Tread calender rotating speed PID control method and system, storage medium and equipment

Abstract

The invention relates to the field of PID control, and provides a tread calender rotating speed PID control method and system, a storage medium and equipment. The tread calender rotating speed PID control method comprises the following steps: processing an initial solution space of a plurality of to-be-optimized parameters based on Logistic-Tent chaotic mapping and dynamic reverse learning to obtain an initial population matrix of a Sabot swarm algorithm; according to the evaluation function, calculating the initial fitness of the soloat group individuals, and updating the global optimal position of the soloat individual with the optimal fitness to the current optimal position; executing a salmons swarm algorithm, and searching the to-be-optimized parameters by simulating a search behavior or an attack behavior of a salmons; in the process of executing the sodat swarm algorithm, if it is judged that the algorithm enters a development stagnation state, executing a transverse crossing strategy and a longitudinal crossing strategy to enable the algorithm to get rid of the development stagnation state; and when a set termination condition is satisfied, outputting a solution corresponding to the current optimal position, and controlling the direct current brushless motor. The method can improve the response speed.

Description

Technical Field

[0001] The present invention relates to the field of PID control technology optimization, and in particular to a tread calender speed PID control method, system, storage medium and equipment. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] PID controller is a widely used controller in industrial production process. It controls the stability, accuracy and response speed of the system by adjusting the output of the controller based on the three parts of error: proportional, integral and differential. )、Integral coefficient( )、Differential coefficient( )The setting of the three parameters directly affects the quality of the control effect. Therefore, the tuning of the PID controller parameters has also been a focus of attention. Most tire companies use the traditional PID control method to control the width of the rubber strip during the tread winding process. When the parameters are set correctly and the working conditions do not change, the width of the rubber strip can be well controlled. However, when the working conditions change, such as the rubber material, temperature, die size, extruder calender spacing, and width measurement position, it will cause a large error, and the original PID parameters cannot be used anymore, and the PID parameters need to be re-tuned. At present, the tuning method adopted by most companies is generally the manual experience tuning method, which is very dependent on the knowledge level of engineers and requires engineers to understand some control principles. Engineers go to the site to tune the PID control parameters, which is very inefficient, takes a long time to adjust, and has poor adjustment effects. During the tuning period, a lot of waste rubber that does not meet the width requirements will be generated, and these rubber materials cannot be reworked, resulting in a large amount of rubber waste. Therefore, optimizing the PID control method of the tread calender speed and improving its control accuracy and stability in actual production are the key to improving production efficiency and product quality. Summary of the invention

[0004] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides a tread calender speed PID control method, system, storage medium and equipment. The present invention enables the tread calender speed control system to have a faster response speed, a lower overshoot and a stronger robustness; by improving the sand cat swarm optimization algorithm, the problems of insufficient initial solution accuracy, slow convergence speed and easy falling into local optimum are solved; by improving the sand cat swarm optimization algorithm to optimize the PID parameters, the mechanical robustness and response speed of the tread calender speed control system are enhanced, and the optimization speed of the three parameters is accelerated.

[0005] In order to achieve the above object, the present invention adopts the following technical solution: A first aspect of the present invention provides a tread calender rotation speed PID control method.

[0006] A PID control method for rotating speed of a tread calender, comprising: Obtain multiple parameters to be optimized of the PID controller of the tread calender speed; Based on Logistic-Tent chaotic mapping and dynamic reverse learning, the initial solution space of multiple parameters to be optimized is processed to obtain the initial population matrix of the improved sand cat swarm algorithm; the initial fitness of the sand cat swarm individuals is calculated according to the evaluation function, and the global optimal position of the sand cat individual with the best fitness is updated to the current optimal position; the sand cat swarm algorithm is executed to search for the parameters to be optimized by simulating the search behavior or attack behavior of the sand cat; during the execution of the sand cat swarm algorithm, if it is determined that the algorithm has entered a development stagnation state, the horizontal crossover strategy and the vertical crossover strategy are executed to make the algorithm get rid of the development stagnation state; When the set termination condition is met, the solution corresponding to the current optimal position is output as the target value of the parameter to be optimized to control the brushless DC motor.

[0007] Furthermore, the horizontal cross strategy is expressed by the following formula:

[0008]

[0009] in, and Indicates the first dimension, , Represents the dimension of the problem to be solved; and Represents its parent individual and In the The offspring individuals produced by the horizontal crossover strategy on the dimension; and is a random number distributed between (0, 1); and is a random number distributed between [-1, 1]; The vertical crossover strategy is expressed by the following formula:

[0010] in, and Indicates the vertical cross strategy and Two dimensions of parent individuals; For the parent By generating offspring individuals through vertical crossover strategies in two different dimensions, is a random number distributed between (0, 1).

[0011] Furthermore, the following formula is used to determine whether development has entered a stagnant state:

[0012]

[0013] in, , is the number of consecutive iterations of triggering the judgment mechanism; is an infinitesimal quantity; For the The individual with the best fitness in the population in the iteration; For the The fitness value of the individual with the best fitness in the population in the iteration; To develop stagnation determination factors; is the maximum number of iterations; Is a positive integer.

