JP2009198298A - Temperature estimation method and apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a temperature estimation method and a temperature estimation apparatus used for a heating process system having a to-be-heated object thermometer for measuring a temperature of a to-be-heated object, the to-be-heated object accommodating a heater and a control device for manipulating an output from the heater as it monitors a to-be-heated object temperature measurement value obtained by the to-be-heated object temperature, estimating a heater temperature, and reducing a temperature estimation error. <P>SOLUTION: The temperature estimation method generates two different transfer function models for estimating the heater temperature from different input time-series data, and estimates a plurality of the heaters by using both of two different transfer function models when the heater temperature is estimated. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention includes a heat treatment target that accommodates a heating target thermometer that measures the temperature of the heating target and a heater, and a control device that operates the output of the heater while monitoring the heating target temperature measurement value by the heating target thermometer. The present invention relates to a temperature estimation method and a temperature estimation device for estimating a heater temperature in a heat treatment system provided.

  A temperature control device such as a temperature controller is applied to a control target using a heater as a heat source. In many cases, the temperature to be controlled is the temperature inside the furnace away from the heater, but even in such a case, the heater temperature may be required for management or diagnostic purposes.

  Although it is not easy to directly measure the heater temperature, it is possible to measure the temperature near the heater. However, taking in a temperature sensor that measures the temperature in the vicinity of the heater into the apparatus increases the number of measurement points handled by the temperature control device, so that an expensive temperature control device that can handle many measurement points is used. Therefore, a method for substituting actual measurement by estimating the temperature in the vicinity of the heater is effective.

  For example, Patent Document 1 is disclosed as a temperature estimation technique. In such a temperature estimation technique, when viewed from the control amount PV that is the temperature measurement point or the operation amount MV that is the output of the control device, the temperature corresponding to the downstream in terms of energy transfer is estimated, In principle, a temperature estimation model approximated by a first-order lag, second-order lag, or higher-order lag transfer function is employed. When estimating the temperature in the vicinity of the heater, it is usual to calculate the estimated temperature value by using a first-order lag, second-order lag, or higher-order lag transfer function with the operation amount MV as the output of the control device as an input signal. Method. This adds signal equipment (eg, a temperature sensor that measures temperature not directly related to control) other than the control amount PV (temperature measurement value) and the operation amount MV (heater output value) that are essential for temperature control. It is reasonable to assume that this is not the case.

  However, since the inside of the apparatus has a heat capacity, the heater temperature cannot always be determined uniformly depending on the operation amount MV (heater output value). In some cases, it may be necessary to allow for a large temperature estimation error.

Incidentally, Patent Document 2 is cited for the explanation to be described later.
JP 2006-329869 A JP 2004-38428 A

  In view of the above circumstances, an object of the present invention is to provide a technique for reducing an estimated temperature estimation error in estimating the temperature of a heater (including the temperature in the vicinity of the heater).

The temperature estimation method of the present invention that achieves the above object includes: a heating target that contains a heating target thermometer and a heater that measures the temperature of the heating target; and a heater while monitoring the heating target temperature measurement value by the heating target thermometer. In a temperature estimation method for estimating the temperature of a heater in a heat treatment system including a control device for operating the output of
Temporary installation of a heater thermometer that measures the temperature of the heater, operation amount time-series data representing the temporal change in the operation amount that is an instruction for operating the heater output of the control device, and the heating target Heating target temperature time series data representing a temporal change in the heating target temperature measurement value measured by the thermometer, and heater temperature time series data representing a temporal change in the heater temperature measurement value measured by the heater thermometer. A time-series data input step to input;
A first transfer function model for obtaining the heater temperature from the manipulated variable is obtained by fitting the manipulated variable time series data as input time series data and fitting the heater temperature time series data as output time series data to the transfer function. 1 modeling step,
The second transfer function for obtaining the heater temperature from the measured temperature of the heating target temperature by fitting the heating target temperature time series data as input time series data and fitting the heater temperature time series data as output time series data to the transfer function. A second modeling step for obtaining a model;
And a heater temperature estimating step of estimating a heater temperature using both the first transfer function model and the second transfer function model.

  The temperature estimation method of the present invention creates two different transfer function models for estimating the heater temperature from different input time series data in both the first modeling step and the second modeling step, In estimating the heater temperature, the temperature of the heater is estimated using both of these two transfer function models, an estimated value having a large error can be avoided, and the temperature estimation error can be reduced.

