JPH02259802A - Pid controller adjusting method - Google Patents

Abstract

PURPOSE:To reduce the error of a control response by finding a time scale factor in a partial model matching method by using a specific equation when a process that is a controlled system can be approximated with a (1st-order lag+dead time) system. CONSTITUTION:A control parameter decision system 4 finds the time scale factor (sigma) in the partial model matching method by, for example, equation I(approximate equation) based on the parameter, the gain K, the time constant T, and the dead time L of the transfer function Gp(S) of the process 1 approximately expressed with the (1st-order lag+dead time) system obtained by a process identification system 3, and decides the control parameter, the proportional gain Kp, the integral action time Ti, the derivative action time Td of a PID controller 2 by using the time scale factor (sigma). In equation I, it is assumed as n=L/T. In such a way, the characteristics of the dead time L and the time constant T can be affected on the control parameter of the PID controller, and a safe control response can be secured by suppressing the change of the amount of overshoot.

Description

[Detailed Description of the Invention] (Industrial Application Field) The present invention relates to a method of adjusting a PID (proportional, integral, differential) controller, and particularly when the controlled object is a process that can be approximated by a first-order lag vector dead time system. The present invention relates to a suitable method for adjusting a PID controller.

[Conventional technology]

When controlling a process using a PID controller, it is necessary to adjust the control parameters of the PID controller based on the characteristics of the process. One way to do this is to
“Control system design method based on partial knowledge of the controlled object” (
Proceedings of the Society of Instrument and Control Engineers, Volume 5, No. 4, 54915
55. There is a partial model matching method described in 1982-8). The outline is explained below.

FIG. 2 is a system diagram of a control system when a process is controlled by a PID controller.

The partial model matching method uses the target value r (s) s
Method for determining control parameters of PID controller 2 such that closed loop transfer function W(s) of control amount y(s) for Niraplus operator partially matches transfer function Wr(s) of reference model showing desired response It is. A case will be considered in which the transfer function GF(8) of process 1 can be approximated by a first-order slow ninety dead time system expressed by the following equation.

Here, K gain, T: time constant, L: waste, and PI
The transfer function of the D controller is Gc(s), where KP: proportional gain, 'rt: 1 minute time, T4:
In the differential time diagram 2, the control amount y (
The closed-loop transfer function W(s) of s) is (1), (2
) is substituted into equation (3),...(4) When the dead time transfer function e-LS is expanded by Macro-Lin.

Time (5) On the other hand, the transfer function Wr(s) of the reference model is given by the following equation.

...(6) Here, αI: coefficient, σ: time scale factor Target value r (s
) of the controlled variable y(s) with respect to the closed-loop transfer function W (s
) and the transfer function W(s) of the reference model shown in equation (6) partially match, the following equation must hold.

The following equations (8) to 11 are obtained from equation (7), and these equations determine the control parameter K of the PID controller.
p, Tt+''r4 and the time scale factor σ can be determined.

I...(10) f(σ)=(2α2α3-α23-α4)σ'+(L+
T)(α22−α3)σ2 By the way, equation (11) is a cubic equation, and complex calculations are required to solve this cubic equation and determine the minimum positive real root as the time scale factor σ. There is a problem in that it takes time to perform this calculation using a microcomputer.

Therefore, a simple calculation formula is required, and the Kitamori model (αz
=0.5. αa=0.15. αa=0.03. ...)
(11)
After calculating the minimum positive real root of the equation and organizing the results, we found that it can be approximated by the following equation.

σ valve 1.37L ・
...(12) [Problem to be solved by the invention] - In the above conventional technology, the ratio L/T of dead time and time constant T
There has been a problem in that the approximation accuracy of equation (12) deteriorates in areas where .

The purpose of the present invention is to accurately obtain an approximate solution to the cubic equation shown in equation (11) over a wide range of dead time and time constant T ratio L/T, and to use this approximate solution to determine the control parameters of the PID controller. The goal is to provide a way to adjust the

Further, in the above-mentioned conventional technology, it was not possible to adjust the rise time of the control response.

Another object of the present invention is to provide a control parameter adjustment method for a PID controller that can adjust the rise time of a control response of a PID controller that determines control parameters using equations (8), (9), and (10). .

[Means to solve the problem]

In order to achieve the above purpose, f(
σ), and based on this rough shape, (1
1) An approximate solution to the equation was found, and this approximate solution was used to determine the control parameters of the PID controller.

Furthermore, in order to provide a control parameter adjustment method for a PID controller that can adjust the rise time of the control response of a PID controller whose control parameters are determined by equations (8), (9), and (10), the time scale factor σ is It is expressed as a function of L, and by increasing or decreasing the coefficient of this function, the rise time of the control response can be adjusted to be slower or faster.

