An automatic cutting speed control method for precision stone cutting

Abstract

The present invention discloses an automatic cutting speed control method for precision stone cutting, belonging to the field of control technology, including: S1, constructing an automatic cutting speed control system; S2, improving the neural population dynamics optimization algorithm by improving the attractor tendency strategy and proposing an adaptive quantum-guided perturbation strategy, and constructing an improved neural population dynamics optimization algorithm module; S3, optimizing the Kp, Ki, and Kd of the PID closed-loop control algorithm through the improved neural population dynamics optimization algorithm to achieve the optimization of the PID closed-loop control; S4, inputting the error value between the stone cutting speed at the t-th moment and the target cutting speed into the PID closed-loop control module, outputting the cutting speed control increment at the t-th moment, and inputting it into the speed drive module of the permanent magnet synchronous motor to output the stone cutting speed; S5, returning to execute S4 until the error value between the stone cutting speed and the target cutting speed is zero, realizing the precise control of the automatic cutting speed of stone cutting.

Description

Technical Field

[0001] The present invention belongs to the field of control technology optimization, and particularly relates to an automatic cutting speed control method for precision stone cutting. Background Art

[0002] During the stone cutting process, the control of the precision cutting speed plays a crucial role in ensuring cutting quality, prolonging tool life, reducing energy consumption, and improving production efficiency. Precise cutting speed can ensure a smooth cutting surface, without cracks or excessive wear; too high or too low cutting speed will result in a rough cutting surface, crack generation, or uneven cutting, affecting the appearance and quality of the final product. Especially for some high-value stones, the appearance and quality of the stone directly affect its value.

[0003] The PID closed-loop control method is widely used in the adjustment of cutting speed and feed rate. In stone cutting, factors such as cutting force, cutting temperature, or vibration will affect the cutting quality. The closed-loop control system adjusts the cutting speed process in real time through a feedback mechanism. A major drawback of the PID closed-loop control is that it assumes the system model is known and stable. However, in practical applications, especially in a complex and variable process like stone cutting, factors such as cutting force, friction coefficient, and material hardness may change continuously, making it difficult for the PID closed-loop control to cope with the complexity and uncertainty of the system.

[0004] The mathematical model of the Neural Population Dynamics Optimization Algorithm (NPDOA) is based on the theory of neural population dynamics and simulates the neural state changes in the cognitive and decision-making processes of the brain; the algorithm contains three key dynamic strategies: attractor trend strategy, coupling interference strategy, and information projection strategy. NPDOA optimizes problems by simulating the dynamic behavior of neural populations. However, in the optimization problem of precision stone cutting speed control, the coupling and local attraction between the agent individuals of the algorithm will cause the population of the entire algorithm to fall into a local optimal solution. Especially during the optimization process, the attractors will be too concentrated, resulting in the loss of diversity in the search space, thus losing the ability of global exploration, leading to a lower accuracy of the optimal solution and affecting the precision stone cutting speed control. Summary of the Invention

[0005] Based on the above problems, the present invention improves and optimizes the traditional PID closed-loop control method and the neural population dynamics optimization algorithm, making the neural population dynamics optimization algorithm and the traditional PID closed-loop control method more suitable for the precision cutting speed control of stone cutting. The core lies in using the improved neural population dynamics optimization algorithm to optimize the PID closed-loop control method for the precision cutting speed of stone cutting, improving the precision of the precision stone cutting speed control.

[0006] To achieve the above object, the present invention adopts the following technical solutions: An automatic cutting speed control method for precision stone cutting, wherein the cutting speed of the stone is realized by driving a permanent magnet synchronous motor, and the rotation speed of the permanent magnet synchronous motor directly controls the stone cutting speed. The specific steps are as follows:

[0007] S1. Construct an automatic cutting speed control system, which includes: a PID closed-loop control module, an improved neural population dynamics optimization algorithm module, and a rotation speed driving module of the permanent magnet synchronous motor;

[0008] S2. Improve the standard neural population dynamics optimization algorithm by improving the attractor tending strategy and proposing an adaptive quantum-guided perturbation strategy to construct an improved neural population dynamics optimization algorithm module;

[0009] S3. Optimize the PID closed-loop control method by optimizing the Kp, Ki, and Kd of the PID closed-loop control algorithm through the improved neural population dynamics optimization algorithm;

[0010] S4. Input the error value between the stone cutting speed at the t-th moment and the target cutting speed into the PID closed-loop control module, and output the cutting speed control increment at the t-th moment The cutting speed control increment is input into the rotation speed driving module of the permanent magnet synchronous motor to output the stone cutting speed ;

[0011] S5. Return to execute S4 until the stone cutting speed meets the error value with the target cutting speed is zero, realizing the automatic cutting speed control of precision stone cutting.

[0012] Preferably, the stone cutting speed depends on the rotation speed of the permanent magnet synchronous motor, and the stone cutting speed is controlled by driving the rotation speed of the permanent magnet synchronous motor at the t-th moment , and the mathematical model is:

[0013] ;

[0014] wherein, is the rotation speed of the permanent magnet synchronous motor at the t-th moment, is a proportional constant, and is obtained by collecting n groups of and values.

[0015] Preferably, the rotation speed driving module of the permanent magnet synchronous motor is a second-order conversion model between the cutting speed control increment at the t-th moment and the rotation speed of the permanent magnet synchronous motor. Input the cutting speed control increment at the t-th moment, and obtain the rotation speed of the permanent magnet synchronous motor at the t-th moment through the rotation speed driving module of the permanent magnet synchronous motor. The mathematical model is:

[0016] ;

[0017] where J is the inertia of the permanent magnet synchronous motor, is the rotational speed of the permanent magnet synchronous motor at the t-th moment, is the first derivative of the rotational speed of the permanent magnet synchronous motor at the t-th moment, is the torque constant of the permanent magnet synchronous motor, is the cutting speed control quantity at the (t - 1)-th moment, where, , is the cutting speed control quantity at the t-th moment.

