A multi-zone temperature control system for a heating tray

Abstract

The present application relates to heating disc temperature control technology field, disclose a kind of heating disc multi-partition temperature control system, comprising: steady gain calculation module, obtain edge partition steady gain, inner ring partition steady gain and lateral coupling coefficient;Inner ring heat back threshold point estimation module, obtain the estimated value of inner ring heat back threshold point;Edge set temperature difference calculation module, obtain the proportion close to threshold point;Power increment calculation module, obtain edge power increment and inner ring power increment;Rolling update module, update parameter;Power instruction issuing module, issue power instruction.The present application quantifies the strength of thermal coupling by applying small power step to edge and inner ring partition, avoids temperature deviation caused by coupling interference;With the help of trace scanning edge set temperature difference and linear interpolation, accurately locate the inner ring heat back threshold point;According to fixed interval rolling update parameter, it can adapt to material aging, environmental fluctuation and other working condition changes in real time, avoid local overheating or underheating, greatly improve the reliability of temperature control.

Description

Technical Field

[0001] This invention relates to the field of heating plate temperature control technology, and more specifically, to a multi-zone temperature control system for a heating plate. Background Technology

[0002] Heating plates are widely used in many fields such as semiconductor wafer annealing and food baking. These scenarios have extremely high requirements for temperature uniformity and stability, so they often adopt zoned temperature control technology. By dividing the heating plate into zones such as the edge and inner ring, the power of each zone can be adjusted independently to achieve precise temperature control.

[0003] In existing multi-zone temperature control schemes for heating plates, only simple power adjustments are typically made to each zone, without fully considering the thermal coupling effect between the edge and the inner ring. Changes in the power of the edge zone affect the temperature of the inner ring through heat conduction, while fluctuations in the inner ring temperature in turn interfere with the edge temperature control, forming dynamic coupling interference. This makes it difficult to accurately correct the temperature deviation between the two rings. At the same time, the inner ring has a critical state of regeneration. When the set temperature difference at the edge exceeds a specific threshold, i.e., the regeneration threshold point of the inner ring, the regeneration effect of the inner ring will be triggered, causing a sudden rise or fall in temperature, which seriously interferes with the stability of the process. However, existing technologies lack precise identification methods for this threshold point and rely solely on experience to set the upper limit of power. This cannot adapt to the changes in the threshold point under different operating conditions and is prone to problems such as over-limit triggering of regeneration or overly strict limiting that compresses the adjustment space.

[0004] Furthermore, core parameters such as the steady-state gain and lateral coupling coefficient of the heating plate will drift with the increase of usage time and changes in operating conditions such as ambient temperature fluctuations. Existing solutions mostly use fixed parameters for power calculation and do not update the parameters in time to match the current operating conditions, resulting in an increase in the conversion deviation between temperature and power. Moreover, most solutions only achieve zone-level temperature control and do not refine it to the sector level. Within the same zone, each sector receives the same power allocation due to temperature differences, which can easily lead to local overheating or underheating, further reducing the temperature control accuracy.

[0005] The aforementioned technical problems make it difficult for existing temperature control systems to balance accuracy, stability, and process safety, becoming a key bottleneck restricting the application effect of heating plates. Summary of the Invention

[0006] This invention provides a multi-zone temperature control system for a heating plate, which solves the technical problems mentioned in the background.

[0007] This invention provides a multi-zone temperature control system for a heating plate, comprising:

[0008] The steady-state gain calculation module is used to apply a small-power step to the edge partition set and the inner loop partition set to obtain the steady-state gain of the edge partition, the steady-state gain of the inner loop partition, and the lateral coupling coefficient.

[0009] The inner ring regeneration threshold estimation module is used to set the temperature difference at the edge of the micro-scan and determine the estimated value of the inner ring regeneration threshold based on the average temperature of the inner ring zone.

[0010] The parameters set for micro-scanning include: edge temperature difference, scan step size, and scan direction;

[0011] The edge setting temperature difference calculation module is used to determine the threshold safety margin based on the standard deviation of temperature measurement, obtain the maximum edge setting temperature difference, and calculate the proportion of the threshold point.

[0012] The power increment calculation module is used to determine the edge allocation coefficient and inner loop allocation coefficient based on the proportion of the threshold point and the lateral coupling coefficient, calculate the edge power increment and inner loop power increment based on the edge partition steady-state gain and the inner loop partition steady-state gain, and limit the edge setting temperature difference with the maximum edge setting temperature difference.

[0013] The rolling update module is used to update the estimated value of the inner loop regeneration threshold point, the edge partition steady-state gain, the inner loop partition steady-state gain, and the lateral coupling coefficient at fixed intervals.

[0014] The power command issuing module is used to allocate the edge power increment and inner loop power increment according to the sector temperature error ratio and issue power commands, synchronously update the edge set temperature and inner loop set temperature, and keep the edge set temperature difference from not exceeding the maximum edge set temperature difference.

[0015] Furthermore, the value of the small power step is between the upper limit of the edge partition's safe power and the lower limit of the edge partition's safe power;

[0016] Obtain the difference between the average temperature of the edge zone before and after the quasi-steady state. This difference is the steady-state change of the average temperature of the edge zone.

[0017] Obtain the difference between the average temperature of the inner ring section before and after the quasi-steady state. This difference is the steady-state change of the average temperature of the inner ring section.

