High-temperature superconducting magnet temperature equalization control method for circulating cold helium

Abstract

The invention provides a high-temperature superconducting magnet temperature equalization control method for circulating cold helium, and belongs to the field of superconducting magnet temperature control, and the method comprises the steps: calculating a difference value between a target temperature and an actual measurement temperature, and obtaining a steady-state error of each group of magnets; constructing a mathematical model of the cold helium cooling system according to a singular perturbation theory; a control target is determined, and the overall performance and stability of the cold helium cooling system are improved; and constructing a singular perturbation control model based on the variable universe Smith. According to the invention, the response speed and precision of the cold helium cooling system can be improved.

Description

Technical Field

[0001] The invention belongs to the field of superconducting magnet temperature control, and in particular relates to a temperature balance control method for a high-temperature superconducting magnet with circulating cold helium gas. Background Art

[0002] The stable operation of superconducting synchronous condensers depends on an efficient cooling system, especially in a low-temperature environment. The efficiency and stability of the cooling technology directly affect the working performance of superconducting materials. The superconducting magnets of high-temperature superconducting synchronous condensers usually operate at a low temperature of about 20 K, which requires the system to maintain a stable working state in a low-temperature vacuum container. In order to ensure that the heat generated by the superconducting magnets and other key components during operation can be removed in time, an efficient and precise cooling solution is required. The superconducting rotor magnet will generate a variety of heat loads during operation, mainly including heat leakage from the superconducting magnet itself, heat leakage caused by radiation or heat conduction of the cooling system, and heat loss on the electrical conductors. These heat loads need to be removed by effective cooling methods to ensure that the superconducting magnets are maintained at the required low temperature state. At present, the refrigeration system of circulating cold helium is widely used in the cooling of superconducting magnets, using the good thermophysical properties of cold helium at low temperatures to provide a stable low-temperature environment.

[0003] Cold helium plays a key role in the temperature balance control of high-temperature superconducting magnets due to its excellent low-temperature characteristics. Through the cold helium circulation system, efficient heat exchange can be achieved and the temperature of the superconducting magnet can be kept within a stable working range. Many studies at home and abroad have shown that cold helium circulation cooling technology can effectively solve the problem of superconducting magnet temperature control and show broad prospects in various application scenarios. For example, Dai Yijun and others used a closed cold helium circulation cooling system in their research, analyzed the cooling process of the rotor by the lumped parameter method, and successfully reduced the rotor temperature to 25 K, achieving a significant technological breakthrough. Shi Zhengjun and others designed a circulating cold helium low-temperature thermal management system in a vacuum environment to meet the cooling needs of the 10 Mvar high-temperature superconducting synchronous condenser of the Southern Power Grid. The test results show that the system can stably control the rotor temperature at 22.4 K, verifying its feasibility and stability in actual engineering.

[0004] Although the cold helium circulation cooling technology has been applied to superconducting motors and phase regulators, there are still some challenges, especially in temperature balance control. Superconducting magnets may experience temperature imbalance under different working conditions, which will affect their superconducting performance and system stability. Therefore, how to further improve the uniformity of cold helium flow and the balance of temperature distribution has become the key to improving the performance of the cooling system. In the existing technology, the optimization of parameters such as the flow rate, pressure and flow path of cold helium is still a research hotspot.

[0005] In summary, although the existing cooling technology has solved the temperature control problem of superconducting magnets to a certain extent, in practical applications, how to achieve more precise and balanced temperature regulation is still the key to improving the performance of the cooling system of superconducting synchronous condensers. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a temperature balance control method for a high-temperature superconducting magnet with circulating cold helium gas, which further improves the temperature balance and system stability of the superconducting magnet by optimizing the flow and cooling parameters of the cold helium gas, so as to meet the higher performance requirements of future superconducting synchronous phase shifters.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] A method for controlling the temperature balance of a high-temperature superconducting magnet by circulating cold helium gas comprises the following steps:

[0009] Step 1, by calculating the difference between the target temperature and the actual measured temperature, the steady-state error of each group of magnets is obtained;