[0018] Preferably, the PID closed-loop control module is the core of the automatic cutting speed control system, and the cutting speed of the stone is controlled by the incremental PID closed-loop control algorithm. Among them, the mathematical model of the incremental PID closed-loop control algorithm is:

[0019] ;

[0020] where, is the adjustment amount of the stone cutting speed, , and are the proportional coefficient, integral coefficient, and differential coefficient of the PID closed-loop control algorithm, and are the cutting speed error values at the (t - 1)-th and (t - 2)-th moments, is the error value between the rotational speed of the permanent magnet synchronous motor at the t-th moment and the set target rotational speed.

[0021] Preferably, in order to improve the precision of stone cutting, a material adaptability factor is introduced to adjust the cutting speed of the stone. The dynamic adjustment formula of the cutting speed is:

[0022] ;

[0023] where, is the cutting speed after dynamic adjustment, is the cutting speed of the stone.

[0024] Preferably, the friction force will cause the temperature between the teeth and the stone to rise, which will affect the efficiency of the cutting process. The friction force not only increases with time but also causes a temperature effect as the cutting time increases. This effect will affect the hardness of the material and the cutting speed. The present invention introduces a temperature factor , which will increase with the increase of the friction force and the cutting time. The mathematical model is:

[0025] ;

[0026] Among them, is the temperature factor value at the t-th moment, is the initial temperature factor, that is, the initial temperature value, γ is the temperature gain coefficient caused by friction, which controls the influence of friction on temperature, and T is the total running time;

[0027] As the temperature increases, the influence of friction force will be more significant. The present invention introduces a non-linear friction coefficient , which changes with the increase of temperature, to represent the influence of friction force on the cutting speed. It reflects the friction increase effect brought by high temperature. The mathematical model is:

[0028] ;

[0029] Among them, is the maximum value of the temperature factor value, that is, the maximum value of the temperature factor value, is the adjustment coefficient, which represents the influence intensity of temperature on the friction force;

[0030] According to the temperature factor and the non-linear friction coefficient design the material adaptability factor , and the mathematical model is:

[0031] ;

[0032] Among them, is the material adaptability factor at the t-th moment.

[0033] Preferably, in the process of optimizing the PID closed-loop control algorithm by the improved neural population dynamic optimization algorithm, the position of the agent individual represents the solutions of Kp, Ki, and Kd of the PID closed-loop control algorithm, that is, the position of the agent individual is a solution containing three parameters (proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd) of the PID closed-loop control algorithm. Each agent individual corresponds to a parameter combination in the parameter space of the PID closed-loop control algorithm. The mathematical model is: , in the formula, is the position of the i-th agent individual, , and are the proportional coefficient, integral coefficient, and differential coefficient of the i-th agent individual.

[0034] Preferably, a fitness function is designed to guide the improved neural population dynamic optimization algorithm to optimize the proportional coefficient Kp, integral coefficient Ki, and derivative coefficient Kd of the PID closed-loop control algorithm through the fitness function. The input of the fitness function is the position of the surrogate individual, that is, a parameter combination in the parameter space of the PID closed-loop control algorithm, which is input into the automatic cutting speed control system. The cutting speed control increment output by the automatic cutting speed control system acts on the permanent magnet synchronous motor to obtain the rotational speed state. The mathematical model of the fitness function is as follows:

[0035] ;

[0036] Among them, and are weight coefficients, T is the total running time, is the rotational speed control stone cutting speed at the t-th moment, is the target cutting speed.

[0037] Preferably, the scaling factor of the current attractor tendency strategy is based on a fixed ratio. The present invention proposes an adaptive non-linear scaling factor method based on local sensitivity and optimal solution information, in which the scaling factor is adjusted according to the similarity between each neural population and its neighbor surrogate individuals and the dynamic change of the optimal solution, making the convergence more intelligent and dynamic. When the current surrogate individual is very similar to other surrogate individuals, the scaling factor becomes smaller, meaning that the attractor trend of the population weakens, encouraging more exploration; when the current surrogate individual is quite different from other surrogate individuals, the scaling factor increases, enhancing the attractor tendency and promoting faster convergence. The specific steps are as follows:

[0038] S201. Design a non-linear scaling factor adjustment mechanism based on similarity, and define the local similarity as the similarity degree between the position of the i-th surrogate individual and the positions of other surrogate individuals in the search space [lb, ub]. The mathematical model is as follows:

[0039] ;

[0040] Among them, iter is the current iteration number, iter = 1, 2,..., Max_iter; Max_iter is the maximum iteration number;

[0041] S202. Based on the local similarity and the best fitness value , improve the scaling factor of the attractor tendency strategy. The mathematical model is as follows:

[0042] ;

[0043] Among them, is the scaling factor of the i-th agent individual at the iter-th iteration, is the initial scaling factor, is the optimal fitness in the current population, is the fitness value of the position of the i-th agent individual at the iter-th iteration;

[0044] S203. Improve the attractor tendency strategy of the neural population dynamic optimization algorithm by using the improved scaling factor; In the present invention, the agent individual corresponding to the minimum fitness value of each iteration is used as the attractor att, and the mathematical model is:

[0045] ;

[0046] In the formula, is the updated position of the i-th agent individual in the attractor tendency strategy stage, is a random number within 0 to 1, is the attractor position at the iter-th iteration, represents Gaussian noise of external input interference, is the position of the i-th agent individual at the iter-th iteration.

