JPH07101207B2 - Method for controlling sample temperature of thermal analysis apparatus and control apparatus thereof - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for controlling a sample temperature of a thermal analysis apparatus and a control apparatus therefor, and particularly to setting a target temperature curve for raising and lowering the temperature of a sample at a constant speed. It relates to the above method and device characterized by the method.

[Prior Art] A thermal analyzer measures changes in various characteristics of a sample by changing the temperature of the sample. In order to measure accurate thermal characteristics, it is necessary to control the temperature of the sample with high accuracy.

In such a thermal analyzer, temperature control is often performed so that the temperature of the sample is raised and lowered at a constant speed. In this case, changes in the thermal properties of the sample are a function of temperature and elapsed time, and are generally irreversible. Therefore, in order to accurately obtain the thermal characteristics of the sample, it is desirable that the temperature change of the sample faithfully follows the target temperature change, and in particular, overshoot is not allowed. This point is different from the general tracking control system.

FIG. 6 is an exaggerated view of a conventional temperature curve and power curve when the sample is heated at a constant speed. In order to control the sample temperature, first, the ideal temperature curve 111 is set.
The ideal temperature curve 111 is a temperature curve that changes from the _first holding temperature T ₁ to the second holding temperature T ₂ at a constant speed (that is, keeping the temperature change per unit time constant). The ideal temperature curve 111 is input as a target value of the servo system so that the sample temperature 145 follows the ideal temperature curve 111.

[Problems to be Solved by the Invention] In the above-described conventional temperature control method, as shown in FIG. 6, in the obtained sample temperature curve 145, transient turbulent portions 146 and 147 are seen. Especially overshoot 147
Is fatal for some measurement purposes. The cause of such a transient disturbance is that the ideal temperature curve 111, which is a polygonal line, is used as it is as the target value of the servo system. The ideal temperature curve 111 is bent at a point J where the first holding temperature T ₁ shifts to a constant temperature rise. The same can be said at the point K where the temperature rises from the constant speed to the second holding temperature T ₂ . At such a bent portion, transient disturbance occurs in the sample temperature curve 145.

The bending of the ideal temperature curve 111 also adversely affects the electric power required for heating. In the power curve 150 of FIG. 5, the power increases sharply immediately after the start of temperature rise, often reaching the maximum heating power 151 of the device. That is, clipping occurs at the maximum power value. Further, in the vicinity of the end of the temperature rise, the electric power sharply decreases with the rapid change in the temperature rise rate, and finally reaches the zero level 152. The big difference from the normal servo system is that there is no negative power. Therefore, clipping occurs at the minimum power value. Such power clipping invalidates the control of the servo system and adversely affects the temperature control. If the capacity of the heating device is made very large, clipping at the maximum value of the electric power does not occur, but it becomes very uneconomical as the life of the heater becomes shorter. on the other hand,
Since the clipping at the minimum value of the electric power is at the zero level, the electric power cannot be further reduced, and even if the heating device is improved, the clipping at the zero level cannot be avoided.

After all, in order to avoid the above-mentioned problems, it is desirable that the ideal temperature curve 111 is not used as it is as the target value of the servo system but the bent portion is smoothed and then input as the target value of the servo system. For that, the bent part,
For example, it suffices if they are smoothly connected by equal acceleration curves. However, such an arithmetic process takes too much time and is not practical.

The present invention has been made in view of the above circumstances, and an object thereof is to convert an ideal temperature curve for constant-speed temperature increase / decrease into a smooth target temperature curve by a simple calculation process, and to convert it into a servo target temperature curve. It is to control the sample temperature with high accuracy by using it as the target value of the system.

[Means and Actions for Solving the Problems] In order to achieve the above-mentioned object, the sample temperature control method of the thermal analysis device according to the present invention has the following features. First, the first
An ideal temperature curve that changes at a constant speed from the holding temperature to the second holding temperature is determined. Next, this ideal temperature curve
It is input to a first-order lag element having a predetermined time constant and its output is used as a target temperature curve. The target temperature curve is used as a target value to follow and control the sample temperature. When the ideal temperature curve is input to the first-order lag element, the output is smoothed at the original bent portion. In addition, the curve is "smooth" means
It means that the derivative (derivative) of a curve is continuous. If this smoothed curve is used as the target value of the servo system, the sample temperature will not be disturbed and highly accurate temperature control will be possible.