  Here, the “heater temperature” in the present invention means that the temperature of the heater itself or the temperature near the heater may be used.

  In the temperature estimation method of the present invention, the heater temperature estimation step includes the first temperature estimation value of the heater obtained using the first transfer function model and the heater temperature obtained using the second transfer function model. The heater temperature may be estimated by a weighted average with the estimated temperature value of 2. Alternatively, the heater temperature estimation step may be a first heater temperature estimation obtained using a first transfer function model. The heater temperature may be estimated by adding a correction based on the second estimated temperature value of the heater obtained using the second transfer function model to the value. A correction based on the first estimated temperature value of the heater obtained using the first transfer function model is added to the second estimated temperature value of the heater obtained using the second transfer function model. It may be a step of estimating the temperature of the motor.

  Whichever method is employed, the heater temperature estimation error can be reduced.

In addition, the temperature estimation device of the present invention that achieves the above object monitors a heating target object that contains a heating target thermometer and a heater that measures the temperature of the heating target, and a heating target temperature measurement value by the heating target thermometer. In the temperature estimation device for estimating the temperature of the heater in the heat treatment system provided with a control device that operates the output of the heater while
Operation amount time-series data representing temporal changes in the operation amount, which is an instruction for operating the heater output of the control device, in a state where a heater thermometer for measuring the temperature of the heater is temporarily installed; Heating target temperature time series data representing temporal changes in the heating target temperature measurement values measured by the heating target thermometer, and heater temperature time series data representing temporal changes in the heater temperature measurement values measured by the heater thermometer A time-series data input unit for inputting
A first transfer function model for obtaining the heater temperature from the manipulated variable is obtained by fitting the manipulated variable time series data as input time series data and fitting the heater temperature time series data as output time series data to the transfer function. 1 modeling part,
The second transfer function for obtaining the heater temperature from the measured temperature of the heating target temperature by fitting the heating target temperature time series data as input time series data and fitting the heater temperature time series data as output time series data to the transfer function. A second modeling unit for obtaining a model;
It has a heater temperature estimation part which estimates the temperature of a heater using both the 1st transfer function model and the 2nd transfer function model.

  According to the present invention described above, an estimated heater temperature value with a reduced temperature estimation error can be obtained.

[Technology / Important points]
The influence of the heat capacity inside the apparatus usually has an influence on the control amount PV (temperature measurement value). When viewed from the control amount PV (temperature measurement value), the temperature in the vicinity of the heater corresponds to the upstream in terms of energy transfer. Therefore, if a lead transfer function corresponding to an inverse function with respect to the first-order lag or the like is used, it is possible in principle to estimate the temperature in the vicinity of the heater using the control amount PV as an input signal. When the transfer function of the lead is used, measurement noise is amplified. Therefore, it is not practical to merely estimate the temperature near the heater using the control amount PV as an input signal. However, as described above, it is important to consider the influence of the heat capacity inside the apparatus as an element lacking in temperature estimation based on the manipulated variable MV. Therefore, if the estimated temperature value based on the control amount PV is used as an estimated value for correcting the temperature estimation by cutting unnecessary high frequency components, the temperature estimation error can be reduced as compared with the temperature estimation based only on the manipulated variable MV. To be possible, the inventors of the present invention have taken notice. For example, if a synthesis method is adopted in which the estimated temperature value based on the manipulated variable MV and the estimated temperature value based on the controlled variable PV are weighted and averaged to obtain the final estimated temperature value, the problem can be solved (the estimated temperature estimation error is reduced). The inventors of the present invention have conceived that the present invention is effective.
[Embodiment]
FIG. 1 is an instrumentation example of a temperature controller to which the temperature estimation method and the temperature estimation apparatus of the present invention are applied, and is a diagram showing a configuration when time-series data is input, and FIG. It is the same example as a temperature control instrumentation example, Comprising: It is a figure which shows the structure at the time of temperature estimation.

  Here, a heat treatment furnace 10 is shown, and a heater 11 and a temperature sensor 12 are arranged inside the heat treatment furnace 10. Further, as shown in FIG. 1, a temperature sensor 13 for measuring the heater temperature is also disposed in the vicinity of the heater 11 when inputting time-series data. The temperature sensor 13 is removed after the time series data is input (see FIG. 2). A partition wall 10A is disposed in the heat treatment furnace 10, and the air heated by the heater 11 circulates in the heat treatment furnace 10 as indicated by an arrow, and the entire inside of the heat treatment furnace 10 is circulated by the circulating air. Be warmed up.