[0018] The steady-state gain of the edge partition is obtained by calculating the ratio of the steady-state change of the average temperature of the edge partition to the small-power step applied to the set of edge partitions.

[0019] The steady-state gain of the inner ring partition is obtained by calculating the ratio of the steady-state change of the average temperature of the inner ring partition to the small-power step applied to the inner ring partition set.

[0020] The lateral coupling coefficient is obtained by calculating the ratio between the steady-state change of the average temperature of the inner ring partition caused by a small-power step applied to the edge partition set and the steady-state change of the average temperature of the edge partition.

[0021] If the absolute value of the rate of temperature change is consistently below the upper limit of the measurement noise within a preset sampling period, the heating plate is considered to have reached a quasi-steady state.

[0022] Further, determining the estimated value of the inner loop heat return threshold point includes the following steps:

[0023] Step S201: Set the edge temperature difference, scanning step size, and scanning direction to complete the micro-scan initialization;

[0024] The edge temperature difference, scan step size, and scan direction are all custom parameters;

[0025] Step S202: Each time, change the edge set temperature difference by one scan step while keeping other settings unchanged, wait for the heating plate to reach a quasi-steady state, and record the average temperature of the inner ring partition and the edge set temperature difference.

[0026] Step S203: Calculate the ratio between the difference of the average temperature of the inner ring zone recorded in two consecutive records and the difference of the edge setting temperature difference after two consecutive adjustments to obtain the steady-state sensitivity.

[0027] Step S204: Perform linear interpolation between two scans in which the steady-state sensitivity shows a sign reversal to obtain an estimated value of the inner loop regenerative threshold.

[0028] Furthermore, the standard deviation of temperature measurements within the estimated time window of the inner loop regenerative threshold is statistically analyzed, multiplied by three-half to obtain the threshold safety margin. Then, the difference between the estimated value of the inner loop regenerative threshold and the threshold safety margin is calculated to obtain the maximum edge setting temperature difference. The current edge setting temperature difference is read, and the ratio of the current edge setting temperature difference to the maximum edge setting temperature difference is calculated. The ratio is then truncated, with the lower limit set to 0 and the upper limit set to 1, to obtain the proportion close to the threshold.

[0029] Furthermore, the allocation index is obtained by adding 1 to the horizontal coupling coefficient; the allocation index is raised to the power of the proportions close to the threshold, and the result of the power operation is subtracted from 1 to obtain the marginal allocation coefficient; the allocation index is raised to the power of the proportions close to the threshold to obtain the inner ring allocation coefficient.

[0030] Further, the edge temperature error is obtained by subtracting the average temperature of the edge zone from the target temperature; the inner loop temperature error is obtained by subtracting the average temperature of the inner loop zone from the target temperature; the edge allocation coefficient is multiplied by the edge temperature error to obtain the first product; the edge zone steady-state gain is multiplied by the closed-loop time constant to obtain the second product; the first product is then divided by the second product to obtain the edge power increment; the inner loop allocation coefficient is multiplied by the edge temperature error to obtain the third product; the third product is added to the inner loop temperature error to obtain the sum; the inner loop zone steady-state gain is multiplied by the closed-loop time constant to obtain the fourth product; the sum is then divided by the fourth product to obtain the inner loop power increment; the current edge set temperature difference is limited, and the limiting rule is that if the current edge set temperature difference is greater than the maximum edge set temperature difference, then the current edge set temperature difference is adjusted to the maximum edge set temperature difference to obtain the limited edge set temperature difference.

[0031] Furthermore, when the current time reaches a preset multiple of the sampling period, the current edge temperature difference is set sequentially by adding the scanning step size, subtracting the scanning step size, and returning to the original value. After each micro-scan, the heating plate is waited to reach a quasi-steady state, and the estimated value of the inner loop heat return threshold point, the edge partition steady-state gain, the inner loop partition steady-state gain, and the lateral coupling coefficient are updated respectively. The sampling period and the preset multiple of the sampling period are both custom parameters.

[0032] Furthermore, for each sector within the edge partition, the target temperature is subtracted from the edge sector temperature to obtain the temperature difference value of that sector. The temperature difference values ​​of all sectors within the edge partition are summed, and a numerical protection factor is added to the sum to obtain the denominator. The temperature difference value of each sector is used as the numerator, and the ratio of the numerator to the denominator is the edge sector weight of that sector. The inner ring sector weight is calculated in the same way. That is, for each sector within the inner ring partition, the target temperature is subtracted from the inner ring sector temperature of that sector to obtain the temperature difference value of that sector. The temperature difference values ​​of all sectors within the inner ring partition are summed, and a numerical protection factor is added to the sum to obtain the denominator. The temperature difference value of each sector is used as the numerator, and the ratio of the numerator to the denominator is the inner ring sector weight of that sector.

[0033] Furthermore, the edge power command at the previous sampling time is added to the result of multiplying the edge sector weight of the current sector by the edge power increment. The sum is then truncated between the lower and upper limits of the edge power to obtain the edge power command of the current sector. The inner loop power command is calculated in the same way, that is, the inner loop power command at the previous sampling time is added to the result of multiplying the inner loop sector weight of the current sector by the inner loop power increment. The sum is then truncated between the lower and upper limits of the inner loop power to obtain the inner loop power command of the current sector.

