A real-time calibration method for multi-region temperature distribution based on heating body

Abstract

The present invention relates to the field of temperature measurement technology, and more particularly to a real-time calibration method for multi-region temperature distribution based on a heating element, comprising the following steps: Step 1: etching the surface of a metal alloy heating element having a resistance temperature coefficient greater than a preset material threshold to form N discrete series resistance heating units that are electrically connected in series but thermally separate; Step 2: establishing a resistance-temperature dynamic relationship library for each discrete series resistance heating unit; Step 3: while the heating element is operating, synchronously measuring the real-time resistance value of each unit; Step 4: using the real-time resistance value to infer the unit center point temperature using a unit-specific relationship, and combining this with the heat conduction equation to reconstruct a continuous temperature distribution matrix on the heating element surface; Step 5: comparing the target temperature field with the real-time temperature field matrix, and adjusting the drive power of the corresponding unit in the out-of-tolerance area. Through continuous calibration and temperature adjustment, the temperature field can be precisely controlled under different usage environments.

Description

Technical Field

[0001] The present invention relates to the technical field of temperature measurement, and in particular to a real-time calibration method for multi-region temperature distribution based on a heating body. Background Art

[0002] In the field of semiconductor wafer thermal processing (such as rapid thermal annealing), the uniformity of the temperature field on the surface of the heating element directly affects the electrical performance of the device. Current mainstream temperature monitoring technology has the following inherent defects:

[0003] Interference defects: Drilling holes or installing infrared temperature measurement windows on the heating element surface to install thermocouples can distort the heat flow path. For example, in a vacuum annealing furnace, the local thermal conductivity difference at the opening can reach over 200% of that in the undamaged area, creating an asymmetric hot spot exceeding ±2°C at the center of the wafer, making it impossible to meet the ±0.5°C temperature control requirements of advanced processes.

[0004] Hysteresis defects: The microstructure of the heater material evolves under long-term high-temperature operation. For example, after 1000 hours of service, the temperature coefficient of resistance at the edge of a nickel-chromium alloy heater can drift by 3.8 times that of the center. Traditional offline calibration, performed only quarterly, fails to capture this regional, time-varying drift, resulting in a continuous increase in the deviation between the actual temperature and the setpoint.

[0005] Therefore, there is an urgent need for a real-time calibration method for multi-region temperature distribution based on a heating body to solve the above problems. Summary of the Invention

[0006] Based on the above objectives, the present invention provides a real-time calibration method for multi-region temperature distribution based on a heating body, comprising the following steps:

[0007] Step 1: Etching N discrete series resistance heating units electrically connected in series but thermally discrete on the surface of a metal alloy heating body having a resistance temperature coefficient greater than a preset material threshold, wherein each unit has a centrally symmetrical trapezoidal structure with a wide end toward the edge and a narrow end toward the center;

[0008] Step 2: Build a resistance-temperature dynamic relationship library for each discrete series resistive heating unit: inject a step-by-step constant current sequence into each unit, simultaneously measure its resistance value and actual surface temperature, and fit a unit-specific relationship.

[0009] Step 3: When the heating element is working, a pulse detection current that does not cause temperature disturbance is circulated into all units, and the real-time resistance value of each unit is measured synchronously;

[0010] Step 4: Use the real-time resistance value to infer the unit center point temperature through the unit-specific relationship, and combine it with the heat conduction equation to reconstruct the continuous temperature distribution matrix on the heating body surface;

[0011] Step 5: Compare the target temperature field with the real-time temperature field matrix, adjust the corresponding unit drive power for the out-of-tolerance area, and trigger step 2 to update the relationship library when the temperature difference of all areas is lower than the update trigger threshold for multiple consecutive times.

[0012] Preferably, the method for determining the geometric proportion of the trapezoidal structure in step 1 includes:

[0013] When the heating body is in the no-load state, an infrared thermal imager is used to measure the steady-state temperature difference between the edge area and the center area at the same power density;

[0014] Based on the temperature difference, a heat loss compensation model is established to calculate the proportion of equivalent power density that needs to be increased in the edge area;

[0015] According to the square relationship between power density and current density, the length ratio of the wide end to the narrow end of the trapezoid is determined so that the current density at the wide end is a set multiple of that at the narrow end to achieve thermal compensation;

[0016] The temperature uniformity is verified by finite element thermal simulation, and the length ratio is iteratively optimized until the global temperature difference is less than the preset verification threshold.

[0017] Preferably, the gradient setting method of the constant current sequence in step 2 includes:

[0018] Apply a step current to the discrete series resistance heating unit and record its temperature rise curve. The time when the temperature change rate drops to a set ratio of the initial value is extracted as the thermal relaxation time.