  A control amount PV, which is measured by the temperature sensor 12 and represents the temperature in the heat treatment furnace 10, is input to the temperature controller 20. The operation amount MV is output from the temperature controller 20 so that the control amount PV becomes a desired value, that is, the desired temperature is measured by the temperature sensor 12. This manipulated variable MV is input to the power regulator 30. The power adjuster 30 receives supply of electric power corresponding to the operation amount MV from the electric power supply circuit 31 and supplies the electric power to the heater 11. The heater 11 generates heat with an amount of generated heat corresponding to the supplied electric power, and heat treatment furnace Warm the air in 10.

  Moreover, the temperature estimation apparatus 100 which is one Embodiment of this invention is provided here. In the temperature estimation device 100, in the stage of acquiring time-series data, as shown in FIG. 1, in the state where the temperature sensor 13 is arranged in the vicinity of the heater, the manipulated variable MV, the controlled variable PV, and the temperature by the temperature sensor 13 Three signals of the heater temperature Th, which is a measured value, are monitored, and three time series data sampled at each corresponding time are collected. In the temperature estimation stage shown in FIG. 2, the estimated temperature value of the heater 11 is obtained with the temperature sensor 13 (see FIG. 1) removed.

  FIG. 3 is a diagram illustrating an example of time-series data collected by the temperature estimation device 100 at the time of data collection illustrated in FIG.

  In the figure, the solid line graph is the time series data of the manipulated variable MV, the broken line graph is the time series data of the controlled variable PV, and the alternate long and short dash line is the time series data of the heater temperature Th measured by the temperature sensor 13. It represents. These time series data are 1.0 sec. The data is sampled every other time, and the numerical value on the horizontal axis represents seconds (sec.). The left vertical axis represents the values of the control amount PV and the heater temperature Th, and specifically represents the temperature (° C.) measured by the two temperature sensors 12 and 13 shown in FIG. Further, the right vertical axis represents the value of the manipulated variable MV. Here, it is represented by the ratio (%) of electric power when the operation amount MV corresponding to the maximum electric power that can be supplied to the heater 11 is 100%.

  That is, the graph of FIG. 3 shows the control amount PV representing the temperature measured by the temperature sensors 12 and 13 and the heater temperature Th when the manipulated variable MV representing the power to be supplied to the heater 11 is changed as shown in the figure. However, it represents that it changes with a delay compared with the manipulated variable MV.

  FIG. 4 is a block diagram of a temperature estimation device as one embodiment of the present invention, shown as one block in FIGS. 1 and 2.

  A temperature estimation apparatus 100 shown in FIG. 4 includes a heat treatment furnace 10 containing a temperature sensor 12 and a heater 11 for measuring the temperature in the furnace shown in FIGS. A temperature estimation device that estimates the temperature of the heater 11 in a heat treatment system that includes a temperature controller 20 that controls the temperature of the heater 11 while monitoring a value (control amount PV), the time series data input unit 110 , The first modeling unit 120, the second modeling unit 130, and the heater temperature estimation unit 140.

  Here, as shown in FIG. 1, the time-series data input unit 110 operates the output of the heater 11 of the temperature controller 20 in a state where the temperature sensor 13 for measuring the temperature of the heater 11 is temporarily installed. Manipulated variable time series data representing a temporal change in manipulated variable MV, which is an instruction to perform, and a heating target temperature time series representing a temporal change in controlled variable PV, which is a heating target temperature measurement value measured by the temperature sensor 12 Data and heater temperature time series data representing a temporal change in the temperature measurement value Th measured by the temperature sensor 13 are input.

  Further, the first modeling unit 120 obtains the heater temperature Th from the operation amount MV by fitting the operation amount time series data as input time series data and fitting the heater temperature time series data as output time series data to a transfer function. A first transfer function model is obtained.

  Further, the second modeling unit 130 performs control representing the heating target temperature measurement value by fitting the heating target temperature time series data as input time series data and fitting the heater temperature time series data as output time series data to a transfer function. A second transfer function model for obtaining the heater temperature Th from the quantity PV is obtained.