[0034] Furthermore, the inner ring temperature error is obtained by subtracting the average temperature of the inner ring partition from the target temperature; the inner ring set temperature is obtained by multiplying the current inner ring set temperature by the inner ring temperature error by the sampling period and then dividing by the closed-loop time constant; the inner ring set temperature at the next moment is obtained by adding the result of multiplying the current inner ring set temperature error by the sampling period and then dividing by the closed-loop time constant; the current edge set temperature difference is compared with the maximum edge set temperature difference, and the smaller value of the two is taken as the candidate edge set temperature difference; the inner ring set temperature at the next moment is added with the candidate edge set temperature difference to obtain the edge set temperature at the next moment.

[0035] The beneficial effects of this invention are as follows: By applying small power steps to the edge and inner ring partitions, this invention can accurately obtain the steady-state gain and lateral coupling coefficient of both, quantify the thermal coupling strength, provide an accurate conversion benchmark for power allocation, and avoid temperature deviations caused by coupling interference; by using micro-scanning of the edge to set the temperature difference and linear interpolation, it can accurately locate the inner ring regeneration threshold point, and combine the temperature measurement standard deviation to construct a safety margin and set an upper limit for the temperature difference, thereby avoiding sudden temperature changes caused by the regeneration effect from the root; by updating the threshold point estimate, steady-state gain, and other core parameters at fixed intervals, it can adapt to changes in operating conditions such as material aging and environmental fluctuations in real time, ensuring that the parameters always match the characteristics of the actual equipment; by allocating the power increment according to the sector temperature error ratio, it can achieve sector-level fine adjustment, allowing the temperature deviation area to obtain accurate power compensation; the overall process ensures that the temperature converges quickly to the target value, avoids local overheating or underheating, and significantly improves the temperature control reliability and process adaptability in scenarios such as semiconductor annealing and food baking. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of a multi-zone temperature control system for a heating plate according to the present invention;

[0037] Figure 2 This is a flowchart illustrating the estimated value of the inner loop regeneration threshold point according to the present invention.

[0038] In the figure: steady-state gain calculation module 101, inner loop regeneration threshold point estimation module 102, edge set temperature difference calculation module 103, power increment calculation module 104, rolling update module 105, power command issuance module 106. Detailed Implementation

[0039] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0040] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should 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 one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" indicate that the element or object preceding the term encompasses the elements or objects listed following the term 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.

[0041] like Figures 1-2 As shown, a multi-zone temperature control system for a heating plate includes:

[0042] Steady-state gain calculation module 101 is used to apply a small-power step to the edge partition set and the inner loop partition set to obtain the steady-state gain of the edge partition, the steady-state gain of the inner loop partition, and the lateral coupling coefficient.

[0043] The inner ring regeneration threshold estimation module 102 is used to set the temperature difference at the edge of the micro-scan and determine the estimated value of the inner ring regeneration threshold based on the average temperature of the inner ring partition.

[0044] The parameters set for micro-scanning include: edge temperature difference, scan step size, and scan direction;

[0045] Edge setting temperature difference calculation module 103 is used to determine the threshold safety margin based on the standard deviation of temperature measurement, obtain the maximum edge setting temperature difference, and calculate the proportion close to the threshold.

[0046] The power increment calculation module 104 is used to determine the edge allocation coefficient and inner loop allocation coefficient based on the proportion of the approach threshold point and the lateral coupling coefficient, calculate the edge power increment and inner loop power increment based on the edge partition steady-state gain and the inner loop partition steady-state gain, and limit the edge setting temperature difference with the maximum edge setting temperature difference.

[0047] The rolling update module 105 is used to update the estimated value of the inner loop regeneration threshold point, the edge partition steady-state gain, the inner loop partition steady-state gain, and the lateral coupling coefficient at fixed intervals.

[0048] The power command issuing module 106 is used to allocate the edge power increment and the inner loop power increment according to the sector temperature error ratio and issue power commands, synchronously update the edge set temperature and the inner loop set temperature, and keep the edge set temperature difference from not exceeding the maximum edge set temperature difference.

[0049] It should be noted that the edge zone set is a structure around the outer edge of the heating plate, consisting of several sectors that can be independently adjusted in power, and each sector is equipped with a temperature sensor; the inner ring zone set is a structure adjacent to the inner side of the edge zone set. Its constituent sectors have the same independent adjustment function, temperature sensor configuration, and other structural and functional characteristics as the edge zone set. The average temperature of both sets is calculated by arithmetically averaging the temperature values ​​measured by all temperature sensors within the set.

[0050] It should be noted that applying a small power step can obtain a near-linear and repeatable mapping relationship between power input and temperature output without affecting the normal operation of the heating plate. This mapping relationship can be used to identify steady-state gain and lateral coupling coefficient. At the same time, this method can avoid the interference of phase and integral effects in the dynamic process on the parameter identification results, ensuring that the identified parameters are accurate and reliable.

[0051] In one embodiment of the present invention, the value of the small power step is between the upper limit of the edge partition safe power and the lower limit of the edge partition safe power.

[0052] Obtain the difference between the average temperature of the edge zone before and after the quasi-steady state. This difference is the steady-state change of the average temperature of the edge zone.

[0053] Obtain the difference between the average temperature of the inner ring section before and after the quasi-steady state. This difference is the steady-state change of the average temperature of the inner ring section.

