JP2000187514A - Controller, temperature controller and thermal treatment equipment - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce interference and to make it possible to carry out autotunning correctly and set control parameters in the control of an object having interference. SOLUTION: This device is provided with plural separately corresponding heaters and plural temperature sensors and also is provided with plural PID control means 61 to 6n, a mean temperature and gradient temperature calculating means 5 calculates a gradient temperature based on the mean temperature of detected temperatures of plural temperature sensors and the detected temperatures, an operation signal is outputted to each PID control means 61 to 6n so that the average temperature or each gradient temperature can respectively be a target value, and a distributing means 7 distributes an operation signal from each PID control means 61 to 6n to each heater so that the control by the each PID control means 61 to 6n can not affect the control of the other PID controlling means.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control device for controlling a physical state such as a temperature and a pressure of a control object, a temperature controller for controlling the temperature of the control object, and a heat treatment apparatus using the temperature controller. The present invention relates to a technique suitable for controlling a controlled object having so-called interference, in which a plurality of state control means for controlling a physical state of a controlled object are provided, and the control by each state controlling means affects the control by another state controlling means. .

[0002]

2. Description of the Related Art As an object to be controlled of this kind, for example, as a heat treatment apparatus for a semiconductor process, there is a thermal oxidation apparatus shown in FIG. 29. This thermal oxidation apparatus 18 oxidizes a silicon wafer. An oxide film is formed while flowing a necessary gas through a reaction tube 19 as a furnace.
The thermal oxidation device 18 is provided with a heat equalizing tube 2 surrounding a reaction tube 19.
In this example, three heaters 21 _{1 to} 21 ₃ and first to third temperature sensors 22 _{1 to} 22 ₃ individually corresponding to the plurality of heaters 21 _{1 to} 21 ₃ are provided. And
The temperature control is individually performed by the microcomputer 23 for each area (hereinafter, referred to as “zone”) corresponding to each set of the heater and the temperature sensor.

That is, the first heater 21 ₁ and the first heater 21 1
In the first zone of the upper temperature sensor 22 ₁ is disposed in, on the basis of the detection output of the first temperature sensor 22 _1, the first heater 21 ₁ so that the target temperature is operated, the second In a _second intermediate zone where the heater 21 ₂ and the second temperature sensor 22 ₂ are arranged, the second temperature sensor 22 ₂
The second heater 21 ₂ is operated to reach the target temperature on the basis of the detection output of, and in the lower third zone in which the third heater 21 ₃ and the third temperature sensor 22 ₃ are arranged, based on the detection output of the third temperature sensor 22 _3, the third heater 21 ₃ is operated so that the target temperature.

However, since each zone is thermally continuous, the amount of heat generated by the heater in one zone affects not only that zone but also the temperature sensors in other zones, so-called interference occurs.

[0005] Such interference occurs not only in the thermal oxidation apparatus but also in the temperature control of the wafer stage in a single-wafer CVD apparatus as described in, for example, Utility Model Registration Publication No. 2565156. As shown in FIG. 30, a wafer mounting table 61 on which a wafer 60 is mounted is concentrically formed with an outer circular portion 62, an intermediate portion 63, and a central portion 64.
The heater 6 is divided into three sections and individually corresponds to each section.
5 to 67 are provided to control the temperature for each zone.

[0006]

Due to such interference, temperature fluctuations become remarkable, especially during transients and disturbances, making it difficult to perform uniform temperature control. It is not easy to control.

Further, an optimum PID for a temperature controller
There is also a drawback that auto tuning for determining control parameters cannot be executed correctly.

Hereinafter, the reason why the auto tuning cannot be executed correctly will be described with reference to an example using simulation software for control (MATLAB).

First, as an example in which auto-tuning can be performed normally, a case will be described in which independent first and second controlled objects 24 ₁ and 24 ₂ without interference shown in FIG. 31 are controlled. This example is independent of what controls the two control target 24 _1, 24 _2, the first PID control means 25 _1, running auto-tuning, the second PID controller 25 _2, the target value Is used as ground to execute PID control. Here, 26 ₁ and 26 ₂ are adders for outputting a control deviation between the target value and the feedback amount.

FIG. 32 shows a first feedback amount PV1 (broken line) from the _first control object 241 in this system, a first operation amount MV1 (solid line) from the _first PID control means 251, Feedback amount PV2 (two-dot chain line) and second PID from the _second control target 24 ₂
The second manipulated variable from the control means 25 ₂ MV2 (dashed line)
Shows a waveform displayed on a scope, a limit cycle in which the first manipulated variable MV1 is turned on and off occurs, and the first PID control unit 25 uses the cycle and amplitude of the first feedback amount PV1. _One PID control parameter can be determined.

The feedback amounts PV1, PV2
Corresponds to, for example, a temperature detected by a temperature sensor in the temperature control, and the manipulated variables MV1 and MV2 are operations provided to operation means including a heater for heating the control target and an electromagnetic switch for turning on and off the power supply to the heater. Quantity.

Next, as shown in FIG. 33, a description will be given of a case where independent control is performed on a control target 27 having two-input (MV1, MV2) and two-output (PV1, PV2) interference.

As shown in FIG. 34, the control object 27 receives the first manipulated variable MV1 from the _first PID control means 251 to the first adder 28 and performs the first attenuation. Attenuated to 0.9 by the adder 29 and the second adder 30
On the other hand, the second manipulated variable MV2 from the _second PID control means 252 is supplied to the second adder 30 and is attenuated to 0.9 by the second attenuator 31 to the first operation amount MV2.
, And the added outputs of the adders 28 and 30 are respectively provided to the first and second delay elements 32 and 33. In this example, each operation amount MV
1, MV2 are added to the other at a ratio of 0.9 to cause interference with each other.

In the control object 27 having such interference,
When the first PID control unit 25 ₁ executes auto-tuning and the second PID control unit 25 ₂ executes PID control with the target value set to ground, as shown in FIG. In some cases, the ON / OFF limit cycle does not occur in MV1 (solid line). In such a case, the amplitude and cycle of the vibration of the first feedback amount PV1 (dashed line) cannot be measured correctly, and the parameters of PID control are also calculated. You will not be able to do it.

[0015] The reason that not the first on-off operation amount MV1 as the change of the first feedback amount PV1 Autotuning side second PID control means 25 ₂ on the side not the automatic tuning and interference occurs This is because it operates without permission. This is because the second manipulated variable MV2 (dotted line) is the first feedback quantity P
It can also be seen from the movement in the opposite direction to the change in V1.

As described above, in the case of a controlled object having interference, P
Auto-tuning for setting the control parameters of the ID cannot be performed, and the setting must be performed by trial and error. Therefore, it takes time to set, and it is difficult to obtain desired control characteristics.

SUMMARY OF THE INVENTION The present invention has been made in view of the above points, and has as its object to reduce the interference and to set a control parameter even for a controlled object having interference. I do.

[0018]

In order to achieve the above-mentioned object, the present invention is configured as follows.

That is, the control device according to the present invention converts information from a plurality of detecting means for respectively detecting the physical state of the control object into information indicating the gradient of the physical state, and converts the representative state of the physical state. Converting means for converting the information into the information to be shown; a plurality of state control means to which each piece of information from the converting means is individually given; an operation signal from each of the state control means; And a distribution means for allocating the control so that the influence on the control by the other state control means is eliminated or reduced.

Here, the physical state refers to various physical quantities such as temperature, pressure, flow rate, speed, and liquid level.

The gradient of the physical state refers to a gradient of various physical quantities such as a temperature gradient, a pressure gradient, a flow rate gradient, and a speed gradient.

Furthermore, the representative state of the physical state refers to a state representatively representing the physical state of the control target. For example, if the temperature is a temperature, the average temperature of the control target, the temperature at a certain position (for example, the center position), etc. Say.

