A 24 / 7 mobile magnetic resonance permanent magnet temperature control device and method

Abstract

This invention discloses an all-weather mobile magnetic resonance permanent magnet temperature control device and method, relating to the field of magnetic resonance permanent magnet temperature control technology. It includes a control component, an amplification component, a heating component, a measuring component, a first permanent magnet, and a second permanent magnet. The first and second permanent magnets measure their temperatures through the measuring component. The control component amplifies voltage through a first amplification component and a second amplification component to control the first and second heating components, respectively. The first and second heating components adjust the temperatures of the first and second permanent magnets, respectively. This invention, employing the aforementioned all-weather mobile magnetic resonance permanent magnet temperature control device and method, ensures that even with ambient temperature fluctuations of more than ten degrees Celsius, the magnet temperature fluctuation is less than 0.05 degrees Celsius, allowing the magnetic resonance permanent magnet to maintain highly stable temperature conditions even under natural conditions of large and rapid fluctuations in ambient temperature.

Description

Technical Field

[0001] This invention relates to the field of magnetic resonance permanent magnet temperature control technology, and in particular to an all-weather mobile magnetic resonance permanent magnet temperature control device and method. Background Technology

[0002] Magnetic resonance (MR) technology, as a high-precision analytical tool, has been widely applied in various fields such as chemistry, physics, biology, and medicine for molecular structure analysis, material composition detection, and disease diagnosis. However, the magnetic properties of permanent magnets in MR systems are extremely sensitive to temperature changes. Temperature fluctuations can cause changes in the magnetic field strength, thus affecting the stability of the MR signal and the accuracy of measurements. Therefore, ensuring the temperature stability of the permanent magnets is crucial for improving the performance of MR systems and guaranteeing the reliability of experimental results.

[0003] Traditional magnetic resonance (MRI) systems typically operate in a constant-temperature environment. For example, the ambient temperature fluctuation of the magnet in the paper "Design and Implementation of a Precision Temperature Controller for NMR Permanent Magnets" is only about 2°C, and the magnet is placed in a heat-insulated cavity. The inner loop of the dual-loop temperature control algorithm controls and regulates the air temperature, further improving the working environment of the MRI permanent magnet. However, patent application CN201710626836.6, entitled "A Temperature Control Device for an Industrial Nuclear Magnetic Resonance Permanent Magnet System," employs a three-stage temperature control method: the first stage stabilizes the temperature at a level close to room temperature; the second stage controls the temperature at a constant level near the magnet's operating temperature; and the third stage controls the magnet temperature to the target operating temperature. These methods essentially involve adjusting the ambient temperature or increasing the microenvironment, directly leading to increased equipment costs and overly complex systems. For example, the invention patent with patent application number CN202111388986, entitled "An Event-Triggered Fuzzy Neural Network Temperature Control System and Method", adopts a cascade control loop that combines an outer loop control loop and an inner loop control loop. Rapid changes in external temperature can easily cause self-excitation of the multi-level loop system connected in series, resulting in poor environmental adaptability.

[0004] To adapt to environments with large and rapid temperature fluctuations throughout the day and to achieve a portable magnetic resonance main magnet at extremely low cost, this application will simplify the system structure as much as possible and, through the design of a better control algorithm, realize a highly stable temperature control system for the magnetic resonance main magnet in an environment without external air conditioning. Summary of the Invention

[0005] The purpose of this invention is to provide an all-weather mobile magnetic resonance permanent magnet temperature control device and method, which solves the problem that existing temperature control technologies cannot meet the high temperature stability requirements of magnetic resonance equipment when operating in natural environments, so that the magnetic resonance permanent magnet temperature fluctuation is less than 0.05 degrees Celsius when the ambient temperature fluctuates by more than ten degrees.

[0006] To achieve the above objectives, the present invention provides an all-weather mobile magnetic resonance permanent magnet temperature control device, comprising a control component, an amplification component, a heating component, a measurement component, a first permanent magnet and a second permanent magnet. The temperature of the first and second permanent magnets is measured by the measurement component. The control component amplifies the voltage through the first and second amplification components to control the first and second heating components, respectively. The first and second heating components adjust the temperature of the first and second permanent magnets, respectively.

