PID (Proportion Integration Differentiation) temperature control optimization method for cascade refrigerating unit

Abstract

The invention belongs to the field of temperature control optimization, and relates to a PID temperature control optimization method for a cascade refrigerating unit, and the method specifically comprises the steps: S1, building a PID temperature control model of the cascade refrigerating unit which comprises two refrigerating cycle stages connected in series; s2, setting initial parameters of the PID temperature controller, wherein the initial parameters comprise a proportionality coefficient, an integral coefficient and a differential coefficient; s3, based on the real-time refrigeration effect and the operation load of the cascade refrigeration unit, the temperature error of each refrigeration cycle stage is calculated, and the temperature errors are used for adjusting PID parameters; and S4, carrying out global optimization on the PID parameters of the high-temperature cold circulation stage by adopting an improved animation oat optimization algorithm, and determining the PID parameters of the high-temperature cold circulation stage suitable for the cascade refrigerating unit through global optimization so as to realize PID temperature control optimization of the cascade refrigerating unit. According to the method, the PID temperature control precision of the cascade refrigerating unit can be improved.

Description

Technical Field

[0001] The present invention belongs to the field of temperature control optimization, and particularly relates to a PID temperature control optimization method for cascade refrigeration units. Background Art

[0002] Cascade refrigeration technology is widely used in scenarios with extremely high requirements for temperature control accuracy and stability, such as ultra-low temperature refrigeration, biological medicine preservation, and liquefied gas production; a cascade refrigeration unit generally consists of two or more refrigeration cycle stages connected in series, and a typical structure includes two subsystems, a low-temperature stage and a high-temperature stage, which achieve energy transfer through a heat exchanger. Due to the dynamic coupling and mutual influence of heat loads between multiple systems, the entire unit exhibits complex characteristics such as nonlinearity, strong coupling, and dynamic changes during operation, which pose high requirements for its temperature control system in terms of control accuracy and response speed.

[0003] To improve control performance, researchers have tried to introduce intelligent optimization algorithms to tune PID parameters, such as particle swarm optimization, genetic algorithms, ant colony algorithms, etc. These methods have improved control accuracy to a certain extent, but are prone to falling into local optima in high-dimensional parameter spaces. Especially when facing a cascade refrigeration system with highly coupled characteristics, traditional optimization methods are difficult to fully utilize their global search capabilities, resulting in the temperature control performance being difficult to reach the optimal level.

[0004] The Animated Oat Optimization algorithm simulates the natural propagation behavior of seeds and constructs an optimization strategy for global search and local development. The global search strategy model has a random wind diffusion mechanism, and the local development strategy simulates barrier-free rolling and ejection mechanisms. The existing ejection mechanism is based on a simplified parabolic motion model, and the energy storage and release are a one-time simple process, which does not truly reflect the multi-stage energy accumulation and complex release mechanism of oat seeds after encountering obstacles. When the Animated Oat Optimization algorithm is used for PID temperature control optimization of cascade refrigeration units, it is prone to low temperature control optimization accuracy. In reality, after an oat seed encounters an obstacle, its main awn does not immediately complete ejection, but undergoes multiple subtle non-linear energy accumulations and step-by-step release processes. This progressive and non-linear energy storage-release mode enables oat seeds to more effectively break through obstacles, achieve greater displacement, and more effective dispersion; among them, the main awn is a slender appendage structure on the surface of plant seeds such as oat seeds, usually in the form of slender hairs or spines, with a certain rigidity; secondly, the exploration stage of the Animated Oat Optimization algorithm mainly relies on random position perturbations to achieve global exploration, lacking directional control and comprehensive consideration of the global potential energy field, which is prone to repeated exploration and slow convergence speed, resulting in slow PID temperature control adjustment of cascade refrigeration units and poor use effects. Summary of the Invention

[0005] Aiming at the problems of difficult parameter tuning and insufficient regulation accuracy of traditional PID control in cascade multi-stage systems, a parameter optimization mechanism based on an improved animated oat optimization algorithm is designed by combining the structural coupling characteristics of the system and the temperature control requirements. This method realizes the global search and dynamic adjustment of the low-temperature stage PID parameters by constructing independent PID control models for the high and low temperature stages, setting initial control parameters, and introducing strategies for simulating the dynamic potential energy field of oat seeds and the critical transition ejection strategy of the structure. At the same time, the local optimization accuracy is enhanced through the local structure guiding vector, effectively improving the temperature control response speed and steady-state control performance of the whole machine. This method combines globality and self-adaptability, significantly improving the temperature control efficiency and control stability of the cascade refrigeration unit.

[0006] A PID temperature control optimization method for a cascade refrigeration unit, and the specific method is as follows: S1. Establish a PID temperature control model for the cascade refrigeration unit. The cascade refrigeration unit includes two series-connected refrigeration cycle stages, and each cycle stage has an independent PID temperature controller. S2. Set the initial parameters of the PID temperature controller, including the proportional coefficient, integral coefficient, and differential coefficient. S3. Based on the real-time refrigeration effect of the cascade refrigeration unit, calculate the temperature error of each refrigeration cycle stage. The temperature error constructs a fitness function for adjusting the PID parameters of the low-temperature refrigeration cycle stage. S4. Use the improved animated oat optimization algorithm to globally optimize the PID parameters of the low-temperature refrigeration cycle stage. Through global optimization, determine the PID parameters of the low-temperature refrigeration cycle stage applicable to the cascade refrigeration unit, and realize the PID temperature control optimization of the cascade refrigeration unit.

