1) and formula (2).

[0024] S2, select the optimization objective function for calculating the fitness value, and the formula of the objective function is: ;

[0025] In the formula, is the objective function, is the expected value, The current value.

[0026] 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 to be included in the elite pool.

[0027] S4, in the speed updating stage of snow geese, simulate the significant influence of key factors such as air resistance and energy consumption in the real migration environment on the flight dynamics of snow geese: that is, the energy level of snow geese in the early migration stage shows an upward trend with the group synergy gain, while the energy gradually decreases due to continuous consumption as it approaches the target area. Based on this behavior characteristic, a speed dynamic updating mechanism is constructed, and the speed updating formula is: ; ; ; ;

[0028] In the formula, is the speed weight factor, which quantifies the correlation between the current and previous generations of the population speed, and its value change simulates the dynamic characteristics of the group energy first rising and then falling in flight, is the current iteration number, is the maximum iteration number, is the inherent energy of individual i, is the position vector of the current population optimum, is the position vector of individual i, is the air resistance experienced by individual i during flight, is a random number between 0 and 1, representing the difference in resistance experienced by the individual through random disturbance, is the speed vector of individual i, is the air resistance influence factor, which is formed by the combined action of the resistance coefficient, cross-sectional area and the angle of snow geese flight, is the mass of the individual in the population.

[0029] S5, use the group cooperative flight behavior of simulated snow geese (its unique V-shaped and straight-line formation) to update the position of the population, including two ways, as follows.

[0030] Method one: V-shaped formation, if the included angle between snow geese during flight (formation phase factor ) is less than the threshold value , then use the simulated V-shaped formation of snow geese (exploration stage) to update the position, at this time, according to the individual fitness performance, implement a hierarchical position updating strategy, for the top The individual uses formula (14) to update the position, the individual with poor fitness in the population (including weak, sick or disabled individuals, i.e. the individual with the lowest fitness ) uses formula (4) to update the position, and finally, for the remaining individuals in the population, formula (15) is used to update the position. The above hierarchical strategy can dynamically adjust the position update rule according to the fitness level of the individual, adapt to the differences in ability and state of individuals in the population, and balance the optimization efficiency and diversity protection. Formula (14) and formula (15) are as follows: ; ; ;

[0031] In the formula, is a navigation factor, which is a random number with a value of [-2, 2], used to guide the individual to converge to the global optimal solution, is a cohesion factor, which is a random number with a value of [-1.5, 1.5], used to drive the individual to gather around the weighted center of the population, is a repulsive factor, which is a random number with a value of [-1, 1], used to produce avoidance and repulsion effect on the weakest or farthest individual in the population, and enhance the diversity of the population, is the center position vector of the population, is the position vector of the worst individual in the population, used to realize the avoidance mechanism, , is the upper and lower bounds of the search space, and the remaining parameters and functions have the same meaning as S4.

[0032] Method two: linear formation, if the included angle between the snow geese (formation phase factor ) exceeds the threshold value , the linear formation of the simulated snow geese (development stage) is used to update the position, which focuses more on improving the escape ability of the local optimal solution region. In this stage, a double-strategy dynamic selection mechanism is adopted. If the strategy selection factor r>0.5, the golden ratio reverse exploration method mentioned in step two is used to improve the group guidance to update the position, and the update formula is shown in formula (6). The simulated snow geese follow the experienced strong individual to search for the optimal target region. If the strategy selection factor r<=0.5, the enhanced multi-directional adaptive Lévy flight mentioned in step two is used to improve the random Brownian motion behavior to update the position, and the update formula is shown in formula (8).

[0033] S6, based on biological evolution, simulation of survival of the fittest, the worst reset strategy mentioned in step two is introduced to update the position of the snow goose in the population, eliminate the worst w individuals, and inject new individuals to enhance the diversity of the solution space, avoid the population from falling into local optimum due to premature, and dynamically balance the exploration and development ability of the algorithm, see formula (5) for the specific reset formula.