According to the control device of the present invention, control is performed by converting information from the plurality of detecting means into information indicating the gradient of the physical state and information indicating the representative state, that is, independent information without interference. Since the control by the state control means is distributed by the distribution means so as to eliminate or reduce the influence on the control by the other state control means, it is possible to reduce the interference in the control of the control target having the interference. Becomes

Further, the temperature controller according to the present invention converts the detected temperatures obtained from the plurality of temperature detecting means for detecting the temperature of the control object into a gradient temperature based on the plurality of detected temperatures. Conversion means for converting into temperature, a plurality of temperature control means each outputting an operation signal with the inclination temperature or the representative temperature from the conversion means as a control amount, and an operation signal from each of the temperature control means, A plurality of heating (or cooling) means for heating (or cooling) are provided with a distribution means for distributing the control by each temperature control means so as to eliminate or reduce the influence on the control by other temperature control means. is there.

According to the temperature controller of the present invention, control is performed by converting the detected temperatures obtained from the plurality of temperature detecting means into the gradient temperature and the representative temperature, that is, independent information having no interference. Since the control by each temperature control means is distributed so as to eliminate or reduce the influence on the control by the other temperature control means, it is possible to reduce the interference in the control of the control target having the interference. In addition, for example, when temperature control is performed by dividing a control target into a plurality of zones, control can be performed focusing on a specific zone using a detected temperature of a specific zone as a representative temperature.

In one embodiment of the temperature controller of the present invention, the representative temperature is an average temperature based on a plurality of detected temperatures. According to the present invention, temperature control is performed using the average temperature and the gradient temperature as control amounts. For example, the degree of interference between zones can be reduced as compared with a case where a control target is divided into a plurality of zones and temperature control is performed using a detected temperature of each zone as a control amount.

In one embodiment of the temperature controller of the present invention, the converting means divides the plurality of temperature detecting means into two, and detects the temperature detected by the temperature detecting means in one section and the temperature detected in the other section. According to the present invention, for example, when a control target is divided into a plurality of zones and the temperature detection means is arranged in each zone, a difference between the temperature and the temperature detected by the detection means is regarded as a gradient temperature. The gradient temperature, which is the difference between the detected temperature detected by the temperature detecting means and the detected temperature detected by the temperature detecting means of the adjacent zone, can be used as the control amount, and the control has a temperature difference for each zone. Can be performed.

Further, in one embodiment of the temperature controller according to the present invention, the plurality of temperature control means operate with the control deviation between the average temperature and the target average temperature or the control deviation between the gradient temperature and the target gradient temperature as an input. A gain of the temperature control means for inputting a control deviation between the slope temperature and the target slope temperature, and an amplification factor of the temperature control means for inputting a control deviation between the average temperature and the target average temperature. According to the present invention, the amplification factor of the temperature control means for controlling the inclination temperature is set to be larger than the amplification rate of the temperature control means for controlling the average temperature. When the target average temperature is changed without changing the target tilt temperature, it is possible to change the average temperature while maintaining the tilt temperature state, that is, the temperature distribution state more strongly. Can.

In one embodiment of the temperature controller according to the present invention, the plurality of temperature control means perform control including integral control, and perform temperature control using a control deviation between the gradient temperature and the target gradient temperature as an input. The control means can perform control not including integral control. According to the present invention, by performing control not including integral control, for example, PD control, the steady-state deviation is increased, and based on the steady-state deviation, temperature detection is performed. It is possible to improve the offset of the temperature sensor which is a means.

In one embodiment of the temperature controller according to the present invention, the temperature control means for outputting an operation signal with the control deviation between the ramp temperature and the target ramp temperature as an input, controls the average temperature and the target average temperature. It is possible to switch between control with a smaller steady-state gain and at least one control without control than a temperature control means that outputs an operation signal with the deviation as an input. According to the present invention, only control of the average temperature is substantially performed. Thus, as will be described later, the offset of the temperature sensor serving as the temperature detecting means appears as the control deviation of the tilt temperature, and the offset adjustment can be easily performed.

Further, in one embodiment of the temperature controller of the present invention, the distribution ratio by the distribution means is determined by the transfer coefficient (際) when the heat quantity of the plurality of heating (or cooling) means is transmitted to the plurality of temperature detection means. Or transfer function).

In one embodiment of the temperature controller according to the present invention, when the amount of heat of one of the plurality of heating (or cooling) means is transmitted to the plurality of temperature detecting means. A coefficient (or transfer function) measures the detection output of each temperature detecting means when an operation signal is given to the one heating (or cooling) means and the other heating (or cooling) means is kept constant. Can be calculated.

Further, the heat treatment apparatus of the present invention comprises a temperature controller of the present invention, a heat treatment furnace to be controlled, a plurality of heating (or cooling) means for heating (or cooling) the heat treatment furnace, A plurality of temperature detecting means for detecting the temperature of the furnace are provided. According to the present invention, the temperature control of the heat treatment furnace is performed by the temperature controller of the present invention, so that the temperature control can be performed with reduced interference.

[0034]

Embodiments of the present invention will be described below in detail with reference to the drawings.

FIG. 1 is a schematic configuration diagram of a temperature control system using a temperature controller according to one embodiment of the present invention.

The temperature control system of this embodiment is
A plurality of heaters 1 for heating the control target 3 ₁~ 1n and multiple
Heater 1₁Temperature of the controlled object 3 individually corresponding to .about.1n
Temperature sensors 2 for detecting temperature₁~ 2n and these temperatures
Sensor 2₁2n based on the detection outputs of₁~
Control 1n by operating it via an electromagnetic switch (not shown)
A temperature controller 4 for controlling the temperature of the object 3 according to the present invention;
Have.

The controlled object 3, which generates heat continuously to interference, a plurality of zones and each temperature sensor 2 ₁ to 2n is arranged close respectively corresponding to the heaters 1 ₁ 1n are Each is formed.

This temperature control system can be applied to, for example, the thermal oxidation apparatus 18 shown in FIG. 29 described above, and the control target 3 is a reaction tube 19 as a heat treatment furnace.
The first to third heaters ₁ 1 to 1 _3, by dividing the periphery of the reaction tube 19 and the first to third heaters 21 ₁ to 21 ₃ which is disposed, the first to third temperature sensors 2 ₁ the ~ 2 _3, in which can be applied as the first to third temperature sensors 22 ₁ to 22 ₃ which detects the temperature of each zone.

[0039] FIG. 2 is a block diagram of a temperature controller 4 of Figure 1, the temperature controller 4 of this embodiment is based on the average temperature and the detected temperature of the temperature detected by the plurality of temperature sensors 2 ₁ to 2n Mean temperature / inclination temperature calculation means (hereinafter also referred to as "mode converter") for calculating the inclination temperature as described later.
5, the PID control means 6 ₁ ～6N as a plurality of temperature control means the average temperature or the gradient temperature calculated by the calculating means 5 are input, the PID control means 6 ₁
And a distribution means (hereinafter also referred to as a "pre-compensator") 7 for distributing the operation signal (operation amount) from 6n to each of the heaters _{11 to} 1n constituting the heating means at a predetermined distribution ratio as described later. ing. Mean temperature and gradient temperature calculating means 5, PID control means 6 ₁ ~6n and allocation means 7 is composed of, for example, a microcomputer.

Conventionally, as shown in FIG. 29 described above, the temperature is detected for each zone and the corresponding heater is individually controlled, but in this embodiment, in order to eliminate interference, Temperature control is performed using the average temperature as the representative temperature calculated by the temperature / inclination temperature calculation means 5 and the plurality of inclination temperatures as control amounts.