[0019] Set the current step interval to an integer multiple of the thermal relaxation time. This integer multiple value is determined by testing the temperature acquisition stability at different multiples.

[0020] The current step amplitude increment is set according to the maximum allowable temperature rise rate of the unit to ensure that the single step temperature rise does not exceed the material thermal stress threshold.

[0021] Preferably, the method for determining the amplitude of the pulse detection current in step 3 includes:

[0022] After the discrete series resistance heating unit reaches a steady-state operating temperature, the heating power is cut off and its natural cooling curve is recorded;

[0023] Calculate the heat dissipation power at this temperature point based on the slope of the cooling curve;

[0024] The Joule heat power generated by the pulse current is set as a set ratio of the heat dissipation power. This ratio is determined by comparing the temperature fluctuation amplitude when there is a pulse and when there is no pulse;

[0025] The pulse width is set to be less than a set fraction of the unit's thermal time constant to ensure that temperature perturbations decay within the sampling period.

[0026] Preferably, the specific process of reconstructing the continuous temperature distribution matrix of the heating body surface by the heat conduction equation in step 4 includes:

[0027] The heating body is divided into a three-dimensional grid, and the grid nodes coincide with the center points of the discrete series resistance heating units;

[0028] The energy conservation equation is applied at each node: the change in thermal energy in the control volume is equal to the sum of the net heat conduction flow and the heat generation power;

[0029] Taking the temperature of the cell center as a strong constraint, the explicit time marching method is used to solve the transient temperature field.

[0030] During the iteration process, the working voltage and current of each unit are collected in real time to dynamically correct the heating power;

[0031] When the root mean square difference of the global temperature between two adjacent iterations is less than the convergence threshold, the temperature distribution matrix is ​​output.

[0032] Preferably, the dynamic correction of the heating power includes:

[0033] Measure the resistance of the electrode lead at the rated temperature and establish the lead resistance-temperature compensation curve;

[0034] During the pulse detection current, the lead voltage drop is synchronously collected to calculate the lead heat loss power;

[0035] The effective heating power actually acting on the heating element is obtained by deducting the heat loss power of the lead wire from the total electrical power of the unit.

[0036] Preferably, the method for setting the update trigger threshold in step 5 includes:

[0037] Record the slope change of each unit's resistance-temperature relationship during the historical calibration period;

[0038] Calculate the moving average of the slope change over multiple consecutive periods as the drift reference value;

[0039] The update trigger threshold is set to a set multiple of the drift reference value, and the multiple is determined by a correlation model between the drift amount and the temperature control deviation in the aging accelerated test.

[0040] Preferably, the driving power adjustment strategy in step 5 includes:

[0041] Establish a transfer function model between the unit drive power change and the temperature response rate;

[0042] Calculate the proportional-differential adjustment amount based on the real-time temperature deviation value and the deviation change rate;

[0043] When the temperature deviation exceeds the dynamic allowable threshold, a feedforward compensation term is added to overcome the thermal inertia lag.

[0044] Preferably, the method for determining the dynamic allowable threshold includes:

[0045] Get the minimum response time for the heating element to rise from the current temperature to the target temperature;

[0046] Calculate the maximum allowable temperature deviation change rate based on the target temperature tolerance band width and minimum response time required by the process;

[0047] The dynamic allowable threshold is set as the product of the maximum temperature deviation change rate and the control system sampling period.

[0048] Preferably, the linkage execution of step 2 and step 5 includes:

[0049] When the relationship library update is triggered, the target area is switched to open-loop constant current mode and the adjacent units are kept in closed-loop temperature control;

[0050] During the step current test, the temperature field of adjacent cells is used as the boundary condition to modify the heat conduction equation solution parameters;

[0051] After the new relationship is verified, the gradient restores the closed-loop control weight of the unit to avoid power mutation.

[0052] Beneficial effects of the present invention:

[0053] 1. This invention etches multiple discrete series-connected resistive heating units onto the surface of the heater and monitors temperature using a resistance-temperature dynamic relationship library. These units are independent of the heater surface, avoiding the heat flow interference associated with traditional temperature monitoring techniques. This ensures uniform temperature distribution across the heater surface, significantly reduces the occurrence of localized hot spots, and meets the temperature control precision requirements of advanced manufacturing processes.

[0054] 2. This invention uses a real-time calibration method to infer the center temperature of discrete series resistance heating units using their real-time resistance values. This method dynamically updates the temperature distribution matrix on the heating element's surface using the heat conduction equation. This method continuously captures changes in the resistance temperature coefficient of each region of the heating element and, through calibration, updates the temperature distribution database, ensuring precise, real-time temperature control, eliminating the lag associated with traditional methods.