[0047] Preferably, by introducing the improved attractor trend strategy, NPDOA can optimize the PID algorithm for automatic cutting speed control of stone cutting. In the dynamic adjustment process, the improved attractor trend strategy can improve the adaptability of the NPDOA algorithm to the changing environment, ensure local search while enhancing the global search ability, and refine the parameter adjustment of the PID closed-loop control algorithm, so as to achieve more efficient and accurate automatic cutting control, which not only improves the cutting quality and speed, but also makes the control system more stable.

[0048] Preferably, the coupling interference simulates the interaction between neural populations, including additive coupling and diffusion coupling; The additive coupling is represented by the following formula:

[0049] ;

[0050] Among them, is the position of the i-th agent individual adjusted by diffusion and additive coupling under the coupling interference strategy; N is the total number of agent individuals, is the position of the i-th agent individual at the iter-th iteration; is a random number within 0 to 1;

[0051] The diffusion coupling is represented by the following formula:

[0052] ;

[0053] wherein, is the position of the i-th agent individual adjusted by differential action under the coupled interference strategy; is the position of the j-th agent individual at the iter-th iteration; is a random number within 0 to 1;

[0054] The additive coupling and diffusion coupling are combined to update the position of the agent individual, and the mathematical model is:

[0055] ;

[0056] wherein, is the updated position of the i-th agent individual in the coupled interference strategy phase, and d is the proportionality factor of the coupled perturbation.

[0057] Preferably, the present invention abandons the information projection strategy of the original NPDOA algorithm and proposes an adaptive quantum-guided perturbation strategy, so that the solutions in the process of optimizing the Kp, Ki, and Kd of the PID closed-loop control algorithm of the automatic cutting speed control system are not limited to the existing solution space, but utilize the superposition and coherence of quantum states to explore and calculate simultaneously among multiple possible solutions, and then select the optimal solution according to the interference effect; the solution is denoted as the position of the agent individual, and the specific steps are as follows:

[0058] S301. Represent each solution as a quantum state ψ(x), and the fitness function value of each solution corresponds to the energy of the quantum state. The mathematical model is:

[0059] ;

[0060] wherein, is a complex coefficient, i = 1, 2,..., N; represents the amplitude of the solution in the quantum state, is the position of the i-th agent individual at the iter-th iteration, i = 1, 2,..., N;

[0061] S302. Simulate quantum tunneling to allow the NPDOA algorithm to pass through the poorer local optimal solution in the solution space and directly transition to a better solution. The mathematical model is:

[0062] ;

[0063] wherein, is the tunneling probability of the i-th agent individual from the current solution to the global optimal solution of the current iteration, is the position of the i-th agent individual at the iter-th iteration, i = 1, 2,..., N; is the position of the best agent individual at the iter-th iteration, R is the tunneling coefficient, and controls the intensity of the tunneling effect; is The fitness value of is the fitness value of

[0064] S303. Generate a random number rand ∈ [0, 1]. If rand is less than , then allow the solution to jump, that is, update the position of the solution to approach the position of the best proxy individual. Otherwise, execute S304. The mathematical model is:

[0065] ;

[0066] where is the updated position of the proxy individual, is the step size, controlling the amplitude of the jump;

[0067] S304. Through simulating quantum interference, during the optimization process of the NPDOA algorithm, competition is carried out among multiple potential solutions, and the optimal solution is selected according to the interference result. The mathematical model is:

[0068] ;

[0069] where is the interference probability of the solution under the interference effect, h is the Planck constant, determining the frequency of the interference effect;

[0070] S305. Through the interference effect, adaptively guide the perturbation process. During the optimization process, first select the most promising solution according to the interference result of the quantum state, and then apply the quantum tunneling effect to explore within the neighborhood of this solution. The mathematical model is:

[0071] ;

[0072] where is the updated position of the proxy individual, is the perturbation amplitude, controlling the size of the position update; is the perturbation direction of the i-th proxy individual.

[0073] Preferably, by simulating quantum tunneling, which describes the ability of a quantum particle to pass through an energy barrier that cannot be penetrated in classical mechanics, during the process of optimizing the Kp, Ki, and Kd of the PID closed-loop control algorithm for an automatic cutting speed control system, the simulated quantum tunneling proposed by the present invention can be used to break through local optima and thus explore a broader solution space. Specifically, the search process of the solution space does not strictly follow traditional local search, but allows the algorithm to "tunnel" through inferior local optima in the solution space and directly transition to a better solution; quantum interference occurs when multiple quantum states interact, and constructive interference and destructive interference can occur, thereby affecting the solution search in the optimization process. Quantum interference usually determines the "phase" or "direction" of a quantum state, and in the optimization process, it reflects the "importance" or "priority" of a solution. Through quantum interference, it is determined which solutions will affect the update of the current solution, and based on the results of quantum interference, the present invention calculates the direction of solution update. , quantum interference is equivalent to the interaction between multiple solutions in the solution space.

[0074] Preferably, the optimization of the PID closed-loop control method is achieved by optimizing the Kp, Ki, and Kd of the PID closed-loop control algorithm through an improved neural population dynamics optimization algorithm. The specific steps are as follows:

[0075] S401. Map the Kp, Ki, and Kd parameters as a spatial vector to the surrogate individuals of the improved neural population dynamics optimization algorithm; initialize the maximum number of iterations Max_iter, the total number of surrogate individuals N, the upper bound ub and lower bound lb of the search space, and the problem dimension D.

[0076] S402. Initialize the positions of the surrogate population of the improved neural population dynamics optimization algorithm by using a random assignment method. The surrogate population includes N surrogate individuals.

[0077] S403. Calculate the fitness value of each surrogate individual position using the fitness function, and retain the position of the surrogate individual corresponding to the current minimum fitness value as the best surrogate individual position at the iter-th iteration.