[0007] Preferably, the control component controls the voltage through a neural network, which includes an input layer, a hidden layer, and an output layer.

[0008] The inputs to the input layer include the target temperature, ambient temperature, permanent magnet temperature, and bias.

[0009] The output layer includes multiple sets of PIDs. The number of PIDs is twice the number of temperature-controlled objects, and the number of PIDs is at least the number of temperature-controlled objects plus 1.

[0010] Preferably, the heating assembly includes a first heating assembly and a second heating assembly. Both the second heating assembly and the first heating assembly are heating wires. The heating wires are placed inside permanent magnet one and permanent magnet two, and the exterior of permanent magnet two and permanent magnet one are wrapped with heat-insulating material.

[0011] Preferably, the amplification device includes a first amplification component and a second amplification component, both of which are adjustable power supplies.

[0012] Preferably, the measuring components include a first temperature probe for measuring the temperature of permanent magnet one, a second temperature probe for measuring the temperature of permanent magnet two, and an ambient temperature probe for measuring the ambient temperature.

[0013] A method for an all-weather mobile magnetic resonance permanent magnet temperature control device includes the following steps:

[0014] Step S1: Set the target temperature x (K) for permanent magnet one and permanent magnet two;

[0015] Step S2: Use the target temperature x (k), the ambient temperature s (k) measured by the ambient temperature probe, the actual temperature y1 (k) of permanent magnet one measured by the first temperature probe, and the actual temperature y2 (k) of permanent magnet two measured by the second temperature probe as the input of the neural network input layer.

[0016] Step S3: After receiving the input, the neural network input layer calculates n sets of PID parameters and outputs them through the output layer.

[0017] Step S4: Update the neural network weights for the next iteration calculation;

[0018] Step S5: The control component uses the n sets of PID parameters output by the neural network in step S3 to calculate the control voltage based on the fluctuation of ambient temperature and the deviation between the permanent magnet temperature and the target temperature.

[0019] Step S6: The two control voltages obtained in step S5 are passed through the first amplification component and the second amplification component respectively to enhance the driving capability of the control component.

[0020] Step S7: Use the control voltage amplified in step S6 to control the first heating component and the second heating component respectively, and adjust the temperature of permanent magnet one and permanent magnet two.

[0021] Step S8: Repeat steps S2 to S7 to stabilize the temperature of permanent magnet one and permanent magnet two within the error range.

[0022] Preferably, the input to the neural network input layer in step S2 is as shown in the following formula:

[0023] I(k)=[x(k),y1(k),y2(k),s(k),…,1] (1)

[0024] In the formula, I(k) represents the input of the neural network input layer, which is a 1*j-dimensional row vector, j represents the number of neurons at the input end of the neural network, x(k) represents the target temperature, y1(k) represents the temperature of permanent magnet one, y2(k) represents the temperature of permanent magnet two, s(k) represents the ambient temperature, 1 is used as the bias, and k represents the number of iterations, which always corresponds to the current time.

[0025] Preferably, the output of the neural network output layer in step S3 is as shown in the following formula:

[0026]

[0027] In the formula, O(k) represents the output of the output layer, and the output result is n sets of PID parameters, where n is equal to twice the number of temperature-controlled objects. w1 represents the input weight, w2 represents the output weight, a and b can be real numbers greater than 1, usually taking the natural constant e, I(k) represents the input of the neural network input layer, and k represents the number of iterations, which always corresponds to the current time.

[0028] Preferably, the formula for calculating the updated weights in step S4 is as follows:

[0029]

[0030] In the formula, w m (k-1) represents the weight of the previous iteration, w m (k-2) represents the weight of the iteration before the previous one. The loss function is expressed as a function of w. mThe partial derivatives of η represent the learning rate, α represent the inertia coefficient, and m = 1 and m = 2 represent the input weight and output weight, respectively.

[0031] The expression for the loss function is as follows:

[0032]

[0033] In the formula, loss represents the loss function, x(k) represents the target value, y1(k) represents the temperature of permanent magnet one, and y2(k) represents the temperature of permanent magnet two.