[0010] Step 2. Construct a mathematical model of the cold helium cooling system based on the singular perturbation theory. By decomposing the cold helium cooling system into a fast subsystem and a slow subsystem, the fast adjustment of the cold helium flow rate and the long-term stability of the magnet temperature are controlled respectively; the fast subsystem is responsible for rapid response when the steady-state error is large, and the slow subsystem ensures that the entire system maintains temperature equilibrium over a long period of time;

[0011] Step 3: Define the control objectives, including maximizing total heat dissipation, minimizing total pressure drop, and optimizing time; by optimizing these objectives, avoid overheating, reduce energy consumption, and quickly respond to temperature fluctuations, ensure that the superconducting magnet is always maintained within the temperature range of 30±1.5K, and ultimately improve the overall performance and stability of the cold helium cooling system;

[0012] Step 4: Construct a singular perturbation control model based on variable domain Smith to ensure that the cold helium cooling system can flexibly adjust control parameters under different working conditions to cope with local hot spots and temperature fluctuations; at the same time, use the Smith predictor to compensate for sensor delays and actuator response lags in the cold helium cooling system to improve the response speed and accuracy of the cold helium cooling system.

[0013] Beneficial effects:

[0014] 1. The present invention provides a temperature balance control method for a high-temperature superconducting magnet based on a variable domain Smith singular perturbation control model. By accurately adjusting the flow rate, pressure and temperature of cold helium gas, the present invention can effectively deal with the instability caused by local hot spots and achieve precise control of the temperature of the superconducting magnet, thereby avoiding the quenching phenomenon caused by excessively high or low temperature and ensuring the stability and safety of the superconducting system during operation.

[0015] 2. The present invention introduces the temperature control strategy of the fast and slow subsystems and uses the singular perturbation theory to perform hierarchical management of the cold helium cooling system. The fast subsystem can quickly respond to local hot spots, adjust the flow and pressure of the cold helium, and eliminate transient temperature deviations in time; the slow subsystem handles the distribution and stability of the overall temperature field to ensure temperature balance among multiple magnets, thereby avoiding quenching problems caused by excessive temperature differences.

[0016] 3. The present invention adopts a combination of variable domain control and fuzzy adaptive PID control, which can dynamically adjust the control parameters according to the real-time steady-state error. When the steady-state error is small, the system maintains a low control sensitivity and reduces energy consumption; when the steady-state error increases, the system automatically increases the sensitivity, quickly adjusts the cold helium flow and pressure, maximizes the heat dissipation, minimizes the system pressure drop, thereby improving the cooling efficiency and reducing energy consumption.

[0017] 4. The present invention combines the Smith predictor to perform time delay compensation, effectively solving the time delay problem between the temperature sensor and the actuator. By predicting the system dynamics in advance, the Smith predictor can perform delay compensation during the temperature adjustment process, thereby improving the system response speed, avoiding temperature oscillation and overshoot caused by hysteresis effects, and ensuring accurate regulation of the cold helium flow rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of the temperature balance control method of the high temperature superconducting magnet with circulating cold helium gas of the present invention;

[0019] Figure 2 Detailed step diagram of the improved singular perturbation theory control strategy;

[0020] Figure 3 This is a schematic diagram of the Smith predictive PID controller structure. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0022] The temperature balance control method of high-temperature superconducting magnets with circulating cold helium proposed in the present invention effectively solves the temperature balance problem of high-temperature superconducting magnets in actual work by combining variable domain control and Smith predictor. In the cold helium circulation system, local hot spots are first dealt with by precisely controlling the flow and pressure of cold helium, and the magnet temperature is adjusted in real time to ensure that all magnets operate stably within the temperature range of 30±1.5K. By combining the coordinated control of fast and slow subsystems with the steady-state error feedback mechanism, the method can achieve dynamic adjustment under different working conditions to ensure maximum cooling efficiency and optimization of energy efficiency.

[0023] The cold helium circulation system adopts a variable domain control strategy, adaptively adjusting the control parameters according to the steady-state error to ensure that the cold helium circulation system maintains low energy consumption and stability under normal operating conditions with small temperature differences; and rapidly increases the cold helium flow rate to eliminate hot spots under local hot spot conditions with large temperature differences. The Smith predictor compensates for the delay between the sensor and the actuator in the system to ensure the timeliness and accuracy of the control response.