[0055] 3. This invention also proposes a drive power regulation strategy. By establishing a transfer function model between the unit drive power change and the temperature response rate, it achieves dynamic adjustment of temperature deviation. When the temperature deviation exceeds the set dynamic allowable threshold, a feedforward compensation term can be added to overcome the thermal inertia lag of the heater. This strategy effectively avoids temperature overshoot and lag while ensuring temperature control accuracy, thereby improving the heater's response speed and stability.

[0056] 4. The present invention also uses a real-time resistance measurement through pulse detection current and dynamically adjusts the current to ensure an update mechanism for temperature field uniformity. When temperature deviation occurs, the system adjusts the unit drive power in real time and triggers an update of the relationship library. This adaptive calibration method not only effectively avoids temperature control deviations caused by material aging, but also ensures the accuracy of temperature control through a rapid feedback mechanism, further improving the stability and reliability of the heater during long-term use. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0058] Figure 1 is a flow chart of the steps of the method of the present invention;

[0059] Figure 2 This is a flowchart of the driving power adjustment strategy of step 5 of the method of the present invention;

[0060] Figure 3 This is a flow chart of the steps of the method for determining the dynamic allowable threshold value according to the method of the present invention. DETAILED DESCRIPTION

[0061] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. It is also noted that, to provide a more detailed description, the following embodiments are best and preferred embodiments, and those skilled in the art may employ alternative methods for implementing certain known technologies. Furthermore, the accompanying drawings are intended only to provide a more detailed description of the embodiments and are not intended to limit the present invention.

[0062] See Figure 1-Figure 3 An embodiment of the present invention provides a real-time calibration method for multi-region temperature distribution based on a heater. In step 1, a metal alloy material with a resistance temperature coefficient greater than a preset threshold is selected as the heater material. Etching is performed on the surface of the metal alloy heater to form multiple discrete series resistance heating units that are electrically connected in series but thermally discrete. Each unit has a centrally symmetrical trapezoidal structure, with the wide end facing the edge of the heater and the narrow end facing the center. This design can achieve a more uniform temperature distribution and avoid the interfering defects (such as distortion of the heat flow path) associated with traditional temperature monitoring technologies, ensuring the uniformity and stability of the temperature field.

[0063] In step 2, a series of step-by-step constant currents is injected into each discrete series resistive heating element while simultaneously measuring the element's resistance and actual surface temperature. This data is fitted to a unique resistance-temperature relationship for each element, forming a dynamic relationship library for each element. This operation accurately reflects the changes in the unit's resistance and temperature during operation, facilitating subsequent temperature monitoring and control.

[0064] In step 3, while the heater is operating, pulsed detection currents are injected into each unit. The amplitude and frequency of these pulsed currents are optimized to ensure they do not cause temperature fluctuations. Simultaneously, by measuring the real-time resistance of each discrete unit, the system can obtain the current resistance change of each unit in real time, which serves as the basic data for inferring the temperature.

[0065] In step 4, based on the real-time resistance value and the established resistance-temperature relationship library, the system infers the center point temperature of each unit. Furthermore, by combining the heat conduction equation and taking into account the heat conduction characteristics of the heating element, the system reconstructs a continuous temperature distribution matrix on the heating element's surface. This allows the system to accurately calculate the real-time temperature of each area on the heating element's surface, ensuring temperature control accuracy and uniformity.

[0066] In step 5, the system compares the target temperature field with the real-time temperature field matrix to identify areas with temperature deviations. For these areas, the system adjusts the drive power of the corresponding units to restore the temperature to the target value. If the temperature difference in all areas falls below the set update trigger threshold multiple times in a row, the system triggers step 2 and updates the resistance-temperature relationship library to accommodate time-varying effects such as material aging and microstructural changes caused by long-term use.

[0067] The use of a discrete series resistance heating unit design avoids interference with the heating body surface in traditional temperature monitoring methods, ensures uniform temperature distribution, and can meet high-precision temperature control requirements.

[0068] By measuring the resistance value in real time, inferring the temperature based on the resistance-temperature relationship, and reconstructing the temperature distribution based on the heat conduction model, the accuracy and real-time performance of temperature monitoring are guaranteed, hysteresis defects are avoided, and the system response speed is improved.

[0069] During the long-term use of the heating element, the system can adapt to temperature deviations caused by material aging and structural changes by updating the resistance-temperature relationship library, thereby ensuring the long-term stability and temperature control accuracy of the system.