[0014] Furthermore, the evaluation function adopts the following formula:

[0015] in, represents the ITAE evaluation index, is the feedback deviation between the actual speed and the expected speed, For time.

[0016] Furthermore, the multiple parameters to be optimized include a proportional coefficient, an integral coefficient and a differential coefficient of a PID controller for the rotation speed of the tread calender.

[0017] Furthermore, the algorithm develops the decision factor To determine whether the sand cat is searching or attacking.

[0018]

[0019]

[0020]

[0021] in, is the sand cat hearing parameter, take 2; is the current iteration number, is the maximum number of iterations; is the sensitivity parameter of the sand cat; represents the sensitivity range of the sand cat; is a random number between [0, 1].

[0022] Furthermore, when When , the algorithm enters the search phase. In the search phase, each sand cat updates its own position through the hyperbolic trigonometric inertia weighted strategy according to the current optimal position, the current position of itself and its corresponding circle coefficient and sensitivity range; when , the algorithm enters the attack phase; in the attack phase, each sand cat updates its own position according to the current optimal position, current own position, sensitivity range, moving distance and moving direction angle.

[0023] The position update formula of the sand cat under the hyperbolic trigonometric inertia weighted strategy is:

[0024]

[0025]

[0026] in, Represents the updated position of the sand cat; is the global optimal position in the current iteration; is the position of the sand cat in the current iteration; represents the sensitivity range of the sand cat; , , is a random number between [0, 1]; To control the coefficient of exploration accuracy of this strategy, it is taken as 0.3; is a monotonically decreasing function; Represents the current iteration number, Represents the maximum number of iterations; The position update formula of the sand cat in the attack phase is:

[0027]

[0028] in, is a random angle between 0° and 360°, where Represents the updated position of the sand cat, is the global optimal position in the current iteration, is the position of the sand cat in the current iteration, Represents the distance between the sand cat and its prey.

[0029] Furthermore, in the initialization phase, the algorithm uses Logistic-Tent chaotic mapping and dynamic reverse learning strategy to process the initial solution space of multiple parameters to be optimized, and obtains the initial population matrix of the improved sand cat swarm algorithm; Furthermore, the Logistic-Tent chaotic mapping is expressed by the following formula:

[0030] in, =0.3, The first Sand cat individuals, The first population generated by the Logistic-Tent chaotic map sand cat individuals; , is the number of individuals in the population; is a random number between 0 and 1, Represents remainder operation; Furthermore, the dynamic reverse learning strategy is expressed by the following formula:

[0031] in, represents the population generated by the dynamic reverse learning strategy; represents the initialization population generated by Logistic-tent chaotic mapping; and is a random number distributed between [0, 1]; is the upper bound of the sand cat population location; is the lower bound of the sand cat population location; Furthermore, the method for obtaining the initial population matrix of the improved sand cat swarm algorithm is as follows:

[0032]

[0033] in, Indicates that it contains and The new population of all individuals, for Fitness value of individual Chinese sand cats, calculation of new population The fitness values ​​of all sand cats in the game are calculated to make them fully compete with each other and select the one with the best fitness. Sand cat individuals as the final initial population .

[0034] A second aspect of the present invention provides a tread calender speed PID control system.

[0035] A tread calender speed PID control system, comprising: A data acquisition module is configured to: acquire a plurality of parameters to be optimized of a tread calender speed PID controller; The improved sand cat algorithm module is configured as follows: based on Logistic-Tent chaotic mapping and dynamic reverse learning, multiple parameters to be optimized are processed to obtain the initial position of the sand cat group; the initial fitness of the sand cat group individuals is calculated according to the evaluation function, and the global optimal position of the sand cat individual with the best fitness is updated to the current optimal position; the sand cat group algorithm is executed to search for the parameters to be optimized by simulating the search behavior or attack behavior of the sand cat; during the execution of the sand cat group algorithm, if it is determined that the algorithm has entered a development stagnation state, the horizontal cross strategy and the vertical cross strategy are executed to make the algorithm get rid of the development stagnation state; The output control module is configured to: when the set termination condition is met, output the solution corresponding to the current optimal position as the target value of the parameter to be optimized to control the brushless DC motor.

[0036] A third aspect of the present invention provides a computer-readable storage medium.

[0037] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the tread calender speed PID control method as described in the first aspect above.

[0038] A fourth aspect of the present invention provides a computer device.

[0039] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the tread calender speed PID control method as described in the first aspect above are implemented.

[0040] Compared with the prior art, the present invention has the following beneficial effects: The invention optimizes and sets the PID parameters of the tread calender speed controller by improving the sand cat group optimization algorithm, thereby realizing the optimal control of the calender speed control system; the calender speed control system has a faster response speed and higher control accuracy, and the system has better robustness.

[0041] The present invention utilizes the fusion of Logistic-Tent chaotic mapping and dynamic reverse learning strategy to update the population individuals in the sand cat population optimization algorithm, increases the randomness and ergodicity of the initial population in the feasible domain, increases the quality of the initial population, and improves the accuracy of the initial solution.

