Rotating speed control method of servo loading system

Abstract

The invention relates to the technical field of servo loading, and discloses a rotating speed control method of a servo loading system, which comprises the following steps: constructing the servo loading system; the servo motor is driven to work at a constant torque; establishing a disturbance estimation model under servo loading disturbance; rotating speed data of the tested motor are obtained in real time, rotating speed errors are input into a speed PID controller, a basic control signal is generated, disturbance compensation and error response are fused, and a master control signal is constructed; pID parameters of a speed PID controller are optimized and adjusted on line through an improved fast exploration random tree algorithm; and fixing the speed PID parameter according to an error stability criterion, keeping the current control output, and readjusting the PID parameter when the disturbance trend changes. According to the invention, the rotating speed control precision and the operation stability of the servo loading system under complex disturbance conditions can be improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of servo loading, and particularly relates to a rotating speed control method of a servo loading system. BACKGROUND

[0002] The servo loading system is widely applied in the field of mechanical test and automatic production, and plays a key role in the performance test of motors, transmission mechanisms and other power systems. The servo loading system is usually composed of a servo motor, a coupling and a measured motor. The servo motor is connected with the measured motor through the coupling, and is used for applying a controllable load to simulate the running state under actual working conditions.

[0003] As a main driving source, the servo motor realizes the test and evaluation of the performance, efficiency and load capacity of the measured motor by adjusting the output torque. The traditional test method depends on simple mechanical structures and manual adjustment, and it is difficult to meet the requirements of high precision and high reliability in the current test process. In comparison, the servo loading system can apply precise controllable load and rotating speed control, so that the measured motor can be tested under more complex and dynamic working conditions, and through high-precision control and real-time monitoring means, more comprehensive and scientific performance analysis basis can be provided.

[0004] In the servo loading system, the speed type PID controller adjusts the running speed of the measured motor to maintain it at the preset target value to meet the requirements of various test conditions. The speed PID controller has the advantages of simple design, easy implementation, and can effectively solve many static and dynamic control problems. It can quickly respond to changing load conditions, stabilize the rotating speed of the measured motor, and maintain the precision and stability of the system under various working conditions. However, the disadvantages are also obvious. Especially in the case of fast load change or high system complexity, the traditional PID control may have the problems of delayed adjustment, overshoot or response lag, which leads to the system unable to achieve the expected dynamic performance.

[0005] RRT-Based Optimizer (RRTO) is a new meta-heuristic algorithm, which is based on the Rapidly Exploring Random Tree (RRT) algorithm originally used for robot path planning. The main innovation of RRTO is to combine the random tree exploration mechanism of RRT with optimization strategies, such as adaptive step size adjustment, to enhance the global search and local optimization capabilities. The core features of this algorithm include adaptive step size wandering strategy, dynamic random walk to escape local optimal solution, and adaptive step size strategy based on boundary and absolute difference, which effectively improve the search accuracy and efficiency. However, despite its strong exploration ability in complex solution space, the algorithm still faces some challenges, especially as the problem size increases, the computational complexity and solution cost also increase accordingly. SUMMARY

[0006] The purpose of the embodiment of the application is to provide a rotational speed control method of a servo loading system, which solves the shortcomings of the traditional rotational speed control method in the case of system response lag, dynamically adjusts the step size penalty factor based on the population distribution dispersion degree and the optimal fitness fluctuation, effectively improves the position update process of the rapid exploration random tree algorithm in the exploration stage, and combines the rotation transformation operator R i (t) with the difference between the current optimal position q best and the current individual position q i,j to construct the rotated difference direction, effectively improve the position update process of the rapid exploration random tree algorithm in the local development stage, improve the solution space search accuracy and control stability, and use the improved rapid exploration random tree algorithm to optimize the PID parameters of the speed PID controller. Through the closed-loop feedback mechanism, the output rotational speed of the measured motor can be adjusted in real time under the condition of fixed torque output of the servo motor, the rotational speed of the measured motor is stable and accurate, and high-precision rotational speed control of the servo loading system is realized.

[0007] To achieve the above application purposes, the technical solutions are adopted as follows:

[0008] The application relates to a rotational speed control method of a servo loading system, which comprises the following steps:

[0009] S1: constructing a servo loading system;

[0010] The servo loading system comprises a servo motor, a measured motor in driving connection with the servo motor, and a rotational speed detection unit for detecting the rotational speed of the measured motor.

[0011] S2: driving the servo motor to work at a constant torque to form a disturbance load on the measured motor side;

[0012] S3: Establish a disturbance estimation model under servo loading disturbance to predict the disturbance trend of the measured motor speed;

[0013] S4: Real-time acquisition of the speed data of the measured motor, input of the speed error into the speed PID controller to generate a basic control signal u0(τ), fusion of disturbance compensation △u d (τ) and error response E(τ) to construct a total control signal u(τ) = u0(τ) + △u d (τ) + E(τ);

[0014] Wherein, the disturbance compensation is a linear mapping output by the disturbance estimation model, and the error response E(τ) is obtained based on the real-time speed error and the disturbance estimation model;

[0015] S5: On-line optimization and adjustment of the PID parameters of the speed PID controller by using an improved fast exploration random tree algorithm;