  The heater temperature estimation unit 140 estimates the heater temperature using both the first transfer function model and the second transfer function model.

  FIG. 5 is a flowchart showing an embodiment of the temperature estimation method of the present invention.

  The temperature estimation method shown in FIG. 5 includes a time series data input step (S1), a first modeling step (S2), a second modeling step (S3), and a heater temperature estimation step (S4). Each of the time series data input step (S1), the first modeling step (S2), the second modeling step (S3), and the heater temperature estimation step (S4) includes a temperature estimation device 100 shown in FIG. 5 corresponds to the time series data input unit 110, the first modeling unit 120, the second modeling unit 130, and the heater temperature estimation unit 140 in FIG. It also serves as an explanation of the estimation method.

  In addition, here, the temperature estimation method executed in the temperature estimation device 100 is also represented by the description of the temperature estimation device 100, but the temperature estimation method of the present invention is performed in one device. Instead of being executed, it may be shared by a plurality of devices. For example, the temperature estimation method of the present invention may be executed by sharing a time series data collection device, a modeling device, and a temperature estimation device.

  FIG. 6 is a diagram showing in more detail the components used during data collection of the temperature estimation apparatus 100 shown in FIG.

  The time-series data input unit 110 includes an operation amount MV input unit 111, a heater temperature Th input unit 112, and a control amount PV input unit 113. In the manipulated variable MV input unit 111, the heater temperature Th input unit 112, and the control amount PV input unit 113, as shown in FIG. 1, the temperature sensor 13 for measuring the temperature of the heater 11 is temporarily installed. Operation amount time-series data representing temporal changes in the operation amount MV, heater temperature time-series data representing temporal changes in the heater temperature Th measured by the temperature sensor 13, and heating targets measured by the temperature sensor 12, respectively. The heating target temperature time-series data representing the temporal change of the control amount PV representing the temperature measurement value is input. Of these three types of time series data, the operation amount time series data input from the operation amount MV input unit 111 is input to the first modeling unit 120 and the heater temperature time series input from the heater temperature Th input unit 112. The data is input to both the first modeling unit 120 and the second modeling unit 130, and the heating target temperature time-series data input from the control amount PV input unit 113 is input to the second modeling unit 130. .

  In the first modeling unit 120, as described above, the first transfer function model is created using the manipulated variable time-series data as input time-series data and the heater temperature time-series data as output time-series data. At 130, a second transfer function model is created using the heating target temperature time-series data as input time-series data and the heater temperature time-series data as output time-series data.

  FIG. 7 is a detailed block diagram of the heater temperature estimation unit 140 that is a component used in the heater estimation of the temperature estimation apparatus 100 shown in FIG.

  The heater temperature estimation unit 140 includes a first model storage unit 141, a second model storage unit 142, a first temperature estimation unit 143, a second temperature estimation unit 144, and a heater temperature calculation unit 145. Yes.

  The first model storage unit 141 and the second model storage unit 142 are generated by the first transfer function model and the second modeling unit 130 created by the first modeling unit 120 shown in FIGS. 4 and 6. The second transfer function model is an element for storing each.

  Further, the first temperature estimation unit 143 and the second temperature estimation unit 144 respectively estimate the heater temperature based on the first transfer function model stored in the first model storage unit 141, and the second temperature estimation unit 144 This is an element for estimating the heater temperature based on the second transfer function model stored in the model storage unit 142. Further, the heater temperature calculation unit 145 uses both the heater temperature estimated by the first temperature estimation unit 143 and the heater temperature estimated by the second temperature estimation unit 144, so that the final temperature estimation value of the heater is obtained. Is an element for calculating.

  Hereinafter, this embodiment will be described in more detail.

  First, a temporary temperature sensor 13 for measuring the heater temperature Th is arranged, and time series data for modeling is collected for the temperature Th in the vicinity of the heater together with the operation amount MV and the control amount PV (temperature measurement value). . For example, Patent Document 2 discloses a technique (curve fitting) for collecting the time series data of the control amount PV and the time series data of the manipulated variable MV and modeling the control target. A transfer function model can be created. However, the modeling disclosed in Patent Document 2 targets the relationship between the “operation amount MV and the control amount PV (temperature measurement value)”, but in the present embodiment, “the operation amount MV and the heater temperature”. Two models for the relationship between “Th” and “heater temperature Th and control amount PV (temperature measurement value)” are obtained.