[0054] The steady-state gain of the edge partition is obtained by calculating the ratio of the steady-state change of the average temperature of the edge partition to the small-power step applied to the set of edge partitions.

[0055] The steady-state gain of the inner ring partition is obtained by calculating the ratio of the steady-state change of the average temperature of the inner ring partition to the small-power step applied to the inner ring partition set.

[0056] The lateral coupling coefficient is obtained by calculating the ratio between the steady-state change of the average temperature of the inner ring partition caused by a small-power step applied to the edge partition set and the steady-state change of the average temperature of the edge partition.

[0057] It should be noted that the edge zone steady-state gain represents the change in the average temperature of the edge zone itself after reaching steady state when one watt of power is input into the power regulation channel; the inner loop zone steady-state gain represents the change in the average temperature of the inner loop zone itself after reaching steady state when one watt of power is input into the power regulation channel; the lateral coupling coefficient is the ratio of the steady-state change in the average temperature of the inner loop zone to the steady-state change in the average temperature of the edge zone when only a small power step is applied to the edge zone set. This parameter is dimensionless and its value ranges from 0 to 1. It is mainly used to reflect the intensity of the thermal influence of the edge zone on the inner loop zone.

[0058] In one embodiment of the present invention, if the absolute value of the temperature change rate is lower than the upper limit of the measurement noise for a continuous preset sampling period, the heating plate is determined to have reached a quasi-steady state.

[0059] It should be noted that the small power step adjustment involves adjusting the input power of the target partition set by a small amount within a safe power range, and then maintaining this power state until the heating plate reaches a quasi-steady state. The temperature difference and power difference before and after the heating plate reaches the quasi-steady state are then recorded. The power adjustment range needs to meet two conditions: first, it must be higher than the power range corresponding to the minimum resolvable temperature difference caused by temperature measurement noise; second, it must be lower than the power threshold that would cause nonlinear changes in the heating plate material or disturbances in the process. The quasi-steady state is determined by the absolute value of the temperature change rate being lower than the threshold obtained by converting the standard deviation of temperature measurement for several consecutive sampling periods.

[0060] It should be noted that during temperature measurement, the sensor itself will have a slight error, i.e., temperature measurement noise. This noise will cause the instrument to be unable to detect temperature changes below a certain value, i.e., the minimum resolvable temperature difference. Assuming that the temperature sensor in the edge zone of the heating plate has a measurement noise of ±0.15℃, it means that the sensor cannot detect temperature changes less than 0.3℃, and the minimum resolvable temperature difference is 0.3℃. Given that the steady-state gain of the edge zone is 0.5℃ / W, i.e., every 1W power change corresponds to a 0.5℃ temperature change, the power amplitude corresponding to the minimum resolvable temperature difference can be calculated as 0.3℃ ÷ 0.5℃ / W = 0.6W.

[0061] It should be noted that the materials of the heating plate (such as aluminum alloy, ceramic, etc.) have a linear range of thermal conductivity characteristics. When the power is too high and the temperature exceeds a certain critical value, the thermal resistance, specific heat capacity, and other characteristics of the material will change abruptly, i.e., nonlinearly. At the same time, the processes served by the heating plate (such as semiconductor wafer heating, food baking, etc.) have strict requirements for temperature stability. A sudden increase in power may cause process deviations. Therefore, the power adjustment range must be lower than this value to ensure that the mapping relationship between power and temperature is linear and does not affect the normal process. Assuming that the heating plate is made of aluminum alloy, its thermal conductivity characteristics are linear when the temperature is below 200℃ (1W power change corresponds to 0.5℃ temperature change), but when the temperature exceeds 200℃, the thermal resistance will suddenly increase (1W power change corresponds to 0.8℃ temperature change, showing nonlinearity). The current baseline temperature for the edge partition is 180℃. If the power adjustment reaches 5W, the corresponding temperature change is 2.5℃, which, when superimposed on the baseline temperature, is 182.5℃ (not exceeding 200℃). If the adjustment is 10W, the corresponding temperature change is 5℃, which, when superimposed, is 185℃ (still not exceeding the baseline temperature). However, when the adjustment reaches 45W, the corresponding temperature change is 22.5℃, which, when superimposed, is 202.5℃, exceeding the critical value of 200℃, and the material exhibits nonlinearity. At this point, the power threshold corresponding to the material nonlinearity is 40W (40W corresponds to a temperature change of 20℃, which, when superimposed, is 180+20=200℃, not exceeding the critical value). If the heating plate is used for pre-lithography heating of semiconductor wafers, the process requires temperature fluctuations not exceeding ±3℃, otherwise it will lead to uneven photoresist coating. The current reference temperature is 180℃. If the power adjustment range is 7W, the corresponding temperature change is 3.5℃, which exceeds the allowable range of ±3℃ and causes process disturbance. When the adjustment range is 5W, the corresponding temperature change is 2.5℃, which does not exceed the allowable range. At this point, the power threshold corresponding to process disturbance is 6W (6W corresponds to a temperature change of 3℃, which just reaches the critical value). Therefore, the power adjustment range must be lower than the minimum of the two (6W) in order to avoid both material nonlinearity and process disturbance. Thus, the power adjustment range must simultaneously meet the requirements of being higher than 0.6W and lower than 6W to ensure that it is not masked by measurement noise due to being too small, nor to cause abrupt changes in material properties or process deviations due to being too large, thus ensuring that the small-power step test can obtain accurate and linear parameter identification data.