[0042] The invention introduces a hyperbolic trigonometric inertia weighting strategy in the exploration stage of the sand cat, so that the algorithm can perform a large-scale search in the early stage of exploration, narrow the search range in the late stage of exploration, and accelerate the convergence speed, thereby improving the search ability of the algorithm.

[0043] The invention introduces a vertical and horizontal crossover strategy based on development stagnation judgment into the sand cat population optimization algorithm to improve the algorithm. When the algorithm falls into development stagnation, the global search ability of the algorithm is enhanced by horizontal crossover, and the diversity of the sand cat population is maintained by vertical crossover to prevent the algorithm from falling into local optimum.

[0044] The present invention solves the problem that the initial population quality of the standard sand cat swarm algorithm is not high, resulting in insufficient initial solution accuracy, slow convergence speed, and easy to fall into the local optimum during the iteration process. The algorithm can quickly find the optimal , , The three parameters improve the convenience, and the calender speed control system has a faster response speed and higher control accuracy, and the system has good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0046] Figure 1 It is a flow chart of the PID control method of the rotation speed of the tread calender based on the improved sand cat group algorithm proposed by the present invention; Figure 2 The block diagram of the tread calender speed control system of the tread calender speed PID control method based on the improved sand cat group algorithm proposed for the invention; Figure 3 This is a model diagram of the tread calender speed PID controller optimized by the improved sand cat swarm algorithm of the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed by the present invention; Figure 4 are population distribution diagrams, wherein (a) is a distribution fork diagram of a population initialized by Logistic-Tent chaotic mapping in the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed in the present invention, (b) is a histogram of a population initialized by Logistic-Tent chaotic mapping in the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed in the present invention, (c) is a population distribution fork diagram generated by using the Rand pseudo-random number sequence in the original sand cat swarm algorithm proposed in the present invention, and (d) is a population distribution histogram generated by using the Rand pseudo-random number sequence in the original sand cat swarm algorithm proposed in the present invention; Figure 5It is a convergence curve diagram of the Improved Sand Cat Swarm Optimization (ISCSO) and the comparison algorithm in the Sphere function of the PID control method for the rotation speed of the tread calender based on the Improved Sand Cat Swarm Optimization proposed by the present invention; Figure 6 It is the convergence curve diagram of ISCSO and the comparison algorithm in Schwefel's Problem 2.22 function of the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed by the present invention; Figure 7 It is a convergence curve diagram of ISCSO and the comparison algorithm in the Generalized Penalized 1 function of the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed by the present invention; Figure 8 It is a convergence curve diagram of ISCSO and the comparison algorithm in the Generalized Penalized 2 function of the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed by the present invention; Fig. 9 This is a response comparison diagram of optimizing the calender speed PID by comparing the ISCSO algorithm of the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed in the present invention with other algorithms.

[0047] Fig.10 This is an error comparison diagram of optimizing the calender speed PID by comparing the ISCSO algorithm of the tread calender speed PID control method based on the improved sand cat swarm algorithm proposed in the present invention with other algorithms. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0049] Embodiment 1 like Figure 1 As shown, this embodiment provides a tread calender speed PID control method, which optimizes the parameters of the speed PID controller of the tread calender system by improving the sand cat group algorithm, so that the tread calender has a faster response speed and better stability, including the following steps: Step 1: If Figure 2As shown, a simulation model of the tread calender speed control system is established using MATLAB / SIMULINK. The MATLAB / SIMULINK module is used to establish a simulation model of the speed control system of the tread calender, including: a DC brushless motor unit for simulating the DC brushless motor; a speed error detection unit for calculating the difference between the target speed and the actual speed of the calender; a current error detection unit for calculating the difference between the given current value and the actual current value of the calender motor; an improved sand cat group algorithm unit for optimizing and adjusting the three parameters of the motor speed PID controller, and transmitting the optimal PID parameters after the algorithm iteration is completed to the speed PID control unit; an actual speed detection unit for detecting the angular velocity of the motor rotation; a current detection unit for detecting the actual current value of the DC brushless motor; a tread calender speed PID controller unit for receiving the difference between the target speed and the actual speed of the calender transmitted by the error unit, and outputting the control amount after the error value is adjusted by the PID controller as the given current and transmitting it to the tread calender current PID controller; a tread calender current PID control unit for receiving the current error transmitted by the error unit and outputting a value as the duty cycle to control the PWM control unit; and a PWM unit for outputting a PWM signal to control the DC brushless motor.

[0050] like Figure 3 As shown, the tread calender speed PID controller includes: expected speed , used to set the desired motor speed; error calculation , used to calculate the actual speed With expected speed The PID controller unit receives the speed error between the desired speed unit and the actual speed unit from the error calculation unit, receives the optimal control parameters calculated by the improved sand cat swarm algorithm, and outputs the optimal control quantity. to the controlled object; the improved sand cat swarm optimization algorithm unit is used to find the optimal parameters according to the evaluation function index; the evaluation function is used to give the fitness function of the improved sand cat swarm optimization algorithm; the controlled object unit receives the control quantity and simulates the operation of the motor to finally obtain the actual speed .