[0007] Specifically, the cascade refrigeration unit includes two series-connected refrigeration cycle stages, which are composed of a low-temperature stage and a high-temperature stage respectively, and gradually achieve lower temperatures. Among them, the high-temperature stage is responsible for the pre-cooling in the first stage, and the low-temperature stage further cools the gas discharged from the high-temperature stage to obtain a lower temperature. The evaporator of the high-temperature stage cycle acts as the condenser of the low-temperature stage. Through this intermediate condenser, the heat absorbed by the low-temperature stage is transferred to the high-temperature stage and released, thus realizing a cycle feedback. Among them, the intermediate condenser is the heat exchange link connecting the two cycles. Therefore, the high-temperature stage and the low-temperature stage temperature control can be realized by a cascade PID controller. The high-temperature stage undertakes to raise the heat to the level that can be dissipated by the environment, while the low-temperature stage directly undertakes the deep cooling of the target space to achieve the target low-temperature environment. Therefore, the low-temperature stage directly controls the ultimately required ultra-low temperature. The present invention optimizes the parameters of the PID controller of the low-temperature refrigeration cycle stage by proposing a new method. By optimizing the PID, the temperature at the outlet of the low-temperature evaporator is controlled, and the output of the high-temperature stage compressor is adjusted to maintain the target temperature. The high-temperature stage controls the temperature of the intermediate condensation evaporator to ensure a suitable condensation environment for the low-temperature stage.

[0008] Specifically, in the PID temperature control model of the cascade refrigeration unit, a cascade control structure is adopted. The PID controller uses the position-type and incremental PID algorithms. A main controller with the final low temperature as the control target is set, that is, the low-temperature stage PID controller, and its output is used as the set value of the secondary controller (high-temperature stage PID controller). Specifically, the main controller outputs a target intermediate temperature according to the temperature deviation of the low-temperature stage evaporator, and the secondary controller drives the high-temperature stage compressor to achieve this target intermediate temperature. Among them, the proportional coefficient, integral coefficient, and differential coefficient of the secondary controller are manually set and fixed according to experience and the working characteristics of the high-temperature area; the proportional coefficient, integral coefficient, and differential coefficient of the main controller are adaptively adjusted through global optimization.

[0009] Specifically, the initial parameter settings of the PID temperature controller are based on the working characteristics of multiple refrigeration cycle stages of the cascade refrigeration unit. The working characteristics of the two refrigeration cycle stages of the cascade refrigeration unit are different. The high-temperature stage refrigeration cycle stage is used to adjust the intermediate condensation temperature and drive the compressor to operate. Its dynamic response is fast, the lag is small, but the inertia is large. Its interference mainly comes from the change of the target intermediate temperature output by the low-temperature stage. According to its working characteristics, the control parameters of the PID controller of the high-temperature stage refrigeration cycle stage of the present invention are set empirically. The proportional coefficient can be set relatively large to improve the response speed; the integral coefficient should be smaller than the differential coefficient to ensure that the steady-state error can be eliminated; the differential coefficient can not be set to avoid frequent control of the compressor; the low-temperature stage refrigeration cycle stage is used to keep the temperature at the outlet of the low-temperature evaporator stable and respond to small load changes; however, the response speed is slow, the lag time is large, the load disturbance is significant, and it is relatively sensitive to the fluctuation of the intermediate condensation temperature from the high-temperature stage. However, the present invention uses an improved animated oatmeal optimization algorithm to optimize it, and it is suitable to adopt a lower initial value.

[0010] Specifically, for the global optimization of the PID parameters of the low-temperature cold cycle stage, first select the performance index as the fitness function according to the control requirements, and then use the improved animated oatmeal optimization algorithm to iteratively adjust the Kp, Ki, and Kd of the PID of the low-temperature cold cycle stage. Evaluate the fitness of each group of parameters on the simulation and experimental models, and then tend to the optimal parameter values, and input the optimal parameter values into the PID controller of the low-temperature cold cycle stage.

[0011] Specifically, the actual outlet temperature of the low-temperature stage evaporator and the actual outlet temperature of the high-temperature stage condensing evaporator are respectively collected as the input variables of the main controller and the secondary controller. The difference between the set target low temperature and the actual temperature is calculated to obtain the error term of the main controller. According to the error term of the main controller, the target temperature value of the intermediate heat exchanger is output through the optimized low-temperature stage PID controller as the set value of the secondary controller. The set intermediate temperature value output by the main controller is compared with the current actual intermediate condensation temperature to obtain the error term of the secondary controller. The high-temperature stage secondary controller uses the error term of the secondary controller for incremental PID regulation and outputs the control signal of the high-temperature stage compressor. The control signal of the high-temperature stage compressor acts on the high-temperature stage compressor, and the refrigeration capacity of the high-temperature stage compressor is driven by the control signal u(t), thereby adjusting the temperature of the intermediate condenser, affecting the low-temperature stage condensation pressure ratio and efficiency, and finally making the outlet temperature of the low-temperature stage evaporator approach the target value, forming a cascade double closed-loop adaptive control model.

[0012] Specifically, in the global search stage of the animated oat optimization algorithm, global exploration mainly relies on random position perturbation, lacking directional control and comprehensive consideration of the global potential energy field, which easily causes problems of repeated exploration and slow convergence speed. The strategy of the present invention proposes a strategy for simulating the dynamic potential energy field of oat seeds, regarding the oat seed population as charged particles distributed in a multi-dimensional space. Each agent individual forms a corresponding potential energy charge according to the current fitness value, and interacts with each other to form a potential energy field that changes dynamically with iteration. The agent individual updates its position according to the gradient of this potential energy field to achieve more efficient and non-intuitive global exploration.