[0024] In addition, the cold helium circulation system also has a redundant design and fault response mechanism. Through real-time monitoring and temperature sensor feedback, it can respond to sudden faults in a timely manner to ensure the stable operation of the cold helium circulation system and the consistency of the magnet temperature. The present invention has strong adaptability and robustness, and can effectively solve the problems of uneven temperature distribution and excessive temperature fluctuations in the cold helium cooling system in practical applications, ensuring that the high-temperature superconducting magnet is always in the best working state under different working conditions.

[0025] like Figure 1 As shown, the temperature balance control method of a high-temperature superconducting magnet circulating cold helium gas in an embodiment of the present invention comprises the following steps:

[0026] Step 1: Calculate the steady-state error, including:

[0027] Step 1.1. Build a temperature accuracy model:

[0028] The temperature accuracy model includes the calculation and feedback mechanism of temperature error, the dynamic change of temperature distribution, and the coupling relationship between cold helium flow and temperature regulation. These features work together to ensure that the system can accurately monitor and adjust the temperature of the superconducting magnet to keep it within the target range:

[0029] In a high-temperature superconducting phase shifter, six groups of magnets contain a total of 18 groups of double-pancake coils, and each group of magnets needs to be maintained within a temperature range of 30±1.5K during operation. Since the temperature of the magnet directly affects the superconducting performance, if the temperature of any double-pancake coil exceeds this precision range, it may cause partial quenching of the magnet (i.e., the superconducting state is destroyed), thereby affecting the stability and safety of the entire system. Therefore, it is the core task of the cold helium cooling system to accurately control the uniformity of the temperature of each group of magnets and maintain a consistent thermal balance between different coils. A temperature accuracy model for temperature uniformity and precision control is added to monitor and adjust the temperature of the six groups of magnets and 18 groups of double-pancake coils.

[0030] Step 1.2 describes the error state of the temperature field:

[0031] Define the real-time temperature of the i-th double-pancake coil as , the target temperature is The steady-state error is defined by the following formula: :

[0032] (1)

[0033] In order to accurately control the temperature of each set of magnets and each coil in the entire cooling system, an index is used To represent each specific coil, the range is , indicating the and A double pancake coil, t represents time.

[0034] The steady-state error needs to satisfy:

[0035] (2)

[0036] Step 1.3 Control the uniformity of the temperature gradient:

[0037] In order to avoid the quench problem caused by uneven temperatures of different coils, it is defined that represents the actual temperature of the th double-pancake coil, represents the actual temperature of the th double-pancake coil, and the maximum temperature difference It can be expressed as:

[0038] (3)

[0039] in, That is, the real-time temperature of the i-th group of magnets is ; That is, the real-time temperature of the jth group of magnets.

[0040] Control objectives ensure:

[0041] (4)

[0042] Step 2. Construct a mathematical model of the system based on singular perturbation theory. By decomposing the system into a fast subsystem and a slow subsystem, the present invention can control the rapid adjustment of the cold helium gas flow and the long-term stability of the magnet temperature respectively. The fast subsystem is responsible for rapid response when the steady-state error is large, and the slow subsystem ensures that the entire system maintains temperature equilibrium over a long period of time.

[0043] The cold helium cooling system has multi-time scale characteristics: the temperature distribution changes slowly, while the flow and pressure change quickly. In order to effectively deal with this multi-time scale phenomenon, the system is divided into two subsystems, fast and slow, using singular perturbation theory: the fast subsystem is mainly responsible for real-time response to local hot spots, and quickly eliminates transient temperature deviations by adjusting the cold helium flow and pressure; the slow subsystem focuses on the long-term temperature balance of the system, handles the distribution and stability of the overall temperature field, and ensures that multiple sets of magnets maintain a consistent temperature during operation.

[0044] The mathematical models of the fast and slow systems are:

[0045] (5)

[0046] (6)

[0047] in, is a slow-changing variable, i.e., the temperature state, is a fast-changing variable, namely the flow rate and pressure state of helium, is the time scale ratio, satisfying . Represents a slowly changing variable The rate of change of, that is, the change of the temperature field in the system. Represents fast-changing variables The rate of change. and They represent the functions of the slow system and the fast system respectively, and t represents time.