In the above-described invention, the output of the first-order lag element is directly used as the target temperature curve, but in actual temperature control, the degree of smoothness of the target temperature curve can be changed at the temperature change start point and the temperature change end point. desirable. For example, at the start of the temperature rise, the sample temperature is less likely to be disturbed even if the transition period when the target temperature curve shifts from the first holding temperature to the constant rate temperature rise is short. On the contrary, when the temperature is increased from the constant speed to the second holding temperature, it is necessary to take a consideration such as prolonging the transition period to avoid overshoot due to non-power clip. Therefore, it is desirable to set the time constant of the first-order lag element to different values with respect to the bending at the start of temperature change and the bending at the end of temperature change in the ideal temperature curve.

Hereinafter, the case of raising the temperature will be described as an example. First, a first ideal temperature curve that raises the temperature from the first holding temperature at a constant speed is determined. The first ideal temperature curve is input to the first-order lag element having the first time constant, and its output is used as the first corrected temperature curve. The first corrected temperature curve is a target temperature curve at the start of temperature increase. Next, the switching point is determined on this first corrected temperature curve. As this switching point, an arbitrary time point until the first ideal temperature curve reaches the second holding temperature can be selected. Preferably, the time point at which the first corrected temperature curve reaches a substantially constant temperature rise is set as the switching point. After this switching point, the second time constant is used.

The second ideal temperature curve is a curve that changes at the same constant speed as the first ideal curve from a point where the temperature is higher than the switching point by the initial temperature difference with the above-mentioned switching point as the origin of the coordinates, and the second hold When it reaches the temperature, it keeps that temperature. This second ideal temperature curve is input to the first-order lag element having the second time constant, and its output is used as the second corrected temperature curve. In this case, it is important that the first modified temperature curve and the second modified temperature curve have the same slope at the switching point. For that purpose, the above-mentioned initial temperature difference and the second time constant are brought into a predetermined relationship. And first before the switch point
The target temperature curve can be obtained by selecting the modified temperature curve of, and the second modified temperature curve after the switching point. This target temperature curve is smoothed with a first time constant at the start of temperature increase and smoothed with a second time constant at the end of temperature increase. By properly selecting the combination of these time constants, an optimum target temperature curve suitable for various purposes can be obtained. The sample temperature is controlled so as to follow this target temperature curve.

Even when the sample temperature is lowered, the target temperature curve can be obtained in the same manner as when raising the temperature.

[Embodiment] Next, an embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram of a sample temperature control device used in an embodiment of the present invention. In this sample temperature control device, an ideal temperature curve setting means 10, a first-order lag element 20, a target temperature curve calculation means 30, and a servo control means 40 are connected in series.

The ideal temperature curve setting means 10 is for setting an ideal temperature curve (see curve 111 in FIG. 6) when the sample is heated and lowered at a constant speed.

The first-order lag element 20 is for smoothing the bent portion of the ideal temperature curve.

The output of the primary delay element 20 is input to the target temperature curve calculation means 30. The target temperature curve calculating means 30 calculates the target temperature curve based on the two corrected temperature curves, as will be described later. One modified temperature curve can be used as it is as the target temperature curve. In that case, the target temperature curve calculation means 30 sends the corrected temperature curve output from the first-order lag element 20 to the servo control means 40 as it is.

In the servo control means 40, a minor loop for feeding back the temperature 46 of the heating furnace is formed in the main loop for feeding back the sample temperature 45. In the servo control means 40, the target temperature curve 31 and the sample temperature 45 are compared, and the difference is input to the PID control unit 41. PID control unit 41
Output is compared with the furnace temperature 46, and the difference is compared to the PID control unit 4
Entered in 2. The furnace 43 is heated by the output of the PID control unit 42, and the sample 44 is further heated. The temperature of the sample 44 follows the target temperature curve 31 by the action of the servo control means 40.

Next, with reference to FIG. 2, FIG. 3, and FIG. 4, a process of obtaining the target temperature curve when the sample is heated at a constant speed will be described. In these graphs, the direction of the time axis is exaggerated for clarity.

FIG. 2 illustrates the process of obtaining the first sample temperature curve at the start of temperature increase. First ideal temperature curve A (t)
Is a curve in which the temperature rises from the _first holding temperature T ₁ to the second holding temperature T ₂ at a constant temperature change rate R (for example, 20 ° C. per minute). That is, A (t) = Rt When this first ideal temperature curve A (t) is input to the first-order lag element having the time constant τ ₁ , its output becomes the first sample temperature curve F (t). .