[0034] S7, update the fitness and merge the elite solution, recalculate the objective function value of all individuals updated in the current iteration, obtain the new fitness, combine the current population with the historical optimal solution reserved in the elite pool, and select and update the elite pool to provide continuous optimization guide benchmark for subsequent iteration.

[0035] S8, judge whether the maximum iteration number of the population is reached, if yes, stop iteration, and analyze the optimal solution into proportional coefficient Kp, integral coefficient Ki and differential coefficient Kd, and input them into the PID controller to complete parameter optimization setting, otherwise return to S4 for continuous iteration optimization.

[0036] Further, in step four, the transfer function formula of the selected controlled object is: ;

[0037] In the formula, is the transfer function, is the function variable.

[0038] As described above, due to the adoption of the above technical scheme, the beneficial effects of the present application are:

[0039] The present application proposes a Taylor space external support PID control method based on improved snow goose algorithm, which introduces boundary excitation and chaotic elite method, elite reservation method, worst reset method, golden ratio reverse exploration method and improved Lévy flight mechanism on the basis of the original snow goose algorithm, significantly enhances the global optimization ability and local search precision of the algorithm. Compared with the premature convergence, insufficient search efficiency and other problems of the original algorithm, the improved algorithm has stronger robustness and adaptability in complex environments such as high dimension, strong coupling and dynamic disturbance, can effectively jump out of local optimum, speed up the convergence speed, and improve the precision and stability of the solution. The algorithm is applied to PID parameter optimization, which can dynamically adjust Kp, Ki and Kd coefficients according to the feedback of support motion, so that the control system can maintain good response characteristics and stable control performance in complex load and uncertain environment, and is suitable for the control of such precise actuator as Taylor space external support, and has good engineering practical value. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 The improved snow goose algorithm is used to optimize the PID controller model of the Taylor space external support system.

[0041] Figure 2Taylor space external support control system block diagram.

[0042] Figure 3 The improved snow goose algorithm is used for optimizing the PID control flow chart of the Taylor space external support system.

[0043] Figure 4 The improved snow goose optimization algorithm and the basic snow goose optimization algorithm are used for optimizing the Kp parameter of the PID.

[0044] Figure 5 The improved snow goose optimization algorithm and the basic snow goose optimization algorithm are used for optimizing the Ki parameter of the PID.

[0045] Figure 6 The improved snow goose optimization algorithm and the basic snow goose optimization algorithm are used for optimizing the Kd parameter of the PID.

[0046] Figure 7 The improved snow goose optimization algorithm and the basic snow goose optimization algorithm are used for optimizing the Kd parameter of the PID.

[0047] Figure 8 The improved snow goose optimization algorithm and the basic snow goose optimization algorithm are used for optimizing the Kd parameter of the PID. DETAILED DESCRIPTION

[0048] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0049] Please refer to Figures 1-8 , the present application provides a technical solution: A Taylor space external support PID control method based on an improved snow goose algorithm, which uses the improved snow goose optimization algorithm to realize fast optimization and determine the PID control parameters of the Taylor space external support system, so as to improve the reliability, stability, response speed and control accuracy of the system. The specific steps are as follows.

[0050] Step one: as Figure 2 shown, a Taylor space external support control model based on a PID controller is established.

[0051] Step two: improve the snow goose optimization algorithm, including the introduction of boundary excitation and chaos elite strategy to initialize the population, the introduction of elite retention strategy, the improvement of the update of the population center position and the weak group position and the introduction of the worst reset strategy, the periodic elimination of poor performing individuals, the use of golden ratio reverse exploration method to improve the group guide, and the use of enhanced multi-directional adaptive Levy flight to improve the random Brownian motion behavior.

[0052] Among them, the algorithm improvement in step two has four places, which are improved as follows.