[0070] Through continuous calibration and temperature adjustment, it is possible to maintain precise control of the temperature field under different usage environments, avoiding the problems of unstable temperature control or deviation expansion in traditional methods. It is particularly suitable for high-end fields such as semiconductor manufacturing that require strict temperature control.

[0071] In one possible implementation, an infrared thermal imager is used to measure the heater while it is unloaded, focusing on the steady-state temperature difference between the edge and center of the heater under the same power density conditions. The key to this step is to accurately determine the temperature distribution differences at different locations on the heater, particularly areas where heat may be lost to the edges. The measured steady-state temperature difference provides a basis for subsequent optimization of temperature uniformity.

[0072] Based on the temperature difference measured in step 1, a heat loss compensation model is used to estimate heat loss at the edges of the heater. Heat loss typically occurs at the edges of the heater because heat conduction and heat dissipation are less efficient at the edges than at the center. Based on the temperature difference, the compensation model calculates the required increase in equivalent power density at the edges. This percentage reflects the design adjustments needed to compensate for heat loss at the edges to ensure a uniform temperature distribution across the heater surface.

[0073] The square relationship between power density and current density yields a formula that correlates current density with the dimensions of the heater structure. To achieve thermal compensation, the current density at the wide end must be greater than that at the narrow end, roughly by a multiple of the desired setting. By adjusting the length ratio of the wide to narrow ends of the trapezoidal structure, the current density at the wide end of the heater can be tailored to the desired thermal compensation requirements, thus achieving thermal compensation at the edge.

[0074] After finalizing the preliminary design for the trapezoidal structure, finite element thermal simulation software was used to simulate and analyze the heat conduction within the heater. This simulation verifies the uniformity of temperature distribution under different geometric proportions. If the simulation results indicate excessive or unintended temperature variations, the design team adjusts the ratio of the wide to narrow ends of the trapezoidal structure and repeatedly optimizes this ratio. This process is iterative, ensuring that the temperature difference across the entire heater surface is below a pre-determined threshold, ensuring that the final design provides uniform temperature distribution.

[0075] By implementing these steps, the structure of the heating body can be optimized while ensuring high-temperature control accuracy, thereby improving its overall performance and stability.

[0076] In one possible implementation, first, a step current is applied to the discrete series resistance heating unit. During this process, the application of current causes the temperature of the heating unit to gradually rise. By recording the temperature rise curve of the heating unit, the rate of temperature change over time can be clearly understood. The key to this process is to extract the time when the rate of temperature change drops to a set proportion of the initial value, which is called the "thermal relaxation time." The thermal relaxation time reflects the time required for the system to gradually recover to a thermal equilibrium state under the action of external excitation (such as a step current). This time is crucial for the subsequent current step setting because it provides a reasonable time window to ensure that temperature acquisition does not cause data instability due to excessively rapid changes.

[0077] After obtaining the thermal relaxation time in step 1, the next step is to determine the current step interval time. According to the size of the thermal relaxation time, the interval time between the current steps is set to an integer multiple of the thermal relaxation time. The specific multiple value is determined by testing the stability of temperature acquisition under different multiples. The core purpose of this process is to ensure that the current does not change too frequently, so as to avoid the temperature not being fully stabilized, thereby affecting the accuracy of the temperature data. By setting the appropriate interval, it can be ensured that the heating unit has enough time to stabilize the temperature after the current step changes, reducing the measurement error caused by too rapid temperature changes.

[0078] After setting the current step interval, you need to determine the amplitude increment for each current step. This amplitude increment is based on the unit's maximum allowable temperature rise rate. The goal is to ensure that each step change does not cause excessive temperature changes on the unit surface or within the material, preventing thermal stress from exceeding the material's tolerance threshold. The thermal stress threshold is the critical temperature change rate at which a material may crack or deform during heating. Therefore, setting an appropriate current step amplitude increment ensures that the heating unit does not exceed the material's thermal stress threshold during temperature rise, thereby preventing damage to the device.

[0079] In one possible implementation, after the discrete series resistor heating unit reaches a steady-state operating temperature, the heating power is turned off and the unit's natural cooling curve is recorded. This cooling curve reflects the temperature drop of the unit due to heat exchange with the surrounding environment after the heating is stopped. By recording the temperature changes during this cooling process, the heat dissipation characteristics at that temperature point can be analyzed. This cooling data is crucial for subsequent steps, as it provides the basis for determining the pulse current amplitude.