[0013] Specifically, the method for simulating the dynamic potential energy field of oat seeds is as follows: S101. Calculate the potential energy charge of the i-th agent individual It is defined as: ; Where and are the maximum and minimum values of the potential energy charge of the agent individual, is the maximum fitness value of the population at the t-th iteration, is the minimum fitness value of the population at the t-th iteration, rand(0, 0.1) is a random number within 0 to 0.1; individuals with good fitness carry larger charges and are more likely to attract other agent individuals to approach. Agent individuals with poor fitness carry smaller charges and are easily attracted to approach the positions of agent individuals with small fitness; S102. Design the potential energy field intensity vector of the agent individual population, including: updating the potential energy field intensity vector at the t-th iteration according to the potential energy charge of the i-th agent individual as: ; where N is the population size, α is the minimum value, is the position of the i-th agent individual at the t-th iteration, is the position of the j-th agent individual at the t-th iteration; through the potential field intensity, the agent individual position can sense the overall potential energy gradient formed by the positions and fitnesses of other individuals, and thus more efficiently determine the moving direction; S103. Determine the new position of the i-th agent individual through the potential energy gradient and the adaptive step size. The mathematical model is: ; where is the position of the i-th agent individual at the (t + 1)-th iteration, and the step size is adaptively adjusted as: ; The step size is negatively correlated with the individual charge. The step size of individuals with high fitness is small for more detailed exploration, and the step size gradually increases with the number of iterations to control the exploration range; is the perturbation term at the t-th iteration, and the mathematical model is: ; where T is the maximum number of iterations, UB is the upper limit position value, LB is the lower limit position value, is a Dim-dimensional random number within -1 to 1.

[0014] Specifically, based on the existing ejection strategy based on a simplified parabolic motion model, energy storage and release are a one-time simple process, which leads to low temperature control optimization accuracy in the PID temperature control process for cascade refrigeration units. The present invention proposes a structural critical transition ejection strategy, which simulates the critical structural mutation caused by the accumulation of structural strain during the spread of oat seeds. When the structural geometric stress exceeds a certain irreversible threshold, the entire structure undergoes a transition to complete long-range ejection; this behavior does not depend on weight control or speed regulation, but is endogenously driven by the geometric shape and state transition mechanism, and the ejection amplitude is completely determined by the state mutation amplitude.

[0015] Specifically, the structural critical transition ejection strategy is specifically as follows: S201. Define the structural state vector of each agent individual at the t-th iteration, including: representing the current structural state vector by the difference between the current position of the agent individual and the position of the i-th agent individual at the (t - 1)-th iteration; further constructing an elastic deformation response through non-linear sine perturbation and defining the state energy modulus , and the mathematical model is: ; where Dim is the optimization parameter dimension for the PID temperature control of cascade refrigeration units; d is the d-th optimization parameter; is the position difference between the i-th agent individual in the d-th dimension at the t-th iteration and the previous iteration; is the position value of the i-th agent individual in the d-th dimension at the t-th iteration, is the upper limit position value of the d-th dimension; S202. Define the critical transition determination mechanism through the structure state vector and the state energy modulus as: ; where, is the critical transition value of the i-th agent individual at the t-th iteration; μ takes the value of 0.0001; When it is greater than 1, it enters the critical transition area, otherwise it continues to accumulate deformation; S203. After triggering the transition, generate a transition ejection displacement, update the position of the agent individual, otherwise maintain the structure inertia perturbation evolution, mathematical model: ; where, the transition ejection displacement is designed as: ; is the transition ejection displacement, is the element-level direction multiplication, is the local structure guiding drive vector, which drives the i-th agent individual to have a direction-preferred state transition in the local neighborhood.

[0016] Specifically, the specific method of the local structure guiding drive vector is: S301. In the t-th iteration, for the i-th agent individual, construct a local structure neighborhood from the current population, and the neighborhood consists of agent individuals that meet the following conditions: ; where, is the set neighborhood search radius, and f is the fitness function; S302. Based on the neighborhood construct the local structure gravitational direction vector of the i-th agent individual, and its calculation formula is as follows: ; where, is the position of the i-th agent individual at the t-th iteration, is the position of the j-th agent individual at the t-th iteration, is the fitness value of the position solution of the j-th agent individual at the t-th iteration, is the fitness value of the position solution of the i-th agent individual at the t-th iteration.

