A cooling control method and system for a conduction-cooled superconducting cavity
By constructing a hybrid 0D/1D heat dissipation network model and performing real-time online correction, combined with MLP and MPC models, the problem of temperature difference control during the transient cooling process of a conductive cooling superconducting cavity was solved, achieving efficient temperature difference constraint and cooling control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF HIGH ENERGY PHYSICS CHINESE ACAD OF SCI
- Filing Date
- 2026-04-07
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies struggle to accurately predict and control the transient cooling process of conductive cooling superconducting cavities, especially within the superconducting transition temperature range between Nb3Sn and Nb, where issues such as excessive temperature differences and low cooling efficiency exist.
A hybrid 0D/1D heat dissipation network model is adopted, and online correction is performed using real-time temperature data to construct a nonlinear transient thermal network model. Predictive control is then performed using an MLP multilayer sensor and an MPC model to achieve coordinated control of heater power and temperature difference constraint.
It achieves predictable, constrainable, and executable cooling control of conductive cooling superconducting cavities, improves the accuracy of temperature difference prediction and cooling efficiency, and is suitable for miniaturized and modular conductive cooling superconducting modules.
Smart Images
Figure CN122160988A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radio frequency superconducting technology and cryogenic engineering, and relates to a cooling control method and system for conductive cooling superconducting cavities. Background Technology
[0002] In superconducting particle accelerators, the superconducting cavity plays a crucial role as the primary accelerating component. Typically, superconducting cavities achieve superconductivity through liquid helium immersion. With the continuous development of superconducting cavity technology and the widespread application of miniaturized accelerators in industrial and medical fields, a novel cooling scheme has been proposed that utilizes a small refrigerator to directly remove the heat load from the superconducting cavity through heat conduction. Compared to the traditional liquid helium immersion cooling method, this scheme offers advantages such as lower cost, easier maintenance, and modularity.
[0003] Existing research has shown that the cooling process (cooling rate and temperature gradient / temperature difference) of a superconducting cavity as it traverses the superconducting transition temperature range significantly affects magnetic flux repulsion / trapping behavior, thereby influencing surface resistivity and radio frequency performance. Therefore, for conduction-cooled superconducting cavities, achieving control that satisfies both temperature difference / gradient constraints and maximizes cooling efficiency within the superconducting transition temperature range of Nb3Sn and Nb is a critical issue directly related to the performance of the superconducting cavity and the stable operation of conduction-cooled accelerators.
[0004] In existing thermal analysis work related to conduction-cooled superconducting cavities, a common approach is to use commercial simulation software to perform steady-state temperature field analysis on the cavity / thermal bridge structure, assuming a constant cold-end temperature or a given heat flux boundary in the boundary conditions to assess the influence of factors such as contact thermal resistance, structural dimensions, and material thermal conductivity on the steady-state temperature distribution. However, in actual conduction cooling processes, the cooling capacity of the cryostat is strongly correlated with temperature, and material properties, contact thermal resistance, and multi-branch heat conduction are all nonlinear transient processes. Commercial software relying solely on steady-state or simplified boundary conditions cannot accurately solve for the transient cooling process. Furthermore, in cooling control, conduction-cooled superconducting cavity systems also suffer from uncertainties in contact thermal resistance caused by preload and interface conditions, uncertainties in heat leakage, and sensor noise. This makes open-loop control relying solely on offline thermal models prone to exceeding temperature limits. Summary of the Invention
[0005] To address the problems existing in the prior art, the present invention aims to provide a cooling control method and system for conductively cooled superconducting cavities. This invention targets a superconducting cavity system using a small refrigerator for conductive cooling. First, M1 establishes and solves the transient thermal network model of the conductive cooling system. Then, M2 acquires real-time temperature data, and M3 performs online correction of key uncertain parameters. Based on this, M4 generates warm-start initial values, M5 forms a constraint set, M6 outputs constrained control variables, and M7 performs supervision and degradation under abnormal operating conditions. Specifically: 1. Construct a hybrid 0D / 1D heat dissipation network model. Components with compact structural dimensions and negligible internal temperature differences in the conductive cooling system are represented as 0D lumped heat nodes; components with non-negligible axial temperature differences or where temperature difference itself is a key control indicator are discretized in 1D, i.e., divided into several segments along the axial direction, each segment corresponding to a 0D lumped heat node, with adjacent heat nodes connected by axial heat conduction.
[0006] 2. In the thermal network model, considering factors such as the temperature variations of material specific heat capacity Cp(T) and thermal conductivity λ(T), surface radiative heat transfer, MLI radiative heat transfer, contact thermal resistance R(T), cold head cooling capacity-temperature characteristics, and heater power input, energy conservation equations for each thermal node are established and simultaneously formed into a nonlinear transient thermal network model. 3. An implicit numerical method combining backward Euler and Newton iterations with step-doubling adaptive step size is used to stably solve the above nonlinear transient thermal network model, thereby obtaining the evolution of the temperature of each thermal node over time, as well as the average temperature, maximum temperature difference, and cooling rate of the superconducting cavity.