[0041] The average temperature-gradient temperature calculating means 5 as the conversion unit, information from a plurality of temperature sensors 2 ₁ to 2n,
This is converted into information of one average temperature and a plurality of gradient temperatures. The reason for this is to make the information independent and easy to understand without interference. For example, the following calculation is performed. .

[0042] That is, the first temperature sensor 2 ₁ detection output S1, a second temperature sensor 2 _second detection output S2, ...
Calculation When the detection output Sn of the temperature sensor 2n of the n, the average temperature Tav shown below, the first gradient temperature Tt1, the second gradient temperature Tt2, the gradient temperature Tt _n-1 of ... the (n-1) I do.

Tav = (S1 + S2 +... Sn) ÷ n Tt1 = (S1 + S2 +._n-1) ÷ (n−1) −Sn Tt2 = (S1 + S2 +... S_n-2) ÷ (n-2) -S_n-1 ・ ・ Tt_n-1= S1−S2 where Tav is the number of temperature sensors 2₁~ 2n detection
The temperature is an average temperature, and the slope temperature Tt1 is a plurality of temperatures.
Sensor 2₁２2n to the temperature sensor 2₁~ 2_n-1And temperature sen
Temperature sensor 2 when divided into two₁~ 2_n-1
Is the difference between the average detected temperature and the detected temperature of the temperature sensor 2n.
The inclination temperature Tt2 is determined by a plurality of temperature sensors 2₁~ 2
_n-1To the temperature sensor 2₁~ 2_n-2And temperature sensor 2_n-1And two
Temperature sensor 2 when divided into two₁~ 2_n-2Average detected temperature
Degree and temperature sensor 2_n-1Is the difference from the detected temperature of
Thus, the slope temperature Tt_n-1Is the temperature sensor 2₁And temperature
Sensor 2 _TwoAnd the detected temperature difference.

Summarizing the above equations, the mode conversion matrix Gm
It can be expressed as follows using a matrix called.

[0045]

(Equation 1)

[0046] T = Gm · S However, T = the _{[Tav Tt1 Tt2 ...... Tt n-} 1] T S = [S1 S2 S3 ...... S n] T this embodiment, these average temperature Tav and a plurality of inclined The temperature is controlled using the temperatures Tt1 to Ttn _{- 1} as control amounts.

Note that the gradient temperature is not limited to this embodiment, and for example, the following mode conversion matrix Gm
As shown in (2), various gradient temperatures such as a temperature difference between detected temperatures of adjacent temperature sensors and a plurality of temperature sensors divided into two groups can be used.

[0048]

(Equation 2)

The gradient temperature is defined as a temperature difference between the average detected temperatures of each group obtained by dividing a plurality of temperature sensors into two groups, a temperature difference between the average detected temperatures of each group obtained by further dividing each group into two groups, Further, a range from a macro gradient temperature to a micro gradient temperature may be calculated and used, such as a temperature difference between the average detected temperatures of each group obtained by dividing each group into two.

In short, what is necessary is just to be able to separate and control the information indicating the temperature gradient and the average information.

The first PID control means 6 _1, average temperature,
Based on the control deviation of the average temperature and the target average temperature from gradient temperature calculating means 5, and outputs an operation signal so that the average temperature of the target average temperature distribution unit 7, the second PID controller 6 _2, An operation signal is distributed based on a control deviation between the first slope temperature and the first target slope temperature from the average temperature / slope temperature calculation means 5 so that the first slope temperature becomes the first target slope temperature. outputs to the means 7, a third PID controller 6 ₃ based on the control deviation between the second gradient temperature and a second target gradient temperature from the average temperature and gradient temperature calculating means 5,
An operation signal is output to the distributing means 7 so that the second inclination temperature becomes the second target inclination temperature, and so on.
The ID control means 6n determines the (n-1) th slope temperature based on the control deviation between the (n-1) th slope temperature and the (n-1) th target slope temperature from the average temperature / slope temperature calculation means 5. An operation signal is output to the distribution unit 7 so that the target inclination temperature becomes −1.

That is, the first PID control means 6 ₁
The average temperature is controlled, and each of the second to n-th PID control means 6 ₂
6 to 6n are for controlling the first to (n-1) -th gradient temperatures, respectively.

Next, the distribution means 7 will be described.

The distribution means 7 is provided with each PID control means 6₁
6n from each heater 1₁~ 1_n
To the PID control means 6
₁Control of average temperature or slope temperature by each
The other PID control means 6 ₁~ 6n each flat
Eliminate interference with control of average or ramp temperature
It is to be distributed to.

[0055] For example, in the case of changing the average temperature by the first operational signal of the PID control means 6 _1, without gradient temperature is changed by the operation signal and by a second operation signal PID control means 6 ₂ When the first gradient temperature is changed, the average temperature and other gradient temperatures are not changed by the operation signal, and similarly, the control by the other PID control units is not affected by the operation signal of each PID control unit. It distributes.

The distribution by the distribution means 7 will be described in more detail.

Here, for simplicity, n = 2,
That is, there are two zones, and the first and second heaters 1 ₁ and 1 ₂ , the first and second temperature sensors 2 ₁ and 2 ₂ , and the first PID control means 6 ₁ for controlling the average temperature. FIG. 3 shows a case in which _second PID control means 62 for controlling the gradient temperature, which is the difference between the temperatures detected by both temperature sensors 2 ₁ and 2 ₂ , is provided.

FIG. 3 shows an example in which the present invention is applied to the control target 27 having two-input and two-output interference described in the conventional examples of FIGS. 33 and 34, and the portions corresponding to FIG. Reference numerals are assigned.

The average temperature / inclination temperature detecting means 5 comprises:
The feedback amounts PV1 and PV2 from the control target 3 corresponding to the detection outputs of the second temperature sensors 2 ₁ and 2 ₂ are added by the adder 8 as shown in FIG. while attenuation and outputs the average temperature Tav, feedback variable PV corresponding to detection outputs of the temperature sensors 2 _1, 2 ₂
1 and PV2 are subtracted by the subtractor 10 to output the gradient temperature Tt.

First PID control means 6₁Is the average temperature
Average temperature Tav and target average temperature from inclination temperature calculation means 5
The average temperature reaches the target average temperature based on the
Output the operation signal (operation amount) Hav to the distribution means 7
And the second PID control means 6 _TwoIs the average temperature / gradient temperature
Control of slope temperature Tt and target slope temperature from calculation means 5
Based on the deviation, the slope temperature will be the target slope temperature.
An operation signal (operation amount) Ht is output to the distribution unit 7.

The distributing means 7 comprises the PID control means 6 ₁ , 6 ₂
Operation signal (operation amount) Hav, the heaters in the allocation ratio as follows Ht _{1 1, 1 2} is distributed to.

FIG. 5 is a block diagram of a control system of the system shown in FIG. The first P controlling the average temperature
An operation amount Hav given from the ID controller _61, eliminating the interference in the allocation means 7, i.e., non-interference coefficient which is a coefficient for non-interacting (distribution ratio) k _1, first with k _2, the 2 of the heater ₁ 1, 1 with ₂ respectively distributed to the second
PID control means an operation amount Ht given from 6 _2, non-interacting factor (distribution ratio) k _3, k ₄ in the first, second heater 1
_1, 1 ₂ in allocated respectively, whereby each heater ₁ 1, 1 ₂ to the amount of heat H _1, H ₂ is to be given, respectively.

The amount of heat H ₁ given to the _first heater 11 is determined by the transfer coefficient (interference coefficient) l ₁ and the first temperature sensor 2.
While transmitted to _1, the second transmitted to the temperature sensor 2 ₂ by the transfer factor (interference coefficient) l _2, similarly, the amount of heat H ₂ given to the second heater 1 ₂ transfer coefficient (interference coefficient) l ₃ in the other hand transmitted to the first temperature sensor 2 _1, and transmitted to the transfer coefficient (interference coefficient) l temperature sensor 2 ₂ second at _4.