  Model formula A: The operation amount MV and the heater temperature Th are targeted.

Th = MA ・ MV
KA: Process gain LA: Process dead time TA1, TA2: Secondary delay time constant Model formula B: Target heater temperature Th and controlled variable PV (temperature measurement value)

Th = MB ・ PV
KB: Process gain (reciprocal)
TB1, TB2: Secondary delay time constant (however, reciprocal = secondary read time constant)
In the model formula B, it seems realistic to use the reciprocal of the second-order lag + dead time. However, assuming real-time temperature estimation, the reciprocal of dead time is a theoretically impossible requirement. Therefore, the above formula is used. However, in the case of the relationship between the heater temperature Th and the control amount PV (temperature measurement value), there is only a heat capacity element as an energy storage element, and there is usually no element of pure dead time. There is no problem with the formula without the reciprocal of time. Conventionally, knowledge regarding such practically acceptable range has not been disclosed.

  The above is the part corresponding to the modeling unit (see FIGS. 1 and 6).

  Next, temperature estimation in the vicinity of the heater is obtained as follows based on the operation amount MV actually output and the control amount PV (temperature measurement value) actually measured.

Estimated temperature A: ThA = MA · MV
Estimated temperature B: ThB = MB · PV
Estimated temperature: ThE = αThA + (1-α) ThB
α: Weight of weighted average defined in advance 0 ≦ α ≦ 1
The above weights may be switched to different values at the time of temperature rise and at the time of steady state. Or you may switch to a different numerical value according to a temperature range.

  In addition to the method using the weighted average, for example, a mathematical formula that adds a correction based on the estimated temperature value B (ThB) using the estimated temperature value A (ThA) as the main estimated value may be adopted.

Estimated temperature: hE = ThA + f (ThB) = ThA + β · ThB
β: Correction coefficient defined in advance Alternatively, for example, a mathematical formula may be adopted in which the temperature estimation value B (ThB) is used as the main estimation value and correction based on the temperature estimation value A (ThA) is added.

Estimated temperature: ThE = ThB + g (ThA) = ThB + γ · ThA
γ: Preliminary correction coefficient The above is the part corresponding to the temperature estimation unit (see FIGS. 2 and 7).

  If there is no change in the ambient conditions in the temperature control system as a whole when modeling is performed, ThA = ThB is generally satisfied. For example, the temperature around the heater rises due to the heat capacity around the heater arranged in the manufacturing apparatus. Even when the operation amount MV is low, the heater temperature itself maintains a high temperature. At this time, the control amount PV is closely related to the temperature around the heater. Therefore, when the heater temperature estimation based on the control amount PV is added in the meaning of the correction function, compared to the heater temperature estimation based only on the operation amount MV, More accurate temperature estimation becomes possible.

  As a specific application, there may be a case where algorithms for estimating heater power consumption and heater life are operating in parallel. In the case of a resistance heater, the heater resistance value increases as the heater temperature is high, so that the power consumption to be estimated tends to be higher than the power consumption simply calculated from the operation amount MV. The heater temperature estimation according to the present embodiment improves the utility of heater power estimation. In addition, since the heater life can be estimated in consideration of the accumulation of energization time when the heater temperature is high, the practicality of the heater life estimation is improved.

  In the example of FIG. 3, the following model formula is obtained.

  Model Formula A: Targeting the manipulated variable MV and the heater temperature Th

ThA = MA ・ MV
Model formula B: Heater temperature Th and control amount PV (temperature measurement value) are targeted

ThB = MB ・ PV
The modeling method used here is curve fitting, but the numerical results obtained by the search method and the search procedure are different. The heater temperature estimated value ThE may be calculated as follows, for example.