F (t) = R [t−τ ₁ {1-exp (−t / τ ₁ )}] The first corrected temperature curve F (t) approaches the slope R over time.

FIG. 3 illustrates the process of obtaining the second corrected temperature curve at the end of the temperature rise. Second ideal temperature curve B (t)
Is a curve in which the temperature rises from the initial value T _{0 at a} constant temperature change rate R, reaches the _second holding temperature T ₂ , and maintains that temperature. That is, when 0 ≦ t ≦ t ₀ B (t) = T ₀ + Rt t ≧ t ₀ B (t) = T ₂ = T ₀ + Rt ₀ This second ideal temperature curve B (t) When input to a first-order lag element with a constant τ ₂ , its output is the second modified temperature curve G (t).

When 0 ≦ t ≦ t ₀ G (t) = Rt + (T ₀ −Rτ ₂ ) {1-exp (−t / τ ₂ )} When t ≧ t ₀ G (t) = T ₀ {1-exp (−t / τ ₂ )} + R [t ₀ −τ ₂ exp
(−t / τ ₂ ) {1-exp (t ₀ / τ ₂ )}] The second corrected temperature curve G (t) becomes the second with the passage of time.
Approaching the holding temperature T ₂ of.

By the way, at the start of temperature increase, even if the target temperature curve immediately shifts to a predetermined slope, the sample temperature follows the target temperature without being disturbed. On the other hand, when the temperature rise ends, if the target temperature curve shifts from the predetermined slope to the second holding temperature immediately, there is a possibility that the sample temperature may overshoot. Therefore, it is desirable to change the degree of smoothness of the target temperature curve between the temperature rising start time and the temperature rising end time. For this reason, the first sample temperature curve F (t) with a small time constant τ ₁ was adopted at the start of temperature increase, and the large time constant τ ₂ was applied at the end of temperature increase. The second modified temperature curve G (t) is adopted.

To connect the two corrected temperature curves smoothly, do as shown in FIG. First, on the first corrected temperature curve F (t),
The switching point C is determined. Next, using this switching point C as the origin of the coordinates, the second corrected temperature curve G (t) shown in FIG.
Draw. At that time, the initial temperature difference T at the switching point C
₀ is determined as follows.

In FIG. 3, the slope of the second corrected temperature curve G (t) at the origin is as follows.

(DG / dt) _{t = 0} = T ₀ / τ ₂ On the other hand, the slope of the first corrected temperature curve F (t) at the switching point C (t = t ₁ ) in FIG. 4 is (dF / dt) _{t = t1} = the _{R {1-exp (-t 1} / τ 1)}. If the above two slopes are equal, T ₀ = Rτ ₂ {1-exp (-t ₁ / τ ₁ )}. That is, the initial temperature difference T ₀ can be obtained if the time t _{1 at} the switching point C and the two time constants τ ₁ and τ ₂ are given. Normally, the time constant τ _{1 for} starting the temperature rise and the time constant τ _{2 for} ending the temperature rise are determined in advance, and then an appropriate switching point C is set to obtain the initial temperature difference T ₀ . By such processing, the first corrected temperature curve F (t) and the second corrected temperature curve F (t)
The corrected temperature curve G (t) of
Connect with the same inclination. Thereby, the target temperature curve is obtained.

Practically, it is preferable to switch to the second correction temperature curve G (t) when the slope of the first correction temperature curve F (t) substantially matches R. For example, when three times the time constant τ ₁ has elapsed, the slope of the first corrected temperature curve F (t) becomes
If R matches with an error of 5% and 5 times the time elapses, it becomes 0.
Matches R with 67% error.

FIG. 5 shows an example of a temperature curve and a power curve when the sample is heated at a constant speed by the control device of FIG. At this time, the first time constant τ ₁ is 0.5 seconds and the second time constant τ ₂ is 10 seconds. The slope R of the ideal temperature curves A (t) and B (t) is 20 per minute
℃. Before the switching point C, the ideal temperature curve A
The first modified temperature curve F (t) is obtained from (t). However, in FIG. 5, the first correction temperature curve F (t) is not shown because it overlaps with the ideal temperature curve A (t). This is because the first time constant τ ₁ is small. After the switching point C, the second corrected temperature curve G (t) is obtained from the ideal temperature curve B (t). The sample temperature curve 45 has a target temperature curve connecting two modified temperature curves as a target value,
Follow-up control is performed. A curve 47 is an enlarged view of the tracking deviation. The modified temperature curve 45 has no transient disturbance at the start and end of the temperature rise.