[0062] In one embodiment of the present invention, such as Figure 2 As shown, determining the estimated value of the inner loop heat return threshold point includes the following steps:

[0063] Step S201: Set the edge temperature difference, scanning step size, and scanning direction to complete the micro-scan initialization;

[0064] The edge temperature setting, scanning step size, and scanning direction are all custom parameters. The edge temperature setting can be adjusted according to the actual process requirements for the temperature difference between the edge and the reference area, and must be within the temperature difference range allowed by the equipment. The scanning step size must be higher than the temperature measurement noise resolution and lower than the temperature difference change amplitude corresponding to the nonlinearity of the material. Preferably, the edge temperature setting is set to 2℃, the scanning step size is set to 0.1℃, and the scanning direction is set to increasing or decreasing.

[0065] Step S202: Each time, change the edge set temperature difference by one scan step while keeping other settings unchanged, wait for the heating plate to reach a quasi-steady state, and record the average temperature of the inner ring partition and the edge set temperature difference.

[0066] Step S203: Calculate the ratio between the difference of the average temperature of the inner ring zone recorded in two consecutive records and the difference of the edge setting temperature difference after two consecutive adjustments to obtain the steady-state sensitivity.

[0067] Step S204: Perform linear interpolation between two scans in which the steady-state sensitivity shows a sign reversal to obtain an estimated value of the inner loop regenerative threshold.

[0068] It should be noted that micro-scanning enables identification with minute and controllable disturbances without interrupting normal temperature control, ensuring compatibility with actual process scenarios. Waiting for the heating plate to reach a quasi-steady state after each scan step adjustment eliminates the interference of dynamic coupling on subsequent calculations, making the data correspondence more accurate. Calculating steady-state sensitivity based on adjacent data and determining the critical interval through sign reversal transforms the complex engineering judgment of whether regeneration has occurred into a simple sign change identification. Finally, linear interpolation is used to obtain an estimate of the inner loop regeneration threshold point, which can accurately locate the regeneration critical state. This establishes a closed-loop link from measurement to calculation to application, providing a unique and traceable data source for subsequent limiting and allocation.

[0069] In one embodiment of the present invention, the standard deviation of temperature measurements within the estimated time window of the inner loop regenerative threshold is statistically analyzed, multiplied by three-half to obtain the threshold safety margin, and then the difference between the estimated value of the inner loop regenerative threshold and the threshold safety margin is calculated to obtain the maximum edge setting temperature difference; the current edge setting temperature difference is read, and the ratio of the current edge setting temperature difference to the maximum edge setting temperature difference is calculated. The ratio is then truncated, with the lower limit set to 0 and the upper limit set to 1, to obtain the proportion close to the threshold.

[0070] It should be noted that if the temperature measurement noise approximately follows a normal distribution, three times the standard deviation can cover about 99.7% of the measurement fluctuations. Dividing three times the temperature measurement standard deviation by 2 yields a threshold safety margin. This margin provides sufficient safety buffer for the estimated inner loop regeneration threshold, preventing measurement noise from causing the actual temperature to mistakenly reach the regeneration threshold. It also avoids excessive compression of the adjustable range of the edge set temperature difference due to an excessive margin, achieving a balance between safety and control flexibility. Furthermore, the proportion approaching the threshold is a dimensionless parameter, ranging from 0 to 1. The closer the value is to 0, the greater the difference between the current edge set temperature difference and the maximum edge set temperature difference, indicating a more ample safety space from the inner loop regeneration threshold. The closer the value is to 1, the closer the current edge set temperature difference is to the maximum edge set temperature difference, approaching the critical state of inner loop regeneration, with a higher risk of exceeding the limit. This weight is used for subsequent dynamic adjustment of power allocation, making the power allocation more consistent with the safety constraints near the threshold.

[0071] In one embodiment of the present invention, 1 is added to the lateral coupling coefficient to obtain the allocation index; the proportion close to the threshold point is raised to the power of the allocation index, and then 1 is subtracted from the result of the power operation to obtain the edge allocation coefficient; the proportion close to the threshold point is raised to the power of the allocation index to obtain the inner ring allocation coefficient.

[0072] In one embodiment of the present invention, the edge temperature error is obtained by subtracting the average temperature of the edge partition from the target temperature; the inner loop temperature error is obtained by subtracting the average temperature of the inner loop partition from the target temperature; the edge allocation coefficient is multiplied by the edge temperature error to obtain a first product; the edge partition steady-state gain is multiplied by the closed-loop time constant to obtain a second product; the first product is then divided by the second product to obtain the edge power increment; the inner loop allocation coefficient is multiplied by the edge temperature error to obtain a third product; the third product is added to the inner loop temperature error to obtain a sum; the inner loop partition steady-state gain is multiplied by the closed-loop time constant to obtain a fourth product; the sum is then divided by the fourth product to obtain the inner loop power increment.

[0073] Specifically, edge power increment The calculation formula is as follows:

[0074] , ,in Indicates the target temperature. This indicates the average temperature of the edge zone. Indicates edge temperature error. Indicates the marginal allocation coefficient. Indicates the steady-state gain of the edge partition. This represents the closed-loop time constant.

