JPH06161510A - Plant identifying method - Google Patents

Abstract

PURPOSE:To make it possible to easily identify the plant to be identified even when it is difficult or impossible to directly investigate the response characteristic of an identified plant or even when the identified plant is changed in a system including plural plants. CONSTITUTION:A plant indentifying part is composed of microcomputers and functionally has an identifying input generation part 12, an identifying output recovering part 14 and an identifying arithmetic processing part 16. The identifying input generation part 12 generates a prescribed input Sin for plant identification. The identifying output recovering part 14 fetches a system output Sout (20, 30) and holds it in a storage device. The identifying arithmetic processing part 16 calculates the parameter of an wafer heating plant (identified plant) based on the data of the input Sin generated from the identifying input generation part 12, the data of the system output Sout (20, 30) fetched by the identifying output recovering part 14 and the response output of the mathematical model of an wafer temperature measuring plant 30 having known parameters.

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION The present invention relates to a method for determining and identifying unknown parameters for modeling a plant.

[0002]

2. Description of the Related Art In a feedback type control system,
A physical quantity to be controlled, that is, a controlled quantity is observed, the observed value is compared with a target value, and a manipulated variable corresponding to a comparison error (deviation) is given to a plant (controlled object).

Conventionally, in this type of system, if the time delay of the plant can be approximated to second order or less, PI
D controllers have been used. The PID controller calculates a manipulated variable by calculating a predetermined equation that combines proportional action (P), integral action (I), and derivative action (D) based on the difference (deviation) between the control amount detection value and the set value. Ask. However, if the controlled variable is not observable or if the time delay is 3rd or more,
The PID controller does not work effectively. Although the PID controller controls the detected physical quantity to match the set value, it cannot control the unobservable control quantity to exactly match the target value. It cannot be fully compensated.

There is an optimum feedback control method for solving the above-mentioned limitations of the PID controller. This control method is to feed back all the state variables of the plant to obtain the control input (manipulation amount) that minimizes the predetermined evaluation function. It is possible to match the target value.

In the optimal feedback control method, observers such as the same dimension observer and the minimum dimension observer are used to estimate the unobservable state quantity. This type of observer is an algorithm that uses a mathematical model of the plant, and calculates and outputs the unobservable state quantity in response to the input and output of the plant.

In constructing such an observer, a mathematical model of the plant must be determined, and for that purpose, the plant must be identified. In general, this kind of mathematical model is expressed as a transfer function of a polynomial, so that the plant is identified by obtaining the coefficient of the polynomial, that is, the parameter from the response characteristic of the plant.

[0007]

However, since it is practically impossible to examine the response characteristics of the plant, identification may be difficult in some cases. For example, CVD for semiconductor device manufacturing
When the temperature of the semiconductor wafer is controlled to be heated to a predetermined temperature in the process, the original control amount is the temperature of the surface to be processed, that is, the surface. However, since a temperature sensor such as a thermocouple cannot be brought into direct contact with the surface to be processed of the wafer during the CVD process, it is common practice to bring the temperature sensor into contact with the peripheral portion of the back surface of the wafer to detect the temperature at that location. ing.

For this reason, conventionally, the entire system from the heating mechanism to the temperature sensor at the peripheral portion of the back surface of the wafer is set as one plant, and the response characteristics of the entire system are investigated to obtain the parameters of the entire system. However, even if the entire system is identified in this way and a mathematical model or observer is constructed, it is rare that the state quantity of the mathematical model and the actual control quantity match, which is the original control quantity. It was difficult to estimate the state quantity of the wafer surface temperature, and it was practically impossible to perform optimum control.

Further, a temperature sensor is attached to the surface of the wafer for identification, the system from the heating mechanism to the wafer surface is used as one plant, the response characteristic of this plant is investigated based on the output signal of the temperature sensor, and the parameters are set. It is possible to ask. However, if the temperature characteristics of the wafer actually processed in the CVD process are different from the temperature characteristics of the wafer in the identification (experimental) model, or if the heating mechanism is changed or modified, the plant parameters change,
It has to be re-identified. It is practically difficult to re-identify the plant by the above-described experimental model every time the plant parameters are changed as described above, which requires a great deal of labor and cost.