[0053] The first place, based on the basic idea of global search and boundary exploration, the boundary excitation and chaos elite initialization population strategy is introduced. The initial population is constructed as two core components of chaos group and boundary group. Among them, the number of chaos group individuals accounts for 4 / 5 of the total population, and the number of boundary group individuals accounts for 1 / 5 of the total population. The specific initialization process of the two types of individuals is related to the formula: ; ;

[0054] In the formula, is the position vector of individual i of the chaos group initialization, is a random variable of individual i, which is uniformly distributed , increasing the coverage ability of global space, , is the upper and lower boundary vectors of the search space, which ensures that the position is within a certain range, is the position vector of individual i of the boundary group initialization, is the boundary selection probability threshold, which enhances the exploration ability of the boundary region of the solution space.

[0055] The second place, based on the survival of the fittest mechanism in biological evolution theory, the elite retention strategy is introduced. Through the improvement of the population center position and the weak group position update, the other individuals are guided to concentrate in the better area, thereby improving the convergence speed and stability of the algorithm. At the same time, the worst reset strategy is introduced, which periodically eliminates poor performing individuals and generates new individuals, effectively avoiding the defect that the population falls into a local optimal solution due to premature convergence. The related formula is: ; ; ;

[0056] In the formula, is the center position vector of the population, which is used for formation update (exploration stage), is the fitness of individual i, is the position vector of individual i, is the size of the population, is the size of the elite pool, is the position vector of the elite individual j, is the navigation factor, a random number with value [-2, 2], indicating that the dominant individual converges to the global optimal solution, is the position vector of the current population optimum, is the cohesion factor, a random number with value [-1.5, 1.5], indicating that the attractive individual converges to the group weighted center, is the velocity vector of individual i, is the elite guide coefficient, which regulates the guidance strength of the elite individual to the current individual, is the position vector of an elite individual randomly selected from the elite pool, is the position vector of individual i in the w worst individuals, , is the upper bound vector and the lower bound vector of the search space, is the reset condition probability, is the disturbance random factor, used to increase the diversity of solutions.

[0057] Thirdly, the golden ratio reverse exploration method is used to improve the group guidance. The golden section ratio is introduced as the basic weight parameter, and a dynamic scaling coefficient adjustment model is constructed by fusing a random disturbance factor to optimize the search direction and effectively improve the global exploration efficiency and solution space traversal ability of the algorithm. The related formula is: ;

[0058] In the formula, is the position vector of individual i, is the golden ratio (0.618), which is used as a reference scaling factor to balance local and small global movement, is the disturbance factor, which introduces randomness to make the step size of each dimension slightly different, is the position vector of the current population optimum.

[0059] Fourthly, the enhanced multi-directional adaptive Lévy flight strategy is used to improve the random Brownian motion behavior. By introducing a multi-directional disturbance mechanism, the search range limitation of traditional Gaussian distribution is broken through, the global exploration breadth of the algorithm in the solution space is enhanced, and the escape ability and global optimization precision of the population from the local optimal solution region are improved. The related formula is: ; ;

[0060] In the formula, is the step size, is the Lévy index, which is randomly sampled from [1, 2) to dynamically adjust the heavy-tailed distribution and achieve a balance between local fine-tuning and global jumping, , are two independent random numbers, subject to uniform distribution , used to generate S and the random intensity of superposition direction disturbance, is the position vector of individual i, , , is an independent Gaussian random direction vector, ensuring direction diversity, is random noise, enhancing spatial coverage.

[0061] Step three: use the improved snow goose optimization algorithm to optimize the parameters of the PID controller, and through iterative operation, obtain the optimized proportional coefficient Kp, integral coefficient Ki and differential coefficient Kd, and configure the above parameters in the PID controller, to realize fast and accurate regulation and control of the Taylor space outer fixed support control system.

[0062] Step four: use MATLAB and Simulink to simulate the PID controller of the Taylor space outer fixed support control model, and verify the adaptive control of the Taylor space outer fixed support system.