[0075] Specifically, the inner ring power increment The calculation formula is as follows:

[0076] , ,in This represents the average temperature of the inner ring zone. This indicates the inner ring temperature error. Indicates the inner ring allocation coefficient. This represents the steady-state gain of the inner loop partition.

[0077] It should be noted that the target temperature is a pre-set temperature value based on the specific process requirements served by the heating plate. For example, if the heating plate is used for the annealing process of semiconductor wafers, the target temperature needs to be set according to the annealing process requirements. If it is used for food baking, it is set according to the cooking requirements of the ingredients. This temperature value is input into the system by the operator before the temperature control process is started. The closed-loop time constant is a pre-set control parameter to adjust the temperature convergence speed of the heating plate. Its value is determined based on the characteristics of the heating plate itself and the temperature control requirements. The thermal inertia of the heating plate (such as the substrate material, thickness, heat dissipation conditions, etc.) is the core influencing factor. For example, a thick aluminum alloy heating plate needs to be set with a larger closed-loop time constant to avoid temperature fluctuations caused by frequent and large power adjustments. That is, the closed-loop time constant is usually set to 15 to 30 seconds. For example, a thin ceramic heating plate can be set with a smaller closed-loop time constant to speed up the temperature response speed. That is, the closed-loop time constant is usually set to 5 to 10 seconds. This parameter is determined through equipment calibration experiments and process requirements and then pre-written into the temperature control system.

[0078] It should be noted that the edge power increment incorporates the temperature error of the inner loop itself, as well as the edge temperature error after weighting by the inner loop allocation coefficient. Then, through the steady-state gain of the inner loop partition and the closed-loop time constant, it is converted into the amount of power change that the inner loop partition should adjust. This reflects the combined effect of the inner loop's own temperature control requirements and the thermal coupling between the edge and the inner loop. The edge power increment can respond to the temperature deviation of the inner loop itself, and coordinate the power according to the coupling relationship between the edge and the inner loop. This ensures that the power distribution of the edge and the inner loop meets their respective temperature control requirements and adapts to the thermal interaction between them. Ultimately, this achieves accurate and stable temperature control of the heating plate in multiple zones, avoids local temperature imbalances or oscillations, and realizes coordinated temperature control of multiple zones.

[0079] In one embodiment of the present invention, the current edge set temperature difference is limited. The limiting rule is that when the current edge set temperature difference is greater than the maximum edge set temperature difference, the current edge set temperature difference is adjusted to the maximum edge set temperature difference to obtain the limited edge set temperature difference.

[0080] In one embodiment of the present invention, when the current time reaches a preset multiple of the sampling period, the current edge temperature difference is sequentially adjusted by adding the scanning step size, subtracting the scanning step size, and returning to the original value. After each micro-scan, the heating plate is waited to reach a quasi-steady state, and the estimated value of the inner loop regeneration threshold point, the edge partition steady-state gain, the inner loop partition steady-state gain, and the lateral coupling coefficient are updated respectively. The sampling period and the preset multiple of the sampling period are both custom parameters. Preferably, the sampling period is set to 1 second, and the preset multiple of the sampling period is set to 30.

[0081] It should be noted that the three-point reciprocating micro-scan operation—adding the scan step size, subtracting the scan step size, and returning to the original value—quickly detects the real-time status of the inner loop regeneration threshold point under the current operating conditions with minimal temperature difference disturbance, without significantly interfering with normal process operation. Since the thermal characteristics of the heating plate may slowly change over time (e.g., material aging after long-term use) and environmental factors (e.g., ambient temperature fluctuations), this reciprocating micro-temperature difference scan can accurately capture the critical setpoint difference of the inner loop regeneration under the current operating conditions. This ensures that subsequent parameters such as the threshold safety margin and allocation coefficient calculated based on the estimated value of the inner loop regeneration threshold point always match the actual operating conditions. Simultaneously, the return-to-original-value operation restores the edge setpoint temperature difference to its state before the micro-scan, further reducing the interference of the micro-scan on process temperature stability. This ensures that the temperature control process achieves a balance between the detected parameters and the stable process, making subsequent power allocation, limiting, and other control behaviors more accurate and reliable.

[0082] In one embodiment of the present invention, for each sector within an edge partition, the target temperature is subtracted from the edge sector temperature to obtain the temperature difference value of that sector. The temperature difference values ​​of all sectors within the edge partition are summed, and a numerical protection factor is added to the sum to obtain the denominator. The temperature difference value of each sector is used as the numerator, and the ratio of the numerator to the denominator is used as the edge sector weight of that sector. The inner ring sector weight is calculated in the same way, that is, for each sector within an inner ring partition, the target temperature is subtracted from the inner ring sector temperature to obtain the temperature difference value of that sector. The temperature difference values ​​of all sectors within the inner ring partition are summed, and a numerical protection factor is added to the sum to obtain the denominator. The temperature difference value of each sector is used as the numerator, and the ratio of the numerator to the denominator is used as the inner ring sector weight of that sector.

[0083] It should be noted that the numerical protection value is used to avoid the denominator being zero. Its default value is 0.001. Calculating the sector weight allows sectors with larger temperature differences within the same loop to receive higher weights, enabling subsequent power regulation resources to be precisely directed to sectors whose temperatures deviate from the target, achieving fine-grained temperature control at the sector level, and preventing some sectors within the same loop from overheating or underheating.