[0048] Construct the temperature control equation of the fast and slow subsystems:

[0049] Based on the existing singular perturbation theory, the temperature dynamic equation can be described as:

[0050] (7)

[0051] in, It is Real-time temperature of group magnets; is the cooling coefficient related to the cold helium flow rate; is the generation coefficient describing the local hotspot; is the local heat generated inside the magnet. The target temperature is .

[0052] Construct the governing equations for the fast subsystem:

[0053] The generation of local hot spots is instantaneous and unpredictable, requiring the fast subsystem to respond quickly to prevent the temperature from exceeding the range of 30 ± 1.5 K. The fast subsystem mainly achieves rapid heat dissipation by adjusting the flow and pressure of cold helium.

[0054] In the tachyon system, the flow rate and pressure of the cold helium need to be adjusted dynamically to ensure that the steady-state error is eliminated quickly:

[0055] (8)

[0056] in, It is cold helium in the Flow rate in group magnets; It is the control input of the cold helium pump

[0057] This equation ensures that the temperature changes of all coils remain within the allowed accuracy range by adjusting the flow rate in each magnet flow channel in real time.

[0058] Construct the control equations of the slow subsystem:

[0059] The fast subsystem can quickly eliminate short-term temperature fluctuations, but the steady-state temperature control of the system also requires a slow subsystem to achieve global temperature balance. The slow subsystem focuses on the long-term evolution of temperature, which is related to the overall heat transfer and distribution of the system, and can better handle the temperature balance between multiple sets of magnets and their coils.

[0060] Considering the long-term heat conduction and temperature balance of the system, the temperature dynamics of the slow subsystem can be described as:

[0061] (9)

[0062] in, It is Heat capacity of the magnet group; is the thermal conductivity, describing the rate of heat exchange between magnets; It is Real-time temperature of group magnets; It is the outside world Thermal power of the magnet group; It refers to the heat taken away by the cold helium.

[0063] In actual engineering, the fast subsystem and the slow subsystem need to work together to ensure the stability and high-precision temperature control of the entire cooling system. Fast subsystem: When a local hot spot appears, the cold helium flow rate is quickly adjusted to ensure that the hot spot temperature quickly returns to the target range. Slow subsystem: By adjusting the temperature balance between each group of magnets, the temperature consistency and stability of the overall system over a long period of time is ensured.

[0064] The synergy between the two can be achieved in the following ways: the fast subsystem compresses local temperature fluctuations into a controllable range; the slow subsystem refines the adjustment strategy of the cold helium gas according to the global temperature distribution, so that the temperature tends to be balanced among different magnets.

[0065] Step 3. Define the control objectives, including maximizing total heat dissipation, minimizing total pressure drop, and optimizing time; by optimizing these objectives, avoid overheating, reduce energy consumption, and quickly respond to temperature fluctuations, ensure that the superconducting magnet is always maintained within the temperature range of 30±1.5K, and ultimately improve the overall performance and stability of the cold helium cooling system.

[0066] Step 3.1 Maximize total heat dissipation:

[0067] Heat dissipation Calculated as:

[0068] (10)

[0069] in, is the mass flow rate of cold helium, is the specific heat capacity of cold helium. The temperature of the cold helium entering the cooling system (inlet temperature), that is, the temperature of the cold helium at the inlet of the cooling equipment; It is the temperature of the cold helium gas flowing out of the cooling system (outlet temperature), that is, the temperature of the cold helium gas at the outlet of the cooling system.

[0070] Step 3.2 Minimize the total pressure drop:

[0071] Pressure drop of cold helium Calculated as:

[0072] (11)

[0073] in, is the friction coefficient, is the pipe length, is the pipe diameter.

[0074] Step 3.3: Time optimal control:

[0075] The time optimization goal is:

[0076] (12)

[0077] in, is the steady-state error, is the rate of change of error. Indicates the total time during the optimization process.

[0078] Step 4: Figure 2 As shown, a singular perturbation control model based on variable domain Smith is constructed:

[0079] When building a model of a cold helium cooling system, the dynamic characteristics of local hot spots, as well as possible sensor delays, actuator response lags, and controller parameter switching issues must be considered. To this end, variable universe control and Smith predictor combined with singular perturbation theory are used to build the model.

[0080] Step 4.1. Derive variable domain control:

[0081] The core idea of ​​variable domain control is to dynamically adjust the controller parameters according to the changes in system status (such as the size of temperature error or whether local hot spots appear). In this way, the system can achieve the best control effect under different working conditions.