[0016] The individual position q i,j (i = 1, 2,..., n, j = 1, 2,..., d) of each individual involved in the algorithm is represented as a group of PID parameters to be optimized, the improved fast exploration random tree algorithm involves a position update model in the exploration stage and a position update model in the development stage based on the difference between the rotation transformation operator R i (t), the current optimal position q best and the current individual position q i,j , wherein the step penalty factor in the position update model in the exploration stage is dynamically adjusted based on the population distribution dispersion and the optimal fitness fluctuation, and the R i (t) in the position update model in the development stage is calculated as follows:

[0017]

[0018] Wherein, I3 is a three-dimensional unit matrix, e a and e b are geometric algebra orthogonal basis vectors, (e a · e b ) represents the geometric product of two orthogonal basis vectors, ω ab is a coupling weight coefficient and obeys a normal distribution with a mean of 0 and a variance of 0.5×(1+cos(πt / T)), T is the maximum iteration number, t represents the tth iteration, n is the population size, d is the problem dimension, is a target function model for calculating the fitness value, e(τ) is the real-time speed error of the measured motor, ρ is the total running time, and θ(t) represents the dynamic rotation angle;

[0019] S6: fixing the PID parameters of the speed PID controller according to the error stability criterion, keeping the current control output, and returning to S5 to re-adjust the PID parameters when the disturbance trend changes.

[0020] In some embodiments of the present application, the disturbance estimation model in S3 is based on the moment of inertia, friction coefficient and constant disturbance torque of the measured motor, and combines real-time speed data of the measured motor to establish a disturbance estimation model to dynamically calculate a disturbance-induced speed estimation value.

[0021] In some embodiments of the present application, the disturbance estimation model is as follows:

[0022]

[0023] wherein, is the disturbance-induced speed estimation value at time τ, J is the moment of inertia of the measured motor, B is the friction coefficient, ω act (a) is the actual speed of the measured motor at time a, T d is the constant disturbance torque.

[0024] In some embodiments of the present application, the error response E(τ) is specifically:

[0025]

[0026] wherein, α and β are empirical weighting coefficients, and e(τ) is the real-time speed error of the measured motor.

[0027] In some embodiments of the present application, the step penalty factor in the position update model of the exploration stage is dynamically adjusted based on population distribution dispersion and optimal fitness fluctuation, and is specifically:

[0028] The population distribution dispersion σ j (t) is constructed.

[0029]

[0030] The step penalty factor α is obtained using σ j (t) and optimal fitness fluctuation.

[0031]

[0032] wherein, is the mean value of the population position in the jth dimension at the tth iteration, α0 is a preset basic step penalty coefficient, σ j (0) is the population distribution dispersion in the jth dimension at initialization, f best (t) is the optimal fitness value at the tth iteration, f best(t-△t) is the optimal fitness value at the t-△t iteration, and ε is a preset minimum value;

[0033] The position update model of the exploration stage is:

[0034]

[0035] wherein, is the new position of the i th individual in the j th dimension, r1 is a random number between 0 and 1, Ub ij is the upper limit constraint of the search, Lb ij is the lower limit constraint of the search, K is a balance coefficient and is K = ln(T-t) / ln(T).

[0036] In some embodiments of the present application, the position update model of the development stage based on the rotation transformation operator R i (t), the current optimal position q best and the current individual position q i,j is specifically:

[0037]

[0038] wherein, is the inverse rotation transformation operator obtained after the inverse operation of R i (t), α1 is an adaptive step adjustment factor, r2 is a random number between 0 and 1, and m1 is an activation function; wherein, α1 and m1 adopt the following formula:

[0039] α1 = 5·(r2-m1 / 2)·cos(2·π·r2)·e b ;

[0040] m1 = E / 10; b = e cos(π-π / t) ;

[0041] wherein, E is an activation coefficient, and b is a random disturbance coefficient.

[0042] In some embodiments of the present application, the error stability criterion is:

[0043]

[0044] wherein, ∈ is an error amplitude threshold, and δ is an error change rate threshold.

[0045] In some embodiments of the present application, the PID parameters of the PID controller are adjusted online and optimized by using the improved fast exploration random tree algorithm in S5, and the specific steps are:

[0046] S51: configure the initialization parameter environment of the improved fast exploration random tree algorithm;

[0047] S52: jointly encode the PID parameters of the speed PID controller as individual dimension variables in a solution vector;

[0048] S53: in each iteration, iteratively evolve the population individual position vectors according to a position update strategy;

[0049] S54: calculate the fitness value of the PID parameters corresponding to the position of each individual based on the target function model, retrieve the individual with the optimal fitness value in the current population and record its position as the tentative optimal solution of the current iteration;

[0050] S55: determine whether the number of iterations has reached the maximum number of iterations, if so, output the solution vector corresponding to the position of the individual with the optimal global fitness in the historical record, and restore the mapping to the final output PID parameters, if not, return to S53 for further iteration.