[0051] Step 2: Select the standard Sand Cat Swarm Optimization (SCSO) algorithm. In order to avoid the problem of insufficient initial solution accuracy, slow convergence speed, and easy to fall into local optimality of the standard SCSO, the Sand Cat Swarm Optimization algorithm is improved; Step 3: Propose an improved Sand Cat Swarm Optimization (ISCSO); the improved strategies include initializing the population based on Logistic-Tent chaotic mapping and dynamic reverse learning mechanism; introducing a hyperbolic trigonometric inertia weighted strategy to improve the search behavior formula of the sand cat in the search phase; adding a vertical and horizontal cross strategy based on the development stagnation judgment mechanism; It is divided into the following three parts: (1) In the initialization stage of the algorithm, the population is initialized based on the Logistic-Tent chaotic mapping and dynamic reverse learning mechanism to obtain a high-quality initialization population. The Logistic-Tent chaotic mapping formula is:

[0052] in, =0.3, The first Sand cat individuals, The first population generated by the Logistic-Tent chaotic map A sand cat individual. , is the number of individuals in the population. is a random number between 0 and 1, Represents the remainder operation.

[0053] like Figure 4 As shown, Figure 4 (a) and (b) are the population distribution bifurcation diagram and histogram generated by Logistic-Tent chaotic mapping. Figure 4 (c) and (d) are the population distribution fork diagram and histogram generated by the Rand pseudo-random number sequence in the original sand cat swarm algorithm. It can be seen that the population distribution generated by the Logistic-tent fusion chaotic sequence is more uniform, the stacking phenomenon of population individuals is reduced, and the population diversity is improved.

[0054] The formula for dynamic reverse learning is:

[0055] in, represents the population generated by the dynamic reverse learning strategy; represents the initialization population generated by Logistic-tent chaotic mapping; and is a random number distributed between [0, 1]; is the upper bound of the sand cat population location; is the lower bound of the sand cat population location.

[0056] The method to obtain the initial population matrix of the improved sand cat swarm algorithm is as follows:

[0057]

[0058] in, Indicates that it contains and A new population of all individuals. for The fitness value of the individual Chinese sand cat. Calculate the new population The fitness values ​​of all sand cats in the game are calculated to make them fully compete with each other and select the one with the best fitness. Sand cat individuals as the final initial population This method can provide the population with a high-quality initial solution, so that the algorithm can approach the optimal solution faster, improving the convergence speed of the algorithm and the accuracy of the solution.

[0059] (2) In the search phase of the sand cat, the hyperbolic trigonometric inertia weighting strategy is introduced, which enables the algorithm to conduct a large-scale search in the early stage of exploration and narrow the search range in the later stage of exploration, while accelerating the convergence speed, thereby improving the search ability of the algorithm. The improved sand cat position update formula in the search phase is:

[0060]

[0061]

[0062] in, Represents the updated position of the sand cat; is the global optimal position in the current iteration; is the position of the sand cat in the current iteration; represents the sensitivity range of the sand cat; , , is a random number between [0, 1]; To control the coefficient of exploration accuracy of this strategy, it is taken as 0.3; is a monotonically decreasing function; Represents the current iteration number, Represents the maximum number of iterations.

[0063] (3) Introduce a vertical and horizontal cross strategy based on the development stagnation judgment mechanism to prevent the algorithm from falling into local optimality. The formula for the development stagnation judgment mechanism is:

[0064]

[0065] in, , is the number of consecutive iterations of triggering the judgment mechanism; is an infinitesimal quantity; For the The individual with the best fitness in the population in the iteration; For the The fitness value of the individual with the best fitness in the population in the iteration; To develop stagnation determination factors; is the maximum number of iterations; It is a positive integer used to avoid triggering the judgment mechanism at the end of the algorithm and affecting the local exploration ability of the algorithm.

[0066] When the algorithm falls into a state of development stagnation, the algorithm executes the vertical and horizontal crossover strategy, which is divided into horizontal crossover and vertical crossover. The horizontal crossover refers to the arithmetic crossover between two different individuals in the population in all dimensions of the solution space. First, all individuals in the generated population are randomly paired in pairs, and the two successfully paired parent individuals are horizontally crossed to generate offspring individuals. The formula is:

[0067]

[0068] in, and Indicates the first dimension, , Represents the dimension of the problem to be solved; and Represents its parent individual and In the The offspring individuals produced by the horizontal crossover strategy on the dimension; and is a random number distributed between (0, 1); and is a random number distributed between [-1, 1].

[0069] The vertical crossover strategy refers to the arithmetic crossover operation performed by all individuals in the population on two different dimensions. Each individual in the population only optimizes the dimension that is trapped in the local optimum when performing vertical crossover, and the other dimensions remain unchanged, so that the dimension trapped in the local optimum has the ability to jump out of the local optimum and does not affect other dimensions. The mathematical formula of the vertical crossover strategy is:

[0070] in, and Indicates the vertical cross strategy and Two dimensions of parent individuals; For the parent By generating offspring individuals through vertical crossover strategies in two different dimensions, is a random number distributed between (0, 1).