[0084] In one embodiment of the present invention, the edge power command at the previous sampling time is added to the result of multiplying the edge sector weight of the current sector by the edge power increment, and then the sum is truncated between the lower limit and the upper limit of the edge power to obtain the edge power command of the current sector; and the inner loop power command is calculated in the same way, that is, the inner loop power command at the previous sampling time is added to the result of multiplying the inner loop sector weight of the current sector by the inner loop power increment, and then the sum is truncated between the lower limit and the upper limit of the inner loop power to obtain the inner loop power command of the current sector.

[0085] It should be noted that the lower limit of edge power, the upper limit of edge power, the lower limit of inner loop power, and the upper limit of inner loop power are all user-defined parameters, and their values ​​are directly determined by the hardware characteristics of the heating plate, which will not be elaborated here. Based on the instruction at the previous sampling moment, the increment is superimposed to achieve smooth iterative adjustment of power, avoiding violent temperature fluctuations caused by sudden increases or decreases in power, and ensuring a stable temperature control process. The increment is allocated according to the sector weight, so that the power adjustment is precisely matched with the temperature difference requirements of each sector, and the sector with a large temperature difference receives more power compensation. After the upper and lower limits are truncated, the power can be strictly constrained within the hardware safety range to prevent the heating element from being overloaded or damaged, or the temperature control effect from being affected by insufficient power, thus balancing adjustment accuracy and equipment safety.

[0086] In one embodiment of the present invention, the inner ring temperature error is obtained by subtracting the average temperature of the inner ring partition from the target temperature; the inner ring set temperature is obtained by multiplying the current inner ring set temperature by the inner ring temperature error by the sampling period and then dividing by the closed-loop time constant; the inner ring set temperature at the next moment is obtained by adding the result of multiplying the current inner ring set temperature error by the sampling period and then dividing by the closed-loop time constant; the current edge set temperature difference is compared with the maximum edge set temperature difference, and the smaller value of the two is taken as the candidate edge set temperature difference; the inner ring set temperature at the next moment is added with the candidate edge set temperature difference to obtain the edge set temperature at the next moment.

[0087] It should be noted that if the current edge set temperature difference is greater than the maximum edge set temperature difference, the edge power increment will be immediately adjusted to 0, and the original edge power increment value will be added to the inner ring power increment. This operation will continue until the edge set temperature difference returns to the range of the maximum edge set temperature difference. Then, the edge power command and inner ring power command will be regenerated according to the aforementioned operation, and the generated edge power command and inner ring power command will be sent to the power execution unit corresponding to the heating plate. This will not be elaborated here.

[0088] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0089] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A multi-zone temperature control system for a heating plate, characterized in that, include: The steady-state gain calculation module is used to apply a small-power step to the edge partition set and the inner loop partition set to obtain the steady-state gain of the edge partition, the steady-state gain of the inner loop partition, and the lateral coupling coefficient. The inner ring regeneration threshold estimation module is used to set the temperature difference at the edge of the micro-scan and determine the estimated value of the inner ring regeneration threshold based on the average temperature of the inner ring zone. The parameters set for micro-scanning include: edge temperature difference, scan step size, and scan direction; The edge setting temperature difference calculation module is used to determine the threshold safety margin based on the standard deviation of temperature measurement, obtain the maximum edge setting temperature difference, and calculate the proportion of the threshold point. The power increment calculation module is used to determine the edge allocation coefficient and inner loop allocation coefficient based on the proportion of the threshold point and the lateral coupling coefficient, calculate the edge power increment and inner loop power increment based on the edge partition steady-state gain and the inner loop partition steady-state gain, and limit the edge setting temperature difference with the maximum edge setting temperature difference. The rolling update module is used to update the estimated value of the inner loop regeneration threshold point, the edge partition steady-state gain, the inner loop partition steady-state gain, and the lateral coupling coefficient at fixed intervals. The power command issuing module is used to allocate the edge power increment and inner loop power increment according to the sector temperature error ratio and issue power commands, synchronously update the edge set temperature and inner loop set temperature, and keep the edge set temperature difference from not exceeding the maximum edge set temperature difference.

2. The multi-zone temperature control system for a heating plate according to claim 1, characterized in that, The value range of the small power step is between the upper limit of the edge partition safe power and the lower limit of the edge partition safe power; Obtain the difference between the average temperature of the edge zone before and after the quasi-steady state. This difference is the steady-state change of the average temperature of the edge zone. Obtain the difference between the average temperature of the inner ring section before and after the quasi-steady state. This difference is the steady-state change of the average temperature of the inner ring section. The steady-state gain of the edge partition is obtained by calculating the ratio of the steady-state change of the average temperature of the edge partition to the small-power step applied to the set of edge partitions. The steady-state gain of the inner ring partition is obtained by calculating the ratio of the steady-state change of the average temperature of the inner ring partition to the small-power step applied to the inner ring partition set. The lateral coupling coefficient is obtained by calculating the ratio between the steady-state change of the average temperature of the inner ring partition caused by a small-power step applied to the edge partition set and the steady-state change of the average temperature of the edge partition. If the absolute value of the rate of temperature change is consistently below the upper limit of the measurement noise within a preset sampling period, the heating plate is considered to have reached a quasi-steady state.