[0051] The speed control method of the servo loading system proposed in the present application has the following advantages and beneficial effects compared with the prior art:

[0052] (1) The improved fast exploration random tree algorithm involved in the present application dynamically adjusts the step penalty factor based on the population distribution dispersion and the optimal fitness fluctuation. Unlike the traditional fixed step penalty factor, the improved step penalty factor can dynamically adjust the step size so that the algorithm can adaptively adjust the step size. Moreover, the population distribution dispersion reflects the dispersion degree of the population in that dimension. A larger dispersion degree means a wider search range, so a larger step size is helpful for global search and improves search efficiency. A smaller dispersion degree indicates that the population tends to converge, so a smaller step size is helpful for refining the search and improving the accuracy of local solutions. In addition, the optimal fitness fluctuation indicates the recent development of the algorithm. When the fluctuation is large, a larger step size is needed to avoid falling into a local optimum. When the fluctuation is small, it indicates that the algorithm has approached the optimal solution, and the step size should be reduced to enhance the stability and accuracy of the search. Through this step dynamic adjustment mechanism, the algorithm can adaptively adjust the step size according to the current solution space distribution and search progress, avoiding the low efficiency problem under the fixed step size strategy, and improving the overall search performance.

[0053] (2) The dynamic rotation angle θ(t) is adjusted by calculating the normalized Euclidean distance between the current solution and the optimal solution and combining the iteration progress, so that the rotation angle is larger in the early stage of the algorithm, and the exploration is strong, while in the later stage, the rotation angle gradually decreases, promoting local development. The design of the dynamic rotation angle avoids the problem of premature convergence, and maintains good search diversity and accuracy throughout the algorithm process. In addition, the rotation transformation operator R i(t) Consider the geometric algebra basis vector, so that the search direction is more flexible and diversified, so that the individual position update not only depends on the linear distance between the optimal solution and the current solution, but also considers the geometric algebra-based spatial transformation, so that the position update process can rotate from multiple dimensions, increase the diversity of global search, and avoid the search based on local information from getting into trouble.

[0054] Other features and advantages of the present application will become more apparent from the following detailed description when read in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0056] Figure 1 A flow chart of the speed control method of the servo loading system proposed in the present application is shown.

[0057] Figure 2 A PID parameter implementation flow chart of the improved fast exploration random tree algorithm in the present application for online optimization and adjustment of the PID controller is shown.

[0058] Figure 3 A comparison chart of the fitness value change in the iterative optimization process using the existing algorithm and the improved fast exploration random tree algorithm in the present application is shown.

[0059] Figure 4 A process chart of the PID parameter of the PID controller using the existing algorithm for online optimization and adjustment is shown.

[0060] Figure 5 A process chart of the PID parameter of the PID controller using the improved fast exploration random tree algorithm in the present application for online optimization and adjustment is shown.

[0061] Figure 6 A comparison chart of the speed control effect of the servo loading system using the improved fast exploration random tree algorithm in the present application and the existing algorithm is shown. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments.

[0063] All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the scope of the present application. In the description of the present application, it should be understood that the terms "center", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are merely for the purpose of facilitating the description of the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0064] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "connecting", "connection" should be understood broadly, for example, it can be fixed connection, or detachable connection, or integrally connected. For those of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances. In the description of the above embodiments, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0065] The terms "first", "second" are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more features. In the description of the present application, unless otherwise specified, the meaning of "multiple" is two or more.

[0066] In order to realize the precise control of the rotating speed of the servo loading system, the present application relates to a rotating speed control method of a servo loading system, referring to Figure 1 , the implementation of the rotating speed control method is specifically described.

[0067] S1: Constructing a servo loading system.

[0068] In some embodiments of the present application, the servo loading system (not shown) comprises a servo motor, a shaft coupling, a measured motor and a speed detection unit.

[0069] A shaft coupling rigidly centers and connects the servo motor and the measured motor shaft, and the speed detection unit is used to detect the rotating speed of the measured motor.

[0070] In some embodiments of the present application, the speed detection unit selects a speed sensor, which has coaxial two ends, one end is rigidly centered and connected with the measured motor shaft through a shaft coupling and the other end is rigidly centered and connected with the servo motor shaft through another shaft coupling, realizing the synchronous rotation of the servo motor and the measured motor.

[0071] S2: drive the servo motor to work at a constant torque to form a disturbance load on the side of the measured motor.

[0072] The servo motor, as a controllable driving source, outputs a specified constant torque, which acts on the measured motor through the shaft coupling to realize the continuous loading of the shaft end of the measured motor, and further introduces an external disturbance torque in the running process of the measured motor to form a controllable and continuous disturbance load on the measured motor, thereby providing a loading condition for simulating the running state of the measured motor under actual working conditions.

[0073] S3: establish a disturbance estimation model under servo loading disturbance to predict the disturbance trend of the measured motor speed.

[0074] In order to realize accurate speed control of the measured motor, the disturbance affecting the speed of the measured motor needs to be compensated in the present application, therefore, it is necessary to dynamically predict the disturbance trend of the measured motor.

[0075] In some embodiments of the present application, a disturbance estimation model is established, and the disturbance estimation model is used to estimate a disturbance-induced speed estimation value of the disturbance acting on the measured motor to induce speed change.

[0076] The disturbance estimation model is based on the moment of inertia, friction coefficient and constant disturbance torque of the measured motor, and combines real-time speed data of the measured motor to establish the disturbance estimation model to dynamically calculate the disturbance-induced speed estimation value, model and calculate the influence of the disturbance on the speed change in the time domain, thereby realizing dynamic prediction of the disturbance trend of the speed of the measured motor.