Then, the first temperature sensor 2₁Detected by
Detected temperature T₁And the second temperature sensor 2 _TwoDetected by
Temperature T_TwoThe average temperature Tav and the slope temperature Tt are calculated from
Issued and each PID control means 6₁, 6_TwoIs input to
A control loop is configured.

From the above, the average temperature Tav is expressed as follows.

Tav = (T ₁ + T ₂ ) / 2 = {(l ₁ · H ₁ + l ₃ · H ₂ ) + (l ₂ · H ₁ + l ₄ · H ₂ )} / 2 = ｛(l ₁ + l ₂₎ ) H ₁ + (l ₃ + l ₄ ) H ₂ ｝ / 2 = {(l ₁ + l ₂ ) (k ₁ · Hav + k ₃ · Ht) + (l ₃ + l ₄ ) (k ₂ · Hav + k ₄ · Ht)} / 2 = [{(l ₁ + l ₂ ) k ₁ + (l ₃ + l ₄ ) k ₂ ｝ Hav + ｛(l ₁ + l ₂ ) k ₃ + (l ₃ + l ₄ ) k ₄ ｝ Ht] / 2 The average temperature Tav is a function of only the manipulated variable Hav of the average temperature, and the term of Ht is set to 0 so as to eliminate the influence of the manipulated variable Ht of the gradient temperature, that is, to eliminate interference.

That is, (l ₁ + l ₂ ) · k ₃ + (l ₃ + l
₄ ) · k ₄ = 0 Therefore, k ₄ = − {(l ₁ + l ₂ ) / (l ₃ + l ₄ )}
a k _3.

Similarly, the gradient temperature Tt is shown as follows.

Tt = T ₁ −T ₂ = (l ₁ · H ₁ + l ₃ · H ₂ )-(l ₂ · H ₁ + l ₄ · H ₂ ) = (l ₁ -l ₂ ) H ₁ + (l ₃ −l ₄ ) H ₂ = (l ₁ −l ₂ ) (k ₁ .Hav + k ₃ .Ht) + (l ₃ −l ₄ ) (k ₂ .Hav + k ₄ .Ht) = ｛(l ₁ −l ₂ ) k _{1 + (l 3 -l 4)} k 2} Hav + {(l 1 -l 2) k 3 + (l 3 -l 4) k 4} Ht where gradient temperature Tt is the gradient temperature operation amount Ht In order to eliminate the influence of the manipulated variable Hav of the average temperature by using only the function, that is, to reduce the interference, the Hav term is set to 0.
And

That is, (l ₁ −l ₂ ) k ₁ + (l ₃ −
l ₄ ) k ₂ = 0 Therefore, k ₂ = − {(l ₁ −l ₂ ) / (l ₃ −l ₄ )}
k ₁ to become.

From the above, the average temperature is controlled without affecting the gradient temperature, and the gradient temperature is controlled without affecting the average temperature, that is, the interference between the average temperature and the gradient temperature is eliminated. to perform decoupling control, the non-interference coefficients may be apportioned (distribution ratio) k ₁ to k _4, in order to calculate the non-interacting factor (distribution ratio) k ₁ to k ₄ are the heater 1 ₁ of heat is first 1, second temperature sensors 2 _1, 2 ₂ to the transmitted transfer coefficient (interference coefficient) l _1, l ₂ and the second heat quantity of the heater 1 ₂ first, the second It is necessary to know the transfer coefficients (interference coefficients) l ₃ and l ₄ transmitted to the temperature sensors 2 ₁ and 2 ₂ .

The decoupling coefficients (allocation ratios) k _{1 to} k
₄ can be handled by the gain of PID control if the ratio between k ₁ and k ₂ and the ratio between k ₃ and k ₄ are known, so the absolute value is not necessarily required.

The transfer coefficients (interference coefficients) l _{1 to} l ₄ can be obtained as follows. That is, only one heater is changed and the other heaters are fixed at a constant value, for example,
The ratio of the change amount of each temperature sensor to the change amount of the heater is used as the transfer coefficient while the switch is kept on or off.

[0074] For example, in the state of the second heater 2 ₂ off, first heater 1 _1, with variation at a certain temperature amplitude, the first temperature sensor 2 ₁ second, 2 ₂ The transfer coefficients l ₁ and l ₂ can be measured depending on how much the temperature amplitude fluctuates in the detected temperature. For example, when the heater fluctuates at the temperature amplitude 1, the temperature amplitude of the temperature sensor becomes 1
If 0, the transfer coefficient is 10 (= 10/1).

Here, distribution using the decoupling coefficient (distribution ratio) in the distribution means 7 of FIG. 3 will be described more specifically. The characteristic of the control target 27 is shown in FIG. 34 described above, and from this characteristic, the transfer coefficient is l ₁ = 1, l ₂ =
0.9, l ₃ = 0.9, l ₄ = 1.

Therefore, when substituting into the above equation of the decoupling coefficient, k ₄ = − ｛(l ₁ + l ₂ ) / (l ₃ + l ₄ )｝ k ₃ = − ｛(1 + 0.9) / (0.9. 9 + 1)｝ k ₃ = −k ₃ and k ₂ = − ｛(l ₁ −l ₂ ) / (l ₃ −l ₄ )｝ k ₁ = − ｛(1−0.9) / (0.9− 1)｝ k ₁ = k ₁ .

Therefore, the total amount of heat distributed to each heater is assumed to be equal to Hav, that is, k ₁ +
k ₂ = 1, and for simplicity, k ₃
= 1 is added.

As a result, k ₂ = k ₁ = 1/2 and k ₄ = −k ₃ = −1, so that the distribution ratio (decoupling coefficient) is determined.

[0079] That is, as shown in FIG. 5, the operation amount Hav average temperature, 1/2 by the heaters ₁ 1, 1 ₂ allocated to the operation amount Ht of gradient temperature, the first heater 1 ₁ In
As it is, the second heater 1 _2, may be distributed by changing the code.

Here, the distribution ratio (decoupling coefficient) can also be obtained as follows.

That is, from the above-mentioned mode average matrix Gm and the above-mentioned transfer coefficient (interference coefficient) matrix P, a matrix of the distribution ratio (decoupling coefficient) (hereinafter also referred to as “pre-compensation matrix”) G
c can also be obtained as an inverse matrix as follows.

Gc = (Gm · P) ^{-1 When} applied to this embodiment, a matrix P of a transfer coefficient (interference coefficient) which is a characteristic of a controlled object at a certain time is represented by

[0083]

(Equation 3)

Then, the pre-compensation matrix Gc, which is a matrix of the distribution ratio (decoupling coefficient), is

[0085]

(Equation 4)

As a check, it is calculated whether or not Gm · P · Gc = I.

[0087]

(Equation 5)

In this embodiment, the distribution ratio (decoupling coefficient) is calculated using the transfer coefficient. However, as another embodiment of the present invention, instead of the transfer coefficient, frequency characteristics are also represented. You may make it calculate using a transfer function.

In the system shown in FIG. 3, the distribution means 7
As shown in the figure, the average temperature operation signal (operation amount) Ha
v is attenuated by 減 衰 in each of the attenuators 11 and 12, and distributed to the adder 13 and the subtractor 14, respectively. The operation signal (operation amount) Ht of the gradient temperature is supplied to the adder 13 and the subtractor 14. are respectively allocated, the heater 1 ₁ output H ₁ is the first adder 13, the output of H ₂ subtracter 14 is applied to the second heater 1 _2.