[0017] Specifically, use the improved animated oat optimization algorithm to globally optimize the PID parameters of the low-temperature cold cycle stage. The specific method is: S401. Map the i-th agent individual of the improved animated oat optimization algorithm to the PID parameters of the low-temperature cold cycle stage, represented as a three-dimensional vector , where the position of each agent individual is a three-dimensional vector, searching for the optimal solution in the three-dimensional continuous parameter space; among them, the first dimension mapping proportionality coefficient Kp, the second dimension mapping integral coefficient Ki, and the third dimension mapping derivative coefficient Kd of the agent individual position; S402. Initialize the maximum number of iterations, population size, and the optimization parameter dimension, maximum value, and minimum value of the agent individual position for the PID temperature control of the cascade refrigeration unit, and construct the initial position of the agent individual by using the random generation method; S403. Calculate the position fitness value of the i-th agent individual by using the fitness function, and the fitness value is obtained by calculating the temperature error of the control parameters mapped by the agent individual acting on the low-temperature cold cycle stage controller through the fitness function; S404. Use the S103 step in the dynamic potential field strategy to determine the new position of the i-th agent individual through the potential gradient and adaptive step size, and update the position of each agent individual; S405. Update the position of the agent individual by using the S203 step in the dynamic potential field strategy; limit the value of the finally updated agent individual position between the maximum and minimum values of the agent individual position; S406. Calculate the fitness value of the updated agent individual position, retain the position value of the agent individual with the smallest fitness value in the current iteration as the current optimal individual position, and judge whether the current iteration number is equal to the maximum iteration number. If so, resolve the current smallest agent individual position value into the optimal PID parameters of the low-temperature cold cycle stage; otherwise, return to execute S404 to continue the optimization process.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: The improved animated oat optimization algorithm of the present invention includes the following two key mechanisms: (1) Dynamic potential field optimization strategy: Simulate the non-linear diffusion process of oat seeds in a complex environment, regard each individual as a charged particle, construct a charge model according to the fitness, form a dynamic potential field that changes with iteration, and guide the individual to move efficiently in the gradient direction; (2) Structural critical transition ejection model: Introduce a structural transition mechanism triggered by geometric strain, simulate the long-range ejection behavior of oat seeds after reaching the critical state, and realize a non-linear jump search process; First, the dynamic potential field optimization strategy simulates the dynamic potential field strategy of oat seeds. When the potential energy is small (local development), the change amount is close to linear and gradually searches; when the potential energy is large (far from the optimum), the change amount tends to 1 to avoid explosive step sizes; Adopt an asymmetric natural attenuation mechanism to dynamically modulate the potential energy guiding direction transition amplitude. On the basis of avoiding traditional normalization scaling, take into account local fine-grained exploration and global extended search. In the temperature control optimization process of a cascade refrigeration unit, the temperature control of the low-temperature stage evaporator requires rapid response and extremely low steady-state deviation. Through the dynamic potential energy modulation mechanism of the present invention, the problems of early local optimum and late oscillatory fine-tuning in the optimization process can be effectively avoided; Second, the local structure guiding driving vector forms a structural local guiding area by constructing the local structure neighborhood of the individual and only selecting the proxy individuals that are closer to the current proxy individual and have better fitness as neighbors; Further, based on the relative distance and fitness difference of each proxy individual in the neighborhood, jointly construct a gravitational direction vector to form a local gravitational driving force field with directional preference and dominant convergence effect; This gravitational vector can be directly used as a jump control variable to guide the proxy individual to perform a directional state transition to a region with better structure in the local space of the population; Compared with the traditional strategy based on global perturbation or non-offset update, this method has the advantages of high perturbation accuracy, strong local guidance, good structural focusing, and no need for random perturbation. Applying the structural critical transition ejection model of the animated oat optimization algorithm to the PID temperature control of a cascade refrigeration unit can achieve more robust optimization.

[0019] In view of the multi-stage coupling characteristics of the cascade refrigeration unit, the present invention adopts a cascade PID control structure with the low-temperature stage as the main controller and the high-temperature stage as the secondary controller, and uses the incremental PID algorithm to coordinate the temperature control of each stage, effectively improving the temperature control accuracy and system response speed; by introducing an improved animated oat optimization algorithm, a mapping relationship between PID parameters and control performance is established, and considering the steady-state error, overshoot and adjustment time comprehensively, the global optimization of the PID parameters of the low-temperature cold cycle stage is realized, overcoming the problem that traditional optimization is prone to falling into local optima; further, the present invention proposes a dynamic potential field strategy and a structural critical transition ejection strategy, enabling the optimization process to have directional guidance and local jumping ability, greatly improving the optimization efficiency and convergence speed. Overall, the present invention takes into account the optimization effect and the complexity of the control system, and improves the temperature control stability, self-adaptability and engineering practicability of the cascade refrigeration unit. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a schematic diagram of PID temperature control optimization for a cascade refrigeration unit; Figure 2 is a schematic diagram of global optimization of PID parameters for the low-temperature cold cycle stage; Figure 3 is a schematic diagram of the PID temperature control process for a cascade refrigeration unit; Figure 4 is a fitness change diagram for measuring the quality of temperature control performance corresponding to each group of PID parameters; Figure 5 is a change diagram for optimizing the best PID parameters of the low-temperature cold cycle stage using the existing method; Figure 6 is a change diagram for optimizing the best PID parameters of the low-temperature cold cycle stage using the method of the present invention; Figure 7 is an effect diagram of PID temperature control optimization for a cascade refrigeration unit. DETAILED DESCRIPTION OF THE INVENTION

[0021] In order to make the objectives, technical solutions and beneficial effects of the present invention clearer, the present invention will be described in detail below in conjunction with specific embodiments; the present invention provides a PID temperature control optimization method for a cascade refrigeration unit, which is applicable to a cascade refrigeration unit including a series circulation structure of a high-temperature stage and a low-temperature stage; the method specifically includes as Figure 1 shown.

[0022] S1. Establish a PID temperature control model for the cascade refrigeration unit. The cascade refrigeration unit includes two series-connected refrigeration cycle stages, and each cycle stage has an independent PID temperature control system.

[0023] For further implementation, in the PID temperature control model of the cascade refrigeration unit, a cascade control structure is adopted. The high-temperature stage and low-temperature stage PID controllers use the incremental PID algorithm. The low-temperature stage PID controller serves as the outer loop to control the outlet temperature of the low-temperature stage; the high-temperature stage PID controller serves as the inner loop to control the operation of the high-temperature stage compressor to adjust the intermediate condensation temperature. The proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd of the high-temperature stage PID controller are fixed values, and the control coefficients of the low-temperature stage PID controller are variables. The cascade control system of the cascade refrigeration unit constructs a simulation model in Siumulink, including an incremental PID control module, an objective function, an input temperature difference calculation module, and a feedback module. Among them, the feedback module collects the actual outlet temperatures of the low-temperature stage and high-temperature stage. The objective function is established by the fitness function, which feeds back the difference between the actual outlet temperature of the low-temperature stage and the set temperature. The input temperature difference module calculates the difference between the set target low temperature and the actual outlet temperature and the difference between the set value of the intermediate temperature output by the low-temperature stage and the current actual intermediate condensation temperature.

[0024] S2. Set the initial parameters of the PID temperature controller, including the proportional coefficient, integral coefficient, and differential coefficient.