The present invention has been made in view of the above problems, and it is easy even if it is difficult or impossible to directly investigate the response characteristic of the identified plant, or if the identified plant is changed. It is an object of the present invention to provide a method capable of identifying a target identified plant.

[0011]

In order to achieve the above-mentioned object, the plant identification method of the present invention has a plant to be identified having an unknown parameter and a known plant.
Applying a predetermined input to a predetermined system consisting of one or more related plants and observing the output of the system; data of the input, data of the system output, and a mathematical model of the related plant. Determining the parameters of the identified plant based on the response characteristics.

[0012]

For example, if the identified plant having an unknown parameter and the related plant having the known parameter are connected in series to form a system, and each of these plants is a linear system, the system corresponds to those plants. Both can be interchanged between mathematical models. Then, by calculating the response output when the system input is given to the known model corresponding to the related plant, and setting the response output as the known input to the unknown model, the known input and the known system output are The response characteristics of the unknown model can be estimated from. Once the response characteristics of the unknown model are estimated, the parameters of the unknown model are obtained using a predetermined parameter calculation method such as the least square method or Kalman filter. From the parameters thus obtained, a mathematical model or observer of the model to be identified can be obtained.

[0013]

Embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 8 shows a control system in which the identification method is used in this embodiment. The control system 100 is a wafer temperature control mechanism for controlling the temperature of a semiconductor wafer to a predetermined temperature in a CVD process for manufacturing a semiconductor device.

In this wafer temperature control mechanism, the semiconductor wafer 10 as an object to be processed is placed in the vacuum chamber 102.
4 is arranged at a predetermined position by a predetermined supporting member (not shown), and a quartz window 106 is arranged at the bottom of the chamber below the wafer 104. A heating lamp 108 is disposed outside the chamber 102, and light from the heating lamp 108 passes through the quartz window 106 and the wafer 104.
The back surface of the wafer is irradiated with the light energy of the wafer 104.
Is heated. The surface (upper surface) of the wafer 104 is a surface to be processed, and the temperature of the surface to be processed is an original controlled amount. A thermocouple 110 is attached as a temperature sensor to the peripheral portion of the back surface of the wafer, and the output voltage of the thermocouple 110 is the system 10
The output y of 0 is given to the controller 140 via the compensation cable 112.

The heating lamp 108 has a PWM amplifier 114.
Receives power from the slip ring 116,
A rotation drive mechanism including a motor 118 and gears 120 and 122 is configured to emit light toward the wafer 104 side while rotating integrally with the rotation shaft 124.

The PWM amplifier 114 includes a controller 14
A temperature control voltage from 0 is input as a control input u, and the temperature control voltage is power-amplified and then supplied to the heating lamp 108 as a PWM signal. The power control unit 124 performs on / off control of the PWM amplifier 114 at the time of start-up or abnormality.

In the vacuum chamber 102, one end of an optical fiber 126 faces between the wafer 104 and the quartz window 106.
The other end of 6 is connected to the luminous flux monitor 128. The light flux monitor 128 detects the light flux (intensity) of the light supplied to the wafer 104 via the optical fiber 126, and supplies the detected light flux value to the glass breaking interlock unit 130. When the quartz window 106 becomes turbid, the amount of light absorbed therein increases, so that the light energy supplied to the wafer 114 decreases, and the risk of breaking the quartz window 106 increases. Therefore, when the luminous flux monitor value decreases to a predetermined value, the glass breaking interlock unit 130
Further, a heating stop signal is given to the PWM amplifier 114, and the heating lamp 108 is turned off.

In the wafer temperature control mechanism 100 having such a configuration, the output y of the system 100 represents the temperature of the back surface of the wafer 104 and is the control amount of the wafer 104.
It does not represent the temperature of the surface (treated surface). The controller 140 performs temperature control by the optimal feedback control method in order to match such an unobservable wafer surface temperature with a target value. Therefore, the controller 14
Since not all state quantities can be observed at 0 as described above, an observer for optimal feedback control is provided. The identification method according to the present embodiment is used in constructing this optimal feedback control and observer.