[0007] 4. By introducing moving time-domain estimation through online temperature measurement data, the scaling factors of equivalent heat leakage and contact thermal resistance are corrected online to reduce model mismatch and improve the accuracy of temperature difference prediction.
[0008] 5. Based on the current temperature measurement status and online correction parameters, the segmented heater power template of the temperature domain output by the MLP multilayer sensor is used as the initial value for the warm-start of the subsequent model predictive control.
[0009] 6. Construct an MPC model predictive controller that includes hard constraints on temperature difference, cooling rate constraints, power upper limit constraints, and power change rate constraints, and perform rolling optimization and coordinated control on multiple heaters.
[0010] 7. During the solution process, convergence, solution time, and temperature difference risk are monitored in real time. When optimization solution timeout, infeasibility, or high temperature difference risk is detected, a warning is triggered and degradation logic is executed to ensure the safe operation of the system.
[0011] Through the above method, the present invention can realize the predictable, constrainable and executable control of the cooling process of the conductive cooling superconducting cavity, and is applicable to miniaturized and modular conductive cooling superconducting modules.
[0012] The technical solution of this invention is as follows: A method for controlling the cooling of a conductive cooling superconducting cavity, comprising the following steps: Receives various parameters input from the conductive cooling system; Based on various parameters within the conductive cooling system, energy conservation equations for each thermal node within the conductive cooling system are established, and these equations are combined to form a thermal network model of the conductive cooling system. Collect the measured temperatures of each thermal node in the conductive cooling system; Based on the measured temperature of each thermal node, the key uncertain parameters in the thermal network model are recursively corrected to obtain the parameter estimates for the current control cycle. The training dataset generated based on the thermal network model and parameter estimates is used to train the MLP multilayer perceptron and predict the heater power in each temperature range of the conductive cooling system as the initial value for warm-start. A set of temperature difference change constraints is generated based on the real-time temperature of the superconducting cavity; Within each control cycle, based on the measured temperature, parameter estimates, warm-start initial values, and temperature difference change constraint set, the corrected thermal network model is invoked to predict the temperature evolution of each thermal node over a future period. The measured temperature, prediction process and results of each thermal node are monitored in real time, and the temperature of the conductive cooling superconducting cavity is controlled based on the monitoring results.
[0013] Preferably, the temperature difference change constraint set ;in, The maximum temperature difference within the temperature range. As the upper limit of the baseline cooling rate, As a speed limiting factor, This represents the upper limit of the actual cooling rate. This is the temperature difference margin threshold.
[0014] Preferred, ; , This represents the actual temperature difference. Minimum speed limit factor, p This is the temperature difference change control factor.
[0015] Preferably, the method for predicting the temperature evolution of each heat node over a future period by calling the corrected thermal network model is as follows: The objective function is solved iteratively using a numerical optimization solver. The optimal heater control sequence within the future prediction domain is obtained; where, This represents the average temperature of the superconducting cavity at the predicted end time. This represents the reference control input for the i-th prediction step. Let be the control input vector of the heater in the prediction domain at the i-th prediction step within the k-th control cycle; The degree of lateral power asymmetry; , , and These are the weighting coefficients for the terminal temperature term, the reference control tracking term, the control increment smoothing term, and the lateral power difference suppression term, respectively, where N represents the number of prediction steps.
[0016] Preferably, the average temperature of the superconducting cavity is... The key temperature zone of the conductive cooling system is divided into multiple temperature ranges based on the characteristic temperature. Temperature data for each temperature range is calculated using a thermal network model. The temperature data and parameter estimates for each temperature range are then compared. As training data, the heater power within this temperature range is used as the label to generate training samples, resulting in a training dataset.
[0017] Preferably, the energy conservation equation for the i-th hot node is: ;in, It is the equivalent mass of the component or discrete segment corresponding to the i-th hot node. The material at the i-th thermal node is at temperature The specific heat capacity below; It is the temperature of the i-th hot node; and These are the input and output of the heat flow of the i-th hot node, respectively. It is the heat flow generated by the external source term of the i-th hot node.
[0018] Preferably, the parameters in the conductive cooling system include at least: the geometric dimensions of each component of the conductive cooling system, the specific heat capacity function Cp(T) of the material, the thermal conductivity function λ(T), the surface emissivity, the number of layers of the multilayer insulation material MLI, the contact thermal resistance function R(T), the cooling capacity-temperature curve Qcool(T) of the cold head, the ambient temperature, the initial temperature, the equivalent heat leakage parameters of the support and connecting parts, the maximum power of the heater, and the maximum power change rate.