[0090] According to the allocation means 7, in the case of changing the average temperature by the operation amount Hav average temperature, since the operation amount is distributed equally to each heater 1 _1, 1 _2, influence the gradient temperature It is possible to change only the average temperature without, that is, without interference. Further, in the case of changing the gradient temperature by the operation amount Ht slope temperature is one of the heater 1 _1, while the operation amount is given in 1x, to the other heater 1 _2, given by -1 times Therefore, only the gradient temperature can be changed without changing the total amount of heat applied to both heaters, that is, without affecting the average temperature.

FIG. 7 shows the average temperature Tav from the average temperature / inclination temperature calculation means 5 when the _first PID control means 61 performs auto-tuning in the system of FIG.
(Broken line), the manipulated variable Hav of the average temperature from the _first PID control means 61 (solid line), the average temperature / inclination temperature calculation means 5
And the operation amount Ht (single-dot chain line) of the inclination temperature from the _second PID control means 62 is shown on the scope, and the operation amount H of the average temperature is shown.
There is a limit cycle in which av is turned on and off, and parameters of PID control can be determined using the cycle and amplitude of the average temperature Tav. The average temperature Ta
v, the slope temperature Tt, the manipulated variable Hav of the average temperature, and the manipulated variable Ht of the slope temperature are the same as those of the conventional example in FIGS.
1, PV2, MV1, and MV2.

The PID of the first PID control means 6 ₁
After the control parameters are determined, the parameters are set, and then the PID control parameters are determined by performing automatic tuning of the _second PID control means 62 for controlling the tilt temperature.

As described above, by controlling the average temperature and the gradient temperature as control amounts, it becomes possible to perform control without interference, to perform auto-tuning for determining the parameters of the PID control, and to determine the optimal control parameters. By setting, desired control characteristics can be obtained.

In the normal control after the parameters of the PID control are set as described above, control is performed so that the average temperature becomes the target average temperature and the gradient temperature becomes the target gradient temperature.

Next, the results of simulation of this embodiment and the conventional example will be described below. In this simulation, modeling of the control target as described below was performed. That is, as the simplest example of the thermal interference system, the heater 1 ₁ two sets of 8, 1 ₂ and the temperature sensor 2 _1, 2 ₂
And a heat treatment apparatus in which a heat conductor 50 is connected between them. The control purpose is to equalize the temperatures at the two points at an arbitrary set temperature. FIG. 9 shows an electrical equivalent circuit of the control target. R ₁ and R ₂ are the thermal resistance from the temperature sensor to the surrounding air, and C ₁ and C ₂ are the heat capacities near the temperature sensor.

[0096] input of the control object is a two heaters heat, a portion of the heat p ₁ of the heater 1 ₁ transmitted a heat conductor 50, the interference temperature theta ₂ of the temperature sensor 2 ₂ thermal resistance R ₃ then, some of the heat p ₂ of heater 1 ₂ is likewise interfere with the thermal resistance R ₃ on the temperature theta ₁ of the temperature sensor 2 _1. A part of the thermal energy of the heat p ₂ is conducted to the machine body heat treatment apparatus in thermal resistance R ₄ is fixed. However, since the heat capacity of the machine body was very large, it was approximated that the heat capacity coincided with the ambient temperature.

The parameter of the equivalent circuit to be controlled is R ₁
= R ₂ = 10 [° C./W], R ₃ = 1 [° C./W], R ₄ = 0.
2 [° C./W] and C ₁ = C ₂ = 10 [J / ° C.]. The disturbance was in the form of a step of 100 W, and was applied under the same conditions as in the conventional example and this embodiment.

The conventional PI according to the parameters shown in Table 1 below
FIG. 10 shows the response waveform of the D control, and FIG. 11 shows the response waveform of this embodiment according to the parameters shown in Table 2 below.

[0099]

[Table 1]

[0100]

[Table 2]

When comparing FIG. 10 and FIG. 11, a temperature difference of 2 ° C. occurs in the conventional control method. In this embodiment, the temperature difference between the two sensors is 0.8 ° C. It can be seen that it has improved up to.

The reason why such a difference in characteristics can be produced is as follows.
In this embodiment, the PI and the average temperature are independent of each other.
The point is that the D parameter can be set. In this example, Table 2
The proportional gain Kp of the gradient temperature control is set to a value larger than the proportional gain Kp of the average temperature control so as to give a difference to the proportional gain Kp and give priority to the convergence of the gradient temperature over the average temperature as shown in FIG. As a result, high-precision temperature uniformity can be expected despite simple PID control parameter settings.

FIGS. 12 to 15 show comparison results of the target value response and the disturbance response between this embodiment and the conventional example. Note that here, CHR (Chien, Hrones and Re
In the swick) adjustment rule, no target value response overshoot was used for average temperature control, and a disturbance response overshoot of 20% was used for gradient temperature control.

FIGS. 12 and 13 show waveforms of the target value response and the disturbance response of this embodiment, and FIGS. 14 and 15 show the waveforms of the target value response and the disturbance response of the conventional example.

In the target value response of the prior art shown in FIG. 14, the settling time was as long as 29 seconds, and overshoot was recognized. However, in the target value response of this embodiment, the settling time was reduced as shown in FIG. It was as short as 9 seconds and no overshoot was observed.

Further, in the disturbance response of the conventional example shown in FIG. 15, the settling time was as long as 32 seconds, and overshoot was slightly recognized. On the other hand, in the disturbance response of this embodiment, FIG.
As shown in FIG. 3, the settling time was as short as 6 seconds, and no overshoot was observed.

That is, in this embodiment, the average temperature control performs weak and slow control, and the gradient temperature control performs strong and fast control. Therefore, in both the target value response and the disturbance response, the overshoot occurs. The settling time was short and satisfactory.

As another embodiment of the present invention, as shown in the characteristic diagram showing the relationship between the amplification factor and the frequency of the first and second PID control means 6 ₁ and 6 ₂ in FIG. the second amplification factor of the PID controller 6 ₂ for controlling may be set larger than the first amplification factor of the PID control means 6 ₁ to control the average temperature. In FIG. 16, the solid line indicates the characteristic of the _first PID control means 61, and the broken line indicates the second PI
D control means 6 ₂ characteristics are shown, respectively.

In this way, for example, when the target average temperature is changed without changing the target inclination temperature, the state of the inclination temperature, that is, the state of the temperature distribution is maintained more strongly. The average temperature can be changed.

For example, in a concentric heater plate such as the wafer stage 61 of the conventional example shown in FIG. 30 described above, when maintaining the temperature distribution inclined in the radial direction and raising or lowering the entire average temperature, Especially effective.

Further, for example, when it is desired to make the outside of the heater plate higher in temperature than the inside, according to this embodiment, by setting the target inclination temperature,
Moreover, a desired temperature distribution state can be obtained more accurately.

Further, as another embodiment of the present invention, a tilt
Second PID control means 6 for controlling oblique temperature_TwoIs the PID
Switching between control and PD control without integral control
It is good also as a structure which can do. In other words, control the slope temperature
Second PID control means 6 _TwoTo PD control
As a result, the amplification factor of low frequency is
It becomes smaller, and as a result, the steady-state deviation becomes larger. Steady-state deviation
Is larger when the offset of the temperature sensor is large.
Therefore, the information of the steady-state deviation is used to turn on the temperature sensor.
Fset can be improved. Therefore, the temperature
Only when adjusting the sensor offset, the second PID system
Means 6_TwoTo PD control without integral control,
After the offset adjustment is completed, return to PID control to
The offset can be easily adjusted. This offset
To adjust the start timing, specify only the start timing with a command.
It can be done automatically.

Hereinafter, the offset adjustment will be described in detail.

[0114] First, FIG. 17, in the conventional configuration, there is an offset of the temperature sensor indicates a steady state when there is interference in the control target, 6 _1, 6 _2, first, second
PID control means 27 is a controlled object with interference,
The control target 27 is controlled by two zones.