[0078] S404. Determine whether the current iteration number iter satisfies iter > Max_iter. If so, output the best surrogate individual position as the optimal solution, and resolve the best surrogate individual position into the Kp, Ki, and Kd parameter values, denoted as the best Kp, Ki, and Kd parameter values; otherwise, execute S405 to S407 to update the surrogate individual positions.

[0079] S405. Calculate the improved scaling factor , and update the surrogate individual positions using the improved attractor tendency strategy.

[0080] S406. Update the surrogate individual positions using the coupling interference strategy.

[0081] S407. Introduce an adaptive quantum-guided perturbation strategy to guide the perturbation of the states of the neural population agent individuals through the "quantum tunneling effect" and "quantum interference effect" in quantum mechanics, and update the positions of the agent individuals.

[0082] S408. Calculate the fitness value of the current agent individual using the fitness function, and retain the position value of the agent individual corresponding to the minimum fitness value, which is the optimal agent individual position at the iter-th iteration. with the optimal agent individual position in the previous iteration and retain the smaller position value of the two as the global optimal population individual position value. Then return to execute S404.

[0083] Compared with the existing method, the beneficial effects and innovations of the present invention are as follows: By simulating the quantum tunneling and interference effects, the present invention optimizes the parameter search process in the PID closed-loop control, so that the solution space is no longer limited to the traditional local search, but conducts global search and jump through the principles of quantum mechanics, avoiding falling into local optima; By combining the improved attractor tendency strategy, coupling interference strategy and quantum-guided perturbation strategy, the adaptability of the neural population algorithm under complex cutting conditions is enhanced, and the accuracy and stability of the PID closed-loop control algorithm are improved; By combining the improved neural population dynamic optimization algorithm (NPDOA) with the traditional PID closed-loop control, the precise cutting speed control method for stone cutting is optimized, enabling the control system to effectively improve the stone cutting accuracy, reduce the errors in cutting, and improve the cutting quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flowchart of the automatic cutting speed control method for precise stone cutting proposed by the present invention;

[0085] Figure 2 It is a flowchart for realizing the optimization of the PID closed-loop control method;

[0086] Figure 3 It is a curve graph showing the change of the fitness value during the optimization process of the standard NPDOA algorithm and the improved NPDOA algorithm;

[0087] Figure 4 It is a trend graph showing the change of the three parameters of the PID closed-loop control algorithm during the optimization process of the standard NPDOA algorithm;

[0088] Figure 5 It is a trend graph showing the change of the three parameters of the PID closed-loop control algorithm during the optimization process of the improved NPDOA algorithm;

[0089] Figure 6Response curves of three different PID control methods in the automatic cutting speed control system. Detailed implementation manners

[0090] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0091] An automatic cutting speed control method for precision stone cutting according to the present invention, wherein the cutting speed of the stone is achieved by driving a permanent magnet synchronous motor, and the rotation speed of the permanent magnet synchronous motor directly controls the stone cutting speed. The detailed implementation manners include the establishment of a mathematical model and software simulation; the establishment of the mathematical model is specifically as Figure 1 shown in S1 to S5 below.

[0092] S1. Construct an automatic cutting speed control system, which includes: a PID closed-loop control module, an improved neural population dynamics optimization algorithm module, and a rotation speed driving module of the permanent magnet synchronous motor.

[0093] Specifically, build an automatic cutting speed control system simulation model in Simulink, including an improved PID closed-loop control model, an objective function module, and a rotation speed driving module of the permanent magnet synchronous motor. The input of the improved PID closed-loop control model in Simulink is the optimal Kp, Ki, and Kd parameter values; the objective function module uses a fitness function, and the rotation speed driving module of the permanent magnet synchronous motor is the Laplace transform form of the rotation speed driving mathematical model of the permanent magnet synchronous motor; the time-domain form of the rotation speed driving mathematical model of the permanent magnet synchronous motor is:

[0094] ;

[0095] wherein, J is the inertia of the permanent magnet synchronous motor, which is set to 0.444 during the implementation process, is the rotation speed of the permanent magnet synchronous motor at the t-th moment, is the first derivative of the rotation speed of the permanent magnet synchronous motor at the t-th moment, is the torque constant of the permanent magnet synchronous motor, which is set to 2 during the implementation process, is the cutting speed control amount at the (t - 1)-th moment, wherein, , is the cutting speed control amount at the t-th moment.

[0096] Specifically, the rotational speed drive model of the permanent magnet synchronous motor in Siumlink adopts the complex frequency domain form, and the initial rotational speed of the permanent magnet synchronous motor w(0) = 0; the complex frequency domain of the rotational speed drive model of the permanent magnet synchronous motor is as follows:

[0097] ;

[0098] where, is the complex frequency domain form of the rotational speed of the permanent magnet synchronous motor at the t-th moment, is the complex frequency domain form of the cutting speed control quantity at the t-th moment, is the complex frequency domain variable.

[0099] S2. Improve the standard neural population dynamics optimization algorithm by improving the attractor tendency strategy and proposing an adaptive quantum-guided perturbation strategy, and construct an improved neural population dynamics optimization algorithm module.