[0034] Preferably, the formula for calculating the control voltage in step S5 is as follows:

[0035]

[0036] In the formula, U i Represents the control voltage of the i-th magnet, error i This represents the deviation between the magnet temperature and the target temperature, where i takes values ​​of 1 or 2; kpid represents the deviation. i,1 Corresponding to the PID coefficient for magnet temperature deviation, kpid i,2 The PID coefficients correspond to the ambient temperature deviation, where error3 represents the fluctuation of the ambient temperature, and ∫error represents the integral over the temperature deviation or fluctuation. It represents the derivative with respect to temperature deviation or fluctuation.

[0037] Therefore, the present invention employs the above-mentioned all-weather mobile magnetic resonance permanent magnet temperature control device and method, which enables the magnetic resonance permanent magnet to maintain a magnet temperature fluctuation of less than 0.05 degrees Celsius when the ambient temperature fluctuates by more than ten degrees, and enables the magnetic resonance permanent magnet to maintain a highly stable temperature condition even under natural conditions of large and rapid fluctuations in ambient temperature.

[0038] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of an embodiment of the all-weather mobile magnetic resonance permanent magnet temperature control device and method of the present invention;

[0040] Figure 2 This is a schematic diagram of the neural network structure of an embodiment of the all-weather mobile magnetic resonance permanent magnet temperature control device and method of the present invention.

[0041] Figure 3 This is a diagram showing the measured experimental data of an embodiment of the all-weather mobile magnetic resonance permanent magnet temperature control device and method of the present invention;

[0042] Reference numerals: 1. Measurement component; 2. Permanent magnet one; 3. First temperature probe; 4. First heating component; 5. Ambient temperature probe; 6. Permanent magnet two; 7. Second temperature probe; 8. Second heating component; 9. First amplification component; 10. Second amplification component; 11. Control component; 12. Input layer; 13. Hidden layer; 14. Output layer; 15. First temperature PID controller; 16. First ambient temperature fluctuation PID controller; 17. Second ambient temperature fluctuation PID controller; 18. Second temperature PID controller; 19. Control voltage; 191. First control voltage; 192. Second control voltage; 20. Neural network; 21. Target temperature; 22. Temperature of permanent magnet one; 23. Ambient temperature; 24. Temperature of permanent magnet two; 25. Bias. Detailed Implementation

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0045] Example

[0046] Please see Figure 1-3 The present invention provides an all-weather mobile magnetic resonance permanent magnet temperature control device, including a control component 11, an amplification component, a heating component, a measuring component 1, a first permanent magnet 2 and a second permanent magnet 6. The temperature of the second permanent magnet 6 and the first permanent magnet 2 is measured by the measuring component 1. The control component 11 amplifies the voltage through the first amplification component 9 and the second amplification component 10 to control the first heating component 4 and the second heating component 8, respectively. The first heating component 4 and the second heating component 8 adjust the temperature of the first permanent magnet 2 and the second permanent magnet 6, respectively.

[0047] Control component 11 controls the voltage via neural network 20, which includes an input layer 12, a hidden layer 13, and an output layer 14. For example... Figure 1As shown, the inputs of the input layer 12 include target temperature 21, permanent magnet one temperature 22, ambient temperature 23, permanent magnet two temperature 24, and bias 25. The output of the output layer 14 includes multiple sets of PIDs. The number of PIDs is twice the number of temperature-controlled objects, and the number of PIDs is at least the number of temperature-controlled objects plus 1.

[0048] The heating assembly includes a first heating assembly 4 and a second heating assembly 8. Both the second heating assembly 8 and the first heating assembly 4 are heating wires. The heating wires are placed inside permanent magnet 1 2 and permanent magnet 2 6. Both permanent magnet 2 6 and permanent magnet 1 2 are wrapped with a certain thickness of heat-insulating material to reduce temperature control energy consumption.

[0049] The amplification device includes a first amplification component 9 and a second amplification component 10, both of which are adjustable power supplies.

[0050] The measuring component 1 includes a first temperature probe 3 for measuring the temperature of permanent magnet 2, a second temperature probe 7 for measuring the temperature of permanent magnet 6, and an ambient temperature probe 5 for measuring the ambient temperature.