[0025] For further implementation, the proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd of the high-temperature stage PID controller are set to 0.001, 0.0001, and 0.0002 according to experience; the proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd of the low-temperature stage PID controller are all set to 0.1.

[0026] S3. Based on the real-time refrigeration effect of the cascade refrigeration unit, calculate the temperature error of each refrigeration cycle stage. The temperature error constructs a fitness function to adjust the PID parameters of the low-temperature refrigeration cycle stage.

[0027] For further implementation, set the target low temperature value , collect the actual outlet temperature of the low-temperature stage through the feedback module Calculate the main controller error term ; through the intermediate target temperature and the actual outlet temperature of the high-temperature stage , calculate the secondary controller error term , calculate the mean square error of the low-temperature stage and the high-temperature stage over a period of time as the fitness function f. The implementation mathematical model is: ; Among them, K is the total running time, set to 40 seconds, k is the current running time, and f is the fitness function; the position update of the proxy individual of the improved animated oat optimization algorithm is driven by the fitness function, that is, the optimization of the control coefficients of the low-temperature stage PID controller.

[0028] S4. Use the improved animated oat optimization algorithm to globally optimize the PID parameters of the low-temperature cold cycle stage, and determine the PID parameters of the low-temperature cold cycle stage suitable for the cascade refrigeration unit through global optimization, so as to achieve the PID temperature control optimization of the cascade refrigeration unit.

[0029] Furthermore, a strategy of simulating the dynamic potential energy field of oat seeds is proposed. The oat seed population is regarded as charged particles distributed in a multi-dimensional space. Each agent individual forms a corresponding potential energy charge according to the current fitness value, and the agent individuals interact with each other to form a potential energy field that changes dynamically with iteration; the agent individuals update their positions according to the gradient of this potential energy field to achieve more efficient and non-intuitive global exploration; set the maximum value of the potential energy charge of the agent individual to 1, the minimum value to 0.1, limit the minimum value α to 0.0001, and the maximum step size is 2; the specific implementation method is as follows: S101. Calculate the potential energy charge of the i-th agent individual Defined as: ; Among them, and are the maximum and minimum values of the potential energy charge of the agent individual (oat seed), is the maximum fitness value of the population at the t-th iteration, is the minimum fitness value of the population at the t-th iteration, rand(0, 0.1) is a random number within 0 to 0.1; individuals with good fitness carry larger charges and are more likely to attract other agent individuals to approach, while agent individuals with poor fitness carry smaller charges and are easily attracted to approach the positions of agent individuals with small fitness; S102. Design the potential energy field intensity vector of the agent individual population, including: update the potential energy field intensity vector at the t-th iteration according to the potential energy charge of the i-th agent individual as: ; Among them, N is the population size, α is the minimum value, which is set to 0.001 in this implementation, is the position of the i-th agent individual at the t-th iteration, is the position of the j-th agent individual at the t-th iteration; through the potential energy field intensity, the agent individual position can sense the overall potential energy gradient formed by the positions and fitness of other individuals, and thus more efficiently determine the moving direction; S103. Determine the new position of the i-th agent individual through the potential energy gradient and the adaptive step size. The mathematical model is: ; Among them, is the position of the i-th agent individual at the (t + 1)-th iteration, and the step size is adaptively adjusted as follows: ; The step size is negatively correlated with the individual charge. Individuals with high fitness have a small step size and conduct more detailed exploration. The step size gradually increases with the number of iterations to control the exploration range; is the perturbation term at the t-th iteration, and the mathematical model is: ; where T is the maximum number of iterations, UB is the upper limit position value, LB is the lower limit position value, is a Dim-dimensional random number within -1 to 1.

[0030] Furthermore, a critical transition ejection model of the structure is proposed to simulate the critical structure mutation caused by the accumulation of structural strain during the oat seed spreading process. When the structural geometric stress exceeds a certain irreversible threshold, the entire structure undergoes a transition to complete long-range ejection; this behavior does not depend on weight control or speed adjustment, but is endogenously driven by the geometric shape and state transition mechanism. The ejection amplitude is completely determined by the state mutation amplitude. The specific implementation method is as follows: S201. Define the structural state vector of each agent individual at the t-th iteration, including: representing the current structural state vector by the difference between the current position of the agent individual and the position of the i-th agent individual at the (t - 1)-th iteration; further constructing an elastic deformation response through non-linear sine perturbation and defining the state energy modulus , and the mathematical model is: ; where Dim is the dimension of the optimization parameter for the PID temperature control of the cascade refrigeration unit; d is the d-th optimization parameter; is the difference in the position of the i-th agent individual in the d-th dimension between the t-th iteration and the previous iteration; is the position value of the i-th agent individual in the d-th dimension at the t-th iteration, is the upper limit position value of the d-th dimension; S202. Define the critical transition determination mechanism through the structural state vector and the state energy modulus as: ; where, is the critical transition value of the i-th agent individual at the t-th iteration; μ takes a value of 0.0001; When it is greater than 1, it enters the critical transition area, otherwise it continues to accumulate deformation; S203. After triggering the transition, generate a transition ejection displacement to update the position of the agent individual, otherwise maintain the structural inertial perturbation evolution. The mathematical model: ; where the transition ejection displacement is designed as: ; is the transition ejection displacement, is the element-level direction multiplication, is the local structure guiding drive vector, which drives the i-th agent individual to have a direction-preferred state transition in the local neighborhood.