FIG. 1 is a block diagram showing the arrangement of an identification system for carrying out the identification method according to this embodiment.

The plant identification section 10 is composed of a microcomputer and functionally has an identification input generation section 12, an identification output recovery section 14 and an identification calculation processing section 16. The identification input generation unit 12 generates an input signal for plant identification, such as a step signal or a normal random number signal. The identification output recovery unit 14 takes in the response output or system output of the plant, and outputs the output data as, for example, R
It is linearly approximated by a look-up table composed of OM and then stored in a storage device. Identification calculation processing unit 1
6 executes the calculation of the identification process as described later to obtain the parameter of the identified plant.

The wafer heating plant 20 is an internal plant corresponding to the portion of the wafer temperature control mechanism 100 of FIG. 8 which heats the surface temperature of the wafer 104 in accordance with the manipulated variable from the controller 140. The wafer heating plant 20 is a wafer plant 2 as a heat transfer system from the heating lamp 108 to the surface (processed surface) of the wafer 104.
In addition to 2, the D / A converter 140 of the output section in the PWM amplifier 114 and the controller 140 of the electric signal processing system
Also includes a and the like.

The wafer temperature measuring plant 30 is an internal plant corresponding to the portion of the wafer temperature control mechanism 100 of FIG. 8 which feeds back the temperature of the wafer 104 to the controller 104. The wafer temperature measuring plant 30 is provided with a sensor output signal (y) in addition to a sensor plant 32 as a heat transfer / thermoelectric conversion system from the front surface of the wafer 104 to the output terminal of the thermocouple 110 that senses the peripheral edge of the back surface of the wafer. A / A of the sensor output transmission unit 34 such as the compensation cable 112 for transmission and the input unit in the controller 140
The D converter 140b etc. are also included. Sensor output transmitter 3
4 includes a switch or a multiplexer for switching between the output signal of the thermocouple 110 and the output signal of the thermocouple 40 for identification by actual measurement as described later.

Wafer temperature control mechanism (control system) 10
At 0, the wafer heating plant 20 and the wafer temperature measuring plant 30 are each a linear internal plant. Both plants 20 and 30 are plants related to each other in that they are connected in series.

Next, the operation of plant identification in this embodiment will be described. The plant identification method according to the present embodiment is applied to the identification of the wafer heating plant 20 when it has an unknown parameter. In carrying out the plant identification method according to the present embodiment, the parameters of the wafer temperature measuring plant 30 which is a related plant to the wafer heating plant 20 must be known and the mathematical model thereof must be established.

Therefore, the wafer temperature measuring plant 30 is previously identified by actual measurement. In order to perform this identification, as shown in FIG. 2, an identification wafer 104 'is placed in the vacuum chamber 102, and an identification thermocouple 40 is attached to the center of the surface of the wafer 104'. The output terminal of the thermocouple 40 is connected to the other input terminal of the changeover switch in the sensor output transmission section 34 via the cable 42. The same thermocouple 1 as in the CVD process is provided on the peripheral portion of the back surface of the wafer 104 '
10 contacts via the thermally conductive cap 110a.
The thermally conductive cap 110a stabilizes the contact condition between the thermocouple 110 and the wafer 104, and further reduces the thermal influence of the ambient gas on the temperature sensing portion of the thermocouple 110 during the CVD process.

First, the response characteristic of the wafer heating plant 20 is actually measured. For this reason, the sensor output transmission unit 34 is switched to the identification thermocouple 40 side. A predetermined digital signal Sin is generated as an input for identification from the identification input generation unit 12 of the plant identification unit 10. The digital identification input signal Sin is converted into an analog signal by the D / A converter 140a and input to the PWM amplifier 114 as a temperature control voltage. The PWM amplifier 114 supplies the lamp 108 with a PWM signal (power) according to the temperature control voltage. Upon receiving this power supply, the heating lamp 108 emits light, and the energy of the light emitted from the heating lamp 108 heats the wafer 104 ′. As a result, the surface temperature of the wafer 104 'rises with a time delay unique to the wafer plant 22. The wafer surface temperature is detected by the thermocouple 40. The output signal of the thermocouple 40 is sent to the A / D converter 140b via the sensor output transmission unit 34, converted into a digital signal there, and then identified as the response output Sout (20) of the wafer heating plant 20. Part 1
It is taken into the identification output recovery unit 14 of 0. The response output data Sout (20) of the wafer heating plant 20 fetched by the identification output recovery unit 14 is held in the storage device in the identification output recovery unit 14.