[0019] A cooling system for conductive cooling of a superconducting cavity, characterized in that it includes: The cooling system structural parameter configuration module is used to receive various parameters input from the conductive cooling system. The thermal network prediction module is used to establish the energy conservation equations for each thermal node in the conductive cooling system based on various parameters in the conductive cooling system, and to form a thermal network model of the conductive cooling system. The online acquisition and preprocessing module is used to acquire the measured temperature of each thermal node in the conductive cooling system and send it to the online correction module and the MPC model prediction and control module. The online calibration module is used to recursively correct the key uncertain parameters in the thermal network model based on the measured temperature of each thermal node, obtain the parameter estimate for the current control cycle, and send the parameter estimate to the MLP multilayer perceptron learning module and the MPC model predictive control module. The MLP multilayer perceptron learning module is used to generate a training dataset based on the thermal network model and parameter estimates to train the MLP multilayer perceptron and predict the heater power in each temperature range of the conductive cooling system as the warm-start initial value and send it to the MPC model predictive control module. The temperature difference setting and speed limiting module is used to generate a set of temperature difference change constraints based on the real-time temperature of the superconducting cavity. The MPC model predictive control module is used to predict the temperature evolution of each heat node in the future period by calling the corrected thermal network model based on the measured temperature, parameter estimates, warm-start initial values, and temperature difference change constraint set in each control cycle. The solution supervision module is used to monitor the measured temperature, prediction process and results of each thermal node in real time, and to control the cooling of the conductive cooling superconducting cavity based on the monitoring results.
[0020] A computing device, characterized in that it comprises: a processor and a memory storing a computer program, wherein the computer program, when run by the processor, executes the method described above.
[0021] A computer-readable storage medium, characterized in that it stores instructions that, when executed on a computer, cause the computer to perform the above-described method.
[0022] The advantages of this invention are as follows: (1) This invention integrates the cold head performance curve, variable thermal properties, radiation heat transfer, contact thermal resistance and multi-branch heat conduction into the same nonlinear transient thermal network model. It adopts the 0D / 1D hybrid discretization method, which can output the axial multi-point temperature of the superconducting cavity and the maximum temperature difference in the key area while maintaining the model calculation efficiency. It can better reflect the actual cooling process than traditional steady-state analysis or simplified boundary transient analysis, and is particularly suitable for the analysis and control of the cooling process of Nb3Sn superconducting cavity that is more sensitive to temperature difference.
[0023] (2) The present invention introduces an online correction module, which can use real-time temperature data to recursively correct equivalent heat leakage and contact thermal resistance deviation, thereby reducing the impact of assembly errors, interface state changes and external disturbances on prediction accuracy.
[0024] (3) The present invention uses the MLP output heater power template as the initial value (warm-start) and combines it with MPC to realize multi-heater collaborative control, which can improve the cooling efficiency under the premise of meeting the hard constraint of temperature difference.
[0025] (4) The present invention sets up a solution supervision and degradation mechanism, which can maintain the continuous, safe and stable operation of the system even in the case of optimization failure, timeout or high temperature difference risk, and has strong engineering application value. Attached Figure Description
[0026] Figure 1 This is a flowchart of the cooling control process for the conductive cooling superconducting cavity of the present invention.
[0027] Figure 2 This is a schematic diagram of a conductive cooling superconducting cavity system.
[0028] Figure 3 The diagram shows the 0D / 1D hybrid heat dissipation node network and its heat input-output.
[0029] Figure 4 This is a diagram showing the distribution of axial thermal nodes in a superconducting cavity.
[0030] Figure 5 This is a diagram showing the distribution of temperature sensors and heaters.
[0031] Figure 6 This is a schematic diagram of the MLP structure. Detailed Implementation
[0032] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
[0033] In order to accurately predict and control the cooling process and cooling rate of a conductive cooling superconducting cavity, an optional embodiment of the present invention proposes a cooling prediction and control method with the following characteristics: (1) a physical model that can quickly predict transient cooling and temperature difference; (2) the ability to correct key uncertain parameters online; (3) outputting closed-loop control of multiple heaters in coordination under hard constraints of temperature difference; and (4) a supervision mechanism that can maintain safe operation even when the solution fails. It mainly consists of the following modules: cooling system structural parameter configuration module M0, thermal network prediction module M1, online acquisition and preprocessing module M2, online correction module M3, MLP multilayer sensor learning module M4, temperature difference setting and rate limiting module M5, MPC model prediction and control module M6, and solution supervision module M7. The above modules form a closed-loop control: M0 provides modeling parameters for M1; M1 provides the thermal network model; M2 collects and outputs the measured temperature; M3 uses the measured temperature from M2 to perform online calibration of the M1 model; M4 generates a heater power template based on the current state and calibration parameters; M5 generates a constraint set based on the real-time temperature; M6 solves for the control variables under the calibration model, warm-start initial values, and constraints; M7 monitors the solution state of M6 and triggers degraded control when necessary. The specific process is as follows: Figure 1 .