[0077] The disturbance estimation model is specifically:

[0078]

[0079] wherein, is the disturbance-induced speed estimation value at time τ, J is the moment of inertia of the measured motor, B is the friction coefficient, ω act (a) is the actual speed of the measured motor at time a (obtained by a speed sensor), T d is the constant disturbance torque.

[0080] S4: real-time acquisition of speed data of the measured motor, input of speed error into a speed PID controller, generation of a basic control signal u0(τ), fusion of disturbance compensation △u d (τ) and error response E(τ), and construction of a total control signal u(τ) = u0(τ) + △u d (τ) + E(τ).

[0081] In some embodiments of the present application, the PID parameters in the speed PID controller include any combination of one or more of a proportional parameter Kp, an integral parameter Ki, and a derivative parameter Kd.

[0082] In some embodiments of the present application, the PID parameters in the speed PID controller include a proportional parameter Kp, an integral parameter Ki, and a derivative parameter Kd, and a speed error e(τ) at time τ (i.e., a difference between a target speed setpoint ω tar (τ) and a real-time speed ω act (τ) of the motor being measured) is input to the PID controller to obtain a basic control signal u0(τ):

[0083]

[0084] A disturbance compensation △u d (τ) is a linear mapping of the output of the disturbance estimation model, i.e.,

[0085]

[0086] where K c is a disturbance compensation coefficient.

[0087] Based on the disturbance-induced speed estimation value The feedback compensation of the control input is dynamically adjusted to accurately calculate and dynamically adjust the disturbance compensation amount.

[0088] An error response E(τ) is obtained based on the real-time speed error e(τ) and the disturbance estimation model as given above, i.e.,

[0089]

[0090] where α and β are empirical weighting coefficients.

[0091] The error response E(τ) is constructed by combining the speed error information and the disturbance-induced characteristics, and comprehensively reflects the speed deviation and the disturbance characteristics, realizes the feedback compensation of the dynamically adjusted control input, and forms a continuous and adjustable control signal output.

[0092] Thus, after obtaining u0(τ), △u d (τ), and E(τ), a total control signal u(τ) = u0(τ) + △u d (τ) + E(τ) is constructed and used as a control input.

[0093] S5: The PID parameters of the speed PID controller are online optimized and adjusted using an improved fast exploration random tree algorithm.

[0094] As described above, the PID parameters include a proportional parameter Kp, an integral parameter Ki, and a derivative parameter Kd.

[0095] The improved fast exploration random tree algorithm of the present application is an improvement based on RRTO, which mainly involves improvement of the position updating strategy.

[0096] The algorithm of the present application involves n populations, each population including d-dimensional search parameters (i.e. the problem dimension is d), therefore, the individual position of each individual in the population is q i,j (i = 1, 2,..., n, j = 1, 2,..., d) (i.e. q i,j represents the current position of the ith individual in the jth dimension).

[0097] Each individual position q i,j corresponds to a solution vector {Kp, Ki, Kd} in the algorithm, i.e. q i,j = {Kp, Ki, Kd}, thereby defining the individual position of each individual in the solution space as a group of PID parameters to be optimized, wherein the value of each dimension variable in the solution vector represents a control parameter of a controller (Kp represents the proportional parameter of a proportional controller, Ki represents the integral parameter of an integral controller, and Kd represents the differential parameter of a differential controller).

[0098] In this way, as the algorithm iterates, the population individual position is updated, i.e. the solution vector of the algorithm search space is updated, i.e. the PID parameters of the speed PID controller are updated.

[0099] The position updating strategy in the improved fast exploration random tree algorithm involved in the present application is improved compared with the position updating strategy in the traditional RRTO algorithm, mainly including the position updating strategy in the exploration stage and the position updating strategy in the development stage, in which the position updating model in the exploration stage is adopted in the position updating strategy in the exploration stage, and the position updating model in the development stage is adopted in the position updating strategy in the development stage.

[0100] Figure 2 The process of online optimization and adjustment of the PID parameters of the speed PID controller by using the improved fast exploration random tree algorithm is shown.

[0101] Referring to Figure 2 , the process of online optimization and adjustment of the PID parameters of the speed PID controller by using the improved fast exploration random tree algorithm is specifically described.

[0102] S51: Configure the initialization parameter environment of the improved fast exploration random tree algorithm.

[0103] The initialization parameter environment includes: setting the population size n, the maximum number of iterations T, the problem dimension d, and the search upper limit constraint Ub ij and the search lower limit constraint Lb ij of the solution space.

[0104] Step S51 is used for the initialization phase of the algorithm, which involves randomizing the parameters of each individual within the search constraints to effectively distribute the individuals throughout the search space, thereby improving diversity and preventing premature convergence to local optima.

[0105] During the initialization phase, the positions of individuals in the population are randomly generated within the search space:

[0106] q i,j =Lb ij +r1·(Ub ij -Lb ij ), i = 1, 2, ..., n, j = 1, 2, ..., d, r1 is a random number between 0 and 1.

[0107] S52: Jointly encode the PID parameters in the speed PID controller into variables of each dimension in the solution vector.