[0080] The heat dissipation power at that temperature can be calculated based on the slope of the recorded cooling curve. The change in the cooling curve slope represents the rate of temperature change per unit time, while the heat dissipation power reflects the natural heat dissipation capacity of the heating unit when not heated. Accurately calculating this heat dissipation power provides a reference for setting the pulse current amplitude, ensuring that the heat generated by the pulse matches the heat dissipation characteristics of the system.

[0081] Next, the Joule heat generated by the pulse current is set as a set ratio of the heat dissipation power. This ratio is determined by comparing the amplitude of temperature fluctuations with and without the pulse current. Specifically, the system needs to adjust the amplitude of the pulse current based on experimental data to keep the temperature fluctuations within a reasonable range. When there is a pulse current, the temperature fluctuations will be different from those without the pulse current. The ideal ratio ensures that the heat generated by the pulse current is balanced with the heat dissipated by the system, thereby avoiding excessive temperature disturbances that affect the stability of temperature acquisition.

[0082] Finally, the pulse width should be set to a fraction smaller than the unit's thermal time constant. The thermal time constant reflects the heating unit's response time to temperature changes after the external heat source ceases. Setting the pulse width too long can result in excessive temperature fluctuations, which may not decay within the sampling period, affecting temperature stability and measurement accuracy. Therefore, properly setting the pulse width to a fraction smaller than the thermal time constant ensures that temperature fluctuations decay within the sampling period, maintaining measurement stability and accuracy.

[0083] By precisely controlling the characteristics of the pulse current, the stability of the heating body during the temperature distribution calibration process is effectively guaranteed, the accuracy of temperature acquisition is improved, and the thermal management of the overall heating process is optimized.

[0084] In one possible implementation, the heating element is first divided into a three-dimensional grid, with the nodes of the grid coinciding with the center points of the discrete series resistance heating units. Each grid node represents a small area on the surface of the heating element. This gridding method can transform the temperature distribution variation on the heating element surface into a discretization problem consisting of multiple small areas. The fineness of the grid division directly affects the accuracy of the temperature distribution calculation; the finer the grid, the more accurate the temperature distribution reconstruction.

[0085] Applying the energy conservation equation at each grid node ensures that the change in thermal energy within the control volume is equal to the sum of the net heat conduction flow and the heat generation power. In other words, within each small area, the increase or decrease in heat is influenced not only by heat conduction from the surrounding area but also by the Joule heating power generated by the current flowing through the heating element within that area. This equation effectively simulates the heat conduction and heat generation processes within the heated object.

[0086] To obtain the transient temperature field on the heated body's surface, an explicit time-marching method is required. This method decomposes the time step, gradually calculating the temperature change within each time step, and using the temperature at the cell center as a strong constraint to ensure the stability and physical rationality of the solution. This method can handle the time-sensitive temperature changes of the heated body during actual operation and accurately reflects the temperature evolution over time.

[0087] During the iteration process, the operating voltage and current of each unit are collected in real time. This data is used to dynamically correct the heating power of each unit. Since the voltage and current of the heater vary over time, using real-time data for correction ensures a more accurate reconstruction of the temperature distribution, reflecting the actual thermal performance of the heater under different operating conditions.

[0088] Finally, after multiple iterations, when the root mean square difference (RMS) of the global temperature between two consecutive iterations is less than the convergence threshold, the temperature distribution matrix is ​​output. The RMS difference measures the change in the temperature distribution. When the change is less than the set threshold, it indicates that the temperature distribution has stabilized and meets the accuracy requirements. Finally, the temperature distribution matrix is ​​output, completing the temperature field reconstruction.

[0089] This method of reconstructing the temperature distribution matrix from the heat conduction equation combines precise meshing, dynamic data correction, and explicit time marching, making the temperature distribution reconstruction process of the heating body both accurate and stable. It has high application value and can be widely used in real-time calibration of heating bodies and thermal management systems.

[0090] In one possible implementation, the resistance of the electrode lead at a rated temperature is first measured. The resistance of the electrode lead varies with temperature, so accurate measurements of the lead resistance are required at a set operating temperature. Using this measurement data, a compensation curve is constructed between resistance and temperature. This compensation curve reflects the variation in lead resistance at different temperatures and helps us understand the resistance changes caused by temperature fluctuations during operation.

[0091] During the pulsed current measurement, the voltage drop across the electrode leads must be simultaneously measured. This voltage drop is the voltage difference generated by the resistance across the electrode leads. By measuring this voltage drop, the heat loss power of the leads can be further calculated. When current flows through the leads, the resistance generates a certain amount of heat. This heat is wasted and does not effectively contribute to the heating element. Therefore, understanding this heat loss power is crucial.