[0071] Step 4: Use ISCSO and Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Sand Cat Swarm Optimization (SCSO), and Rime Optimization (RIME) to test on four benchmark functions to verify the effectiveness of the improved algorithm. The four benchmark functions are: Sphere, Schwefel's Problem 2.22, Generalized Penalized 1, and Generalized Penalized 2. The four functions are shown in Table 1 (3.31E-99 in the table is represented by 3.31×10 -99 ). The parameters of the ISCSO of the present invention and other comparison algorithms are set as follows: the population size is 50, the number of iterations is The value of the parameter is 500, and the other parameters use the default values.

[0072] Table 1 Parameters related to the four functions

[0073] Each algorithm was run 30 times to obtain the optimal value, average value and standard deviation, and the results are shown in Table 2. In all test functions, the statistical indicators of the ISCSO algorithm are the best, proving that the optimization ability of the ISCSO algorithm in functions F1-F4 is significantly higher than that of the comparison algorithm.

[0074] The size of the fitness is usually used to evaluate the quality of the algorithm solution. A solution with a smaller fitness value is usually better than a solution with a larger fitness value. In addition, the convergence speed of the algorithm is also very important. Figure 5 , Figure 6 They are the convergence curves of ISCSO and the comparison algorithm on function F1 and function F2 respectively. Figure 5 , Figure 6 As shown in the figure, ISCSO has the fastest convergence speed in single-peak functions such as function F1 and function F2, and will not fall into the local optimum, and finally obtains the theoretical optimal value of the function.

[0075] Table 2 The optimal value, average value and standard deviation of each algorithm after running 30 times

[0076] Figure 7 , Figure 8 These are the convergence curves of ISCSO and the comparison algorithm on function F3 and function F4 respectively. Figure 7 , Figure 8 As shown in the figure, ISCSO has achieved the optimal fitness value in multi-peak functions such as F3 and F4, and due to the existence of the population initialized based on Logistic-Tent chaotic mapping and dynamic reverse learning mechanism in the initialization stage of the algorithm, the ISCSO algorithm has achieved the optimal fitness value in the early stage, and when it falls into the local optimum in the middle stage, due to the existence of the hyperbolic trigonometric inertia weighted strategy and the vertical and horizontal cross strategy based on the development stagnation judgment mechanism, the algorithm jumps out of the local optimum in time and achieves the best fitness value among all compared algorithms.

[0077] Step 5: Use the ISCSO algorithm to compare the particle swarm optimization algorithm (PSO), gray wolf optimization algorithm (GWO), sand cat swarm optimization algorithm (SCSO), and frost ice optimization algorithm (RIME) to optimize the PID parameters of the simulation model of the tread calender speed control system, and transmit them to the speed PID controller to compare and verify the superiority of the ISCSO algorithm in the PID parameter setting of the tread calender speed control system. The algorithm parameters are set as follows: the population size is 20, the number of iterations is The value of the parameter is 100, and the other parameters use the default values.

[0078] The specific steps of improving the sand cat swarm algorithm to optimize the PID controller are: Step 1: Initialize the sand cat population and set the population size , Dimension , maximum number of iterations . Determine the three parameters of the PID controller , , The range is [LB, UB].

[0079] Step 2: Generate the initial population based on Logistic-Tent chaotic mapping and dynamic reverse learning , and calculate the initial fitness of the sand cat group individuals according to the ITAE evaluation index, and select the individuals with the best fitness Update to the current optimal individual; the ITAE evaluation index formula is:

[0080] in, is the feedback deviation between the actual speed and the expected speed, For time.

[0081] Step 3: Initialize parameters , , Behavior determination factor And random angles .

[0082]

[0083]

[0084] in, is 2, is the current iteration number, is the maximum number of iterations, is the sensitivity parameter of the sand cat; represents the sensitivity range of the sand cat, is a random number between [0, 1].

[0085] Step 4: Determine factors based on behavior The size of determines whether the algorithm searches for prey or attacks prey. When , the algorithm performs a search, and the position update formula is:

[0086]

[0087]

[0088] in, Represents the updated position of the sand cat; is the global optimal position in the current iteration; is the position of the sand cat in the current iteration; represents the sensitivity range of the sand cat; , , is a random number between [0, 1]; To control the coefficient of exploration accuracy of this strategy, it is taken as 0.3; is a monotonically decreasing function; Given by Step3; Represents the current iteration number; Represents the maximum number of iterations.

[0089] Step 5: When When , the algorithm enters the attack prey stage, and the position update formula is:

[0090]

[0091] in, A random angle between 0° and 360°; is the distance between the sand cat and its prey; the other symbols are the same as Step 4.

[0092] Step 6: If the judgment formula is satisfied, the algorithm enters a development stagnation state. The judgment formula is:

[0093]

[0094] in, , is the number of consecutive iterations of triggering the judgment mechanism; is an infinitesimal quantity; For the The individual with the best fitness in the population in the iteration; For the The fitness value of the individual with the best fitness in the population in the iteration; To develop stagnation determination factors; is the maximum number of iterations; It is a positive integer used to avoid triggering the judgment mechanism at the end of the algorithm and affecting the local exploration ability of the algorithm.