[0115] In the steady state, it is defined by the gain of the integral control, the gain, for example, a 200-fold, the first temperature sensor 2 ₁ Offset + 6 ° C, the second temperature sensor 2 ₂
Is set to −6 ° C., and the operation amount M for the heater
V is 0% ≦ MV ≦ 100%, and the transfer coefficient of the controlled object 27 is 1.0, 0.9.

In this steady state, the first temperature sensor 2₁
Is detected at 96 ° C.
The target temperature SP1 is 95 ° C., and the first PID control
Step 6 ₁Is -1 ° C and the gain is 20
Since it is 0 times, it becomes -200, but the operation amount MV is 0
% Or more, the first manipulated variable MV1 is 0%.

[0117] On the other hand, the detected temperature PV2 detected by the second temperature sensor 2 _2, a 94 ° C, the target temperature SP2
Is 95 ° C., the control deviation to the _second PID control means 62 becomes + 1 ° C., and the gain is 200 times, so that it becomes 200. However, since the manipulated variable MV2 is 100% or less, The second operation amount MV2 becomes 100%.

Accordingly, the true temperature of the first zone of the controlled object 27 is 0 × 1.0 + 100 × 0.9 = 90 ° C., and the true temperature of the second zone is 0 × 0.9 + 100.
× 1.0 = 100 ° C. and stabilized.

Therefore, in this steady state, the detected temperatures PV1 and PV2 are 96 ° C. and 94 ° C., and the difference seems to be as small as 2 ° C.
V1 and MV2 are saturated to 0% and 100%, and the true temperature difference is as large as 10 ° C. (= 100 ° C.-90 ° C.). Become.

The above temperature is considered as a temperature difference from room temperature.

Next, the offset adjustment of the present invention will be described with reference to FIG. In the figure, reference numeral 5 denotes an average temperature / inclination temperature calculating means, and 61 denotes a _first temperature controlling average temperature.
PID control means, 62 is a _second PID for controlling the gradient temperature.
ID (PD) control means that does not include integral control
Assume that D control is being performed. 7 is a distribution means, 27
Is a control target having interference.

[0122] Also, as in the conventional example of FIG. 17, the first temperature sensor 2 ₁ Offset + 6 ° C, the second temperature sensor 2 ₂ offsets and -6 ° C, a first PID controller 6 ₁ of the gain is 200 times, the second PID (PD) gain control means 6 ₂ containing no integral control to 0.01 times, the transmission coefficient of the controlled object 27, and 1.0,0.9 I do.

In this steady state, the first temperature sensor 2 ₁
Is 100.49 ° C., and the detected temperature PV detected by the _second temperature sensor 22 is
2 is 88.52 ° C., the average temperature calculated by the average temperature / gradient temperature calculating means 5 is about 94.5 ° C., and the gradient temperature is about 12 ° C.

Since the target average temperature SPav is 95 ° C., the control deviation to the _first PID control means 61 is about 0.5.
Since the temperature is 5 ° C. and the gain is 200 times, the output is 99.47. On the other hand, the target inclination temperature SPt is
Since the temperature is 0 ° C., the second PID not including the integral control
(PD) control deviation to the control means 6 _2, -12 ° C, and the the gain is 0.01 times, its output is -0.
It becomes 12.

[0125 Accordingly, the first manipulated variable to the first heater 1 ₁ output from the allocation unit 7 MV1 is 99.4
7 × 0.5 + (- 0.12) next × 1.0 = 49.62%, the second manipulated variable MV2 for the second heater 1 ₂
99.47 × 0.5 + (− 0.12) × (−1.0) = 4
It will be 9.86%.

Thus, the true temperature of the first zone of the controlled object 27 is 49.62 × 1.0 + 49.86 × 0.9.
= 94.49 ° C and the true temperature of the second zone is
49.62 × 0.9 + 49.86 × 1.0 = 94.52 ° C.
It becomes stable.

Therefore, in this steady state, the manipulated variables MV1 and MV2 do not saturate, and the true temperature difference is 0.03 ° C. (= 94.52 ° C.-94.49 ° C.).
Thus, the temperature can be controlled with higher accuracy than the conventional example shown in FIG.

Further, the difference between the offsets of the temperature sensor appears as -12 ° C. in the deviation of the inclination temperature. Therefore,
This -12 ° C is added as an offset adjustment value of the temperature sensor to the slope temperature output from the average temperature / slope temperature calculation means 5 to enable offset adjustment. After the offset is adjusted, PD control is performed and PID control is performed. Should be returned to

As a result, the offset of the temperature sensor is adjusted so that the difference between the actual temperature and the manipulated variable MV is kept small.
The saturation of 1, MV2 is also eliminated, and a more accurate temperature control can be performed as compared with the conventional example.

The deviation of the inclination temperature obtained in this embodiment is a value close to the offset of the temperature sensor, but is not the same, so that the adjustment must be repeated many times.

Therefore, the gradient temperature control is performed by using PD without integration.
The offset control may be performed with a small number of adjustments by controlling the control, and further weakening the proportional control or extremely setting the control to be non-control.

[0132] Figure 19 is a second PID (PD) gain control means 6 ₂ corresponds to FIG. 18 in the case of the 0-fold, in FIG 19, is calculated by using the inverse matrix of the above The other components are the same as those in FIG.

The second PI for controlling the gradient temperature as described above
By extremely small constant gain D (PD) controller 6 _2, relative offset of the temperature sensor is, precisely the control deviation of the gradient temperature and gradient temperature obtained from the average temperature-gradient temperature calculating means 5 That is, the number of offset adjustments can be reduced.

The reason why the offset can be easily detected is that the coefficient (the leftmost vertical column) that distributes the manipulated variable of the average control of the decoupling coefficient (the matrix coefficient of the precompensator 7). I can understand it. In other words, the distribution ratio of the manipulated variable of the average control is such that only the average temperature changes and does not affect the slope temperature. Despite the fact that it should not change, the difference is caused by the offset, and the loop for canceling this offset is operated so as to reduce the gain, and the deviation at this time is It will represent the offset. That is, if only the average control is performed, the temperatures of all the sensors are constant, and the deviation at this time represents the offset.

As another embodiment of the present invention, as shown in FIG. 20, two-degree-of-freedom control using target value filters 51, 52 or feedforward elements 53, 54 shown in FIG. 21 are used. It can be combined with the feed-forward type two-degree-of-freedom control, and the overshoot of the target value response can be reduced, for example, when the gain of the PID parameter of the gradient temperature control is increased.
20 and 21, parts corresponding to those in FIG. 3 are given the same reference numerals.

In the above example, for simplicity, n = 2
However, the present invention can be similarly applied to the case where the number of zones is three, that is, the case where the number of heaters, temperature sensors and PID control means is three (n = 3).

That is, as shown in the block diagram of FIG. 22 corresponding to FIG.
A ₁ to 1 _3, first to the corresponding individually to each of the heater ₁ 1 to 1 ₃
The third temperature sensors 21 to 23 are arranged in the _first to _third zones, respectively. The first zone and the second zone are adjacent to each other, and the second zone and the third zone are arranged. the zone and are adjacent, for simplicity, assume that only the interference between adjacent zones, transfer coefficient from the first heater 1 ₁ to the second temperature sensor 2 ₂ (interference coefficient) l ₁ , the second heater 1
₂ first, third temperature sensor 2 _1, transfer factor to 2 ₃ (interference coefficient) l _2, l _3, transfer coefficient from the third heater 1 ₃ to the second temperature sensor 2 ₂ (interference the coefficient) and l _4, opposite transfer coefficient from the first heater 1 ₁ such first temperature sensors 2 ₁ (interference coefficient) is 1.0.