[0108] As mentioned above, PID parameters include proportional parameter Kp, integral parameter Ki, and derivative parameter Kd.

[0109] As mentioned above, each individual position q i,j In the algorithm, there is a corresponding solution vector {Kp, Ki, Kd} (i.e., q). i,j ={K p K i K d In the solution vector, the value of each dimension variable represents a controller parameter (Kp represents the proportional parameter of the proportional controller, Ki represents the integral parameter of the integral controller, and Kd represents the derivative parameter of the derivative controller).

[0110] Therefore, the position of each individual in the algorithm's solution space is represented as a set of PID parameters {Kp, Ki, Kd} to be optimized. When the algorithm updates the position of the individuals in the population, it updates the solution vector in the algorithm's solution space, which is to say, it updates the PID parameters of the speed PID controller.

[0111] S53: In each iteration, the position of individuals in the population is iteratively evolved according to the position update strategy, so that the PID parameters of the speed PID controller gradually converge to the global convergence domain in the search space.

[0112] Step S53 is the iterative process of the algorithm. Before the maximum number of iterations T is reached, the position of individuals in the population is updated iteratively.

[0113] During the iteration process, the location update strategies described above for the exploration phase and the development phase are employed to update the individual location q. i,j Iterative updates will be performed.

[0114] The location update strategies for the exploration phase and the development phase are described in detail below.

[0115] In the location update model during the exploration phase, the step size penalty factor α is dynamically adjusted based on the population distribution dispersion and the fluctuation of the optimal fitness, so as to dynamically and adaptively adjust the step size, which helps to improve search efficiency.

[0116] The step size penalty factor α is dynamically adjusted based on the population distribution dispersion and the fluctuation of optimal fitness.

[0117] In some embodiments of this application, based on the spatial location information of each individual in the current population in the target dimension j, and combined with the population position mean in that dimension, a statistical configuration is formed to reflect the degree of change in the internal structure, and the population distribution dispersion σ is constructed. j (t).

[0118]

[0119] Where, q i,j (i = 1, 2, ..., n, j = 1, 2, ..., d) represents the current position of the i-th individual in the j-th dimension. Let be the mean value of the population position in the j-th dimension during the t-th iteration.

[0120] Population distribution dispersion σ j (t) reflects the dispersion of the population along this dimension. A larger dispersion means a wider search range, in which case a larger step size should be used to facilitate global search and improve search efficiency; while a smaller population distribution dispersion σ j (t) indicates that the population tends to converge in this dimension. At this time, the step size should be small, which helps to refine the search and improve the accuracy of local solutions.

[0121] Therefore, the step size penalty factor α takes into account the population distribution dispersion σ. j (t) can improve search efficiency and local solution accuracy.

[0122] In some embodiments of this application, σ is utilized j (t) and the fluctuation of optimal fitness, in the iterative evolution process, the step size penalty factor α is obtained by flexibly adjusting and temporally adapting the step size penalty factor through a nonlinear recursive mechanism.

[0123]

[0124] Where α0 is the preset base step size penalty coefficient, σ j (0) represents the population distribution dispersion in the j-th dimension during initialization, f best (t) represents the optimal fitness value in the t-th iteration, f best (t-△t) is the optimal fitness value at the t-△t iteration, and ε is the preset minimum value.

[0125] In some embodiments of this application, Δt can be 1 and ε can be 10-8. Adding ε prevents division by zero errors and ensures that the step size adjustment is smooth when the fitness value difference is small.

[0126] Recent developments in optimal fitness fluctuation representation algorithms have shown that when fluctuations are large (i.e., f... best (t) and f best When the difference between (t-Δt) is large, a larger step size is needed to avoid getting trapped in local optima. When the fluctuation is small (i.e., f), a larger step size is needed. best (t) and f best When the difference between (t-△t) is small, it indicates that the algorithm has approached the optimal solution, and the step size should be reduced to enhance the stability and accuracy of the search.

[0127] Therefore, the step size penalty factor α takes into account the fluctuation of the optimal fitness, which can enhance the stability and accuracy of the search.

[0128] Therefore, through this dynamic step size adjustment mechanism, the algorithm can adaptively adjust the step size according to the current solution space distribution and search progress, avoiding the inefficiency problem of the traditional fixed step size strategy and improving the overall search performance.

[0129] Therefore, the improved mathematical model for position update in the exploration phase is as follows:

[0130]

[0131] in, Let r1 be the new position of the i-th individual in the j-th dimension, and Ub be a random number between 0 and 1. ij For upper limit constraints on the search, Lb ij For the lower bound constraint of the search, K is the balance coefficient and is K = ln(Tt) / ln(T).

[0132] As described above, in order to obtain the fitness value of each individual, an objective function model is introduced in some embodiments of this application. The fitness value of each individual is used to calculate the fitness value, where e(τ) is the real-time speed error of the tested motor and ρ is the total running time.

[0133] The objective function model uses the integral absolute error function as a measure of the system control performance. The smaller the fitness value, the better the control effect of the PID parameter.

[0134] The position update strategy during the development phase is based on the rotation transformation operator R. i (t), current optimal position q best and the current individual position q i,j The difference between them, where the rotation transformation operator R i(t) depends on the dynamic rotation angle θ(t) and the geometric algebraic difference direction.