[0095] Step 7: If the algorithm enters a development stagnation state, the algorithm executes horizontal crossover and vertical crossover strategies respectively. The horizontal crossover formula is:

[0096]

[0097] in, and Indicates the first dimension, , Represents the dimension of the problem to be solved; and Represents its parent individual and In the The offspring individuals produced by the horizontal crossover strategy on the dimension; and is a random number distributed between (0, 1); and is a random number distributed between [-1, 1].

[0098] The vertical cross formula is:

[0099] in, and Indicates the vertical cross strategy and Two dimensions of parent individuals; For the parent By generating offspring individuals through vertical crossover strategies in two different dimensions, is a random number distributed between (0, 1).

[0100] If the algorithm has not entered a development stagnation state, proceed to the next step: Step 8: Determine whether the current number of iterations has reached If yes, output the optimal solution to the speed PID controller, otherwise return to Step 3 to continue; Step 9: The optimal solution obtained by the improved sand cat swarm algorithm is passed into the simulation model of the tread calender speed control system to obtain the speed output result of the model.

[0101] Output the optimal value after iteration , , Parameters are input into the established simulation model of the tread calender speed control system.

[0102] When measuring the response curve of a system, we usually focus on the overshoot, rise time, and adjustment time. Overshoot is defined as the maximum degree to which the adjusted parameter dynamically deviates from the given value; rise time is defined as the time it takes for the system to reach 90% of the final value for the first time; adjustment time is defined as the time it takes for the system to enter the 5% error band. Combination Fig. 9 It can be seen that the adjustment time and rise time of the tread calender speed PID control system based on the improved sand cat group algorithm are both the smallest. The adjustment time of the ISCSO response curve is 6.63s, which is better than 8.71s of SCSO and 12.53s of GWO. Since the dynamic process of RIME and PSO is very slow, they did not enter the 5% error band until the end of the simulation, so the adjustment time is much higher than ISCSO. The rise time of ISCSO is 2.67s, which is better than 2.85s of GWO and 3.98s of SCSO. The rise time of RIME is 36.12s. Since the dynamic process of PSO is very slow, it did not reach 90% of the final value at the end of the simulation, so it is much higher than ISCSO. It can be seen that the response curve of the tread calender speed PID control system adjusted by ISCSO has good rapidity and accuracy. The overshoot of ISCSO is 4.5%, which is lower than the overshoot of GWO 42.5% and the overshoot of SCSO 7.3%. Among them, RIME and PSO did not produce overshoot in the end because of their very slow dynamic response.

[0103] Combination Fig.10 It can be seen that the response curve of the tread calender speed PID control system adjusted by ISCSO always has the smallest error in the response process, which is better than other comparison algorithms.

[0104] In summary, the response curve of the tread calender speed PID control method based on the improved sand cat swarm algorithm has a lower overshoot, better robustness, accuracy and speed, and has a high application value.

[0105] Embodiment 2 This embodiment provides a tread calender speed PID control system, comprising: A tread calender speed PID control system, comprising: A data acquisition module is configured to: acquire a plurality of parameters to be optimized of a tread calender speed PID controller; The improved sand cat algorithm module is configured as follows: based on Logistic-Tent chaotic mapping and dynamic reverse learning, the initial solution space of multiple parameters to be optimized is processed to obtain the initial population matrix of the improved sand cat swarm algorithm; the initial fitness of the sand cat swarm individuals is calculated according to the evaluation function, and the global optimal position of the sand cat individual with the best fitness is updated to the current optimal position; the sand cat swarm algorithm is executed to search for the parameters to be optimized by simulating the search behavior or attack behavior of the sand cat; during the execution of the sand cat swarm algorithm, if it is determined that the algorithm has entered a development stagnation state, the horizontal crossover strategy and the vertical crossover strategy are executed to make the algorithm get rid of the development stagnation state.

[0106] The output control module is configured to: when the set termination condition is met, output the solution corresponding to the current optimal position as the target value of the parameter to be optimized to control the brushless DC motor.

[0107] The improved sand cat algorithm module is further configured as follows: the horizontal cross strategy is expressed by the following formula:

[0108]

[0109] in, and Indicates the first dimension, , Indicates the dimension of the problem to be solved; and Represents its parent individual and In the The offspring individuals produced by the horizontal crossover strategy on the dimension; and is a random number distributed between (0, 1); and is a random number distributed between [-1, 1].

[0110] The improved sand cat algorithm module is further configured as follows: the longitudinal cross strategy is expressed by the following formula:

[0111] in, and Indicates the vertical cross strategy and Two dimensions of parent individuals; For the parent By generating offspring individuals through vertical crossover strategies in two different dimensions, is a random number distributed between (0, 1).

[0112] The improved sand cat algorithm module is also configured to: determine the development stagnation state using the following formula:

[0113]

[0114] in, , is the number of consecutive iterations of triggering the judgment mechanism; is an infinitesimal quantity; For the The individual with the best fitness in the population in the iteration; For the The fitness value of the individual with the best fitness in the population in the iteration; To develop stagnation determination factors; is the maximum number of iterations; It is a positive integer used to avoid triggering the judgment mechanism at the end of the algorithm and affecting the local exploration ability of the algorithm.