[0034] The content and function of each module are as follows: Module M0: Cooling system structural parameter configuration module The system receives various parameters from the conductive cooling system, including at least: the geometric dimensions of each component, the material's specific heat capacity function Cp(T), thermal conductivity function λ(T), surface emissivity, the number of MLI layers in the multilayer insulation material, contact thermal resistance function R(T), the cold head's cooling capacity-temperature curve Qcool(T), ambient temperature, initial temperature, equivalent heat leakage parameters of supports and connectors, maximum heater power, and maximum power change rate. These parameters can be obtained from design drawings, material databases, experimental calibrations, or empirical values.
[0035] Module 1 M1: Thermal Network Prediction Module A 0D / 1D hybrid heat dissipation network model and numerical solution method are provided for transient calculation of the cooling process of a superconducting cavity system, enabling: (1) While maintaining the high efficiency and scalability of the thermal network model, it calculates the cooling curves of multiple components such as the cold screen, magnetic shield and superconducting cavity, as well as the axial temperature distribution, and can simultaneously output key indicators such as the maximum axial temperature difference of the superconducting cavity. (2) Under the consideration of complex factors such as material properties changing with temperature, MLI radiation heat transfer, surface radiation, thermal conductivity and contact thermal resistance, a stable solution for a strongly nonlinear rigid system is achieved. (3) The implicit adaptive step size numerical scheme of Backward Euler + Newton + step-doubling is adopted to improve the robustness and efficiency of the solution.
[0036] 1. Hot node partitioning A "thermal node" is the basic discrete unit in a thermal network. For components with relatively compact structural dimensions and negligible internal temperature differences, a single 0D lumped thermal node is used. For components with significant temperature gradients along the axial direction or where the temperature difference itself is a key indicator, 1D equivalent discretization is used, which divides the component into several segments along the axial direction. Each segment is still represented by a single 0D lumped thermal node, and adjacent segments are connected by axial thermal conduction.
[0037] Select the following core components: primary thermal anchor Link1, cold shield, magnetic shield, secondary thermal bridge Link2, and superconducting cavity. Primary thermal anchor Link1 connects the primary cold head and cold shield; the magnetic shield is located inside the cold shield, and the two are not in direct contact, but connected by a copper braided strap; the secondary thermal bridge connects the secondary cold head and superconducting cavity. Figure 2 This is a structural diagram of a conductive cooling superconducting cavity system.
[0038] Specific node division: Due to the long axial heat conduction paths of the cold shield and magnetic shield, and the non-negligible axial temperature difference during cooling, the cold shield and magnetic shield are each divided into n nodes (e.g., n=5) along the axial direction, with adjacent segments connected by axial heat conduction. Furthermore, during cooling, not only the cooling rate of the superconducting cavity is considered, but also the axial temperature difference; therefore, the superconducting cavity is divided into m nodes along the axial direction, m=9. Five thermal nodes are set in the ellipsoidal cavity region, and two thermal nodes are set in each of the two bundle tubes. The three Link2 branches are connected to the 3rd, 5th, and 7th thermal nodes of the superconducting cavity, respectively, i.e., T... CA,3 T CA,5 and T CA,7 A heater is installed on each of the three Link2 branches to achieve distributed collaborative control. Figure 3 and Figure 4 These are the thermal node network and heat input-output diagram and the thermal node diagram of the superconducting cavity.
[0039] 2. Establishment of transient thermal network model For any i-th hot node, by the law of energy conservation: in, It is the equivalent mass of the component or discrete segment corresponding to the i-th hot node. It is the temperature of the node material The specific heat capacity below; It is the temperature of the i-th hot node; and These are the input and output heat flow (heat conduction and radiation) of the thermal node, respectively. External source terms (such as cold head cooling capacity, heater power); heat flow into the hot node is taken as positive, and heat flow out of the hot node is taken as negative; cold head cooling capacity is included as a negative heat flow term, and heater power and ambient heat leakage are included as positive heat flow terms.
[0040] To address the issue of specific heat capacity varying with temperature, a unit mass enthalpy function is introduced. To address the issue of thermal conductivity varying with temperature, a thermal conductivity integral function is introduced. .
[0041] For any two hot nodes p and q, the heat conduction between them... If the number of parallel heat conduction channels or the equivalent number between the two is heat transfer cross-sectional area ,length Then the heat conduction between node p and node q can be expressed as: There are two types of radiative heat calculations: gray body radiative heat and MLI radiative heat. The gray body radiative heat transfer terms and MLI radiative heat transfer terms can be expressed using formulas known in the art and calculated based on the corresponding surface area, emissivity, number of MLI layers, and temperature boundary.