[0031] Furthermore, implement by constructing the local structure guiding drive vector. The specific implementation method is as follows: S301. In the t-th iteration, for the i-th agent individual, construct a local structure neighborhood from the current population , and the neighborhood consists of agent individuals that meet the following conditions: ; wherein, is the set neighborhood search radius, and f is the fitness function; in the implementation process of the present invention, the neighborhood search radius is set to half of the position value of the i-th agent individual; S302. Based on the neighborhood construct the local structure gravitational direction vector of the i-th agent individual, and its calculation formula is as follows: ; wherein, is the position of the i-th agent individual in the t-th iteration, is the position of the j-th agent individual in the t-th iteration, is the fitness value of the position solution of the j-th agent individual in the t-th iteration, is the fitness value of the position solution of the i-th agent individual in the t-th iteration.

[0032] Furthermore, implement as Figure 2 shown, use the improved animated oat optimization algorithm to globally optimize the PID parameters of the low-temperature cold cycle level, set the maximum number of iterations to 80, the population size to 20, the dimension of the optimization parameter to 3, set the maximum value of the agent individual position UB = [80, 80, 80], and the minimum value LB = [0, 0, 0]; the specific implementation method is as follows: S401. Map the i-th agent individual of the improved animated oat optimization algorithm to the PID parameters of the low-temperature cold cycle level, which is represented as a three-dimensional vector , and each agent individual position is a three-dimensional vector to search for the optimal solution in the three-dimensional continuous parameter space; wherein, the first dimension mapping proportionality coefficient of the agent individual position is Kp, the second dimension mapping integral coefficient is Ki, and the third dimension mapping differential coefficient is Kd; S402. Initialize the maximum number of iterations, the population size, and the dimension of the optimization parameters for the PID temperature control of the cascade refrigeration unit, as well as the maximum and minimum values of the agent individual position, and construct the initial position of the agent individual by using the random generation method. S403. Calculate the position fitness value of the i-th agent individual using the fitness function. The fitness value is obtained by calculating the temperature error of the low-temperature cold cycle stage controller with the control parameters mapped by the agent individual through the fitness function. S404. Use the S103 step in the dynamic potential field strategy to determine the new position of the i-th agent individual through the potential gradient and adaptive step size, and update the position of each agent individual. S405. Update the position of the agent individual using the S203 step in the dynamic potential field strategy; limit the value of the finally updated agent individual position between the maximum and minimum values of the agent individual position. S406. Calculate the fitness value of the updated agent individual position, retain the position value of the agent individual with the minimum fitness value in the current iteration as the current optimal individual position, and determine whether the current iteration number is equal to the maximum iteration number. If so, resolve the current minimum agent individual position value into the optimal PID parameters of the low-temperature cold cycle stage; otherwise, return to execute S404 to continue the optimization process.

[0033] Furthermore, the initial position of the agent individual is constructed by the method of random generation, and the implementation mathematical model is: ; where, is the initial position value of the i-th agent individual in the -th dimension, is the minimum value of the agent individual position in the -th dimension, is the maximum value of the agent individual position in the -th dimension, and r is a random number between 0 and 1.

[0034] Furthermore, as shown in Figure 3 , set the target low-temperature temperature value , collect the actual outlet temperature of the low-temperature stage and the actual outlet temperature (intermediate condensation temperature) of the high-temperature stage through the feedback module and input them into the input temperature difference calculation module of each stage; calculate the main controller error term , input the main controller error term into the low-temperature stage PID controller, and output the intermediate target temperature (intermediate condensation set temperature) , and the implementation mathematical model is: ; where, is the proportional coefficient value of the PID of the low-temperature cold cycle stage, is the integral coefficient value of the PID of the low-temperature cold cycle stage, is the differential coefficient value of the PID of the low-temperature cold cycle stage, is the main controller error term at the current moment. is the error term of the main controller at the previous moment, is the error term of the main controller at the i-th moment.

[0035] Furthermore, as implemented, Figure 3 shown, re-enter the optimal PID parameters of the low-temperature cold cycle stage into the PID controller of the low-temperature cold cycle stage, and update the intermediate target temperature (intermediate condensation set temperature) using the optimal parameters , calculate the secondary controller error term through the intermediate target temperature and the actual outlet temperature of the high-temperature stage , input the secondary controller error term into the high-temperature stage PID controller to update the compressor control signal , calculate the output value of the incremental PID , the implementation mathematical model is: ; Among them, is the proportional coefficient setting value of the PID of the high-temperature cold cycle stage, is the integral coefficient setting value of the PID of the high-temperature cold cycle stage, is the differential coefficient setting value of the PID of the high-temperature cold cycle stage, is the secondary controller error term at the current moment, is the secondary controller error term at the previous moment, is the secondary controller error term at the previous moment at k-1 moment.

[0036] Furthermore, as implemented, input the compressor control signal into the high-temperature stage compressor control model, and adjust the suction capacity and load of the high-temperature stage evaporator, thereby adjusting the temperature of the intermediate condenser. The temperature of the intermediate condenser directly affects the condensation efficiency of the low-temperature stage, thereby adjusting the actual outlet temperature of the low-temperature stage , and finally realize the double closed-loop control optimization of the cascade refrigeration unit.

[0037] Furthermore, as implemented, complete the code of the above implementation steps in Maltab, introduce the comparison experiment between the existing animation oat optimization algorithm and the improved animation oat optimization algorithm of the present invention, establish the Main function, and use the high-temperature stage compressor control model as the controlled function. The high-temperature stage compressor control model includes a first-order control model from the refrigeration capacity of the compressor to the adjustment of the intermediate condensation temperature and a second-order control model of the influence of the intermediate condensation temperature on the condensation efficiency of the low-temperature stage. The controlled function model is: ; Among them, is the complex frequency domain of the actual outlet temperature of the low-temperature stage, is the influence of the high-temperature stage compressor control signal on the temperature of the intermediate condenser, set to -3.5, For the influence of the intermediate condensation temperature on the low-temperature stage outlet temperature, it is set to 1.8, For the high-temperature stage evaporator response time constant of 1 second, For the low-temperature stage condensation heat response inertia of 2 seconds, For the low-temperature stage evaporation heat capacity and heat transfer lag of 1 second, For the complex frequency domain form of the compressor control signal, the final controlled module model of Siumulink is: .