[0092] After calculating the heat loss in the lead wires, this loss must be deducted from the total electrical power of the heating unit. Because the heat loss in the lead wires is caused by resistance but does not directly affect the temperature change of the heated element, it must be excluded to determine the actual heat output effectively acting on the heated element. This deduction ensures that the temperature distribution calculation only considers the truly effective heat input, without interference from irrelevant factors.

[0093] By introducing the resistance-temperature compensation curve and real-time monitoring of the voltage drop to accurately calculate the heat loss power and deduct this part from the total power, the accuracy of the temperature distribution calculation is guaranteed, and the thermal management performance of the heating body is optimized, which has strong practical value and reliability.

[0094] In one possible implementation, the relationship between resistance and temperature for each heating unit is first recorded during each calibration cycle. The slope of this relationship reflects the rate at which resistance changes with temperature. By monitoring the changes in the resistance-temperature relationship over multiple cycles, it is possible to identify resistance aging trends and performance changes due to heater usage. At the end of each cycle, the change in slope—that is, the magnitude of the increase or decrease—is recorded. This provides a data foundation for subsequent analysis.

[0095] Next, a moving average of the slope change over multiple consecutive calibration cycles is calculated. This moving average smooths out the effects of occasional fluctuations within a single cycle, preventing accidental deviations from interfering with threshold updates. The resulting drift baseline reflects the overall trend of the heater's resistance over time, which helps predict potential performance changes in future cycles.

[0096] The drift reference value is then used to set the update trigger threshold. The update trigger threshold is a criterion for determining when temperature calibration is necessary; it determines when the temperature control system should initiate the calibration process. By setting this threshold as a multiple of the drift reference value, the calibration frequency can be flexibly adjusted based on the aging rate of the heater. For example, if the heater ages rapidly, the trigger threshold will be lower, ensuring that temperature calibration can be performed in a timely manner. The specific value of the set multiple is determined by a model that correlates drift with temperature control deviation during accelerated aging testing. This model has been experimentally validated and can accurately predict the relationship between drift and temperature control deviation based on actual usage.

[0097] This method of setting the update trigger threshold can effectively track the aging process of the heating body and dynamically adjust the frequency of temperature calibration, thereby ensuring precise control of the temperature distribution of the heating body and improving the stability and responsiveness of the temperature control system.

[0098] In one possible implementation, to precisely adjust the drive power, a transfer function model is first established, linking the change in drive power per unit to the heater's temperature response rate. This model reflects the immediate impact of changes in drive power on temperature, as well as the heater's response to power changes over time. The transfer function, derived by fitting experimental data, accurately describes the heater's response speed and degree to power input, providing a theoretical basis for subsequent adjustments.

[0099] The proportional-derivative control (PDC) is calculated based on the real-time temperature deviation (the difference between the current temperature and the set target temperature) and the rate of change of the temperature deviation (the rate at which the temperature deviation changes over time). The proportional control adjusts based on the magnitude of the temperature deviation, while the differential control considers the rate of change of the temperature deviation. The PD control method enables precise temperature adjustment. By using appropriate proportional and differential control, the system can quickly respond to temperature fluctuations, thereby reducing temperature deviation.

[0100] When the temperature deviation exceeds the dynamic allowable threshold, the temperature control system will experience thermal inertia lag. This means that the temperature response of the heating element is not immediately synchronized with the power change, but rather delayed. To overcome this lag, a feedforward compensation term is added to the control process. This term predicts the temperature change trend in advance and quickly adjusts the system's power input based on the change in drive power, thereby reducing the delay in temperature response. This compensation term provides rapid adjustment during temperature fluctuations, effectively compensating for the lag in the temperature control system and ensuring that the temperature can quickly return to the target value.

[0101] Through the combination of precise mathematical modeling, proportional-differential control and feedforward compensation, precise adjustment of the temperature distribution of the heating body is achieved, which not only improves the response speed of the temperature control system, but also optimizes its stability and accuracy, thus meeting the high requirements for temperature distribution in complex working environments.

[0102] In one possible implementation, the system first determines the minimum response time required for the heater to rise from its current temperature to the target temperature. This time is the shortest amount of time required for the heater to reach the set target temperature from its starting temperature. This response time is affected by various factors, including the heater's power, heat transfer characteristics, ambient temperature, and its thermal inertia. This time value can be obtained through experimental data or system modeling, providing a basis for further temperature change rate calculations.