[0082] In a high-temperature superconducting phase shifter, local hot spots change over time, so the control parameters under different states need to be dynamically adjusted. To achieve this goal, variable universe control is introduced to adaptively adjust the control parameters.

[0083] Design of variable domain controller: In control systems, steady-state error It is used as the basis for adjusting the controller parameters. According to different steady-state error ranges, the controller gain , , Need to change dynamically. The specific settings are:

[0084] When the temperature difference When the system remains in normal operation, the parameter adjustment is slow and the controller sensitivity is low;

[0085] When the temperature difference When the system enters the hot spot state, the cold helium flow rate needs to be increased rapidly. The controller is highly sensitive and the parameters change rapidly.

[0086] When the temperature difference is too large or too small, the system enters an overcooling or abnormal state, and the controller needs to reduce the flow rate to avoid overcooling or wasting energy.

[0087] Formula derivation of variable domain controller: First, define the steady-state error :

[0088] (13)

[0089] Derivative of the steady-state error:

[0090] (14)

[0091] In order to achieve adaptive control, Indicates adjusting the response speed of the system. represents the elimination of steady-state error, Indicates that the controller gain is used to reduce the overshoot of the system. , , All are errors Function:

[0092] = (15)

[0093] (16)

[0094] (17)

[0095] in, is the critical value of the error, which determines the threshold for switching the control parameters. is the sensitivity of the control parameter adjustment. Indicates low proportional gain. When the system temperature error is small or stable, a lower proportional gain is used to reduce the response to temperature fluctuations and reduce over-regulation. Indicates low integral gain. Low integral gain allows the system to avoid over-integration of small errors accumulated over a long period of time when the error is small, thereby improving the stability of the system; Indicates low differential gain. Low differential gain means that in a stable state, the system responds more gently to temperature changes, reducing the risk of overshoot and oscillation. Indicates high proportional gain, which can respond quickly to temperature errors, quickly adjust flow to eliminate local hot spots, and increase the sensitivity of the control system to temperature errors; Indicates high integral gain, which can accelerate the elimination of steady-state errors in the system and prevent the temperature from deviating from the target value for a long time. It is suitable for the rapid elimination of local hot spots. It means that high differential gain can respond to temperature changes more sensitively, quickly suppress temperature fluctuations and overshoot, and thus avoid further increase in hot spot temperature. In the Smith predictor, Is the gain parameter of the system. K usually refers to one of the three gain parameters, namely the proportional gain , integral gain or differential gain , these gain parameters determine how the controller responds to temperature errors, the rate of change of the error, and the accumulation of the error.

[0096] The control input formula of the variable universe PID controller is:

[0097] (18)

[0098] in, represents the control input, which is a control signal representing the flow rate of cold helium gas, and adjusts the cooling system to achieve the target temperature; It represents the integral part of the steady-state error function. It calculates the accumulated steady-state error from the beginning of the system to the current moment. It plays the role of eliminating the steady-state error in the integral term, ensuring that the system maintains accurate temperature during long-term operation. is the integrating variable, which varies in the time range [0.t].

[0099] In practical applications, too drastic parameter switching may lead to control discontinuity or oscillation problems, especially when the system frequently switches between different states. In order to avoid this phenomenon, it is possible to consider introducing a hysteresis control strategy, that is, adding an appropriate hysteresis interval when switching between states to ensure smooth system switching. Therefore, the hysteresis region is introduced. To define the boundary of parameter switching. We can get:

[0100] (19)

[0101] (20)

[0102] (twenty one)

[0103] Apply variable universe control to singularly perturbed models:

[0104] In the singular perturbation model, the fast subsystem describes the rapid changes in the flow and pressure of cold helium gas, and its control input is generated by the variable domain controller. The state equation of the fast subsystem is:

[0105] (twenty two)

[0106] in, Represents the time scale factor, which is the ratio of the fast and slow time scales. Represents the gain factor of flow regulation, Indicates that cold helium is The flow rate in the magnetic coil, Indicates the target flow rate of cold helium gas.