[0042] The k-th hot node of a superconducting cavity is denoted as... Where k∈{3,5,7} corresponds to the three cavity nodes connected to the three Link2 branches, namely the T-junction of the secondary thermal bridge and the superconducting cavity. CA,3 T CA,5 and T CA,7 Three parallel cooling branches are established using three hot nodes. The thermal resistance of each cooling branch consists of the secondary thermal bridge thermal resistance and the contact thermal resistance R(T) between Link2 and the superconducting cavity hot node, connected in series. Let the temperature of the secondary cold head side in the k-th branch be... The temperature of the superconducting cavity thermal node connected by the k-th branch is The thermal conductivity cross-sectional area is Thermal conductivity length is The contact thermal resistance function is The temperature of the intermediate interface is Then the heat flow of the kth branch for: Therefore T int,k It is determined by a univariate nonlinear equation: Find T int,k The heat flow of the kth branch can then be calculated. This heat flow is then incorporated into the energy conservation equation of the corresponding hot node.
[0043] By combining the above methods of "local nonlinear solution and global thermal network solution", the problem of contact thermal resistance changing with temperature can be solved.
[0044] 3. Numerical solution After completing the hot node partitioning and establishing the energy conservation equations for all hot nodes, the temperature state vectors of the hot nodes can be obtained. The nonlinear transient model that satisfies the condition is denoted as . ,in, This represents a vector consisting of the derivatives of the temperatures at each thermal node with respect to time. This represents the right-hand side of the heat network equation, determined by heat conduction, radiation, cooling, heat leakage, and heater power. At step size h: Convert to nonlinear equations: Then, Newton's iteration is used to solve the problem. To improve the stability of the solution, a line search is introduced into Newton's iteration: in Line search is used to ensure residual reduction; to balance accuracy and efficiency, a step-doubling strategy is adopted for adaptive step size control, which compares the difference between the results obtained by "one step h" and "two steps h / 2" to estimate the local truncation error; when the error meets the tolerance requirement, the current step size is accepted and the next step size is appropriately increased; otherwise, the step size is reduced and the calculation is recalculated. First step h is obtained Two steps to get h / 2 Error estimation ; definition: If err≤1, accept the application and update the step size; otherwise, reject the application, decrease the step size, and recalculate.
[0045] Through the above implicit adaptive solution process, the cooling curves of each thermal node can be stably obtained, and then the changes of the average temperature of the superconducting cavity, the maximum temperature difference of the ellipsoidal cavity, and the cooling rate over time can be obtained.
[0046] Module 2 M2: Online Acquisition and Preprocessing Module M2 is used for online acquisition and preprocessing of multi-point temperatures during the actual cooling process. It acquires multi-point temperatures online, removes outliers, and performs filtering to reduce noise, resulting in a smoothed measured temperature sequence, which serves as the real-time input for online calibration in M3 and model predictive control in M6. The actual distribution of temperature sensors and heaters, and the symbolic representation of the measured temperature points, are shown below. Figure 5 As shown.
[0047] Module 3 M3: Online Calibration Module To improve the consistency between the thermal network prediction and the actual device, an online correction module, M3, is set up. This module uses the thermal network model provided by M1 as the prediction model and the measured temperature sequence output by M2 as the observation input. It employs a moving-time-domain estimation method to recursively correct the key uncertain parameters in the thermal network model, thereby obtaining the parameter estimates for the current control cycle. And based on this, the state of the prediction model is corrected.
[0048] Selected actual temperature value T: Temperature values T of the three Link2 branches Li (i=1,2,3) and the temperature T at the five nodes of the ellipsoidal cavity. Cj (j=1,2,…,5). Four key parameters are selected. These are: the deviation in heat leakage of the Link2 branch due to material properties, vacuum level, and support, which is corrected by an equivalent heat leakage term, Q. leak,i (i=1,2,3); the corrected heat leakage terms are added to the corresponding Link2 branches. Additionally, the contact thermal resistance deviation caused by actual assembly preload, interface conditions, etc., is corrected using the overall contact thermal resistance scaling value αR, i.e., R... eff,i (T)=α R R i (T) (i=1,2,3). At the same time, reasonable constraints can be added based on actual conditions: Q min ≤Q leak,i ≤Q max α R,min ≤α R ≤α R,max .
[0049] M3 output corrected parameter estimate The corresponding correction status is used as input to M4 and M6, thereby improving the accuracy of subsequent temperature difference prediction and control decisions.
[0050] Module 4 M4: MLP Multilayer Perceptron Learning Module In actual control processes, without suitable initial values for calculation, problems such as long solution times, iteration failures, and high-frequency fluctuations in output power can easily occur. Therefore, this module uses machine learning methods to calculate the output power in each control cycle based on the current temperature state vector x and the estimated parameter values. In addition, temperature zone coding is used to generate a set of reference control sequences that approximate the feasible optimal solution. U ref As the warm-start initial value provided by M6 to provide a near-feasible optimal solution, that is, to give a theoretically suitable and feasible "three-heater power scheme" as the initial value input in advance, the control module only needs to make a small correction to make the operation more efficient and stable.