[Effect]

The true value of the minimum positive real root of equation (11) is a function of the ratio L/T of the dead time to the time constant T and the dead time.

Therefore, the approximate solution of the least positive real root of equation (11) is also L/T
is calculated as a function of wasted time. By this, (1
1) The accuracy of the approximate solution to the equation is improved.

Furthermore, when the time scale factor σ changes, the rise time of the control response changes. −For processes that can be approximated by the next-order delay + dead time system, the time scale factor σ
is expressed as a function of dead time, which is an important parameter representing the characteristics of this process, and when the time scale factor σ is increased or decreased by increasing or decreasing this function, the control parameter K p is obtained.

This is because the characteristics of dead time are reflected in T1 and Ta.

While maintaining a stable control response, the rise time of the response can be adjusted to be slower or faster.

〔Example〕

FIG. 1 shows an embodiment of the present invention. This embodiment describes a process identification system 3. that identifies the transfer function Gp(s) of a process 1. The system includes a control parameter determination system 4 that determines control parameters of the PID controller 2 based on the identified transfer function Gp(s) of the process 1.

The process identification system 3 has a transfer function Gp of the process 1.
To identify (s), as shown in Equation 1), it is approximated by a =-order lag ten dead time system. The control parameter determination system 4 determines the time scale and time scale based on the parameters of the transfer function Gp(s) of the process 1, which is approximately expressed by a -order lag and ten dead time systems, that is, the gain K, the time constant T, and the dead time. Find the factor σ and use this σ to calculate (8), (9)
, (10), the control parameters of the PID controller, that is, the proportional gain K p and the integral time T t
, the differential time T, are determined. The PID controller 2 controls the process 1 using the determined control parameters Kp, T1, and Td.

The time scale factor σ is determined as the minimum positive real root of equation (11), and in order to shorten the calculation time, this minimum positive real root is determined using an approximate equation. In order to obtain an approximate expression for this root, it is important to understand the approximate shape of f(σ) defined by equation (11). By the way, the control characteristics of the -order delay ten dead time system largely depend on the ratio L/T of the dead time and the time constant T. Therefore, L/T is defined by the following equation.

n=L/T...
・(13) Equation (13) and coefficient α, (in the case of Kitamori model, α2=0.5.(!3=0.15.(!4=0.03
．． -) into equation (11) and sort it out.

From equations (14), (16), and (17), the extreme value of f(σ) and the value of σ that gives the extreme value, and the value of the inflection point of f(σ) and the inflection point are given. The value of σ is calculated and shown in Figure 3. Furthermore, f (0) and f' (0) are (14
), From equation (16), ('',''L,T)O)...(18)...(1
4) The cubic coefficient of equation (14) is negative, and the relationship shown in the following equation is obtained.

Also, f'(σ) and f'(σ) are calculated from equation (14) by (
', "L, T) O) ... (19) (15),
It can be seen from equations (I8) and (19) and FIG. 3 that the approximate shape of f(σ) is as shown in FIG. From this figure, it can be seen that the root f(σ)=0 is a three-root co-regular real root. Furthermore, it can be seen that the minimum positive real root is between 0 and the value of σ that gives the minimum value.

Therefore, f(σ
), and approximating f(σ) with Tiller expansion at each of these points, the minimum distortion real root of σ such that this approximation formula becomes 0...(17) is expressed as f(σ)=O Let us find it as an approximate expression of the minimum distortion real root of . The Tiller expansion approximation formula of f(σ) near σ0 is given by the following formula.

f(σ)=f(σo)+f'(σ)(σ−σ0)...
(20) In equation (20), first, by truncating at the first-order term of σ, the following equation is obtained.

f (cr) = f ((FO) + f' ((F
O)(+7- (FO) -(21)(14), (
By setting σ=σ0 in equation (16) and substituting these equations into equation (21), we obtain the approximate equation (22) at each point of 1.4L, and obtain (2
2) When the value of σ for which the equation becomes zero is calculated, the approximate equation shown in FIG. 5 is derived. From this figure, it can be seen that the approximate expression for the minimum distortion real root of f(σ) is expressed as the product of a function of n and L. Therefore, the true value of the minimum strain real root of f(σ)=O is also n
It is presumed that it is expressed as the product of a function of and L.

Various glues were used to confirm the accuracy of the approximation formula shown in Figure 5.

The minimum distortion real root of f(σ) = 0 for T was actually determined by a computer, and this true value was determined using the rearranged value expressed as the product of the function of n and L and the approximate formula in Figure 5. Approximate values are shown in FIG. As is clear from this figure, σo=
The approximate expression of the minimum distortion real root of f(σ)=0 in 1.4L is the most accurate and matches the true value to two significant figures in the practically sufficient range of n=o to 5.