[0100] Specifically, the present invention proposes an adaptive non-linear scaling factor method based on local sensitivity and optimal solution information, and the specific steps are as follows:

[0101] S201. Design a non-linear scaling factor adjustment mechanism based on similarity, and define the local similarity as the similarity degree between the position of the i-th agent individual and the positions of other agent individuals in the search space [lb, ub], and the mathematical model is:

[0102] ;

[0103] where, iter is the current iteration number, iter = 1, 2,..., Max_iter; Max_iter is the maximum iteration number, which is set to 100 during the implementation process;

[0104] S202. Based on the local similarity and the best fitness value improve the scaling factor of the attractor tendency strategy, and the mathematical model is:

[0105] ;

[0106] where, is the scaling factor of the i-th agent individual at the iter-th iteration, is the initial scaling factor, and the initial value is set to 0.5, and the value range is from 0 to 1; is the optimal fitness in the current population, is the fitness value of the position of the i-th agent individual at the iter-th iteration;

[0107] S203. Improve the attractor tendency strategy of the neural population dynamics optimization algorithm using an improved scaling factor; in the present invention, the agent individual corresponding to the minimum fitness value in each iteration is used as the attractor att, and the mathematical model is:

[0108] ;

[0109] In the formula, is the updated position of the i-th agent individual in the attractor tendency strategy stage, is a random number within 0 to 1, is the position of the attractor in the iter-th iteration, represents Gaussian noise of external input interference, is the position of the i-th agent individual in the iter-th iteration.

[0110] Specifically, an additive coupling mathematical model is constructed through the following formula:

[0111] ;

[0112] Among them, is the position of this i-th agent individual adjusted through diffusion and additive coupling under the coupling interference strategy; N is the total number of agent individuals, is the position of the i-th agent individual in the iter-th iteration; is a random number within 0 to 1;

[0113] Diffusion coupling is represented by the following formula:

[0114] ;

[0115] Among them, is the position of this i-th agent individual adjusted through differentiation under the coupling interference strategy; is the position of the j-th agent individual in the iter-th iteration; is a random number within 0 to 1;

[0116] Combine additive coupling and diffusion coupling to update the position of the agent individual, and the mathematical model is:

[0117] ;

[0118] Among them, is the updated position of the i-th agent individual in the coupling interference strategy stage, and d is the proportionality factor of the coupling perturbation.

[0119] Specifically, the present invention abandons the information projection strategy of the original NPDOA algorithm and proposes an adaptive quantum-guided perturbation strategy. By utilizing the superposition and coherence of quantum states, exploration and calculation are simultaneously carried out among multiple possible solutions, and then the optimal solution is selected according to the interference effect; the solution is denoted as the position of the agent individual, and the specific steps are as follows:

[0120] S301. Represent each solution as a quantum state ψ(x), and the fitness function value of each solution corresponds to the energy of the quantum state. The mathematical model is:

[0121] ;

[0122] Wherein, is a complex coefficient, i = 1, 2,..., N; represents the amplitude of the solution in the quantum state, is the position of the i-th agent individual at the iter-th iteration, i = 1, 2,..., N; N is the total number of agent individuals, which is set to 20 during implementation;

[0123] S302. Simulate quantum tunneling to allow the NPDOA algorithm to pass through poorer local optimal solutions in the solution space and directly transition to a better solution. The mathematical model is:

[0124] ;

[0125] Wherein, is the tunneling probability of the i-th agent individual from the current solution to the global optimal solution at the current iteration, is the position of the i-th agent individual at the iter-th iteration, i = 1, 2,..., N; is the position of the best agent individual at the iter-th iteration, R is the tunneling coefficient, which controls the intensity of the tunneling effect; is 's fitness value, is 's fitness value;

[0126] S303. Randomly generate a number rand ∈ [0, 1]. If rand is less than , then allow the solution to jump, that is, update the position of the solution to approach the position of the best agent individual, otherwise execute S304. The mathematical model is:

[0127] ;

[0128] Wherein, is the updated position of the agent individual, is the step size, which controls the amplitude of the jump;

[0129] S304. Through simulating quantum interference, during the optimization process of the NPDOA algorithm, competition occurs among multiple potential solutions, and the optimal solution is selected according to the interference result. The mathematical model is as follows:

[0130] ;

[0131] Among them, is the interference probability of the solution under the interference effect. h is the Planck constant, which determines the frequency of the interference effect and is set to 0.5 during the implementation of the present invention;

[0132] S305. Through the interference effect, the perturbation process is adaptively guided. During the optimization process, first, the most promising solution is selected according to the interference result of the quantum state, and then the quantum tunneling effect is applied to explore within the neighborhood of this solution. The mathematical model is as follows:

[0133] ;

[0134] Among them, is the updated position of the surrogate individual, is the perturbation amplitude, which controls the magnitude of the position update; during the implementation, the initial value is set to 0.3, and subsequent iterations are randomly generated within 0 to 1; is the perturbation direction of the i-th surrogate individual, and the value is any number from 0 to 1.

[0135] More specifically, in the present invention, the tunneling coefficient R, the step size step, and the proportionality factor d of the coupled perturbation are designed according to the idea that as the number of iterations increases, the tunneling coefficient and the step size gradually decrease, thereby reducing the exploratory, jumping, and coupled perturbation properties and enhancing the exploitation property. The mathematical models for defining R, step, and d are as follows:

[0136] ;

[0137] Among them, iter is the current number of iterations, iter = 1, 2,..., Max_iter; Max_iter is the maximum number of iterations and is set to 100 during the implementation.

[0138] S3. The Kp, Ki, and Kd of the PID closed-loop control algorithm are optimized through the improved neural population dynamic optimization algorithm to realize the optimization of the PID closed-loop control method.

[0139] Specifically, during the optimization of the PID closed-loop control algorithm by the improved neural population dynamics optimization algorithm, the position of the agent individual represents the solutions of Kp, Ki, and Kd of the PID closed-loop control algorithm, that is, the position of the agent individual is a solution containing the three parameters (proportional coefficient Kp, integral coefficient Ki, and derivative coefficient Kd) of the PID closed-loop control algorithm. Each agent individual corresponds to a parameter combination in the parameter space of the PID closed-loop control algorithm, and the mathematical model is: , where is the position of the i-th agent individual, , and are the proportional coefficient, integral coefficient, and derivative coefficient of the i-th agent individual.