3. The multi-zone temperature control system for a heating plate according to claim 2, characterized in that, Determining the estimated value of the inner loop heat return threshold includes the following steps: Step S201: Set the edge temperature difference, scanning step size, and scanning direction to complete the micro-scan initialization; The edge temperature difference, scan step size, and scan direction are all custom parameters; Step S202: Each time, change the edge set temperature difference by one scan step while keeping other settings unchanged, wait for the heating plate to reach a quasi-steady state, and record the average temperature of the inner ring partition and the edge set temperature difference. Step S203: Calculate the ratio between the difference of the average temperature of the inner ring zone recorded in two consecutive records and the difference of the edge setting temperature difference after two consecutive adjustments to obtain the steady-state sensitivity. Step S204: Perform linear interpolation between two scans in which the steady-state sensitivity shows a sign reversal to obtain an estimated value of the inner loop regenerative threshold.

4. The multi-zone temperature control system for a heating plate according to claim 1, characterized in that, The standard deviation of temperature measurements within the estimated time window of the inner loop regenerative threshold is statistically analyzed, multiplied by three-half to obtain the threshold safety margin. Then, the difference between the estimated value of the inner loop regenerative threshold and the threshold safety margin is calculated to obtain the maximum edge setting temperature difference. The current edge setting temperature difference is read, and the ratio of the current edge setting temperature difference to the maximum edge setting temperature difference is calculated. The ratio is then truncated, with the lower limit set to 0 and the upper limit set to 1, to obtain the proportion close to the threshold.

5. A multi-zone temperature control system for a heating plate according to claim 1, characterized in that, Add 1 to the lateral coupling coefficient to obtain the allocation index; raise the allocation index to the power of the proportions close to the threshold, and then subtract the result of the power operation from 1 to obtain the marginal allocation coefficient; raise the allocation index to the power of the proportions close to the threshold to obtain the inner loop allocation coefficient.

6. The multi-zone temperature control system for a heating plate according to claim 1, characterized in that, The edge temperature error is obtained by subtracting the average temperature of the edge zone from the target temperature; the inner loop temperature error is obtained by subtracting the average temperature of the inner loop zone from the target temperature; the edge allocation coefficient is multiplied by the edge temperature error to obtain the first product; the edge zone steady-state gain is multiplied by the closed-loop time constant to obtain the second product; the first product is divided by the second product to obtain the edge power increment; the inner loop allocation coefficient is multiplied by the edge temperature error to obtain the third product; the third product is added to the inner loop temperature error to obtain the sum; the inner loop zone steady-state gain is multiplied by the closed-loop time constant to obtain the fourth product; the sum is divided by the fourth product to obtain the inner loop power increment; the current edge set temperature difference is limited, and the limiting rule is that if the current edge set temperature difference is greater than the maximum edge set temperature difference, the current edge set temperature difference is adjusted to the maximum edge set temperature difference to obtain the limited edge set temperature difference.

7. A multi-zone temperature control system for a heating plate according to claim 1, characterized in that, When the current time reaches a preset multiple of the sampling period, the current edge temperature difference is set sequentially by adding the scanning step size, subtracting the scanning step size, and returning to the original value. After each micro-scan, wait for the heating plate to reach a quasi-steady state, and update the estimated value of the inner loop heat return threshold point, the edge partition steady-state gain, the inner loop partition steady-state gain, and the lateral coupling coefficient respectively. The sampling period and the preset multiple of the sampling period are both custom parameters.

8. A multi-zone temperature control system for a heating plate according to claim 1, characterized in that, For each sector within the edge partition, the temperature difference value of that sector is obtained by subtracting the edge sector temperature from the target temperature. The temperature difference values ​​of all sectors within the edge partition are then summed, and a numerical protection factor is added to the sum to obtain the denominator. The temperature difference value of each sector is used as the numerator, and the ratio of the numerator to the denominator is the edge sector weight of that sector. The inner ring sector weight is calculated in the same way. That is, for each sector within the inner ring partition, the temperature difference value of that sector is obtained by subtracting the inner ring sector temperature from the target temperature. The temperature difference values ​​of all sectors within the inner ring partition are then summed, and a numerical protection factor is added to the sum to obtain the denominator. The temperature difference value of each sector is used as the numerator, and the ratio of the numerator to the denominator is the inner ring sector weight of that sector.

9. A multi-zone temperature control system for a heating plate according to claim 8, characterized in that, The edge power command at the previous sampling time is added to the result of multiplying the edge sector weight of the current sector by the edge power increment. The sum is then truncated between the lower and upper limits of the edge power to obtain the edge power command of the current sector. The inner loop power command is calculated in the same way, that is, the inner loop power command at the previous sampling time is added to the result of multiplying the inner loop sector weight of the current sector by the inner loop power increment. The sum is then truncated between the lower and upper limits of the inner loop power to obtain the inner loop power command of the current sector.

10. A multi-zone temperature control system for a heating plate according to claim 6, characterized in that, The inner ring temperature error is obtained by subtracting the average temperature of the inner ring zone from the target temperature. The inner ring set temperature is obtained by multiplying the current inner ring set temperature by the inner ring temperature error by the sampling period and then dividing by the closed-loop time constant. The inner ring set temperature at the next moment is obtained by adding the result. The current edge set temperature difference is compared with the maximum edge set temperature difference, and the smaller value of the two is taken as the candidate edge set temperature difference. The inner ring set temperature at the next moment is added to the candidate edge set temperature difference to obtain the edge set temperature at the next moment.

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