[0135] In some embodiments of this application, based on the relative spatial position relationship between the current solution and the global optimal solution, and by integrating the iteration progress information of each stage in the iteration process, a dynamic rotation angle θ(t) is collaboratively constructed using the normalized Euclidean distance ratio and the iteration progress.

[0136]

[0137] The dynamic rotation angle θ(t) is calculated by measuring the normalized Euclidean distance between the current solution and the global optimum. The algorithm is adjusted in conjunction with the iteration progress, resulting in a larger rotation angle in the early stages, which promotes exploration, while the rotation angle gradually decreases in the later stages, which promotes local exploration. The design of the dynamic rotation angle θ(t) avoids premature convergence and maintains good search diversity and accuracy throughout the algorithm.

[0138] In some embodiments of this application, a spatial rotation transformation matrix driven by a dynamic rotation angle θ(t) is introduced, along with a nested mechanism of directional weight adjustment and orthogonal geometric operators. Furthermore, a rotation transformation operator R is constructed by applying a coupling perturbation correction to the identity matrix. i (t).

[0139]

[0140] Where I3 is the three-dimensional identity matrix, e a and e b Let e ​​be a geometric algebraic orthogonal basis vector. a ·e b ω represents the geometric product of two orthogonal basis vectors. ab The coupling weights are normal distributions with a mean of 0 and a variance of 0.5×(1+cos(πt / T)).

[0141] In some embodiments of this application, e a Let it be (1,0,0), e b Let it be (0,0,1).

[0142] By introducing orthogonal basis vectors from geometric algebra, the search direction becomes more flexible and diverse.

[0143] In some embodiments of this application, after obtaining the rotation transformation operator R i After (t), the rotation transformation operator R is fused. i (t) and inverse rotation transformation operator (that is, for R) i (t) obtained after inverting the operation), the difference |q| between the optimal solutions best -qi,j Perform a two-way transformation to construct the difference direction vector after bidirectional rotation mapping correction.

[0144] Therefore, the location update model during the development phase is as follows:

[0145]

[0146] Where α1 is the adaptive step adjustment factor, r2 is a random number between 0 and 1, and m1 is the activation function.

[0147] In some embodiments of this application, α1 and m1 are obtained using the following formula.

[0148] α1=5·(r2-m1 / 2)·cos(2·π·r2)·e b .

[0149] m1 = E / 10; b = e cos(π-π / t) .

[0150] Where E is the activation coefficient and b is the random perturbation coefficient.

[0151] In the position update model during the development phase, the rotation transformation operator R is used. i (t) and inverse rotation transformation operator In coordination, the update of individual positions does not solely depend on the difference between the optimal solutions |q best -q i,j Furthermore, it considers spatial transformations based on geometric algebra, enabling the individual position update process to rotate from multiple dimensions, increasing the diversity of global search and avoiding the predicament of searching based solely on local information.

[0152] Using the position update strategy described above, the position of each individual in the population is updated.

[0153] S54: Calculate the fitness value of the PID parameter corresponding to each individual based on the objective function model, retrieve the individual with the best fitness value in the current population and record its position, which is used as the provisional optimal solution for the current iteration.

[0154] As mentioned above, the objective function model is given. Used to calculate the position q of each individual. i,j The fitness value is determined, and the position of the individual with the best fitness value in the population is found and used as the current optimal solution q. best (This is provisional and will be updated as the iteration process continues) for use in continuous iteration.

[0155] S55: Determine if the number of iterations has reached the maximum number of iterations. If yes, output the solution vector corresponding to the position of the globally fitness-optimal individual in the historical record and restore it to the final output PID parameters. If no, return to S53 to continue iterating.

[0156] The maximum number of iterations T is preset by the user.

[0157] If the number of iterations reaches the maximum, output the position q of the globally fitness-optimal individual in the historical records. i,j The corresponding solution vector {Kp, Ki, Kd} is mapped back to the PID parameters Kp, Ki, and Kd of the final output PID controller.

[0158] If the maximum number of iterations has not been reached, return to S53 to continue iterating.

[0159] S6: Fix the PID parameters of the speed PID controller according to the error stability criterion, maintain the current control output, and return to S5 when the disturbance trend changes to readjust the PID parameters.

[0160] The error stability criterion is preset.

[0161] In some embodiments of this application, the error stability criterion is set based on the error response E(τ), and specifically, the error stability criterion is selected as follows:

[0162]

[0163] Where ∈ is the error amplitude threshold and δ is the error rate of change threshold.

[0164] After obtaining the PID parameters Kp, Ki, and Kd using the algorithm, if the error response E(τ) satisfies the error stability criterion, it indicates that the error change is slowing down and the system is becoming stable. In this case, the current PID parameters are kept fixed and no further updates are made. If the error response E(τ) does not satisfy the error stability criterion, the process returns to S5, and the algorithm is used again to optimize the PID parameters online, thus readjusting the PID parameters.