[0140] Specifically, the optimization of the PID closed-loop control method is achieved by optimizing Kp, Ki, and Kd of the PID closed-loop control algorithm through the improved neural population dynamics optimization algorithm. The specific steps are as follows:

[0141] S401. Map the Kp, Ki, and Kd parameters as a spatial vector to the agent individuals of the improved neural population dynamics optimization algorithm; initialize the maximum number of iterations Max_iter, the total number of agent individuals N, the upper bound ub and lower bound lb of the search space, and the problem dimension D;

[0142] S402. Initialize the positions of the agent population of the improved neural population dynamics optimization algorithm by using the method of random assignment. The agent population includes N agent individuals;

[0143] S403. Calculate the fitness value of each agent individual position using the fitness function, and retain the position of the agent individual corresponding to the current minimum fitness value as the best agent individual position at the iter-th iteration;

[0144] S404. Determine whether the current iteration number iter satisfies iter > Max_iter. If so, output the best agent individual position as the optimal solution, and parse the best agent individual position into the Kp, Ki, and Kd parameter values, denoted as the best Kp, Ki, and Kd parameter values; otherwise, execute S405 to S407 to update the agent individual position;

[0145] S405. Calculate the improved scaling factor , and update the agent individual position using the improved attractor tendency strategy;

[0146] S406. Update the agent individual position using the coupling interference strategy;

[0147] S407. Introduce an adaptive quantum guidance perturbation strategy to guide the perturbation of the state of the neural population agent individuals through the "quantum tunneling effect" and "quantum interference effect" in quantum mechanics, and update the positions of the agent individuals;

[0148] S408. Calculate the fitness value of the current agent individual using the fitness function, and retain the position value of the agent individual corresponding to the minimum fitness value, which is the best agent individual position at the iter - th iteration , and the best agent individual position in the previous iteration , retain the smaller position value of the two, which is the global best population individual position value , and return to execute S404.

[0149] Specifically, the fitness function is used to guide the improvement of the neural population dynamic optimization algorithm for optimizing the proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd of the PID closed - loop control algorithm. The input of the fitness function is the position of the agent individual, that is, a parameter combination in the parameter space of the PID closed - loop control algorithm. The input is automatically cut into the speed control system, and the cutting speed control increment output by the automatic cutting speed control system acts on the permanent magnet synchronous motor to obtain the rotational speed state. The mathematical model of the fitness function is:

[0150] ;

[0151] Among them, and are weight coefficients, which are set to 0.5 respectively during the implementation process. T is the total running time, which is set to 20 seconds in the implementation of the present invention. is the rotational speed control for cutting the stone at the t - th moment, is the target cutting speed.

[0152] S4. Input the error value between the stone cutting speed at the t - th moment and the target cutting speed into the PID closed - loop control module, and output the cutting speed control increment at the t - th moment , and input the cutting speed control increment into the rotational speed drive module of the permanent magnet synchronous motor to output the stone cutting speed .

[0153] Specifically, the PID closed - loop control module adopts an incremental PID closed - loop control algorithm, and the mathematical model is:

[0154] ;

[0155] Among them, is the adjustment amount of the stone cutting speed, , and are the proportional coefficient, integral coefficient, and differential coefficient of the PID closed - loop control algorithm, and is the cutting speed error value at the (t - 1)-th and (t - 2)-th moments, is the error value between the rotational speed of the permanent magnet synchronous motor at the t-th moment and the set target rotational speed.

[0156] Specifically, the rotational speed of the permanent magnet synchronous motor at the t-th moment is used to control the stone cutting speed , and the mathematical model is:

[0157] ;

[0158] wherein, is the rotational speed of the permanent magnet synchronous motor at the t-th moment, is the proportionality constant, which is obtained by collecting n groups of and values and is set to 1.

[0159] Specifically, a material adaptability factor is introduced to adjust the stone cutting speed, and the dynamic adjustment formula for the cutting speed is:

[0160] ;

[0161] wherein, is the cutting speed after dynamic adjustment, is the stone cutting speed, and the specific implementation steps are as follows:

[0162] S501. Introduce a temperature factor , which increases with the increase of friction and cutting time, and the mathematical model is:

[0163] ;

[0164] wherein, is the value of the temperature factor at the t-th moment, is the initial temperature factor, that is, the initial temperature value is set to 20, γ is the temperature gain coefficient caused by friction to control the influence of friction on temperature and is set to 0.5, and T is the total running time;

[0165] S502. Introduce a non-linear friction coefficient , which changes with the increase of temperature to represent the influence of friction force on the cutting speed, and it reflects the friction increase effect caused by high temperature, and the mathematical model is:

[0166] ;

[0167] wherein, is the maximum value of the temperature factor value, that is, the maximum value of the temperature factor value is set to 100, is the adjustment coefficient, representing the influence intensity of temperature on friction force, and is set to 0.5;

[0168] S503. Design the material adaptability factor according to the temperature factor and the non - linear friction coefficient , and the mathematical model is:

[0169] ;

[0170] wherein, is the material adaptability factor at the t - th moment.

[0171] S5. Return to execute S4 until the stone cutting speed meets the error value with the target cutting speed is zero, realizing the automatic cutting speed control of precision stone cutting.