  Estimated temperature: ThE = 0.5ThA + 0.5ThB

It is an instrumentation example of a temperature controller to which the temperature estimation method and the temperature estimation apparatus of the present invention are applied, and is a diagram showing a configuration when inputting time-series data. It is the same example as the temperature control instrumentation example shown in FIG. 1, Comprising: It is a figure which shows the structure at the time of temperature estimation. It is a figure which shows the example of the time series data collected by the temperature estimation apparatus shown in FIG. It is a block diagram of the temperature estimation apparatus as one embodiment of the present invention shown by one block in FIG. 1 and FIG. It is a flowchart which shows one Embodiment of the temperature estimation method of this invention. It is the figure which showed in more detail the component used at the time of data collection of the temperature estimation apparatus shown in FIG. FIG. 5 is a detailed block diagram of a heater temperature estimation unit that is a component used in estimating the heater temperature of the temperature estimation device shown in FIG. 4.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Heat processing furnace 10A Bulkhead 11 Heater 12, 13 Temperature sensor 20 Temperature controller 30 Power regulator 31 Power supply circuit 100 Temperature estimation apparatus 110 Time series data input 111 Manipulation amount MV input part 112 Heater temperature Th input part 113 Control amount PV Input unit 120 First modeling unit 130 Second modeling unit 140 Heater temperature estimation unit 141 First model storage unit 142 Second model storage unit 143 First temperature estimation unit 144 Second temperature estimation unit 145 Heater temperature Calculation unit

Claims (5)

A heating target that houses a heating target thermometer that measures the temperature of the heating target and a heater, and a control device that operates the output of the heater while monitoring the heating target temperature measurement value by the heating target thermometer In the temperature estimation method for estimating the temperature of the heater in the heat treatment system,
Temporary installation of a heater thermometer for measuring the temperature of the heater, operation amount time-series data representing a temporal change in the operation amount that is an instruction for operating the output of the heater of the control device; Heating target temperature time series data representing a temporal change in the heating target temperature measurement value measured by the heating target thermometer, and a heater temperature representing a temporal change in the temperature measurement value of the heater measured by the heater thermometer A time-series data input step for inputting time-series data;
A first transfer function for determining the heater temperature from the manipulated variable by fitting the manipulated variable time-series data as input time-series data and fitting the heater temperature time-series data as output time-series data to a transfer function. A first modeling step for obtaining a model;
By fitting the heating target temperature time-series data as input time-series data and the heater temperature time-series data as output time-series data to a transfer function, a first temperature for obtaining the heater temperature from the heating target temperature measurement value is obtained. A second modeling step for obtaining a transfer function model of 2;
A temperature estimation method comprising: a heater temperature estimation step for estimating a temperature of the heater using both the first transfer function model and the second transfer function model.   In the heater temperature estimation step, a first estimated temperature value of the heater obtained using the first transfer function model, and a second estimated temperature value of the heater obtained using the second transfer function model, The temperature estimation method according to claim 1, wherein the temperature of the heater is estimated by a weighted average.   In the heater temperature estimating step, the first temperature estimated value of the heater obtained using the first transfer function model is set to the second temperature estimated value of the heater calculated using the second transfer function model. The temperature estimation method according to claim 1, wherein a step of estimating the temperature of the heater is performed by applying a correction based on the correction.   In the heater temperature estimating step, the second temperature estimated value of the heater obtained using the second transfer function model is set to the first temperature estimated value of the heater obtained using the first transfer function model. The temperature estimation method according to claim 1, wherein a step of estimating the temperature of the heater is performed by applying a correction based on the correction. A heating target that houses a heating target thermometer that measures the temperature of the heating target and a heater, and a control device that operates the output of the heater while monitoring the heating target temperature measurement value by the heating target thermometer In the temperature estimation device for estimating the temperature of the heater in the heat treatment system,
Manipulation amount time-series data representing a temporal change of an operation amount, which is an instruction for operating the output of the heater, of the control device in a state where a heater thermometer for measuring the temperature of the heater is temporarily installed. And heating target temperature time-series data representing a temporal change in the heating target temperature measurement value measured by the heating target thermometer, and a temporal change in the heater temperature measurement value measured by the heater thermometer. A time series data input section for inputting heater temperature time series data;
A first transfer function for determining the heater temperature from the manipulated variable by fitting the manipulated variable time-series data as input time-series data and fitting the heater temperature time-series data as output time-series data to a transfer function. A first modeling unit for obtaining a model;
By fitting the heating target temperature time-series data as input time-series data and the heater temperature time-series data as output time-series data to a transfer function, a first temperature for obtaining the heater temperature from the heating target temperature measurement value is obtained. A second modeling unit for obtaining a transfer function model of 2;
A temperature estimation device, comprising: a heater temperature estimation unit that estimates the temperature of the heater using both the first transfer function model and the second transfer function model.

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