Next, the response characteristic of the wafer temperature measuring plant 30 is measured. For this purpose, the sensor output transmission unit 34
Is switched to the normal temperature detecting thermocouple 110 side. Then, the identification input generation unit 12 of the plant identification unit 10
The same digital identification input signal Sin as described above is applied to the D / A converter 140a of the wafer heating plant 20.
As a result, the lamp 108 emits light, and the light energy heats the wafer 104 ′, and the wafer plant 22 is heated.
The surface temperature of the wafer 104 'rises with a time delay peculiar to the above. Then, the temperature of the peripheral portion of the back surface of the wafer 104 ′ is detected by the thermocouple 110. The output signal of the thermocouple 110 is sent to the A / D converter 140 via the sensor output transmission unit 34.
b, where it is converted to a digital signal,
Wafer heating plant 20 and wafer temperature measurement plant 30
Is output to the identification output recovery unit 14 of the plant identification unit 10 as the output Sout (20,30) of the system including the.

In this case, the wafer temperature measuring plant 30
Receives the output Sout (20) of the wafer heating plant 20 as an input and outputs the output Sout (20, 30). By the way, the output S (20) of the wafer heating plant 20 is held in the storage device in the identification output recovery unit 14 in the previous measurement of the response characteristic of the wafer heating plant 20. Therefore, the data of the input S (20) and the output Sout (20, 30) in the wafer temperature measuring plant 30 are complete, and the response characteristic of the wafer temperature measuring plant 30 is actually measured. The identification calculation processing unit 16 obtains the parameters of the wafer temperature measuring plant 30 based on the response characteristics by using a predetermined parameter calculation method, for example, the least square method. By thus determining the parameters of the wafer temperature measuring plant 30, the wafer temperature measuring plant 30 is identified and its mathematical model is determined.

With respect to the wafer heating plant 20 as well, the parameters can be obtained based on the response output S (20). However, if the wafer 104 in the actual CVD process is different from the identification wafer 104 ′, or if the heating lamp 108, the PWM amplifier 114, or the like is changed or modified, the parameters of the wafer heating plant 20 are changed. In this respect, in the wafer temperature measurement plant 30, even if the identification wafer 104 ′ is replaced with the actual wafer 104, the response characteristics are not affected, and the device circuit is rarely deformed or modified. Does not change, and even if it does change, it can be re-identified by the method described below using a reference wafer with known parameters. Therefore, the parameters or mathematical model of the wafer temperature measuring plant 30 obtained by using the experimental model as described above is the actual CVD.
It is valid even during the process.

3 and 4 show examples of response characteristics of the wafer heating plant 20 and the wafer temperature measuring plant 30 obtained by the above-described actual measurement. Figure 3 shows the input Sin
4 is a case where a step waveform is used as shown in FIG.
This is the case where a normal random number is used as in.

When the parameters of the wafer heating plant 20 are changed for the above reasons, the plant identification method according to this embodiment is used. In this identification method, the thermocouple 40 for identification is not used. Therefore, the sensor output transmission unit 34 is connected to the thermocouple 110 side for normal temperature detection. The identification input generation unit 12 of the plant identification unit 10 generates an appropriate digital signal Sin as an input for identification. This digital signal Sin may be the same signal as that used in the above identification by actual measurement, or may be a different signal. This digital identification input signal Sin is D /
It is converted into an analog signal by the A converter 140a and input as a temperature control voltage to the PWM amplifier 114. The PWM amplifier 114 supplies the lamp 108 with a PWM signal (power) according to the temperature control voltage. Upon receiving this power supply, the heating lamp 108 emits light, and the energy of the light emitted from the heating lamp 108 heats the wafer 104. As a result, the surface temperature of the wafer 104 rises with a time delay unique to the wafer plant 22. Then, the temperature of the peripheral portion of the back surface of the wafer 104 is detected by the thermocouple 110. The output signal of the thermocouple 110 is sent to the A / D converter 140b via the sensor output transmission unit 34, where it is converted into a digital signal, and then the wafer heating plant 2
0 and the output Sout (20,22) of the system including the wafer temperature measurement plant 30 are taken into the identification output recovery unit 14 of the plant identification unit 10.