A first PID for controlling an average temperature for a decoupling coefficient (allocation ratio) for eliminating interference.
Control means 6 _first operation amount Hav second, third heater 1 _2,
K ₁ the non-interacting factor (distribution ratio) for distributing to 1 _3, k
_2, non-interference coefficients for distributing the operation amount Ht ₁ second PID control means 6 ₂ for controlling the first gradient temperature Tt ₁ in first, third heater 1 _1, 1 ₃ (distribution ratio ) To k ₃ and k ₄ , the second
The third PID control means 6 ₃ operation amount Ht2 the first, second heater ₁ 1, 1 decoupling factor to allocate ₂ to the (distribution ratio) k ₅ for controlling the gradient temperature Tt _2, and k _6, facing the non-interference coefficients from the first PID control means 6 ₁ like the first heater 1 ₁ to 1.0. Note that, in this example, the first inclination temperature Tt1 is equal to the second and third temperature sensors 2 ₂ ,
2 ₃ average detected temperature of the detected temperature T _2, T ₃ and has a difference between the first and the detected temperature T ₁ of the temperature sensor 2 _1, and the second
Gradient temperature Tt ₂ of the second temperature sensor 2 ₂ detected temperature T
₂ and the difference between the detected temperature T _{3 of the third} temperature sensor 23.

At this time, the average temperature Tav is expressed as follows.

Tav = (T ₁ + T ₂ + T ₃ ) / 3 = ｛(H ₁ + l ₂ · H ₂ ) + (l ₁ · H ₁ + H ₂ + l ₄ · H ₃ ) + (l ₃ · H ₂ + H ₃₎ )｝ / 3 = ｛(1 + l ₁ ) H ₁ + (1 + l ₂ + l ₃ ) H ₂ + (1 + l ₄ ) H ₃ ｝ / 3 = ｛(1 + l ₁ ) (Hav + k ₃ · Ht ₁ + k ₅ · Ht ₂ ) + (1 + l ₂ + l ₃ ) (k ₁ · Hav + Ht ₁ + k ₆ · Ht ₂ ) + (1 + l ₄ ) (k ₂ · Hav + k ₄ · Ht ₁ + Ht ₂ )｝ / 3 = [｛(1 + l ₁ ) + (1 + l ₂ + l ₃ ) k ₁ + (1 + l ₄ ) k ₂ ｝ Hav + ｛(1 + l ₁ ) k ₃ + (1 + l ₂ + l ₃ ) + (1 + l ₄ ) k ₄ ｝ Ht ₁ + ｛(1 + l ₁ ) k ₅ + (1 + l _{2) + l 3) k 6 + (} 1 + l 4)} Ht 2 ] / 3, where the average temperature Tav is a function of only the operation amount Hav average temperature, the operation of the gradient temperature amounts Ht _1, Ht ₂ To eliminate the influence of the manipulated variable, i.e., in order to non-interference, and 0 to the section Ht _1, Ht _2.

That is, (1 + l ₁ ) k ₃ + (1 + l ₂ +
_{l 3) + (1 + l} 4) k 4 = 0 (1 + l 1) k 5 + (1 + l 2 + l 3) k 6 + (1 + l 4) =
It becomes 0.

This will be simplified as follows.

La + lb · k ₃ + lc · k ₄ = 0... Ld + le · k ₅ + lf · k ₆ = 0... Similarly for the first slope temperature Tt ₁ , the manipulated variable Ht _{1 of} the first slope temperature Tt ₁ By applying the condition that the operation amount Hav of the average temperature and the operation amount Ht2 of the _second gradient temperature are not affected by only the function, the following equation can be obtained.

Lg + lh · k ₁ + li · k ₂ = 0... Lj + l _k · k ₅ + l _l · k ₆ = 0 Also, the following equation is similarly obtained for the second gradient temperature Tt ₂ .

Lm + ln · k ₁ + lo · k ₂ = 0... Lp + lq · k ₃ + lr · k ₄ = 0... Transfer coefficients l _{1 to} l ₄ , and therefore, la to lr are n = 2
Since it is determined in the same manner as in the non-interacting factor k ₁
As a result, the following _six equations, in which the unknowns are set as k ₆ , are obtained, and by solving these equations, the decoupling coefficients (allocation ratios) k _{1 to} k ₆ to be allocated by the allocation unit are obtained. become.

For example, if it is determined by a determinant, the following is obtained.

[0147]

(Equation 6)

[0148]

(Equation 7)

As described above, the present invention can be similarly applied to a control system where n = 3 or more.

The pre-compensation matrix Gc, which is a matrix of the distribution ratio (decoupling coefficient), can be obtained from the mode conversion matrix Gm and the matrix P of the transfer coefficient (interference coefficient) as described above. the first PID controller 6 ₁ first heater 1 ₁
Can be obtained including the opposite decoupling coefficient. Here, a matrix P of a transfer coefficient (interference coefficient) which is a characteristic of the control target at a certain time is represented by

[0151]

(Equation 8)

Assuming that l1 = l2 = l3 = l4 = 0.9,

[0153]

(Equation 9)

The pre-compensation matrix Gc is

[0155]

(Equation 10)

As a check, it is calculated whether or not Gm · P · Gc = I.

[0157]

[Equation 11]

The mode conversion matrix Gm for calculating the average temperature and the gradient temperature can be changed according to the structure of the object to be controlled and the purpose of the control.
Some specific examples are shown below.

[0159] For example, the vacuum chamber 55 as shown in FIG. 23 (a), the temperature is controlled by using two sets of heater is divided into two zones ₁ 1, 1 ₂ and the temperature sensor 2 _1, 2 ₂ If, alternatively, a rectangular heater table shown in FIG. (b) (the heater plate) 56, two sets of heater ₁ 1, 1 ₂
When the temperature is controlled using the temperature sensors 2 ₁ and 2 ₂ , the following mode conversion matrix Gm can be used by focusing on the interference between adjacent sensors.

[0160]

(Equation 12)

[0161] Further, as shown in FIG. 24 (a), the vacuum chamber 55, the heater ₁ 1 three sets of divided three zones, 1 _2, 1 ₃ and the temperature sensor 2 _{1, 2} 2, 2 ₃ using the case temperature control, or rectangular heater table shown in FIG. (b) (the heater plate) 56, three sets of heater 1 _1, 1 _2, 1 ₃ and the temperature sensor 2 _1, 2 ₂ , in the case of temperature control by using a 2 _3, it can be focused on interference between adjacent sensors using the mode conversion matrix Gm as follows.

[0162]

(Equation 13)

Or

[0164]

[Equation 14]

[0165] Also, a rectangle shown in Figure 25, divided into two in and out, further, the heater 1 an outer peripheral portion 2 divided by _1, 1 _2, 1 ₃ heater table as arranged (heater plate) In the case of 56, the following mode conversion matrix Gm can be used by focusing on the interference between adjacent sensors.

[0166]

(Equation 15)

Or

[0168]

(Equation 16)

In the case of a heater base (heater plate) 56 which is rectangular as shown in FIG. 26 and in which heaters ₁₁ to ₁₆ are divided into six parts inside and outside, a heater between adjacent sensors is provided. Focusing on interference, the following mode conversion matrix Gm can be used.

[0170]

[Equation 17]

Furthermore, the rectangle shown in FIG.
Lattice pattern 9 divided heater block, such as placing the heater 1 ₁ to 1 ₉ in the case of (the heater plate) 56 is focused on the interference between adjacent sensors, mode conversion matrix G as follows
m can be used.

[0172]

(Equation 18)

Or

[0174]

[Equation 19]

The shape of the heater base (heater plate) 56 is not limited to a rectangle, but may be concentric or another shape as in the conventional example of FIG.

In another embodiment of the present invention, instead of the average temperature, for example, the temperature of the central zone or the temperature of the central position of the wafer stage is set as the representative temperature, and the representative temperature and the tilt temperature are controlled as control amounts. May be performed.