[0063] Further, in the step one, the Taylor space outer fixed support control model of the PID controller mainly includes the following modules: position difference calculation module, improved snow goose 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 is used to calculate the deviation value of the target position and the actual position. The improved snow goose algorithm module is used to quickly and iteratively obtain the optimal PID parameters Kp, Ki and Kd, and input them into the position PID control module. The position PID control module adjusts the output position control signal to the load compensation calculation module according to the position error value of the position difference calculation module. The load compensation calculation module combines the position control signal of the position PID control module and the load change deviation to adjust the position signal and then output it to the position adjustment module. The position adjustment module adjusts the final position output according to the position signal of the load compensation calculation module to ensure accurate control of the system position. The speed detection module is used to detect the actual speed of the motor and feedback the support movement speed change information to optimize the position control effect. The support pressure detection module is used to detect the support pressure and feedback the key information of the support state to assist accurate position adjustment.

[0064] Further, as shown in Figure 3 , in the step three, the specific steps of optimizing the PID controller by the improved snow goose optimization algorithm are as follows:

[0065] S1, initialize the parameters of the improved snow goose optimization algorithm, including the basic idea of global search and boundary exploration, introduce boundary excitation and chaos elite strategy to initialize the population position, at the same time initialize the population speed, population size N, upper bound ub and lower bound lb of search space, solution space dimension dim and maximum iteration number T, boundary excitation and chaos elite related formula see formula (1) and formula (2).

[0066] S2, select the optimization objective function, which is used to calculate the fitness value, the objective function formula is: ;

[0067] In the formula, is the objective function, is the expected value, is the current value.

[0068] 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 as elite individuals and include them in the elite pool.

[0069] S4, in the speed updating stage of snow goose, simulate the significant influence of key factors such as air resistance and energy consumption on the flight dynamics of snow goose in the real migration environment: that is, the energy level of snow goose increases with the group synergy at the beginning of migration, and gradually decreases due to continuous consumption as it approaches the target area. Based on this behavior characteristic, a speed dynamic updating mechanism is constructed, and the speed updating formula is: ; ; ; ;

[0070] In the formula, is the speed weight factor, which quantifies the correlation between the current and previous generations of population speed, and its value change simulates the dynamic characteristics of the group energy first rising and then falling in the process of population flight, is the current iteration number, is the maximum iteration number, is the inherent energy of individual i, is the optimal position vector of the current population, is the position vector of individual i, is the air resistance suffered by individual i in the flight process, is a random number between 0 and 1, which represents the difference in resistance suffered by the individual through random disturbance, is the speed vector of individual i, Air resistance impact factor, comprehensive resistance coefficient, cross-sectional area and snow goose flight angle jointly form, The quality of the individuals in the population.

[0071] S5, the population position is updated by simulating the cooperative flight behavior of snow geese (its unique V-shaped and straight-line formation), including two ways, as follows.

[0072] Way one: V-shaped formation, if the included angle between snow geese when flying (formation phase factor ) is less than the threshold value , the position is updated using the simulated V-shaped formation of snow geese (exploration stage), at this time, a hierarchical position update strategy is implemented according to the individual fitness performance, for the top individuals in the population with excellent fitness performance, formula (14) is used for position update, for individuals in the population with poor fitness (including weak, sick or disabled individuals, i.e. the lowest fitness ), formula (4) is used for position update, finally, for the remaining individuals in the population, formula (15) is used for position update. The above hierarchical strategy can dynamically adjust the position update rule according to the individual fitness level, adapt to the differences in individual ability and state in the population, and take into account the optimization efficiency and diversity protection, formula (14) and formula (15) are as follows: ; ; ;

[0073] In the formula, is the navigation factor, a random number with a value of [-2, 2], used to guide the individual to converge to the global optimal solution, is the condensation factor, a random number with a value of [-1.5, 1.5], used to drive the individual to gather around the weighted center of the population, is the repulsive factor, a random number with a value of [-1, 1], used to produce avoidance and repulsion effect on the weakest or farthest individual in the population, and enhance the diversity of the population, is the center position vector of the population, is the position vector of the worst individual in the population, used to realize the avoidance mechanism, , is the upper and lower bounds of the search space, and the rest of the parameters and functions have the same meaning as S4.