[0115] The improved sand cat algorithm module is also configured as follows: the evaluation function adopts the following formula:

[0116] in, represents the ITAE evaluation index, is the feedback deviation between the actual speed and the expected speed, For time.

[0117] The data acquisition module is further configured as follows: the multiple parameters to be optimized include a proportional coefficient, an integral coefficient and a differential coefficient of a PID controller of a rotation speed of a tread calender.

[0118] Improved Sand Cat algorithm module, also configured as: algorithm through the development of decision factors To determine whether the sand cat is searching or attacking.

[0119]

[0120]

[0121]

[0122] in, is the sand cat hearing parameter, take 2; is the current iteration number, is the maximum number of iterations; is the sensitivity parameter of the sand cat; represents the sensitivity range of the sand cat; is a random number between [0, 1].

[0123] The improved sand cat algorithm module is also configured as follows: When , the algorithm enters the search phase. In the search phase, each sand cat updates its own position through the hyperbolic trigonometric inertia weighted search strategy according to the current optimal position, the current position of itself and its corresponding circle coefficient and sensitivity range; When , the algorithm enters the attack phase. In the attack phase, each sand cat updates its own position according to the current optimal position, current own position, sensitivity range, moving distance and moving direction angle.

[0124] The improved sand cat algorithm module is also configured as follows: The position update formula of the sand cat under the hyperbolic trigonometric inertia weighted strategy is:

[0125]

[0126]

[0127] in, Represents the updated position of the sand cat; is the global optimal position in the current iteration; is the position of the sand cat in the current iteration; represents the sensitivity range of the sand cat; , , is a random number between [0, 1]; To control the coefficient of exploration accuracy of this strategy, it is taken as 0.3; is a monotonically decreasing function; Represents the current iteration number, Represents the maximum number of iterations. The improved sand cat algorithm module is also configured as follows: The position update formula of the sand cat in the attack phase is:

[0128]

[0129] in, is a random angle between 0° and 360°, where Represents the updated position of the sand cat, is the global optimal position in the current iteration, is the position of the sand cat in the current iteration, Represents the distance between the sand cat and its prey.

[0130] The improved sand cat algorithm module is also configured as follows: in the initialization stage, the algorithm uses Logistic-Tent chaotic mapping and dynamic reverse learning strategy to process the initial solution space of multiple parameters to be optimized, and obtains the initial population matrix of the improved sand cat swarm algorithm.

[0131] The improved sand cat algorithm module is also configured as follows: Logistic-Tent chaotic mapping is expressed by the following formula:

[0132] in, =0.3, The first Sand cat individuals, The first population generated by the Logistic-Tent chaotic map A sand cat individual. , is the number of individuals in the population. is a random number between 0 and 1, Represents the remainder operation.

[0133] The improved sand cat algorithm module is also configured as follows: The dynamic reverse learning strategy is expressed by the following formula:

[0134] in, represents the population generated by the dynamic reverse learning strategy; represents the initialization population generated by Logistic-tent chaotic mapping; and is a random number distributed between [0, 1]; is the upper bound of the sand cat population location; is the lower bound of the sand cat population location.

[0135] The improved sand cat algorithm module is further configured as follows: The method for obtaining the initial population matrix of the improved sand cat swarm algorithm is as follows:

[0136]

[0137] in, Indicates that it contains and A new population of all individuals. for The fitness value of the individual Chinese sand cat. Calculate the new population The fitness values ​​of all sand cats in the game are calculated to make them fully compete with each other and select the one with the best fitness. Sand cat individuals as the final initial population .

[0138] Embodiment 3 This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps in the PID control method for the rotation speed of a tread calender as described in the first embodiment are implemented.

[0139] Embodiment 4 This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the tread calender speed PID control method as described in the first embodiment are implemented.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A PID control method for the rotation speed of a tread calender, characterized in that: include: Obtain multiple parameters to be optimized of the tread calender speed PID controller; Based on Logistic-Tent chaotic mapping and dynamic reverse learning, the initial solution space of multiple parameters to be optimized is processed to obtain the initial population matrix of the improved sand cat swarm algorithm; the initial fitness of the sand cat swarm individuals is calculated according to the evaluation function, and the global optimal position of the sand cat individual with the best fitness is updated to the current optimal position; the sand cat swarm algorithm is executed to search for the parameters to be optimized by simulating the search behavior or attack behavior of the sand cat; during the execution of the sand cat swarm algorithm, if it is determined that the algorithm has entered a development stagnation state, the horizontal crossover strategy and the vertical crossover strategy are executed to make the algorithm get rid of the development stagnation state; When the set termination condition is met, the solution corresponding to the current optimal position is output as the target value of the parameter to be optimized to control the brushless DC motor.