[0051] The temperature state vector x includes the temperature values T of the three Link2 branches. Li (i=1,2,3), the temperature T at the five nodes of the ellipsoidal cavity Cj (j=1,2,…,5), average temperature Temperature difference Cooling rate r. The average temperature of the superconducting cavity. As a characteristic temperature, the critical temperature region (30K-4K) is divided into J temperature ranges, with further segmentation possible before and after the superconducting transition temperature. Within each temperature range, the heater power output changes linearly. Furthermore, based on the characteristics of the cooling structure and heater distribution, it is found that the middle branch (P2) more directly affects the overall average temperature and rate, while the two side branches (P1 and P3) more directly affect the temperature difference between the two ends and the middle of the superconducting cavity. Therefore, the following definition is made: , This transforms "two-dimensional coupling" into "one-dimensional regression".
[0052] Learning can be performed using a multilayer perceptron (MLP). The input layer includes the temperature state vector x and parameter estimates. And J-dimensional one-hot vectors, the output layer is , and The training dataset is derived from solving a hybrid 0D+1D thermal network model and an implicit adaptive step-size model. The training samples in the training dataset consist of offline thermal network model simulations and feasible control sequences. Each training sample contains a set of state and parameter inputs, such as the temperatures of the three Link2 branches, the five-node temperature of the ellipsoidal cavity, the average temperature, the maximum temperature difference, the cooling rate, the estimated online correction parameters, and the temperature zone encoding. The corresponding output is a parameterized representation of the power of the three heaters in each temperature zone.
[0053] When running online, M4 updates the output reference control sequence in each control cycle. U refThis reference control sequence is the initial value of M6's warm-start, used only for optimization initialization and reference trajectory, and not directly used as the final execution instruction.
[0054] Module 5 M5: Temperature Difference Setting and Speed Limiting Module Since the temperature difference before and after the superconducting transition temperature region of the Nb3Sn superconducting cavity during the cooling process will significantly affect the performance of the superconducting cavity, it is necessary to constrain the cooling temperature difference in the key temperature region.
[0055] The average temperature, maximum temperature difference, and cooling rate on the superconducting cavity were obtained from actual temperature measurements. , , ; Typically, the maximum temperature difference of the superconducting cavity within the 30 K–4 K temperature range is required to not exceed 0.2 K, i.e. (j=1,2,…,5); and while satisfying the hard constraint of temperature difference, the cooling rate should be increased as much as possible. Therefore, a baseline cooling rate upper limit is set in the key temperature zone. To avoid excessively limiting the system's cooling rate, i.e. ,in These are key temperature range breakpoints (e.g., several breakpoints covering 30-4K). This represents the upper limit of the cooling rate for the corresponding temperature zone.
[0056] At the same time, issues arising from prediction model errors, measurement noise, and hard constraints need to be considered, such as temperature differences. High-frequency vibrations in the vicinity and high-frequency adjustments of the heater necessitate further improvements in the system's robustness and solution stability. Therefore, a speed limiting factor is defined. : in, , This represents the actual temperature difference within the cavity; This is the temperature difference margin threshold, used to determine whether to begin preventatively reducing the cooling rate; The minimum rate-limiting factor represents the allowable cooling rate when the actual temperature difference in the cavity approaches 0.2K, ensuring controllability as the temperature difference nears its upper limit and reducing the risk of exceeding the limit. p determines whether the change is gradual; the smaller the p, the more gradual the change, and the larger the p, the more abrupt the change.
[0057] Define the upper limit of the actual cooling rate ,Right now Therefore, constraints are imposed within the prediction domain in module six (M6): .
[0058] Therefore, the final output set of this module .
[0059] Module 6 M6: MPC Model Predictive Control Module Since the superconducting cavity cooling system is inherently a slowly changing and highly nonlinear thermal system, the MPC (Model Predictive Control) method is employed to coordinate the control of multiple heaters while satisfying the hard constraint of temperature difference. MPC involves predicting the temperature evolution over a future period using a model in each control cycle, solving for the optimal control sequence under the constraints, and executing only the first control variable. The next control cycle then updates the solution based on the latest measurement results and re-solves the problem. Specific implementation steps: During the k-th control cycle, M6 receives the following input: the measured temperature state vector x output by M2. k Parameter estimates output by M3 M4 output reference control sequence U ref,k (i.e., the initial values of warm-start) and the set of constraints output by M5. Based on the above inputs, the internal M1 thermal network model is invoked to predict the temperature evolution of each thermal node over a future period, and the state recursive equation within the prediction domain is constructed as follows: Initial conditions ,in F represents the system state vector of the i-th deviated step in the prediction domain during the k-th control period; d This represents the state transition function obtained by time discretization of the thermal network model of module M1; This represents the control input vector corresponding to the three heaters in the staggered path; N represents the prediction step number. Actuator constraints are added to ensure control execution and to protect the system and suppress jitter. , (j=1,2,3). Wherein... This represents the power of the j-th heater in the i-th step of the prediction domain during the k-th control cycle; This represents the upper limit of the power of the j-th heater; This represents the maximum allowable power variation of the j-th heater between adjacent walks. Control optimization involves actuator constraints and constraint sets. This is achieved through a combination of factors, ensuring the actuator control input is executable while simultaneously guaranteeing that the predicted process meets the requirements for temperature difference and cooling rate. In other words, actuator constraints are used to constrain the power of each heater. and the change between its adjacent walks; constraint set It is mainly used to constrain the maximum temperature difference and cooling rate of the superconducting cavity within the prediction domain.