[0107] For each set of magnets or cooling circuits, the control objective of the tachyon system is to respond to local hot spots by adjusting the flow of cold helium and maintain the target temperature. It is obtained through the variable domain controller as follows:

[0108] (twenty three)

[0109] Substituting this formula into the state equation of the fast subsystem, we get the dynamic change equation of the cold helium flow rate:

[0110] (twenty four)

[0111] This equation describes how the cold helium flow rate can be adaptively adjusted through variable universe control to cope with changes in steady-state error.

[0112] Step 4.2. Obtain the time delay compensation formula of the Smith predictor in the system:

[0113] like Figure 3 As shown in the figure, in the cold helium cooling system, there may be a certain time delay between the temperature sensor and the actuator, and the temperature data obtained by the sensor is not real-time, which will cause the control system to respond lag. For this, it is necessary to estimate the dynamic mathematical model of the controlled object. A compensator is connected in parallel to the controlled object to form a new controller. In order to make the controller take action in advance, the controlled quantity will be fed back to the input end in advance, so as to weaken or even eliminate the oscillation and overshoot caused by the lag effect of the original system and improve the stability of the system.

[0114] Figure 3 middle, is the expected value of the system; is the measured value of the system; is the controller transfer function; It is a pure lag link; It is the mathematical model of the system; is the lag time; is the mathematical model of Smith's predictor variable; the function of Smith's predictor compensation is expressed as ;in is a complex variable used in Laplace transform to represent the frequency response of the system.

[0115] The model derivation process of Smith predictor is as follows:

[0116] The core idea of ​​the Smith predictor is to separate the delayed model from the non-delayed model and predict the future output through the model to achieve delay compensation. It is given by the following formula:

[0117] (25)

[0118] in, is the reference input of the system (target temperature); It is the model estimate of the system, representing the output of the system without delay; is the actual output of the system with delay; It's a time delay. It is the transfer function of the controller, which represents the response of the controller to the input signal in the control system.

[0119] The state space representation of the Smith predictor is:

[0120] In actual engineering, the state of the system can be described by the state space model. Assume that the state equation of the system is:

[0121] (26)

[0122] (27)

[0123] in, Represents the state variables of the system; Represents the output of the system; represents the control input; A, B, C, and D are the state matrix, input matrix, output matrix, and transfer matrix of the system respectively;

[0124] Delayed output for:

[0125] (28)

[0126] The Smith predictor uses a delay-free model of the system To predict the output of the system and perform delay compensation. The estimated output is:

[0127] (29)

[0128] in, Represents the estimated value of the system output, that is, through Predicted system outputs; represents the estimated value of the control input, that is, the estimated control signal; is an estimated state variable that represents a predicted or estimated value of the system state.

[0129] Control Input The formula is:

[0130] (30)

[0131] The complete governing equations for the fast subsystem combined with the Smith predictor are:

[0132] When combined with the Smith predictor, the state equation of the fast subsystem becomes:

[0133] (31)

[0134] in, is the reference temperature; Compensates for the delay predicted by the Smith predictor.

[0135] This equation describes how to compensate for time delays through the Smith predictor, ensuring that the flow rate of cold helium responds promptly and is not affected by delays.

[0136] Step 4.3. Construct the overall control framework of the helium cooling system of the high-temperature superconducting phase shifter:

[0137] After combining the variable domain controller and the Smith predictor, the overall control framework of the system is as follows:

[0138] The fast subsystem is used to quickly adjust the cold helium flow:

[0139] (32)

[0140] The variable domain controller generates control input by adaptively adjusting PID parameters :

[0141] (33)

[0142] The Smith predictor compensates for system time delays to ensure prompt response.