[0103] After understanding the minimum response time of the heating element, the system determines the maximum allowable temperature deviation rate based on the target temperature tolerance band width required by the process. The target temperature tolerance band width represents the range of temperature deviation allowed by the temperature control system and is typically determined by the process requirements. For example, in certain industrial applications, the temperature must be maintained within a certain narrow range; any deviation outside this range could affect product quality or process stability. By combining the tolerance band width with the minimum response time, the system can calculate the temperature deviation rate—the rate of temperature change—to ensure that excessive temperature changes do not occur during the temperature control process, avoiding excessive system response.

[0104] After determining the maximum temperature deviation rate of change, the dynamic permissible threshold is set as the product of this rate of change and the control system's sampling period. The sampling period is the time interval during which the control system acquires temperature data and performs calculations. Setting the dynamic permissible threshold ensures that the temperature control system does not experience excessive temperature deviations within each sampling period, thereby preventing the heating element's temperature from varying beyond the process requirements. In this way, the system can dynamically adjust the permissible range of temperature deviation, ensuring stability and accuracy during the temperature regulation process.

[0105] By determining the dynamic allowable threshold, the system can achieve fine control of the temperature regulation process, ensuring that the temperature change of the heating body is within a predetermined range, and improving the response speed, stability and accuracy of the temperature control system.

[0106] In one possible implementation, when the system detects that the relationship library needs to be updated, it first needs to adjust the temperature control mode of the target area. At this point, the target area will be switched to open-loop constant current mode. In open-loop constant current mode, the system no longer relies on feedback temperature data to adjust the power input, but instead directly controls the heating element with a constant current, ensuring that the temperature rise process is consistent with the predetermined current. At this time, the adjacent units remain in closed-loop control mode, relying on the feedback temperature signal for precise temperature regulation.

[0107] During the step current test, the system will gradually adjust the current intensity to more accurately measure the temperature changes in each area. The key to this process is to use the temperature field of adjacent units as the boundary condition to correct the solution parameters of the heat conduction equation. The heat conduction equation is used to describe the heat transfer characteristics of the heating body and its surrounding environment. In the step current test, by comparing the temperature change data under different current intensities, the system can accurately adjust and optimize the key parameters in the heat conduction equation, such as thermal conductivity, heat capacity, etc., to ensure that the temperature control model more accurately reflects the actual heat transfer characteristics.

[0108] Once the revised relationship is verified—that is, the new heat conduction equation and temperature distribution relationship are validated and confirmed to be effective—the system gradually restores the closed-loop control weight for that area. Restoring the closed-loop control weight means the temperature control system restarts its feedback mechanism, resuming its reliance on temperature feedback to regulate heating power. Importantly, during this process, the system avoids sudden power surges, meaning it prevents excessive temperature fluctuations caused by the activation of closed-loop control. Through gradient adjustment technology, the system achieves a smooth transition, making the temperature change of the heated element more stable and gradual, thus avoiding sudden temperature fluctuations or overheating and ensuring precise temperature control.

[0109] Through precise control mode switching, optimized correction of the heat conduction equation and smooth transition of closed-loop control, the accuracy and stability of temperature control are effectively improved, unnecessary power mutations are avoided, and the efficient operation of the temperature control system in dynamic changes is ensured.

[0110] The present invention encompasses any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention. To provide a thorough understanding of the present invention, specific details are described in detail below in connection with the preferred embodiments of the present invention, but those skilled in the art will be able to fully understand the present invention without these detailed descriptions. Furthermore, to avoid unnecessary confusion regarding the essence of the present invention, well-known methods, processes, procedures, components, and circuits have not been described in detail.

[0111] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A real-time calibration method for multi-region temperature distribution based on a heating body, characterized in that: The following steps are involved: Step 1: Etching N discrete series resistance heating units electrically connected in series but thermally discrete on the surface of a metal alloy heating body having a resistance temperature coefficient greater than a preset material threshold, wherein each unit has a centrally symmetrical trapezoidal structure with a wide end toward the edge and a narrow end toward the center; Step 2: Build a resistance-temperature dynamic relationship library for each discrete series resistive heating unit: inject a step-by-step constant current sequence into each unit, simultaneously measure its resistance value and actual surface temperature, and fit a unit-specific relationship. Step 3: When the heating element is working, a pulse detection current that does not cause temperature disturbance is circulated into all units, and the real-time resistance value of each unit is measured synchronously; The method for determining the amplitude of the pulse detection current in step 3 includes: After the discrete series resistance heating unit reaches a steady-state operating temperature, the heating power is cut off and its natural cooling curve is recorded; Calculate the heat dissipation power at this temperature point based on the slope of the cooling curve; The Joule heat power generated by the pulse current is set as a set ratio of the heat dissipation power. This ratio is determined by comparing the temperature fluctuation amplitude when there is a pulse and when there is no pulse; The pulse width is set to be less than a set fraction of the unit's thermal time constant to ensure that temperature perturbations decay within the sampling period; Step 4: Use the real-time resistance value to infer the unit center point temperature through the unit-specific relationship, and combine it with the heat conduction equation to reconstruct the continuous temperature distribution matrix on the heating body surface; Step 5: Compare the target temperature field with the real-time temperature field matrix, adjust the corresponding unit drive power for the out-of-tolerance area, and trigger step 2 to update the relationship library when the temperature difference of all areas is lower than the update trigger threshold for multiple consecutive times.

2. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 1, characterized in that: The method for determining the geometric proportion of the trapezoidal structure in step 1 includes: When the heating body is in the no-load state, an infrared thermal imager is used to measure the steady-state temperature difference between the edge area and the center area at the same power density; Based on the temperature difference, a heat loss compensation model is established to calculate the proportion of equivalent power density that needs to be increased in the edge area; According to the square relationship between power density and current density, the length ratio of the wide end to the narrow end of the trapezoid is determined so that the current density at the wide end is a set multiple of that at the narrow end to achieve thermal compensation; The temperature uniformity is verified by finite element thermal simulation, and the length ratio is iteratively optimized until the global temperature difference is less than the preset verification threshold.

3. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 1, characterized in that: The gradient setting method of the constant current sequence in step 2 includes: Apply a step current to the discrete series resistance heating unit and record its temperature rise curve. The time when the temperature change rate drops to a set ratio of the initial value is extracted as the thermal relaxation time. Set the current step interval to an integer multiple of the thermal relaxation time. This integer multiple value is determined by testing the temperature acquisition stability at different multiples. The current step amplitude increment is set according to the maximum allowable temperature rise rate of the unit to ensure that the single step temperature rise does not exceed the material thermal stress threshold.

4. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 1, characterized in that: The specific process of reconstructing the continuous temperature distribution matrix of the heating body surface through the heat conduction equation in step 4 includes: The heating body is divided into a three-dimensional grid, and the grid nodes coincide with the center points of the discrete series resistance heating units; The energy conservation equation is applied at each node: the change in thermal energy in the control volume is equal to the sum of the net heat conduction flow and the heat generation power; Taking the temperature of the cell center as a strong constraint, the explicit time marching method is used to solve the transient temperature field. During the iteration process, the working voltage and current of each unit are collected in real time to dynamically correct the heating power; When the root mean square difference of the global temperature between two adjacent iterations is less than the convergence threshold, the temperature distribution matrix is ​​output.

5. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 4, characterized in that: The dynamic correction of the heating power includes: Measure the resistance of the electrode lead at the rated temperature and establish the lead resistance-temperature compensation curve; During the pulse detection current, the lead voltage drop is synchronously collected to calculate the lead heat loss power; The effective heating power actually acting on the heating element is obtained by deducting the heat loss power of the lead wire from the total electrical power of the unit.

6. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 1, characterized in that: The method for setting the updated trigger threshold in step 5 includes: Record the slope change of each unit's resistance-temperature relationship during the historical calibration period; Calculate the moving average of the slope change over multiple consecutive periods as the drift reference value; The update trigger threshold is set to a set multiple of the drift reference value, and the multiple is determined by a correlation model between the drift amount and the temperature control deviation in the aging accelerated test.

7. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 1, characterized in that: The driving power adjustment strategy of step 5 includes: Establish a transfer function model between the unit drive power change and the temperature response rate; Calculate the proportional-differential adjustment amount based on the real-time temperature deviation value and the deviation change rate; When the temperature deviation exceeds the dynamic allowable threshold, a feedforward compensation term is added to overcome the thermal inertia lag.

8. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 7, characterized in that: The method for determining the dynamic allowable threshold includes: Get the minimum response time for the heating element to rise from the current temperature to the target temperature; Calculate the maximum allowable temperature deviation change rate based on the target temperature tolerance band width and minimum response time required by the process; The dynamic allowable threshold is set as the product of the maximum temperature deviation change rate and the control system sampling period.

9. The method for real-time calibration of multi-region temperature distribution based on a heating body according to claim 1, characterized in that: The linkage execution of step 2 and step 5 includes: When the relationship library update is triggered, the target area is switched to open-loop constant current mode and the adjacent units are kept in closed-loop temperature control; During the step current test, the temperature field of adjacent cells is used as the boundary condition to modify the heat conduction equation solution parameters; After the new relationship is verified, the gradient restores the closed-loop control weight of the unit to avoid power mutation.

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