In the power curve 50 shown in the lower part of FIG. 5, it can be seen that no clipping occurs at the maximum value 51 and the minimum value 52. At the minimum value of 52, the power does not become zero and the temperature control works effectively.

Although the example of the constant speed temperature increase is shown in the above-mentioned embodiment, the present invention can be similarly applied to the constant speed temperature decrease. In this case, a large time constant is used at the start of cooling and a small time constant is used at the end of cooling.

The optimum values of the two time constants for obtaining the two corrected temperature curves differ depending on whether the temperature is increasing or decreasing and the starting temperature and the ending temperature. The optimum value of the time constant is
It can be determined by a prior experiment.

Although the servo control means of the above-described embodiment uses the minor loop relating to the furnace temperature, the present invention may use any other servo system.

[Effects of the Invention] As described above, according to the present invention, the ideal temperature curve is input to the first-order lag element and the output thereof is used as the target temperature curve. Therefore, the bending of the ideal temperature curve can be performed by a very simple calculation process. The part can be smoothed. By inputting such a target temperature curve as the target value of the servo system, transient disturbance does not occur in the sample temperature between the start time and the end time of the temperature raising / lowering.

Furthermore, by changing the time constant of the first-order lag element at the temperature change start time point and the temperature change end time point, a more appropriate target temperature curve can be obtained.

[Brief description of drawings]

FIG. 1 is a block diagram of a sample temperature control device used in an embodiment of the present invention, FIGS. 2, 3, and 4 are graphs showing a process for obtaining a target temperature curve, and FIG. 5 is a sample temperature curve. And a graph showing an example of a power curve, and FIG. 6 is a graph showing a conventional temperature curve and power curve. 10 ... Ideal temperature curve setting means 20 ... First-order lag element 40 ... Servo control means A (t) ... First ideal temperature curve B (t) ... Second ideal temperature curve F (t). first correction temperature curve G (t) ...... second correction temperature curve C ...... switching point T ₁ ...... first holding temperature T ₂ ...... second holding temperature tau ₁ ...... first time constant τ ₂ …… Second time constant

Claims (3)

[Claims] 1. A method for controlling a sample temperature of a thermal analysis apparatus, wherein a sample temperature is changed from a first holding temperature to a second holding temperature, the method having the following steps. (A) Determining an ideal temperature curve that changes at a constant speed from the first holding temperature to the second holding temperature. (B) Inputting the ideal temperature curve to a first-order lag element having a predetermined time constant, and setting the output as the target temperature curve. (C) A step of tracking and controlling the sample temperature with the target temperature curve as a target value. 2. A method for controlling a sample temperature of a thermal analysis apparatus, wherein the sample temperature is changed from a first holding temperature to a second holding temperature, the method having the following steps. (A) A step of determining a first ideal temperature curve that changes at a constant speed from the first holding temperature. (B) The first-order lag element having the first time constant has the first
Inputting the ideal temperature curve of, and using the output as the first corrected temperature curve. (C) Determining a switching point on the first modified temperature curve. (D) With the switching point as the origin of coordinates, the first point is separated from the switching point by an unknown initial temperature difference.
Of the second ideal temperature curve (including an unknown initial temperature difference) that changes at the same constant speed as the ideal temperature curve of No. 1 to reach the second holding temperature and keeps the temperature. The mathematical expression of the second ideal temperature curve is input to the first-order lag element having a time constant of, and the mathematical expression of the second corrected temperature curve (including the unknown initial temperature difference) is obtained as the output, and the switching point In, the initial temperature difference is calculated using the first time constant and the second time constant so that the slope of the second correction temperature curve matches the slope of the first correction temperature curve,
This determines the second modified temperature curve. (E) obtaining the target temperature curve by selecting the first modified temperature curve before the switching point and selecting the second modified temperature curve after the switching point. (F) A step of tracking and controlling the sample temperature with the target temperature curve as a target value. 3. A sample temperature control device for a thermal analysis device for changing a sample temperature from a first holding temperature to a second holding temperature, the sample temperature controlling device having: (A) Ideal temperature curve setting means for setting an ideal temperature curve that changes at a constant speed from the first holding temperature to the second holding temperature. (B) A first-order lag element that receives the output of the ideal temperature curve setting means. (C) Servo control means for tracking and controlling the sample temperature with the output of the first-order lag element as a target value.