[0051] The method for the above-mentioned high-stability magnetic resonance permanent magnet constant temperature control device includes the following steps:

[0052] Step S1, as follows Figure 1 As shown, the target temperature x (K) of permanent magnet 2 and permanent magnet 6 is set.

[0053] Step S2: The target temperature x (k), the ambient temperature s (k) measured by the ambient temperature probe 5, the actual temperature y1 (k) of the permanent magnet 2 measured by the first temperature probe 3, and the actual temperature y2 (k) of the permanent magnet 6 measured by the second temperature probe 7 are used as the inputs of the input layer 12 of the neural network 20.

[0054] The input to layer 12 of neural network 20 is shown in the following formula:

[0055] I1(k)=[x(k),y1(k),y2(k),s(k),…,1] (1)

[0056] In the formula, I1(k) represents the input of the input layer 12 of the neural network 20, which is a 1*j-dimensional row vector, j represents the number of neurons at the input end of the neural network 20, x(k) represents the target temperature, y1(k) represents the temperature of permanent magnet 2, y2(k) represents the temperature of permanent magnet 6, s(k) represents the ambient temperature, 1 is used as the bias 25, and k represents the number of iterations, which always corresponds to the current time.

[0057] Step S3: After receiving input, the input layer 12 of the neural network 20 calculates n sets of PID parameters and outputs them through the output layer 14.

[0058] The output of the neural network output layer in step S3 is shown in the following formula:

[0059]

[0060] In the formula, O(k) represents the output of the output layer 14, and the output result is n sets of PID parameters, where n is equal to twice the number of temperature control objects. w1 represents the input weight, w2 represents the output weight, a and b can be real numbers greater than 1, usually taking the natural constant e, I(k) represents the input of the neural network input layer, and k represents the number of iteration calculation steps, which always corresponds to the current time.

[0061] Step S4: Update the weights of neural network 20 for the next iteration calculation;

[0062] The formula for calculating the updated weights is as follows:

[0063]

[0064] In the formula, w m (k-1) represents the weight of the previous iteration, w m (k-2) represents the weight of the previous iteration. The loss function is expressed as a function of w. m The partial derivatives of η represent the learning rate, α represent the inertia coefficient, and m = 1 and m = 2 represent the input weight and output weight, respectively.

[0065] The expression for the loss function is as follows:

[0066]

[0067] In the formula, loss represents the loss function, x(k) represents the target value, y1(k) represents the temperature of permanent magnet 2, and y2(k) represents the temperature of permanent magnet 6.

[0068] In step S5, the control component 11 uses the n sets of PID parameters output by the neural network 20 in step S3 to calculate the control voltage 19, respectively, for the fluctuation of ambient temperature 23, the temperature 22 of permanent magnet one, the temperature 24 of permanent magnet two and the deviation of the target temperature 21.

[0069] The formula for calculating control voltage 19 is as follows:

[0070]

[0071] In the formula, U i The control voltage of the i-th magnet is 19, error. i This represents the deviation between the magnet temperature and the target temperature, where i takes values ​​of 1 or 2; kpid represents the deviation. i,1 Corresponding to the PID coefficient for magnet temperature deviation, kpid i,2The PID coefficients correspond to the ambient temperature deviation, where error3 represents the fluctuation of the ambient temperature, and ∫error represents the integral over the temperature deviation or fluctuation. It represents the derivative with respect to temperature deviation or fluctuation.

[0072] In this embodiment, the first temperature PID controller 15 for the permanent magnet 2 is represented as follows:

[0073]

[0074] In the formula, Val1 represents the first temperature PID controller 15 of permanent magnet-2, error1 represents the deviation between the temperature of permanent magnet-2 and the target temperature, and ∫error1 represents the integral of the temperature deviation of permanent magnet-2. This represents the derivative of the temperature deviation of the permanent magnet 2.