[0074] Way two: straight-line formation, if the included angle between snow geese when flying (formation phase factor ) exceeds the threshold value If the strategy selection factor r > 0.5, the golden ratio reverse exploration method mentioned in step two is used to improve the group guidance to update the position, and the update formula is shown in equation (6). The snow goose follows the experienced strong individual to search the optimal target area. If the strategy selection factor r <= 0.5, the enhanced multi-directional adaptive Lévy flight mentioned in step two is used to improve the random Brownian motion behavior to update the position, and the update formula is shown in equation (8).

[0075] S6, based on biological evolution, simulating survival of the fittest, introducing the worst reset strategy mentioned in step two to update the position of the snow goose in the population, eliminating the w individuals with the worst fitness, and synchronously injecting new individuals to enhance the diversity of the solution space, avoiding the population from falling into local optimum due to premature convergence, and dynamically balancing the exploration and development capabilities of the algorithm. The specific reset formula is shown in equation (5).

[0076] S7, update the fitness and merge the elite solution. The target function value of all individuals updated in the current iteration is recalculated, the new fitness is obtained, the current population and the historical optimal solution reserved in the elite pool are combined, the elite pool is updated, and the guide benchmark for subsequent iteration is provided.

[0077] S8, judge whether the maximum iteration number of the population is reached. If yes, stop iteration, and analyze the optimal solution as the proportional coefficient Kp, the integral coefficient Ki, and the differential coefficient Kd, and input them into the PID controller to complete parameter optimization setting. Otherwise, return to S4 to continue iteration and optimization.

[0078] Further, as shown in Figure 1 , in step four, the transfer function formula of the selected controlled object is: ;

[0079] In the formula, is the transfer function, is the function variable.

[0080] As shown in Figure 4 , Figure 5 and Figure 6 , the changes of the improved snow goose optimization algorithm and the basic snow goose optimization algorithm in optimizing the PID control parameters are analyzed. The improved snow goose optimization algorithm performs better in optimizing the Kp, Ki and Kd parameters, can quickly converge near the optimal parameter value in fewer iteration times, and effectively shortens the parameter optimization adjustment period. At the same time, the parameter change curve of the improved algorithm has smaller fluctuation amplitude and more stable convergence trend, fully embodying its stronger stability and precision in parameter adjustment in the optimization process.

[0081] Fitness is the core index to measure the performance of algorithm, and its value directly reflects the approximation degree of the algorithm to the optimal solution. According to the evaluation criterion that the smaller the fitness value is, the better the algorithm performance is, the analysis of the fitness value of the improved Snowy Owl Optimization Algorithm and the basic Snowy Owl Optimization Algorithm is shown in the following table. Figure 7 It can be seen from the comparison of the fitness value of the improved Snowy Owl Optimization Algorithm and the basic Snowy Owl Optimization Algorithm that the fitness value of the improved algorithm is always lower than that of the basic version in the same number of iterations, and it can find a better solution. The basic algorithm is easy to stagnate and fall into local optimum, and it is difficult to break through, while the improved algorithm can quickly jump out of the local optimum and continue to optimize, and it can reach a stable state earlier, and it can converge to a lower level with fewer iterations, so the convergence speed and stability are better. Therefore, the performance of the improved Snowy Owl Optimization Algorithm is better than that of the basic algorithm.

[0082] Figure 8 For the comparison of the effect of the improved Snowy Owl Optimization Algorithm and the basic Snowy Owl Optimization Algorithm on optimizing the PID controller, the analysis of the comparison chart is shown in the following table. Figure 8 It can be seen that the improved Snowy Owl Optimization Algorithm optimized PID control system has a significantly lower overshoot, which can reduce system fluctuations and losses; it takes less time to reach a stable state and responds more quickly; in the dynamic adjustment process, the system output can approach the target value with higher efficiency. This shows that the improved Snowy Owl Optimization Algorithm can effectively improve the dynamic performance and steady-state accuracy of the system by optimizing the PID parameters, making the control system more stable, faster in response, and stronger in anti-interference ability.