In this embodiment, the identification calculation processing section 16 of the plant identification section 10 identifies the wafer heating plant 20 having an unknown parameter by the following algorithm. As shown in FIG. 1, since the wafer heating plant 20 and the wafer temperature measuring plant 30 are connected to each other in series as an internal plant, as shown in FIG. Model G
1 (Z ^-1 ) and G2 (Z ^-1 ) are also represented as being connected in series with each other.

These mathematical models G1 (Z ^-1 ) and G2 (Z ^-1 )
Using, for example, a discrete ARMA (autoregressive moving average) model, G1 (Z ^-1 ) = (a11Z ^-1 + ... a1nZ ^-1 ) / (1 + b11Z ^-1 + ... b1nZ ^-1 ) ... (1) G2 ( Z ^-1 ) = (a21Z ^-1 + ... a2nZ ^-1 ) / (1 + b21Z ^-1 + ... b2nZ ^-1 ) ... (2)

Since the wafer heating plant 20 is an identified plant, the parameters a11, ..., A1n, b11, ..., B1n of the mathematical model G1 (Z ^-1 ) are unknown. On the other hand, the wafer temperature measuring plant 30 is previously identified by actual measurement as described above, and its mathematical model G2 (Z
, A2n, b21, ..., B2n of ( ^-1 ) are known.

These mathematical models G1 (Z ^-1 ) and G2 (Z ^-1 )
Since each is a linear model, even if G1 (Z ^-1 ) and G2 (Z ^-1 ) are replaced with each other as shown in (B) of FIG. 5, (A) of FIG. System output Sou
The same system output Sout (30,20) as t (20,30) is obtained. Then, in the system shown in FIG.
The response output [Sout (30)] of the mathematical model G2 (Z ^-1 ) of the wafer temperature measuring plant 30 with respect to the [input Sin] is obtained by the following arithmetic expression. [Sout (30)] = G2 (Z ⁻¹ ) · Sin (3) where [Sin] is the value (data) of the digital signal Sin generated by the identification input generator 12 in the above measurement. .

The model G2 (Z ^-1 ) obtained by the above equation (3)
Response output [Sout (30)] of the wafer heating plant 20
^Is the input of the mathematical model G1 (Z ^-1 ). Therefore, the following equation holds for the mathematical model G1 (Z ^-1 ). G1 (Z ^-1 ) * [Sout (30)] = [Sout (30,20)] = Sout (20,30) (4) where [Sout (30,20)] is ( B) is the response output of the mathematical model G2 (Z ^-1 ) ・ G1 (Z ^-1 ) of [Sout (20,3
0)] is the mathematical model G1 (Z ^-1 ) ・ G2 (Z ^-1 ) of Fig. 5 (A).
Is the response output of Sout (20,30), and Sout (20,30) is the system output Sout (20,30) fetched by the identification output recovery unit 14 in the above actual measurement.
Is the value of.

The unknown parameter a11 of the model G1 (Z ^-1 ),
, A1n, b11, ..., b1n are 2n, [S
If 2n combinations of out (30)] and the corresponding [Sout (20,30)] are given, 2n equations can be obtained from the above equation (4). All parameters a11, ..., A1n, b11, ..., B1n can be obtained. To obtain more accurate parameters, a parameter calculation method such as the least square method or Kalman filter may be used.