[0075] Both the first ambient temperature fluctuation PID controller 16 and the second ambient temperature fluctuation PID controller 17 can be represented as:

[0076]

[0077] Where Val2 represents the first ambient temperature fluctuation PID controller 16, Val3 represents the second ambient temperature fluctuation PID controller 17, error3 represents the ambient temperature fluctuation, and ∫error3 represents the integral of the ambient temperature fluctuation. It represents the differential of ambient temperature fluctuations.

[0078] The second temperature PID controller 18 of permanent magnet 26 is represented as follows:

[0079]

[0080] Where Val4 represents the second temperature PID controller 18 of permanent magnet 6, error2 represents the deviation between the temperature of permanent magnet 6 and the target temperature, and ∫error2 represents the integral of the temperature deviation of permanent magnet 6. This represents the derivative of the temperature deviation of the permanent magnet 26.

[0081] U1 = kpid 1,1 *Val1+kpid 1,2 *Val2 (9)

[0082] Where U1 represents the calculated first control voltage 191 for permanent magnet 2, kpid 1,1 This represents the first set of PID parameters output by neural network 20, kpid. 1,2 The second set of PID parameters output by neural network 20 is represented by Val1 and Val2, which are Equations (6) and (7), respectively.

[0083] U2 = kpid 2，2 *Val3+kpid 2，1 *Val4 (10)

[0084] Where U2 represents the calculated second control voltage 192 kpid for permanent magnet 6. 2,2 This represents the third set of PID parameters output by neural network 20, kpid. 2,1 The fourth set of PID parameters output by neural network 20 is represented by Val3 and Val4, which are Equations (7) and (8), respectively.

[0085] Step S6: The two control voltages obtained in step S5 are passed through the first amplification component 9 and the second amplification component 10 respectively to enhance the driving capability of the control component 11.

[0086] Step S7: Use the control voltage amplified in step S6 to control the first heating component 4 and the second heating component 8 respectively, and adjust the temperature of permanent magnet 2 and permanent magnet 6.

[0087] Step S8: Repeat steps S2 to S7 to stabilize the temperature of permanent magnet 2 and permanent magnet 6 within the error range.

[0088] The number of PID groups n output by neural network 20 is determined according to the number of temperature-controlled objects. The neural network 20 algorithm in this embodiment is only for illustrative purposes.

[0089] The actual test results of this implementation case are as follows: Figure 3 As shown, when the ambient temperature fluctuates by more than ten degrees, the magnet temperature fluctuates by less than 0.05 degrees Celsius.

[0090] Therefore, the present invention employs the above-mentioned all-weather mobile magnetic resonance permanent magnet temperature control device and method, so that when the ambient temperature fluctuates by more than ten degrees, the magnet temperature fluctuation is less than 0.05 degrees Celsius, enabling the magnetic resonance permanent magnet to maintain a highly stable temperature condition even under natural conditions of large and rapid fluctuations in ambient temperature.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A weather-controlled mobile magnetic resonance permanent magnet temperature control device, characterized in that: It includes a control component, an amplification component, a heating component, a measuring component, a permanent magnet one, and a permanent magnet two. The permanent magnet two and the permanent magnet one measure the temperature through the measuring component. The control component amplifies the voltage through the first amplification component and the second amplification component respectively to control the first heating component and the second heating component. The first heating component and the second heating component respectively adjust the temperature of the permanent magnet one and the permanent magnet two. The control component controls the voltage through a neural network, which includes an input layer, a hidden layer, and an output layer. The inputs to the input layer include the target temperature, ambient temperature, permanent magnet temperature, and bias. The output layer includes multiple sets of PIDs. The number of PIDs is twice the number of temperature-controlled objects, and the number of PIDs is at least the number of temperature-controlled objects plus 1. The heating assembly includes a first heating assembly and a second heating assembly. Both the second heating assembly and the first heating assembly are heating wires. The heating wires are placed inside permanent magnet one and permanent magnet two, and the exterior of permanent magnet two and permanent magnet one are wrapped with heat-insulating material. The amplification components include a first amplification component and a second amplification component, both of which are adjustable power supplies; The measuring components include a first temperature probe for measuring the temperature of permanent magnet one, a second temperature probe for measuring the temperature of permanent magnet two, and an ambient temperature probe for measuring the ambient temperature. The control component will output the neural network. n The PID parameters are used to calculate the control voltage based on the fluctuation of ambient temperature and the deviation between the permanent magnet temperature and the target temperature, respectively, and the two control voltages are obtained. The two control voltages calculated by the control component are respectively amplified by the first amplification component and the second amplification component to enhance the driving capability of the control component; The first and second heating components are controlled by two control voltages respectively through the first and second amplification components, thereby adjusting the temperature of permanent magnet one and permanent magnet two.