In the above embodiment, only one average temperature is used as the average temperature. However, as another embodiment of the present invention, for example, each average temperature of each group divided into a plurality of groups, that is, Alternatively, a plurality of average temperatures may be used.

Although the above embodiment has been described by applying to PID control, the present invention is not limited to PID control but can be applied to other control systems such as on / off control, proportional control, and integral control. is there.

The heat treatment apparatus of the present invention can be applied not only to the thermal oxidation apparatus but also to a diffusion furnace, a CVD apparatus, a temperature control of a cylinder portion of an injection molding machine or a temperature control of a heater base of a packaging machine. is there.

In the above embodiment, the description has been given of the case where the present invention is applied to temperature control using a heating means such as a heater, but it is needless to say that the present invention may be applied to temperature control using a Peltier element or a cooler. Further, the present invention may be applied to temperature control using both a heating unit and a cooling unit.

Further, the present invention is not limited to temperature control, but can be applied to control of other physical states such as pressure, flow rate, speed or liquid level.

For example, when a film is formed on a wafer 71 placed on a wafer stage 70 shown in FIG. 28, the film is not detected and controlled, but the film thickness is measured in a non-contact manner. the thickness sensor ₇₂₁ detects the thickness of the wafer 70 of each zone 72 _3, the average thickness, the thickness of the inclined calculated, based on it, the heater 73 _1-7 in each zone
3 ₃ a control to may be carried out an average film thickness and control of the gradient film thickness.

[0183]

As described above, according to the present invention, it is possible to reduce the interference and to set the optimal control parameters in the control of the control object having the interference.

[Brief description of the drawings]

FIG. 1 is a schematic configuration diagram of a temperature control system according to one embodiment of the present invention.

FIG. 2 is a block diagram of the temperature controller of FIG. 1;

FIG. 3 shows a configuration in which a temperature sensor, a heater, and PID control means are 2
FIG.

FIG. 4 is a block diagram of an average temperature / inclination temperature calculation means 5 of FIG. 3;

FIG. 5 is a block diagram of a control system of FIG. 3;

FIG. 6 is a block diagram of a distribution unit of FIG. 3;

FIG. 7 is a waveform chart at the time of auto tuning of the system of FIG. 3;

FIG. 8 is a diagram showing a model of a control target.

FIG. 9 is an equivalent circuit diagram of a control target.

FIG. 10 is a diagram showing a response waveform of a conventional example.

FIG. 11 is a diagram showing a response waveform according to the embodiment.

FIG. 12 is a diagram showing a target value response waveform according to the embodiment.

FIG. 13 is a diagram showing a disturbance response waveform according to the embodiment.

FIG. 14 is a diagram showing a target value response waveform of a conventional example.

FIG. 15 is a diagram showing a disturbance response waveform of a conventional example.

FIG. 16 is a characteristic diagram illustrating a relationship between an amplification factor and a frequency of each PID control unit according to another embodiment of the present invention.

FIG. 17 is a block diagram for explaining the influence of an offset of a conventional temperature sensor.

FIG. 18 is a block diagram corresponding to FIG. 17 of another embodiment of the present invention.

FIG. 19 is a block diagram corresponding to FIG. 17 of still another embodiment of the present invention.

FIG. 20 is a block diagram to which a target value filter type two degree of freedom control is applied.

FIG. 21 is a block diagram to which feedforward type two-degree-of-freedom control is applied.

FIG. 22 is a block diagram of a control system when there are three zones.

FIG. 23 is a diagram showing a control target.

FIG. 24 is a diagram showing another control target.

FIG. 25 is a diagram showing still another control target.

FIG. 26 is a diagram showing a control target.

FIG. 27 is a diagram showing still another control target.

FIG. 28 is a diagram showing another embodiment of the present invention.

FIG. 29 is a diagram showing a configuration of a thermal oxidation device.

FIG. 30 is a diagram showing a wafer mounting table.

FIG. 31 is a configuration diagram of a system that controls two control targets without interference.

FIG. 32 is a waveform chart at the time of auto tuning of the system of FIG. 31.

FIG. 33 is a configuration diagram of a system that controls a control target having interference.

FIG. 34 is a diagram showing a configuration of a control target in FIG. 33;

FIG. 35 is a waveform chart at the time of auto-tuning of the system of FIG. 33;

[Explanation of symbols]

1 ₁ 1n heater 2 ₁ to 2n Temperature sensor 3 controlled object 4 temperature controller 5 average temperature-gradient temperature calculating means 6 ₁ ~6n PID controller 7 allocation means 15 the heater plate 18 thermal oxidizer

Claims (10)

[Claims] A converting means for converting information from a plurality of detecting means for respectively detecting a physical state of a control object into information indicating a gradient of the physical state and converting the information into information indicating a representative state of the physical state; A plurality of state control means to which each information from the conversion means is individually given; an operation signal from each state control means, a plurality of operation means, control by each state control means, other state control And a distribution means for allocating so as to eliminate or reduce the influence on the control by the means. 2. A converting means for converting detected temperatures obtained from a plurality of temperature detecting means for detecting a temperature of a control target into a gradient temperature based on the plurality of detected temperatures and converting the detected temperature into a representative representative temperature, A plurality of temperature control units each outputting an operation signal using the tilt temperature or the representative temperature from the conversion unit as a control amount; and a plurality of operation signals from each of the temperature control units for heating (or cooling) the control target. A temperature controller comprising: a heating (or cooling) unit; and a distribution unit that distributes the control by each temperature control unit so as to eliminate or reduce the influence on the control by another temperature control unit. 3. The temperature controller according to claim 2, wherein the representative temperature is an average temperature based on a plurality of detected temperatures. 4. The converting means divides the plurality of temperature detecting means into two, and determines a difference between a temperature detected by the temperature detecting means in one of the sections and a temperature detected by the temperature detecting means in the other section as an inclined temperature. The temperature controller according to claim 2 or 3, wherein 5. The temperature control means outputs an operation signal with a control deviation between the average temperature and a target average temperature or a control deviation between the gradient temperature and a target gradient temperature as an input. The amplification factor of the temperature control unit that receives the control deviation between the ramp temperature and the target ramp temperature as an input is set to be larger than the amplification factor of the temperature control unit that receives the control deviation between the average temperature and the target average temperature as an input. Item 3. The temperature controller according to Item 3. 6. The plurality of temperature control means performs control including integral control, and the temperature control means which receives a control deviation between the slope temperature and a target slope temperature as input includes a control including integral control. The temperature controller according to any one of claims 2 to 5, wherein switching to control not including integral control is possible. 7. A temperature control means for outputting an operation signal by inputting a control deviation between the inclination temperature and the target inclination temperature as an input, and outputting the operation signal by inputting a control deviation between the average temperature and the target average temperature. The temperature controller according to claim 3, wherein the temperature controller can switch between at least one of control and control in which the steady gain is reduced. 8. The distribution ratio by the distribution unit is calculated using a transfer coefficient (or transfer function) when the amounts of heat of the plurality of heating (or cooling) units are transmitted to the plurality of temperature detection units, respectively. The temperature controller according to claim 2. 9. The transfer coefficient (or transfer function) when the amount of heat of one heating (or cooling) unit of the plurality of heating (or cooling) units is transmitted to the plurality of temperature detecting units. 9. The calculation method according to claim 8, wherein an operation signal is given to one heating (or cooling) means, and a detection output of each temperature detecting means when another heating (or cooling) means is kept in a constant state is calculated. air conditioner. 10. The temperature controller according to claim 2, a heat treatment furnace to be controlled, and a plurality of heating (or cooling) for heating (or cooling) the heat treatment furnace.
And a plurality of temperature detecting means for detecting the temperature of the heat treatment furnace.