Parameter a obtained as described above
, ..., A1n, b11, ..., B1n define the mathematical model G1 (Z ^-1 ) of the wafer heating plant 20. And an observer designed based on this model G1 (Z ^-1 ),
For example, the same dimension observer or the minimum dimension observer is incorporated into the controller 140 of FIG. 8 and the optimal feedback parameters are determined. This allows
In the wafer temperature control mechanism 100, optimal feedback control is performed so that the surface to be processed (surface) of the wafer 104 matches the target value.

In the wafer heating plant 20, for example, when the type of the wafer 104 is changed and the parameters are changed, the plant identification method of this embodiment described above may be performed again. Since the plant identification method of the present embodiment obtains the parameters of the wafer heating plant 20 by an algorithm using the mathematical model G2 (Z ^-1 ) of the wafer temperature measuring plant 30 having known parameters without using the experimental model, It can be easily implemented. Also, instead of identifying the entire system as one plant,
Since the plants to be identified (wafer heating plant 20) are narrowed down and identified by dividing them into the internal plants of the wafer heating plant 20 and the wafer temperature measurement plant 30, highly accurate parameters can be obtained, and thus an observer with a high estimation capability can be obtained. Can be designed.

FIG. 6 shows a verification example in which the response output of the mathematical model G1 (Z ^-1 ) of the wafer heating plant 20 is compared with the response output of the plant 20 by actual measurement. Mathematical model G1 (Z
The response output [Sout (20)] of ^-1 ) is a value calculated by the following equation. [Sout (20)] = G1 (Z ⁻¹ ) · [Sin] (5) On the other hand, the response output Sout (20) of the plant 20 by actual measurement
Is a measured value obtained from the identifying thermocouple 40 using the experimental model as shown in FIG. As shown in FIG. 6, the response output of the mathematical model G1 (Z ^-1 ) [Siut (20)]
Is well approximated to the measured response output Sout (20) of the plant 20. In addition, in FIG. 6, when the sensor plant is changed, the mathematical model of (A) of FIG. 5 by the parameters when G2 (Z ^-1 ) is estimated using the known G1 (Z ^-1 ). A verification example is also shown in which the response output [Sout (20,30)] of G2 (Z ^-1 ) is compared with the response output of the plants 20 and 30 (temperature detected by the thermocouple 110) Sout (20,30) by actual measurement. .

In the above-described embodiment, the system 100 is represented by two internal plants, the wafer heating plant 20 and the wafer temperature measuring plant 30, but other internal plants can be considered. For example, when the feedback thermocouple 110 is directly irradiated with the light from the heating lamp 108, the heat transfer system of this bypass is a “direct heat transfer plant” to the wafer heating plant 20 and the wafer temperature measuring plant 30. It may be connected in parallel. In this case, the response characteristic of the direct heat transfer plant is determined by the identification input generation unit 12 with the wafer 104 removed.
Output signal Sout of thermocouple 110 for input Sin from
(50) can be measured. The parameters of the heat transfer plant can be obtained directly from the response characteristics obtained by this measurement.

Since the direct heat transfer plant is an internal plant connected in parallel to the wafer heating plant 20 and the wafer temperature measuring plant 30, the response output Sout () of the wafer heating plant 20 and the wafer temperature measuring plant 30 to the input Sin is obtained. 20,30) and the response output Sout (50) of the direct heat transfer plant with respect to the input Sin, the output is the response output of the entire system (response output of the thermocouple 110).
Obtained as Sout (20,30 / 50).

Therefore, when the wafer heating plant 20 is identified by the algorithm in this embodiment, a mathematical model as shown in FIG. 7 may be used. G3 (Z- ¹ ) is a mathematical model of the direct heat transfer plant, and its parameters a31, ..., A3n, b31, ..., B3n are known from the above-mentioned actual measurement.

Mathematical model G3 (Z for input [Sin]
^-1 ) response output [Sout (50)] to system output Sout (20,
30/50), the wafer heating plant 20
And the response output Sout (2
0,30) is required. After that, the same processing as in the case of FIG. 5A is performed, and both models G1 are processed as shown in FIG. 5B.
(Z ^-1), substituting G2 (Z ^-1), the system input Sin and the system output Sout (20, 30) and based on the response characteristics of the known model G2 (Z ^-1) the model G1 (Z ^- The response characteristic of ¹ ) or the parameters a11, ..., A1n, b11 ,.