Claims

1. A method for controlling the temperature balance of a high-temperature superconducting magnet by circulating cold helium, characterized in that: The steps include: Step 1, by calculating the difference between the target temperature and the actual measured temperature, the steady-state error of each group of magnets is obtained; Step 2: Construct a mathematical model of the cold helium cooling system based on the singular perturbation theory. Decompose the cold helium cooling system into a fast subsystem and a slow subsystem to control the rapid adjustment of the cold helium flow rate and the long-term stability of the magnet temperature respectively. The fast subsystem is responsible for rapid response when the steady-state error is large, and the slow subsystem ensures that the entire system maintains temperature equilibrium over a long period of time. Step 3: Define the control objectives, including maximizing total heat dissipation, minimizing total pressure drop, and optimizing time; by optimizing these objectives, avoid overheating, reduce energy consumption, and quickly respond to temperature fluctuations, ensure that the superconducting magnet is always maintained within the temperature range of 30±1.5K, and ultimately improve the overall performance and stability of the cold helium cooling system; Step 4: Construct a singular perturbation control model based on variable domain Smith to ensure that the cold helium cooling system can flexibly adjust control parameters under different working conditions to cope with local hot spots and temperature fluctuations; at the same time, use the Smith predictor to compensate for sensor delays and actuator response lags in the cold helium cooling system to improve the response speed and accuracy of the cold helium cooling system.

2. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium according to claim 1, characterized in that: The step 1 comprises: Step 1.

1. Construct a temperature accuracy model, which includes the calculation and feedback mechanism of temperature error, the dynamic change of temperature distribution, and the coupling relationship between cold helium flow and temperature regulation, to ensure accurate monitoring and adjustment of the temperature of the superconducting magnet to keep it within the target range; Step 1.2 describes the error state of the temperature field: Define the real-time temperature of the i-th double-pancake coil as , the target temperature is ; The steady-state error is defined by the following formula : （1） Among them, the index To represent each specific coil, the range is , indicating the and A double pancake coil, t represents time; The steady-state error satisfies: （2） Step 1.3 Control the uniformity of the temperature gradient: Maximum temperature difference It is expressed as: （3） in, Indicates The actual temperature of the double-pancake coil, Indicates The actual temperature of the double-pancake coil; Ensures maximum temperature difference satisfy: （4）。 3. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium according to claim 1, characterized in that: In step 2, the mathematical model of the fast system and the mathematical model of the slow system are respectively: （5） （6） in, is a slow-changing variable, i.e., the temperature state, is a fast-changing variable, namely the flow rate and pressure state of helium, is the time scale ratio, satisfying ; Represents a slowly changing variable The rate of change of, that is, the change of the temperature field in the system; Represents fast-changing variables The rate of change of and Then they represent the functions of the slow system and the fast system respectively, and t represents time; The temperature control equation for constructing the fast and slow subsystems is: Based on the existing singular perturbation theory, the temperature control equation is described as: （7） in, It is Real-time temperature of the double-pancake coil; is the cooling coefficient related to the cold helium flow rate; is the generation coefficient describing the local hotspot; is the local heat generated inside the magnet; the target temperature is ; The control equation of the fast subsystem is constructed as: （8） in, It is cold helium in the Flow rate in a double pancake coil; It is the control input of the cold helium pump; The control equation of the slow subsystem is constructed as: （9） in, It is The heat capacity of a double pancake coil; is the thermal conductivity, describing the rate of heat exchange between magnets; It is Real-time temperature of the double-pancake coil; It is the outside world Thermal power of a double pancake coil; It refers to the heat taken away by the cold helium.

4. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium gas according to claim 3, characterized in that: The coordination of the control equations of the fast subsystem and the slow subsystem is achieved in the following way: the fast subsystem compresses the local temperature fluctuations into a controllable range; the slow subsystem refines the adjustment strategy of the cold helium gas according to the global temperature distribution, so that the temperature tends to be balanced among different magnets.

5. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium gas according to claim 1, characterized in that: The step 3 comprises: Step 3.1 Maximize total heat dissipation: Heat dissipation Calculated as: （10） in, is the mass flow rate of cold helium, is the specific heat capacity of cold helium, is the temperature of the cold helium entering the cooling system, that is, the inlet temperature, that is, the temperature of the cold helium at the inlet of the cooling equipment; is the temperature of the cold helium gas flowing out of the cooling system, that is, the outlet temperature, that is, the temperature of the cold helium gas at the outlet of the cooling system; Step 3.2 Minimize the total pressure drop: Pressure drop of cold helium Calculated as: （11） in, is the friction coefficient, is the pipe length, is the pipe diameter; Step 3.3: Time optimal control: The time optimization goal is: （12） in, is the steady-state error, is the error change rate; Indicates the total time during the optimization process.

6. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium gas according to claim 1, characterized in that: The step 4 comprises: Step 4.