[0038] Furthermore, implement it by setting two stage values for the target low-temperature value. The first-stage temperature is -31.5 °C, and the second-stage temperature is -6.3 °C; then the compressor control signal is required to be 5 and 1 respectively; run the Main function to call the PID control model of the low-temperature cold cycle stage of Siumulink, set it to run for 40 seconds, and the output is as Figures 4 to 7 the experimental graph.

[0039] First, from as Figure 4 analyzed, measure the fitness change graph of the temperature control performance corresponding to each group of PID parameters. The smaller the fitness value, the smaller the difference between the actual output temperature and the target set temperature, indicating that the control coefficient of the PID of the low-temperature cold cycle stage is more accurate. The faster the fitness value reaches a stable region, the faster the optimization speed of the control coefficient of the PID for the low-temperature cold cycle stage; from the joint analysis of the fitness value and the number of iterations in the graph, it can be seen that when the method of the present invention optimizes the PID controller parameters of the low-temperature cold cycle stage of the cascade refrigeration unit, it not only quickly converges to the error minimum of 5.2 at the 16th iteration, while the existing method falls into a local optimum at the 19th iteration and no longer decreases, and finally is 6.8; compared with the existing method, the final convergence error is reduced by 30%, and it can effectively jump out of the local optimum, showing significant optimization efficiency and global performance advantages. The change trend of the fitness curve clearly verifies its improvement effect.

[0040] Secondly, as Figure 5 shown, use the existing method to optimize the PID best parameters of the low-temperature cold cycle stage. The existing method finds the control coefficient values of the best PID of the low-temperature cold cycle stage at the 19th iteration. The proportional coefficient Kp = 1.997; the integral coefficient Ki = 0.2216; the differential coefficient Kd = 1.4432; Figure 6 For the change graph of optimizing the PID best parameters of the low-temperature cold cycle stage by using the method of the present invention, corresponding to the change of the fitness value, the method of the present invention finds the control coefficient values of the best PID of the low-temperature cold cycle stage at the 16th iteration. The proportional coefficient Kp = 13.1471; the integral coefficient Ki = 0.2037; the differential coefficient Kd = 9.7383.

[0041] Finally, obtain asFigure 7 The PID temperature control optimization effect diagram of the cascade refrigeration unit shown. Compared with the PID temperature control of the cascade refrigeration unit of the existing method, the method proposed by the present invention has better control performance in the cascade refrigeration system. The overall response curve of its compressor control signal is smoother, with smaller overshoot, faster convergence speed and better steady-state control effect. Especially in the disturbance response process, it shows strong robustness and anti-disturbance ability, verifying the engineering adaptability and control precision advantages of the method of the present invention in complex multi-stage temperature control systems.

Claims

1. A PID temperature control optimization method for cascade refrigeration units, characterized in that, The specific method is as follows: S1. Establish a PID temperature control model for a cascade refrigeration unit. The cascade refrigeration unit includes two series-connected refrigeration cycle stages, and each cycle stage has an independent PID temperature controller; S2. Set the initial parameters of the PID temperature controller, including the proportional coefficient, integral coefficient, and differential coefficient; S3. Based on the real-time refrigeration effect of the cascade refrigeration unit, calculate the temperature error of each refrigeration cycle stage. The temperature error constructs a fitness function for adjusting the PID parameters of the low-temperature refrigeration cycle stage; S4. Use an improved animated oat optimization algorithm to globally optimize the PID parameters of the low-temperature refrigeration cycle stage. Through global optimization, determine the PID parameters of the low-temperature refrigeration cycle stage applicable to the cascade refrigeration unit, and achieve the PID temperature control optimization of the cascade refrigeration unit. The improved animated oat optimization algorithm includes constructing an optimization mechanism for the animated oat optimization algorithm through a dynamic potential field optimization strategy and a structural critical transition ejection strategy.

2. The PID temperature control optimization method for a cascade refrigeration unit according to claim 1, wherein, In the PID temperature control model of the cascade refrigeration unit, a cascade control structure is adopted. The high-temperature and low-temperature PID controllers use the incremental PID algorithm. The low-temperature PID controller is used as the outer loop to control the outlet temperature of the low-temperature stage; The high-temperature PID controller is used as the inner loop to control the operation of the high-temperature compressor to adjust the intermediate condensation temperature. The low-temperature PID controller outputs a target intermediate temperature according to the temperature deviation of the low-temperature evaporator. The high-temperature PID controller then drives the high-temperature compressor to achieve this target intermediate temperature. Among them, the proportional coefficient, integral coefficient, and differential coefficient of the high-temperature PID controller are manually set and fixed according to experience; the proportional coefficient, integral coefficient, and differential coefficient of the low-temperature PID controller are adaptively adjusted through global optimization.

3. The PID temperature control optimization method for a cascade refrigeration unit according to claim 2, wherein, The improved animated oat optimization algorithm is obtained by improving the global search strategy and local development strategy of the standard animated oat optimization algorithm. Specifically, by introducing a potential charge based on fitness to construct a potential field intensity vector, combining the potential field intensity vector and an adaptive step size regulation mechanism, constructing a dynamic potential field optimization strategy to replace the global search strategy of the standard animated oat optimization algorithm; Secondly, by constructing a critical transition determination mechanism jointly defined by a structural state vector and a state energy modulus, and integrating a local structure guiding drive vector constructed based on fitness and distance weighting, constructing a structural critical transition ejection strategy to replace the local search strategy of the standard animated oat optimization algorithm, and finally obtaining the optimization mechanism of the improved animated oat optimization algorithm.