[0172] More specifically, complete the software design of the mathematical model of the method of the present invention in Matlab. The final parameters during the program operation in the Main function include the maximum number of iterations Max_iter set to 100, the total number of agent individuals N set to 20, the upper bound ub of the search space set to 90, the lower bound lb set to 0.01, the problem dimension D set to 3. Assign the fitness function value to the objective function, and establish the code for parameter mapping in the optimization process of the PID control algorithm of the standard neural population dynamic optimization algorithm and the improved neural population dynamic optimization algorithm of the present invention for the automatic cutting speed control system; and plot the final optimized Kp, Ki, and Kd parameter values, as well as the fitness function value and the control effect. Run the program, and the code is as follows:

[0173] %% Clear the environment

[0174] clear all;

[0175] close all;

[0176] clc;

[0177] warning off;

[0178] Max_iter = 100;

[0179] N = 20;

[0180] lb = 0.01;

[0181] ub = 90;

[0182] D = 3;

[0183] f = @(x) Best_PID(x);

[0184] [Best_score_1, Best_solution_1, K_PID1, fitness_1]=NPDOA(Max_iter, lb, ub, D, fobj);

[0185] [best_score_2, best_solution_2, K_PID2, fitness_2]=GNPDOA(Max_iter, lb, ub, D, fobj);

[0186] Get as Figures 3 to 6 。

[0187] More specifically, the fitness function measures the performance of the PID controller, aiming to minimize the control error. By continuously adjusting the parameters of the PID controller, the fitness function is optimized to reach its minimum value; as Figure 3 shown, the improved NPDOA algorithm is significantly better than the standard NPDOA algorithm; the fitness function value of the standard NPDOA algorithm decreases slowly and there is a long stagnation period in the middle stage, falling into a local optimum, and reaching the best optimization solution at the 46th iteration with a fitness value of 6.57445; the fitness function value of the improved NPDOA algorithm decreases rapidly and stabilizes, indicating that the method of the present invention can find the global optimum solution faster during the optimization process, and finds a better solution than the standard NPDOA algorithm at the 11th iteration with a fitness value of 4.08995; this shows that the improved NPDOA algorithm has higher efficiency and convergence speed when optimizing the parameters of the PID closed-loop control algorithm.

[0188] More specifically, as Figure 4 and Figure 5As shown in the figure, the changing trends of the three parameters of the PID closed-loop control algorithm during the optimization process of the standard and improved NPDOA algorithms, corresponding to the changes in the fitness value. When the standard NPDOA algorithm optimizes the PID parameters, its convergence speed is not as fast as expected. Although the adjustments of Kp, Ki, and Kd gradually tend to be stable, the convergence process is slow. Especially in the initial stage of finding the optimal solution, finally, Kp stabilizes at about 30 iterations without significant fluctuations, Ki tends to be stable after about 35 iterations, and the change of Kd is the slowest, with no obvious change in the early stage and only starting to decrease and tend to be stable until about 46 iterations. Finally, the optimal control parameters are Kp = 10.5216, Ki = 0.559252, and Kd = 1.27043; compared with the standard NPDOA algorithm, the improved NPDOA shows a faster convergence speed during the optimization process of Kp, and is also more efficient in the adjustment of Ki. Although Kd does not change significantly, its stability is well reflected during the optimization process. Finally, the optimal control parameters are Kp = 86.7229, Ki = 0.506707, and Kd = 11.2386.

[0189] More specifically, as Figure 6 shown in the response curves of three different PID control methods in the automatic cutting speed control system. When the cutting speed control amount is set to 7, the standard PID method shows obvious overshoot, slow response speed, and it takes longer for the system to stabilize to the target value, with obvious overshoot phenomenon and the system needs time to stabilize; compared with the standard PID, the ordinary optimization algorithm - PID method reduces overshoot and improves the response speed of the system. However, although the system approaches the target value faster, there is still a certain oscillation and the stability is improved; the optimal control effect of the optimization algorithm - PID method of the present invention has almost no overshoot, the system quickly stabilizes to the target value, and the response speed is the fastest. The improved NPDOA algorithm of the present invention can accurately reach the target in the shortest time without overshoot and oscillation.

Claims

1. An automatic cutting speed control method for precision stone cutting, characterized in that, The specific steps are as follows: S1. Construct an automatic cutting speed control system, which includes a PID closed-loop control module, an improved neural population dynamics optimization algorithm module, and a speed drive module for a permanent magnet synchronous motor; S2. Improve the standard neural population dynamics optimization algorithm by improving the attractor tendency strategy and proposing an adaptive quantum-guided perturbation strategy to construct an improved neural population dynamics optimization algorithm module; the adaptive quantum-guided perturbation strategy uses the superposition and coherence of quantum states to explore and calculate simultaneously among multiple possible solutions, and then selects the optimal solution according to the interference effect; the solution is denoted as the position of the surrogate individual, specifically: S301. Represent each solution as a quantum state ψ(x), and the fitness function value of each solution corresponds to the energy of the quantum state. The mathematical model is: ； wherein, is a complex coefficient, i = 1, 2, ..., N; represents the amplitude of the solution in the quantum state, is the position of the i-th agent individual at the iter-th iteration, i = 1, 2, ..., N; S302. Simulate quantum tunneling to allow the NPDOA algorithm to cross the poorer local optimal solution in the solution space and directly jump to a better solution. The mathematical model is: ； wherein, is the tunneling probability of the i-th agent individual from the current solution to the globally optimal solution of the current iteration, is the position of the i-th agent individual at the iter-th iteration, i = 1, 2,..., N; is the position of the best agent individual at the iter-th iteration, R is the tunneling coefficient, controlling the intensity of the tunneling effect; is the fitness value of, is the fitness value of; S303. A randomly generated number rand ∈ [0, 1]. If rand is less than , then solution jumping is allowed, that is, update the position of the solution to approach the position of the best surrogate individual. Otherwise, execute S304. The mathematical model is as follows: ； Among them, is the updated position of the agent individual, is the step size, which controls the amplitude of the jump; S304. Through simulating quantum interference, the NPDOA algorithm competes among multiple potential solutions during the optimization process and selects the optimal solution according to the interference result. The mathematical model is: ； Among them, is the interference probability under the interference effect, h is the Planck constant, which determines the frequency of the interference effect; S305. Through the interference effect, adaptively guide the perturbation process. During the optimization process, first select the most promising solution according to the interference result of the quantum state, and then apply the quantum tunneling effect to explore within the neighborhood of this solution. The mathematical model is: ； Among them, is the updated position of the agent individual, is the perturbation amplitude, which controls the magnitude of the position update; is the perturbation direction of the i-th agent individual; S3. Optimize the PID closed-loop control method by optimizing the Kp, Ki, and Kd of the PID closed-loop control algorithm through the improved neural population dynamics optimization algorithm; S4. Input the error value between the stone cutting speed at the t-th moment and the target cutting speed into the PID closed-loop control module, and output the cutting speed control increment at the t-th moment , and input the cutting speed control increment into the rotational speed driving module of the permanent magnet synchronous motor to output the stone cutting speed ; S5. Return to execute S4 until the stone cutting speed meets the error value with the target cutting speed is zero to achieve automatic cutting speed control for precision stone cutting.