[0165] The embodiments of this application achieve dynamic simulation of the working state of the tested motor by constructing a servo loading system and combining a constant torque drive mechanism with a disturbance load modeling method. A disturbance estimation model is introduced to predict speed disturbance trends in real time, improving the system's ability to perceive disturbance factors. Furthermore, an improved fast exploratory random tree algorithm is introduced to dynamically optimize the PID parameters of the speed PID controller, effectively enhancing the global search capability and local convergence accuracy during parameter adjustment. Finally, the error stability criterion controls the PID parameter update mechanism, achieving dynamic switching and stable maintenance of the controller's behavior.

[0166] This application improves the speed control accuracy and operational stability of the servo loading system under complex disturbance conditions, and is suitable for various high-precision motor testing and dynamic performance evaluation scenarios.

[0167] In some embodiments of this application, the dynamic response process of the actual speed of the motor under test is described by establishing a speed response model based on a second-order linear system. The input of the speed response model is the total control signal u(τ), and the output is the actual speed of the motor under test. The specific mathematical model is as follows:

[0168]

[0169] Where K is the stiffness coefficient, K n This represents the system gain.

[0170] In some embodiments of this application, in order to verify the improved fast exploration random tree algorithm involved in this application, the mathematical models in the above embodiments are simulated in Matlab. The Matlab code implementation includes the mathematical models of position updates for iterative optimization at each stage of the existing basic fast exploration random tree algorithm and the improved fast exploration random tree algorithm of this application, the disturbance estimation model, the speed PID controller model, the total control signal model, the objective function model, and the main program. The main program is used to implement the mapping between the existing basic fast exploration random tree algorithm and the improved fast exploration random tree algorithm of this application and the PID parameters of the speed PID controller, and to map the objective function model to the objective function of the Simulink simulation model.

[0171] The population size n is set to 30, the maximum number of iterations T is set to 30, the problem dimension d is set to 3, and the upper limit constraint Ub is set to the search limit. ij The lower bound constraint is 300, and the search limit is Lb. ij If the value is 0, run the main program and obtain... Figures 3 to 6 The simulation results are shown in the figure.

[0172] Figure 3 The graph shows a comparison of fitness value changes during the iterative optimization process using existing algorithms and the improved fast exploratory random tree algorithm in this application.

[0173] See Figure 3 It can be seen that the existing algorithm reaches the optimal fitness value of 5.5 in the 23rd iteration, while the algorithm in this application has already reached the optimal fitness value of 4.1 in the 13th iteration.

[0174] By improving the step size penalty factor α and constructing the difference direction after rotation, the algorithm in this application has a high degree of adaptability during the optimization process. It can dynamically adjust the search behavior according to the population state and iteration progress, thereby effectively improving the accuracy of the solution and the overall convergence efficiency. Existing algorithms rely on fixed step size parameters, resulting in poor search stability and a tendency to get trapped in local optima and insufficient convergence. Through comparison, the algorithm in this application shows superior performance in terms of convergence speed, optimal solution quality, and stability, and has stronger generalization ability and robustness, significantly outperforming existing algorithms.

[0175] Figure 4 The diagram illustrates the process of online optimization and adjustment of PID parameters for a speed PID controller using an existing algorithm. Figure 5 The diagram illustrates the process of online optimization and adjustment of PID parameters for a speed PID controller using the improved fast exploratory random tree algorithm described in this application.

[0176] See Figure 4 The optimal PID parameters obtained by tuning the existing algorithm are Kp = 44, Ki = 5.2, and Kd = 1.8; see [link / reference]. Figure 5 The optimal PID parameters obtained by the algorithm tuning in this application are Kp = 23, Ki = 27, and Kd = 6.4.

[0177] Figure 6 The figure shows a comparison of the speed control effects of the improved fast exploratory random tree algorithm of this application and existing algorithms on the servo loading system.

[0178] Will Figure 4 and Figure 5 The optimal PID parameters obtained from the intermediate tuning are input into the speed PID controller to obtain... Figure 6 .

[0179] The Simulink simulation model of the system was set to run for 20 seconds. The target speed value of the motor under test in the servo loading system was set to 1 unit. After 10 seconds of steady-state operation, the target speed value of the motor under test was changed to 2 units.

[0180] See Figure 6 It can be seen that the algorithm of this application has a stronger response adjustment capability when the target speed value of the motor under test changes in the servo loading system, and can achieve stable tracking of the new target value in a shorter time; especially in the dynamic adjustment stage after target switching, it significantly shortens the system response transition time and effectively reduces overshoot.

[0181] Compared with existing algorithms, the algorithm of this application demonstrates higher adjustment accuracy in the iterative optimization of PID parameters of the speed PID controller, enabling the tested motor to maintain a stable and efficient operating state. With the help of the algorithm of this application, the tested motor can achieve more sensitive and stable speed control when dealing with target speed disturbances, thereby comprehensively improving control accuracy and subsequent testing efficiency.

[0182] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions claimed by the present invention.