4. The PID temperature control optimization method for a cascade refrigeration unit according to claim 3, characterized in that, The specific method of the dynamic potential field optimization strategy is as follows: S101. Calculate the potential charge of the i-th agent individual It is defined as: ； Among them, and are the maximum and minimum potential charges of the agent individuals, is the maximum fitness value of the population at the t-th iteration, is the minimum fitness value of the population at the t-th iteration, and rand(0, 0.1) is a random number within 0 to 0.1; S102. Design the potential field intensity vector of the agent individual population, including: according to the potential charge of the i-th agent individual Update the potential field intensity vector at the t-th iteration as follows: ； where N is the population size, α is the minimum value, is the position of the i-th agent individual at the t-th iteration, is the position of the j-th agent individual at the t-th iteration; S103. Determine the new position of the i-th agent individual through the potential gradient and the adaptive step size. The mathematical model is: ； Among them, is the position of the i-th agent individual in the (t + 1)-th iteration, and the step size is adaptively adjusted as: ; the step size is negatively correlated with the individual charge. Individuals with high fitness have a small step size and conduct more detailed exploration. The step size gradually increases with the number of iterations to control the exploration range; is the perturbation term in the t-th iteration, and the mathematical model is: ； where T is the maximum number of iterations, UB is the upper limit position value, and LB is the lower limit position value. It is a random number of Dim dimensions within -1 to 1.

5. The PID temperature control optimization method for a cascade refrigeration unit according to claim 4, wherein The structural critical transition ejection strategy is specifically as follows: S201. Define the structural state vector of each agent individual at the t-th iteration, including: calculate the position difference between the i-th agent individual at the d-th dimension in the t-th iteration and the previous iteration to represent the current structural state vector; further construct the elastic deformation response through non-linear sine perturbation and define the state energy modulus , and the mathematical model is: ； Among them, Dim is the dimension of the optimization parameter for the PID temperature control of the cascade refrigeration unit; d is the d-th dimension of the optimization parameter; is the difference in position between the i-th agent individual at the d-th dimension in the t-th iteration and the previous iteration; is the position value of the i-th agent individual at the d-th dimension in the t-th iteration, is the upper limit position value of the d-th dimension; S202. Define the critical transition determination mechanism through the structural state vector and the state energy modulus as: ； wherein, is the critical transition value of the i-th agent individual at the t-th iteration; μ takes a value of 0.0001; When it is greater than 1, it enters the critical transition region, otherwise it continues to accumulate deformation; S203. After triggering the transition, generate a transition ejection displacement and update the position of the agent individual. Otherwise, maintain the structural inertial perturbation evolution. The mathematical model: ； Among them, the transition ejection displacement is designed as: ; is the transition ejection displacement, is the element-level direction multiplication, is the local structure guiding drive vector, which drives the i-th agent individual to have a direction-preferred state transition in the local neighborhood.

6. The PID temperature control optimization method for a cascade refrigeration unit according to claim 5, characterized in that The specific method of the local structure guiding drive vector is as follows: S301. In the t-th iteration, for the i-th agent individual, construct a local structure neighborhood from the current population , where the neighborhood consists of agent individuals that satisfy the following conditions: ； Among them, is the set neighborhood search radius, and f is the fitness function; S302. Based on the neighborhood Construct the local structural gravitational direction vector of the i-th proxy individual , and its calculation formula is as follows: ； wherein, is the position of the i-th agent individual at the t-th iteration, is the position of the j-th agent individual at the t-th iteration, is the fitness value of the solution of the position of the j-th agent individual at the t-th iteration, is the fitness value of the solution of the position of the i-th agent individual at the t-th iteration.

7. A PID temperature control optimization method for a cascade refrigeration unit according to any one of claims 1-6, characterized in that, Use the improved animated oat optimization algorithm to globally optimize the PID parameters of the low-temperature cold cycle stage. The specific method is as follows: S401. Map the i-th agent individual of the improved animated oat optimization algorithm to the PID parameters of the low-temperature cold cycle stage, represented as a three-dimensional vector , where the position of each agent individual is a three-dimensional vector, and the optimal solution is searched in the three-dimensional continuous parameter space; among them, the first dimension mapping proportionality coefficient Kp, the second dimension mapping integral coefficient Ki, and the third dimension mapping differential coefficient Kd of the agent individual position; S402. Initialize the maximum number of iterations, population size, and the dimension of the optimization parameters for the PID temperature control of the cascade refrigeration unit, as well as the maximum and minimum values of the surrogate individual positions. Use the method of random generation to construct the initial positions of the surrogate individuals; S403. Calculate the position fitness value of the i-th surrogate individual using the fitness function. The fitness value is obtained by calculating the temperature error of the control parameters mapped by the surrogate individual acting on the low-temperature cold cycle stage controller through the fitness function; S404. Use the S103 step in the dynamic potential field strategy to determine the new position of the i-th surrogate individual through the potential gradient and adaptive step size, and update the position of each surrogate individual; S405. Update the position of the surrogate individual using the S203 step in the dynamic potential field strategy; limit the value of the finally updated surrogate individual position between the maximum and minimum values of the surrogate individual positions; S406. Calculate the fitness value of the updated surrogate individual position, retain the position value of the surrogate individual with the minimum fitness value in the current iteration as the current optimal individual position, and determine whether the current iteration number is equal to the maximum iteration number. If so, parse the current minimum surrogate individual position value as the optimal PID parameter of the low-temperature cold cycle stage; otherwise, return to execute S404 to continue the optimization process.

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