2. The automatic cutting speed control method for precision stone cutting according to claim 1, wherein The rotational speed driving module of the permanent magnet synchronous motor is the cutting speed control increment at the t-th moment It is a second-order conversion model between the cutting speed control increment at the t-th moment and the rotational speed of the permanent magnet synchronous motor. By inputting the cutting speed control increment at the t-th moment and passing it through the rotational speed driving module of the permanent magnet synchronous motor, the rotational speed of the permanent magnet synchronous motor at the t-th moment is obtained. The mathematical model is as follows: ； where J is the inertia of the permanent magnet synchronous motor, is the torque constant of the permanent magnet synchronous motor, is the cutting speed control quantity at the (t - 1)-th moment.

3. The automatic cutting speed control method for precision stone cutting according to claim 2, wherein, The improved neural population dynamics optimization algorithm module includes improving the standard neural population dynamics optimization algorithm by improving the attractor tendency strategy, specifically: S201. Design a non - linear scaling factor adjustment mechanism based on similarity and define local similarity as the position of the i - th agent individual and the positions of other agent individuals in the search space [lb, ub], and the mathematical model is as follows: ； where iter is the current iteration number, iter = 1, 2,..., Max_iter; Max_iter is the maximum iteration number; S202. Based on local similarity and the best fitness value Improve the scaling factor of the attractor tendency strategy , the mathematical model is as follows: ； Among them, is the scaling factor of the $i$-th agent individual at the $iter$-th iteration, is the initial scaling factor, is the optimal fitness in the current population, is the fitness value of the position of the $i$-th agent individual at the $iter$-th iteration; S203. Use the improved scaling factor to improve the attractor tendency strategy of the neural population dynamics optimization algorithm; take the surrogate individual corresponding to the minimum fitness value of each iteration as the attractor att. The mathematical model is: ； wherein, is the updated position of the i-th agent individual in the attractor tendency strategy stage, is a random number within 0 to 1, is the attractor position at the iter-th iteration, represents Gaussian noise of external input interference, is the position of the i-th agent individual at the iter-th iteration.

4. An automatic cutting speed control method for precision stone cutting according to claim 3, characterized in that, The optimization of the Kp, Ki, and Kd of the PID closed-loop control algorithm by the improved neural population dynamics optimization algorithm specifically includes the following steps: ​ ​ ​ S404. Determine whether the current iteration number iter satisfies iter > Max_iter. If so, output the position of the best surrogate individual as the optimal solution, and parse the position of the best surrogate individual into the parameter values of Kp, Ki, and Kd, denoted as the best Kp, Ki, and Kd parameter values; Otherwise, execute S405 to S407 to update the position of the surrogate individual; S405. Calculate the improved scaling factor , and update the position of the agent individual by using the improved attractor tendency strategy; S406. Update the position of the surrogate individual using the coupled interference strategy; S407. Introduce an adaptive quantum-guided perturbation strategy to guide the perturbation of the state of the neural population surrogate individual through the "quantum tunneling effect" and "quantum interference effect" in quantum mechanics, and update the position of the surrogate individual; S408. Calculate the fitness value of the current surrogate individual using the fitness function, and retain the position value of the surrogate individual corresponding to the minimum fitness value, which is the position of the best surrogate individual in the iter-th iteration. , and the position of the best surrogate individual in the previous iteration . Retain the smaller position value of the two, which is the position value of the best individual in the global population , and return to execute S404.

5. An automatic cutting speed control method for precision stone cutting according to claim 1, characterized in that, Introduce a material adaptability factor , adjust the stone cutting speed, and the dynamic adjustment formula for the cutting speed is: ； Among them, is the cutting speed after dynamic adjustment, is the stone cutting speed; the steps of the material adaptability factor design method are as follows: S501. Introduce a temperature factor , which increases with the increase of friction force and cutting time. The mathematical model is as follows: ； Among them, is the temperature factor value at the t-th moment, is the initial temperature factor, that is, the initial temperature value, γ is the temperature gain coefficient caused by friction, which controls the influence of friction on temperature, and T is the total running time; S502. Introduce a non-linear friction coefficient , which varies with the increase in temperature, to represent the influence of friction force on the cutting speed. It reflects the friction increase effect caused by high temperature. The mathematical model is as follows: ； Among them, is the maximum value of the temperature factor, that is, the maximum value of the temperature factor, is the adjustment coefficient, indicating the influence intensity of temperature on the frictional force; S503. Design the material adaptability factor according to the temperature factor and the non-linear friction coefficient , and the mathematical model is as follows: ​ ； Among them, is the material adaptability factor at the t-th moment.

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