[0060] The objective function for building module M6 is: ;in This represents the average temperature of the superconducting cavity at the predicted end time. This represents the i-th prediction step reference control input output by module M4; This indicates the power difference between the left and right heaters, used to characterize the degree of lateral power asymmetry; , , and The weighting coefficients for the terminal temperature term, reference control tracking term, control increment smoothing term, and left-right power difference suppression term are respectively obtained through offline tuning, simulation calibration, or empirical setting.
[0061] The optimal heater control sequence in the future prediction domain is obtained by iteratively solving using a numerical optimization solver (SQP / internal point method, etc.). The predicted evolution of temperatures at each thermal node is determined by a discretized thermal network prediction model within the optimal control sequence. The result is obtained recursively under the action of the action, namely: During online execution, only the control quantity of the first step in the optimal control sequence is used. The solution is applied to the actual system; in the next control cycle k+1, the above optimization problem is solved again based on the latest measured data, the latest parameter estimates, and the updated reference control sequence, thereby achieving rolling optimization closed-loop control.
[0062] In addition, the M6 module needs to output a solution status packet to the M7 module, including whether the solution has converged, the number of iterations, and the solution time.
[0063] Module 7 M7: Solution Supervision Module This module is mainly used to monitor the solution process and results of the M6 module in real time. It performs health classification based on indicators such as convergence, feasibility, computational resources and constraint margin, and triggers degradation control and solution configuration adjustment for the next cycle when necessary to ensure that the closed-loop control can operate continuously, safely and stably.
[0064] The input to this module mainly comes from the solution status packet of module M6, the measured temperature and various temperature parameters of module M2. When module M6 fails to solve or times out (solve_time > 0.9Δt), or... It triggers a high-risk alarm and outputs a downgrade command, while the executor retains the last feasible command; and it adaptively adjusts the M6 module, including shortening the prediction time domain and increasing the smoothing weight.
[0065] An optional embodiment of the present invention provides a cooling system for conductive cooling of a superconducting cavity, characterized in that it includes... The cooling system structural parameter configuration module is used to receive various parameters input from the conductive cooling system. The thermal network prediction module is used to establish the energy conservation equations for each thermal node in the conductive cooling system based on various parameters in the conductive cooling system, and to form a thermal network model of the conductive cooling system. The online acquisition and preprocessing module is used to acquire the measured temperature of each thermal node in the conductive cooling system and send it to the online correction module and the MPC model prediction and control module. The online calibration module is used to recursively correct the key uncertain parameters in the thermal network model based on the measured temperature of each thermal node, obtain the parameter estimate for the current control cycle, and send the parameter estimate to the MLP multilayer perceptron learning module and the MPC model predictive control module. The MLP multilayer perceptron learning module is used to generate a training dataset based on the thermal network model and parameter estimates to train the MLP multilayer perceptron and predict the heater power in each temperature range of the conductive cooling system as the warm-start initial value and send it to the MPC model predictive control module. The temperature difference setting and speed limiting module is used to generate a set of temperature difference change constraints based on the real-time temperature of the superconducting cavity. The MPC model predictive control module is used to predict the temperature evolution of each heat node in the future period by calling the corrected thermal network model based on the measured temperature, parameter estimates, warm-start initial values, and temperature difference change constraint set in each control cycle. The solution supervision module is used to monitor the measured temperature, prediction process and results of each thermal node in real time, and to control the cooling of the conductive cooling superconducting cavity based on the monitoring results.
[0066] An optional embodiment of the present invention provides a computing device, characterized in that it includes: a processor and a memory storing a computer program, wherein the computer program is executed by the processor to perform the above-described method.
[0067] An optional embodiment of the present invention provides a computer-readable storage medium, characterized in that it stores instructions that, when executed on a computer, cause the computer to perform the above-described method.