Claims

1. A PID control method for an external fixed support in Taylor space based on an improved snow goose algorithm, characterized in that: By improving the snow goose optimization algorithm, the three parameters of the PID controller of the Taylor space external support system, that is, Kp, Ki and Kd, are optimized, and the specific steps are as follows: Step one: establish a Taylor space external support control model based on a PID controller; Step two: improve the snow goose optimization algorithm; Step three: use the improved snow goose optimization algorithm to optimize and solve the parameters of the PID controller, obtain the optimized proportional coefficient Kp, integral coefficient Ki and differential coefficient Kd through iterative operation, and configure the above parameters in the PID controller to realize the regulation and control of the Taylor space external support control system; Step four: use MATLAB and Simulink to simulate the PID controller of the Taylor space external support control model to verify the adaptive control of the Taylor space external support system.

2. The Taylor space PID control method based on the improved snow goose algorithm of claim 1, wherein, Step two includes: D1, based on the idea of global search and boundary exploration, the boundary excitation and chaotic elite initialization population strategy is adopted, and the related formula is: ； ； wherein, is the position vector of the individual i initialized by chaos group, is the random variable of the individual i, subject to uniform distribution , increase the coverage ability of the global space, , is the upper bound vector and the lower bound vector of the search space, which ensures that the position is within a certain range, is the position vector of the individual i initialized by the boundary group, is the boundary selection probability threshold, which enhances the exploration ability of the boundary region of the solution space; D2, based on the survival of the fittest mechanism in biological evolution theory, the elite reservation and worst reset strategy is introduced, and the related formula is: ； ； ； wherein, is the center position vector of the population for the swarm update, is the fitness of individual i, is the position vector of individual i, is the size of the population, is the size of the elite pool, is the position vector of elite individual j, is the leader factor, a random number with value [-2, 2], is the position vector of the current population optimum, is the cohesion factor, a random number with value [-1.5, 1.5], is the velocity vector of individual i, is the elite guide coefficient, which regulates the guidance strength of the elite individual to the current individual, is the position vector of a randomly selected elite individual from the elite pool, is the position vector of individual i in the w worst individuals, , is the upper bound vector and the lower bound vector of the search space, is the reset condition probability, is the perturbation random factor.

3. The Taylor space PID control method based on the improved snow goose algorithm with external support according to claim 2, characterized in that, Step two also includes: D3, the golden ratio reverse exploration method is used to improve the group guidance, and the related formula is: ； wherein is the position vector of individual i, is a reference scaling factor, balancing local and a small amount of global movement, is a perturbation factor, is the position vector of the current population optimum; D4, the enhanced multi-directional adaptive Lévy flight strategy is used to improve the random Brownian motion behavior, and the related formula is: ； ； where, is the step size, is the Lévy exponent, randomly sampled from [1,2), dynamically adjusting the heavy-tailed distribution to achieve a balance between local fine-tuning and global jumping, , are two independent random numbers, following a uniform distribution , used to generate S and the random intensity of the superposition direction perturbation, is the position vector of individual i, , , is an independent Gaussian random direction vector, ensuring direction diversity, is random noise, enhancing spatial coverage.

4. The improved snow goose algorithm-based Taylor space outer-fixed support rack PID control method according to claim 1, characterized in that, In step one, the Taylor space external support control model of the PID controller mainly includes the following modules: position difference calculation module, improved snow goose algorithm module, position PID control module, load compensation calculation module, position adjustment module, speed detection module and support pressure detection module; wherein, the position difference calculation module is used to calculate the deviation value of the target position and the actual position; the improved snow goose algorithm module is used to quickly iterate to obtain the optimal PID parameters Kp, Ki and Kd, and input into the position PID control module; the position PID control module adjusts the output position control signal to the load compensation calculation module according to the position error value of the position difference calculation module; the load compensation calculation module combines the position control signal of the position PID control module and the load change deviation to adjust the position signal and then output to the position adjustment module; the position adjustment module adjusts the final position output according to the position signal of the load compensation calculation module to ensure accurate control of the system position; the speed detection module is used to detect the actual speed of the motor to feedback the support speed change information to optimize the position control effect; the support pressure detection module is used to detect the support pressure to feedback the key information of the support state and assist accurate position adjustment.