1. Derive the specific formula of variable domain control: In a control system, the steady-state error It is used as the basis for adjusting the controller parameters. According to different steady-state error ranges, the controller gain , , Dynamic changes, specific settings are: When the steady-state error When the system remains in normal operation, the parameter adjustment is slow and the controller sensitivity is low; When the steady-state error When the system enters the hot spot state, the cold helium flow rate needs to be increased rapidly. The controller is highly sensitive and the parameters change rapidly. When the temperature difference is too large or too small, the system enters an overcooling or abnormal state, and the controller needs to reduce the flow rate to avoid overcooling or wasting energy; First, we define the steady-state error : （13） Derivative of the steady-state error: （14） In order to achieve adaptive control, Indicates adjusting the response speed of the system. represents the elimination of steady-state error, Indicates that the controller gain is used to reduce the overshoot of the system. , , Steady-state error Function: = （15） （16） （17） in, is the critical value of the error, which determines the threshold for switching the control parameters. is the sensitivity of the control parameter adjustment; represents proportional gain; represents the integral gain; represents the differential gain; Indicates high proportional gain; Indicates high integral gain; This means that a high differential gain can respond more sensitively to temperature changes.

7. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium gas according to claim 6, characterized in that: The control input formula of the variable universe PID controller is: （18） in, represents the control input, which is a control signal representing the flow rate of cold helium gas, and adjusts the cooling system to achieve the target temperature; Represents the integral part of the steady-state error function, which calculates the steady-state error accumulation from the beginning of the system to the current moment. is the integral variable, which varies in the time range [0, t]; Introducing hysteresis regions To define the boundary of parameter switching, we get: （19） （20） （21） Apply variable universe control to singularly perturbed models: In the singular perturbation model, the fast subsystem describes the rapid changes in the flow and pressure of cold helium gas, and its control input is generated by the variable domain controller, and the state equation of the fast subsystem is: （22） in, represents the time scale factor, which is the ratio of the fast and slow time scales. Represents the gain factor of flow regulation, Indicates that cold helium is The flow rate in the magnetic coil, Indicates the target flow rate of cold helium; For each set of magnets or cooling circuits, the control objective of the tachyon system is to respond to local hot spots by adjusting the flow of cold helium and maintain the target temperature; the control input It is obtained through the variable domain controller as follows: （23） Substituting this formula into the state equation of the fast subsystem, we get the dynamic change equation of the cold helium flow rate: （24）。 8. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium gas according to claim 7, characterized in that: The step 4 also includes: Step 4.

2. Obtain the time delay compensation formula of the Smith predictor in the system. The model derivation process of the Smith predictor is: Control Input It is given by the following formula: （25） in, is the reference input of the system (target temperature); It is the model estimate of the system, representing the output of the system without delay; is the actual output of the system with delay; It is a time delay; is the transfer function of the controller, which represents the response of the controller to the input signal in the control system; The state space representation of the Smith predictor is: In actual engineering, the state of the system can be described by the state space model. Assume that the state equation of the system is: （26） （27） in, Represents the state variables of the system; Represents the output of the system; represents the control input; A, B, C, and D are the state matrix, input matrix, output matrix, and transfer matrix of the system respectively; Delayed output for: （28） The Smith predictor uses a delay-free model of the system To predict the output of the system and perform delay compensation, the estimated output is: （29） in, Represents the estimated value of the system output, that is, through Predicted system outputs; represents the estimated value of the control input, that is, the estimated control signal; is an estimated state variable, used to represent the predicted or estimated value of the system state; Control Input The formula is: （30） The complete governing equations for the fast subsystem combined with the Smith predictor are: When combined with the Smith predictor, the state equation of the fast subsystem becomes: （31） in, is the reference temperature; Compensates for the delay predicted by the Smith predictor.

9. The method for controlling the temperature balance of a high-temperature superconducting magnet with circulating cold helium gas according to claim 8, characterized in that: The step 4 also includes: Step 4.

3. Combine the variable domain controller and Smith predictor to build the overall control framework of the helium cooling system of the high-temperature superconducting phase shifter: The fast subsystem is used to quickly adjust the cold helium flow: （32） The variable domain controller generates control input by adaptively adjusting PID parameters : （33） The Smith predictor compensates for system time delays to ensure prompt response.

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