[0068] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for controlling the cooling of a superconducting cavity through conduction, comprising the following steps: Receives various parameters input from the conductive cooling system; Based on various parameters within the conductive cooling system, energy conservation equations for each thermal node within the conductive cooling system are established, and these equations are combined to form a thermal network model of the conductive cooling system. Collect the measured temperatures of each thermal node in the conductive cooling system; Based on the measured temperature of each thermal node, the key uncertain parameters in the thermal network model are recursively corrected to obtain the parameter estimates for the current control cycle. The training dataset generated based on the thermal network model and parameter estimates is used to train the MLP multilayer perceptron and predict the heater power in each temperature range of the conductive cooling system as the initial value for warm-start. A set of temperature difference change constraints is generated based on the real-time temperature of the superconducting cavity; Within each control cycle, based on the measured temperature, parameter estimates, warm-start initial values, and temperature difference change constraint set, the corrected thermal network model is invoked to predict the temperature evolution of each thermal node over a future period. The measured temperature, prediction process and results of each thermal node are monitored in real time, and the temperature of the conductive cooling superconducting cavity is controlled based on the monitoring results.
2. The method according to claim 1, characterized in that, The set of temperature difference change constraints ;in, The maximum temperature difference within the temperature range. As the upper limit of the baseline cooling rate, As a speed limiting factor, This represents the upper limit of the actual cooling rate. This is the temperature difference margin threshold.
3. The method according to claim 2, characterized in that, ; , This represents the actual temperature difference. Minimum speed limit factor, p This is the temperature difference change control factor.
4. The method according to claim 1, 2, or 3, characterized in that, The method for predicting the temperature evolution of each heat node over a future period using the corrected thermal network model is as follows: The objective function is solved iteratively using a numerical optimization solver. The optimal heater control sequence within the future prediction domain is obtained; where, This represents the average temperature of the superconducting cavity at the predicted end time. This represents the reference control input for the i-th prediction step. Let be the control input vector of the heater in the prediction domain at the i-th prediction step within the k-th control cycle; The degree of lateral power asymmetry; , , and These are the weighting coefficients for the terminal temperature term, the reference control tracking term, the control increment smoothing term, and the lateral power difference suppression term, respectively, where N represents the number of prediction steps.
5. The method according to claim 1, 2, or 3, characterized in that, With the average temperature of the superconducting cavity The key temperature zone of the conductive cooling system is divided into multiple temperature ranges based on the characteristic temperature. Temperature data for each temperature range is calculated using a thermal network model. The temperature data and parameter estimates for each temperature range are then compared. As training data, the heater power within this temperature range is used as the label to generate training samples, resulting in a training dataset.
6. The method according to claim 1, 2, or 3, characterized in that, The energy conservation equation for the i-th hot node is: ;in, It is the equivalent mass of the component or discrete segment corresponding to the i-th hot node. The material at the i-th thermal node is at temperature The specific heat capacity below; It is the temperature of the i-th hot node; and These are the input and output of the heat flow of the i-th hot node, respectively. It is the heat flow generated by the external source term of the i-th hot node.
7. The method according to claim 1, characterized in that, The parameters of the conductive cooling system include at least the following: the geometric dimensions of each component of the conductive cooling system, the specific heat capacity function Cp(T) of the material, the thermal conductivity function λ(T), the surface emissivity, the number of layers of the multilayer insulation material MLI, the contact thermal resistance function R(T), the cooling capacity-temperature curve Qcool(T) of the cold head, the ambient temperature, the initial temperature, the equivalent heat leakage parameters of the support and connecting parts, the maximum power of the heater, and the maximum power change rate.
8. A cooling system for conductive cooling of a superconducting cavity, characterized in that, include The cooling system structural parameter configuration module is used to receive various parameters input from the conductive cooling system. The thermal network prediction module is used to establish the energy conservation equations for each thermal node in the conductive cooling system based on various parameters in the conductive cooling system, and to form a thermal network model of the conductive cooling system. The online acquisition and preprocessing module is used to acquire the measured temperature of each thermal node in the conductive cooling system and send it to the online correction module and the MPC model prediction and control module. The online calibration module is used to recursively correct the key uncertain parameters in the thermal network model based on the measured temperature of each thermal node, obtain the parameter estimate for the current control cycle, and send the parameter estimate to the MLP multilayer perceptron learning module and the MPC model predictive control module. The MLP multilayer perceptron learning module is used to generate a training dataset based on the thermal network model and parameter estimates to train the MLP multilayer perceptron and predict the heater power in each temperature range of the conductive cooling system as the warm-start initial value and send it to the MPC model predictive control module. The temperature difference setting and speed limiting module is used to generate a set of temperature difference change constraints based on the real-time temperature of the superconducting cavity. The MPC model predictive control module is used to predict the temperature evolution of each heat node in the future period by calling the corrected thermal network model based on the measured temperature, parameter estimates, warm-start initial values, and temperature difference change constraint set in each control cycle. The solution supervision module is used to monitor the measured temperature, prediction process and results of each thermal node in real time, and to control the cooling of the conductive cooling superconducting cavity based on the monitoring results.
9. A computing device, characterized in that, include: A processor, a memory storing a computer program, wherein the computer program, when executed by the processor, performs the method as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, A storage instruction that, when executed on a computer, causes the computer to perform the method as described in any one of claims 1 to 7.