2. The tread calender speed PID control method according to claim 1, characterized in that: The horizontal crossover strategy is expressed by the following formula: in, and Indicates the first dimension, , Represents the dimension of the problem to be solved; and Represents its parent individual and In the The offspring individuals produced by the horizontal crossover strategy on the dimension; and is a random number distributed between (0, 1); and is a random number distributed between [-1, 1]; The vertical crossover strategy is expressed by the following formula: in, and Indicates the vertical cross strategy and Two dimensions of parent individuals; For the parent By generating offspring individuals through vertical crossover strategies in two different dimensions, is a random number distributed between (0, 1).

3. The tread calender speed PID control method according to claim 1, characterized in that: The following formula is used to determine whether development has entered a stagnant state: in, , is the number of consecutive iterations of the triggering decision mechanism; is an infinitesimal quantity; For the The individual with the best fitness in the population in the iteration; For the The fitness value of the individual with the best fitness in the population in the iteration; To develop stagnation determination factors; is the maximum number of iterations; Is a positive integer.

4. The tread calender speed PID control method according to claim 1, characterized in that: The evaluation function adopts the following formula: in, represents the ITAE evaluation index, is the feedback deviation between the actual speed and the expected speed, For time.

5. The PID control method for the rotation speed of a tread calender according to claim 1, characterized in that: The multiple parameters to be optimized include a proportional coefficient, an integral coefficient and a differential coefficient of a PID controller for a rotation speed of a tread calender.

6. The PID control method for the rotation speed of a tread calender according to claim 1, characterized in that: The Sand Cat Swarm Algorithm develops a decision factor To determine whether the sand cat is searching or attacking; in, is the sand cat hearing parameter, take 2; is the current iteration number, is the maximum number of iterations; is the sensitivity parameter of the sand cat; represents the sensitivity range of the sand cat; is a random number between [0, 1]; when When , the algorithm enters the search phase. In the search phase, each sand cat updates its own position through the hyperbolic trigonometric inertia weighted strategy according to the current optimal position, the current position of itself and its corresponding circle coefficient and sensitivity range; when When , the algorithm enters the attack phase. In the attack phase, each sand cat updates its own position according to the current optimal position, current own position, sensitivity range, moving distance and moving direction angle; The hyperbolic trigonometric inertia weighting strategy is expressed by the following formula: in, Represents the updated position of the sand cat; is the global optimal position in the current iteration; is the position of the sand cat in the current iteration; represents the sensitivity range of the sand cat; , , is a random number between [0, 1]; To control the coefficient of exploration accuracy of this strategy, it is taken as 0.3; is a monotonically decreasing function; Represents the current iteration number, Represents the maximum number of iterations; The position update formula of the sand cat in the attack phase is: in, is a random angle between 0° and 360°, where Represents the updated position of the sand cat, is the global optimal position in the current iteration, is the position of the sand cat in the current iteration, Represents the distance between the sand cat and its prey.

7. The PID control method for the rotation speed of a tread calender according to claim 1, characterized in that: In the initialization stage, the sand cat swarm algorithm uses Logistic-Tent chaotic mapping and dynamic reverse learning strategy to process the initial solution space of multiple parameters to be optimized, and obtains the initial population matrix of the improved sand cat swarm algorithm; The Logistic-Tent chaotic mapping is expressed by the following formula: in, =0.3, The first Individual sand cats, The first population generated by the Logistic-Tent chaotic map sand cat individuals; , is the number of individuals in the population; is a random number between 0 and 1, Represents remainder operation; The dynamic reverse learning strategy is expressed by the following formula: in, represents the population generated by the dynamic reverse learning strategy; represents the initialization population generated by Logistic-tent chaotic mapping; and is a random number distributed between [0, 1]; is the upper bound of the sand cat population location; is the lower bound of the sand cat population location; The method to obtain the initial population matrix of the improved sand cat swarm algorithm is as follows: in, Indicates that it contains and The new population of all individuals, for The fitness value of the individual Chinese sand cat is used to calculate the new population The fitness values ​​of all sand cat individuals in the sand cat are adjusted to make them fully compete with each other and select the one with the best fitness. Sand cat individuals as the final initial population .

8. The tread calender speed PID control system is characterized by: include: A data acquisition module is configured to: acquire a plurality of parameters to be optimized of a tread calender speed PID controller; The improved sand cat algorithm module is configured as follows: based on Logistic-Tent chaotic mapping and dynamic reverse learning, the initial solution space of multiple parameters to be optimized is processed to obtain the initial population matrix of the improved sand cat swarm algorithm; the initial fitness of the sand cat swarm individuals is calculated according to the evaluation function, and the global optimal position of the sand cat individual with the best fitness is updated to the current optimal position; the sand cat swarm algorithm is executed to search for the parameters to be optimized by simulating the search behavior or attack behavior of the sand cat; during the execution of the sand cat swarm algorithm, if it is determined that the algorithm has entered a development stagnation state, the horizontal cross strategy and the vertical cross strategy are executed to make the algorithm get rid of the development stagnation state; The output control module is configured to: when the set termination condition is met, output the solution corresponding to the current optimal position as the target value of the parameter to be optimized to control the brushless DC motor.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the tread calender speed PID control method as described in any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the tread calender speed PID control method according to any one of claims 1 to 7 are implemented.

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