5. The improved snow goose algorithm-based Taylor space outer-fixed support rack PID control method according to claim 1, characterized in that, Step three includes: S1, initialize the parameters of the improved snow goose optimization algorithm, including the basic idea of global search and boundary exploration, introduce the boundary excitation and chaotic elite strategy to initialize the population position, initialize the population speed, population size N, upper bound ub and lower bound lb of the search space, solution space dimension dim and maximum iteration number T, the boundary excitation and chaotic elite related formula is shown in formula (1) and formula (2); S2, select the optimization objective function to calculate the fitness value, the objective function formula is: ； In the formula, is the target function, is the expected value, is 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 as elite individuals to be included in the elite pool.

6. The improved snow goose algorithm-based Taylor space outer-fixed support rack PID control method according to claim 5, characterized in that, Step three also includes: S4, in the speed updating stage of the snow goose, simulate the significant influence of air resistance and energy consumption on the flight dynamics of the snow goose in the real migration environment: that is, the energy level of the snow goose rises with the group synergy at the beginning of migration, and gradually decreases due to continuous consumption as it approaches the target area. Based on this behavior characteristic, a speed dynamic updating mechanism is constructed, and the speed updating formula is: ； ； ； ； wherein, is the velocity weight factor, quantifying the correlation between the current and previous generation population velocity, is the current iteration number, is the maximum iteration number, is the intrinsic energy of individual i, is the position vector of the current population optimum, is the position vector of individual i, is the air resistance experienced by individual i during flight, is a random number between (0, 1), representing the variability of the resistance experienced by individual i through random perturbation, is the velocity vector of individual i, is the air resistance impact factor, which is formed by the combined action of the resistance coefficient, the cross-sectional area and the flight angle of the snow goose, is the mass of individual i in the population.

7. The improved snow goose algorithm-based Taylor space outer-fixed support rack PID control method according to claim 5, characterized in that, Step three also includes: S5, update the position by simulating the group cooperation flight of the snow goose, including two ways, as follows: Method 1: If the snow goose is flying at an angle less than , the simulated snow goose V-shaped formation is used to update the position, and the front of the population with excellent fitness value is Individual, use formula (14) to update the position, for the lowest fitness For each individual, use formula (4) to update the position. For the remaining individuals in the population, use formula (15) to update the position. Formulas (14) and (15) are as follows: ； ； ； Where, is the pilot factor, a random number between -2, 2. is the cohesion factor, a random number between [-1.5, 1.5], is the repulsion factor, a random number between [-1, 1], is the center position vector of the population, is the position vector of the worst individual in the population, used to implement the avoidance mechanism, , are the upper and lower bounds of the search space, and the rest of the parameters and functions have the same meanings as S4; Method two: if the included angle exceeds then the position is updated using the simulated snow goose linear formation, if the strategy selection factor r>0.5, the position is updated using the golden ratio reverse exploration method mentioned in step two to improve the group guidance, the update formula is seen 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 two, the update formula is seen in equation (8).

8. The improved snow goose algorithm-based Taylor space outer-fixed support rack PID control method according to claim 5, characterized in that, Step three also includes: S6, based on biological evolution heuristic, simulate survival of the fittest, introduce the worst reset strategy mentioned in step two to update the position of the snow goose in the population, eliminate the worst w individuals, and inject new individuals to enhance the diversity of the solution space, avoid the population from falling into local optimum due to precocity, and dynamically balance the exploration and development ability of the algorithm, the specific reset formula is shown in equation (5); S7, update the fitness and merge the elite solution, recalculate the target function value of all individuals updated in the current iteration, obtain the new fitness, combine the current population with the historical optimal solution reserved in the elite pool, and select and update the elite pool to provide continuous optimization guide benchmark for subsequent iteration; S8, judge whether the maximum number of iterations of the population is reached, if yes, stop iteration, and analyze the optimal solution into the proportional coefficient Kp, the integral coefficient Ki, and the differential coefficient Kd, and input them into the PID controller to complete parameter optimization setting, otherwise, return to S4 for continuous iteration optimization.

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