Claims

1. A speed control method for a servo loading system, characterized in that, include: S1: Construct the server loading system; The servo loading system includes a servo motor, a test motor connected to the servo motor, and a speed detection unit for detecting the speed of the test motor. S2: Drive the servo motor to operate at a constant torque to create a disturbance load on the side of the motor under test; S3: Establish a disturbance estimation model under servo loading interference to predict the disturbance trend of the measured motor speed; S4: Acquire the speed data of the motor under test in real time, input the speed error into the speed PID controller, generate the basic control signal u0(τ), and integrate the disturbance compensation Δu d Given the error response E(τ), construct the total control signal u(τ) = u0(τ) + Δu(τ). d (τ)+E(τ); Among them, the disturbance compensation is a linear mapping of the output of the disturbance estimation model, and the error response E(τ) is obtained based on the real-time speed error and the disturbance estimation model; S5: An improved fast exploratory random tree algorithm is used to optimize and adjust the PID parameters of the speed PID controller online; The individual position q of each individual involved in the algorithm i,j (i = 1, 2, ..., n, j = 1, 2, ..., d) represents a set of PID parameters to be optimized. The improved fast exploration random tree algorithm involves a position update model in the exploration phase and a rotation transformation operator R. i (t), current optimal position q best and the current individual position q i,j The position update model for the development phase of the difference between the two phases, wherein the step size penalty factor in the position update model of the exploration phase is dynamically adjusted based on the population distribution dispersion and the fluctuation of the optimal fitness, and R in the position update model of the development phase. i (t) is calculated as follows: Where I3 is the three-dimensional identity matrix, e a and e b Let e ​​be a geometric algebraic orthogonal basis vector. a ·e b ω represents the geometric product of two orthogonal basis vectors. ab The coupling weights are normally distributed with a mean of 0 and a variance of 0.5 × (1 + cos(πt / T)), where T is the maximum number of iterations, t represents the t-th iteration, n is the population size, and d is the problem dimension. Here is the objective function model used to calculate the fitness value, e(τ) is the real-time speed error of the motor under test, ρ is the total running time, and θ(t) represents the dynamic rotation angle; S6: Fix the speed PID parameters according to the error stability criterion and maintain the current control output. When the disturbance trend changes, return to S5 and readjust the PID parameters.

2. The speed control method according to claim 1, characterized in that, The disturbance estimation model in S3 is based on the moment of inertia, friction coefficient, and constant disturbance torque of the motor under test, and combined with the real-time speed data of the motor under test to establish a disturbance estimation model in order to dynamically calculate the disturbance-induced speed estimate.

3. The speed control method according to claim 2, characterized in that, The disturbance estimation model is as follows: in, Let J be the estimated disturbance-induced velocity at time τ, B be the moment of inertia of the tested motor, and ω be the coefficient of friction. act (a) represents the actual rotational speed of the motor being measured at time a, T d It is a constant disturbance torque.

4. The speed control method according to claim 3, characterized in that, The error response E(τ) is specifically: Where α and β are empirical weighting coefficients, and e(τ) is the real-time speed error of the motor under test.

5. The speed control method according to claim 1, characterized in that, In the location update model during the exploration phase, the step size penalty factor is dynamically adjusted based on the population distribution dispersion and the fluctuation of optimal fitness. Specifically: Constructing the population distribution dispersion σ j (t); Using σ j (t) and the historical trend of optimal fitness are used to obtain the step size penalty factor α; in, Let α0 be the mean position of the population in the j-th dimension during the t-th iteration, and σ be the preset base step size penalty coefficient. j (0) represents the population distribution dispersion in the j-th dimension during initialization, f best (t) represents the optimal fitness value in the t-th iteration, f best (t-△t) is the optimal fitness value at the t-△t-th iteration, and ε is the preset minimum value; The location update model for the exploration phase is as follows: in, Let r1 be the new position of the i-th individual in the j-th dimension, and Ub be a random number between 0 and 1. ij For upper limit constraints on the search, Lb ij For the lower bound constraint of the search, K is the balance coefficient and is K = ln(Tt) / ln(T).

6. The speed control method according to claim 1, characterized in that, Based on rotation transformation operator R i (t), current optimal position q best and the current individual position q i,j The location update model for the development phase of the difference between them is as follows: in, For R i (t) The inverse rotation transform operator obtained after the inverse operation, where α1 is the adaptive step adjustment factor, r2 is a random number between 0 and 1, and m1 is the activation function; where α1 and m1 are expressed as follows: α1=5·(r2-m1 / 2)·cos(2·π·r2)·e b ; m1=E / 10; b=e cos(π-π / t) ; Where E is the activation coefficient and b is the random perturbation coefficient.

7. The speed control method according to claim 1, characterized in that, The error stability criterion is as follows: Where ∈ is the error amplitude threshold and δ is the error rate of change threshold.

8. The speed control method according to claim 1, wherein the improved fast exploration random tree algorithm is used in step S5 to optimize and adjust the PID parameters of the speed PID controller online, the specific steps of which are as follows: S51: Configure the initialization parameter environment for the improved fast exploratory random tree algorithm; S52: Jointly encode the PID parameters in the speed PID controller into variables of each dimension in the solution vector; S53: In each iteration, the position of individuals in the population is iteratively evolved according to the position update strategy; S54: Calculate the fitness value of the PID parameter corresponding to each individual's position based on the objective function model, retrieve the individual with the best fitness value in the current population and record its position, which is used as the provisional optimal solution for the current iteration; S55: Determine if the number of iterations has reached the maximum number of iterations. If yes, output the solution vector corresponding to the position of the globally fitness-optimal individual in the historical record and restore it to the final output PID parameters. If no, return to S53 to continue iterating.

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