2. The method for using the all-weather mobile magnetic resonance permanent magnet temperature control device according to claim 1, characterized in that, Includes the following steps: Step S1: Set the target temperatures for permanent magnet one and permanent magnet two. ; Step S2: Set the target temperature Ambient temperature measured by the ambient temperature sensor The actual temperature of permanent magnet one as measured by the first temperature probe. The actual temperature of the permanent magnet 2 as measured by the second temperature probe. As input to the input layer of a neural network; Step S3: After receiving the input, the neural network input layer performs calculations to obtain... The PID parameters are grouped and output through the output layer; Step S4: Update the neural network weights for the next iteration calculation; Step S5: The control component will output the neural network from step S3. The PID parameters are used to calculate the control voltage based on the fluctuation of ambient temperature and the deviation between the permanent magnet temperature and the target temperature. Step S6: The two control voltages obtained in step S5 are passed through the first amplification component and the second amplification component respectively to enhance the driving capability of the control component. Step S7: Use the control voltage amplified in step S6 to control the first heating component and the second heating component respectively, and adjust the temperature of permanent magnet one and permanent magnet two. Step S8: Repeat steps S2 to S7 to stabilize the temperature of permanent magnet one and permanent magnet two within the error range.

3. The method for an all-weather mobile magnetic resonance permanent magnet temperature control device according to claim 2, characterized in that, The input to the neural network input layer in step S2 is shown in the following formula: （1） In the formula, This represents the input to the input layer of the neural network, which is a dimensional row vectors, This indicates the number of neurons at the input end of the neural network. Indicates the target temperature. This indicates the temperature of permanent magnet one. This indicates the temperature of permanent magnet two. This represents the ambient temperature, with 1 as a bias. This represents the number of iterations, always corresponding to the current time step.

4. The method for an all-weather mobile magnetic resonance permanent magnet temperature control device according to claim 3, characterized in that, The output of the neural network output layer in step S3 is shown in the following formula: （2） In the formula, This indicates the output layer output, and the output result is... Group PID parameters, Equal to twice the number of temperature-controlled objects, Indicates the input weights. These represent the output weights, where a and b can be real numbers greater than 1, but are usually taken as the natural constant e. This represents the input to the input layer of the neural network. This represents the number of iterations, always corresponding to the current time step.

5. The method for an all-weather mobile magnetic resonance permanent magnet temperature control device according to claim 4, characterized in that, The formula for calculating the updated weight in step S4 is as follows: （3） In the formula, Indicates the weight of the previous iteration. This represents the weight from the previous iteration. Represents the loss function pair The partial derivative, Indicates the learning rate. Represents the coefficient of inertia. Take 1 and The value 2 represents the input weight and the output weight, respectively. The expression for the loss function is as follows: （4） In the formula, Represents the loss function. Indicates the target value. This indicates the temperature of permanent magnet one. This indicates the temperature of permanent magnet two.

6. The method for an all-weather mobile magnetic resonance permanent magnet temperature control device according to claim 5, characterized in that, The formula for calculating the control voltage in step S5 is as follows: （5） In the formula, Indicates the first The control voltage of each magnet This indicates the deviation between the magnet temperature and the target temperature. Choose 1, 2; Corresponding to the PID coefficient for magnet temperature deviation, The PID coefficient corresponding to the ambient temperature deviation, This indicates fluctuations in ambient temperature. This represents the integral over the deviation between the magnet temperature and the target temperature. This represents the integral over fluctuations in ambient temperature. This represents the derivative of the deviation between the magnet temperature and the target temperature. It represents the derivative with respect to fluctuations in ambient temperature.

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