As described above, even if a large number of plants are included, if all the plants other than the plant to be identified have known parameters, the input / output data of the system and the mathematical models of those other plants. The response characteristic of the mathematical model of the plant to be identified can be obtained based on the response characteristic of 1 and the parameter of the plant to be identified can be obtained from the response characteristic of the mathematical model by a predetermined parameter calculation method.

In the algorithm identification process in the above-described embodiment, as shown in FIG. 5B, the mathematical model G1 (Z
^-1 ), G2 (Z ^-1 ) are replaced, and the response output [Sout (30)] when the input [Sin] is given to the known model G2 (Z ^-1 ) is calculated, and the response output [Sout (30)] is the unknown model G
1 (Z ^-1 ) is a known input, and this known input [Sout (3
0)] and the response output [Sout (30,20)] of the model G1 (Z ^-1 ) corresponding to the known system output Sout (20,30), and the response characteristic of the unknown model G1 (Z ^-1 ) is obtained. It was This method has an advantage that the arithmetic processing can be easily completed.

However, the response characteristics of the unknown model G1 (Z ^-1 ) without replacing both models G1 (Z ^-1 ) and G2 (Z ^-1 ), that is, in the state shown in FIG. 5A. It is also possible to obtain parameters. That is, the model G is calculated from the parameters of the known model G2 (Z ^-1 ) and the known system output Sout (20,30).
The input of 2 (Z ^-1 ) is back-calculated, and the input of the back-calculated model G2 (Z ^-1 ) is unknown model G1 (Z
^-1 ) response output [Sout (20)]
The response characteristic or parameter of (Z ^-1 ) can be obtained.

Although the above embodiment is an example applied to the wafer temperature control mechanism, the plant identification method of the present invention can be applied to other temperature control mechanisms and various control mechanisms.

[0049]

As described above, according to the plant identification method of the present invention, the parameters of the identified plant can be calculated by using the known mathematical model of the related plant included in the same system as the identified plant. Since it is determined, even if it is difficult or impossible to directly investigate the response characteristic of the identified plant, or even if the identified plant is changed, the identified plant can be easily identified.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an identification system for implementing an identification method according to an embodiment of the present invention.

FIG. 2 is a diagram showing a main part of an experimental model for actually measuring a response characteristic of a wafer temperature measuring plant 30 in an example.

FIG. 3 shows a wafer heating plant 20 and a wafer temperature measuring plant 30 for step waveform input in the embodiment.
It is a figure which shows the example of the response characteristic of.

FIG. 4 is a diagram showing an example of response characteristics of the wafer heating plant 20 and the wafer temperature measuring plant 30 with respect to a normal random number input in the embodiment.

FIG. 5 is a diagram showing a mathematical model used in an algorithm for identifying an identified plant having an unknown parameter in the example.

FIG. 6 is a diagram showing a verification example showing the response output of the mathematical model of the wafer heating plant 20 and the wafer temperature measuring plant 30 identified in the embodiment in comparison with the response output by the actual measurement.

FIG. 7 is a diagram showing a mathematical model used in an identification algorithm when a direct heat transfer plant is considered in the example.

FIG. 8 is a block diagram showing a control system in which the plant identification method according to the embodiment is used.

[Explanation of symbols]

 10 Plant Identification Unit 12 System Input Generation Unit 14 System Output Recovery Unit 20 Wafer Heating Plant 30 Wafer Temperature Measurement Plant 40 Identification Thermocouple 100 Wafer Temperature Control Mechanism (Control System) 104 Semiconductor Wafer 110 Feedback Thermocouple

Claims (1)

[Claims] 1. A step of applying a predetermined input to a predetermined system consisting of an identified plant having unknown parameters and one or a plurality of related plants having known parameters, and observing an output of the system. And a step of obtaining parameters of the plant to be identified based on the input data, the system output data, and the response characteristics of the mathematical model of the related plant.