Referring to Figure 3, ao=O, L, 1.2L.

For this formula, as can be seen from Figure 6.

Equation (12) has an error of ±1% in the range of n=o to 5, and Equation (23) is more accurate. However, in equation (22), n
When is brought close to ω, the minimum distortion real root is larger than the value of σ, 1.3962L, which indicates the minimum value of f(σ) in FIG. This is the point (1,4L) on f(σ).

This is because the tangent to f (1,4L)) has a positive slope when n increases beyond a certain level, and equation (23) becomes an approximate expression of a positive real root between the minimum strain real root and the maximum pressure real root. Therefore, when n becomes 10 or more, f at σ0=1.3L
The following equation (24), which is an approximate equation for the minimum distortion real root of (σ)=O, has better accuracy.

Find 0.331 0.0196366+. In the Tiller expansion approximation formula (20) near 00 of f(σ), the following formula is obtained by truncating at the quadratic term of σ.

f(σ)=f(σo)+f' ((FO)(17−σo
)+ -f' (σo) (σ-170)2...(25
) In equations (14), (16), and (17), let σ = σ0 and substitute these equations into equation (25). However, in practice, n is almost never greater than 10, so ( There seems to be no problem with formula 23).

The first-order approximation formula for the minimum distortion real root of f(σ)=O in equation (14) was obtained first, but next, as shown in FIG. 3L and σ0=1.4L, the accuracy of the linear approximation formula for the minimum strain real root was good. Therefore, for these cases, a quadratic approximation formula for the minimum distortion real root is determined. In equation (26).

By setting cr□=1.3L and σo=1.4L, equations (17) and (213) are obtained, respectively.

(σo=1.3L) ・(29) (σo=1,3L) ...(27) (σo=1.4L) (29), The roots of equations (30) are, respectively, ...( 3
0) (σo=1.4L) ...(28)'(27)
, In equation (28), if we set f(σ)=O, then (3
In equation 1), if n=1 and n=5, σo=1
．． The quadratic approximation formula for the minimum strain real root at 3L is... (33) Also, in equation (32), if n = 1 and n = 5, then the quadratic formula for the minimum strain real root at σo = 1.4L is The approximate formula is...
・(34) Comparing the quadratic approximation formula for the minimum distortion real root shown in equations (33) and (34) with the true value of the minimum distortion real root shown in FIG. 6, it can be seen that they still match by four orders of magnitude. While the minimum strain real root determined by the -th order approximation formula matched the true value to within two fingers, -folding accuracy has been improved. Also, (31).

As can be seen from equation (32), the quadratic approximation equation for the minimum distortion real root of f(σ)20 is also expressed as the product of the function of n and L, similar to the -order approximation equation, and f'(σ )=0, it can be inferred with more confidence that the true value of the minimum distortion real root is expressed by the product of the function of n and L.

Next, using the formula of the root of the cubic equation, f in equation (14)
Find the true value of the minimum positive real root of (σ)=0. First, we will show the formula for the root of the cubic equation. The general form of the cubic equation is a a”+b ty2+a σ+d=o”
・(35) The standard form of the cubic equation is obtained.

3 + P + q = Q...
(36) The standard form root formula (Kardame's formula) of the cubic equation shown in equation (36) is given by the following equation.

In addition, the root discriminant is D= a'(ct -β)z(f3-y)z(y-
a) 2=-4p"-27q2...(
41) When the coefficients of equation (35) are real numbers, the relationship between the root discriminant and the roots is: (a) If D>O, there are three real roots.

(b) If D=O, it is heavy machinery (at least two real roots overlap).

(c) If D<O, one real root, two conjugate complex numbers.

Next, using the formula of the root of the cubic equation, f in equation (14)
Find the true value of the minimum positive real root of (σ)=0.

Comparing the coefficients of f(σ)=0 in equation (14) and equation (35), we find that ω = ...(40) To convert f(σ)=O in equation (14) to standard form,
d a It can be seen from equation (46) that the discriminant D>O. Therefore, all three roots of f(σ)=0 in equation (14) are real roots, and match the result obtained from the approximate shape of f(σ).

Substituting equation (45) into equations (38) and (39), we get
Substituting equation (43) into equation (14) and rearranging it, and setting f(σ) as 20, ・(47) Comparing the coefficients of equation (36) and equation (44),...
44) ...(48) (47), Substituting equation (48) into equation (37), we get (
The root of equation 44) is: Substituting equation (45) into equation (41), the discriminant of the root is:
d % Shi-J (49), (so), (sl) From formulas, (44
) where gα(n), gβ(n), and gγ(n) are all functions of n Substituting equation (52) into equation (43), we obtain the cubic equation (1
4) The three roots of f (σ) = 0 in equation (14) are: In other words, the three roots of f (σ) = O in equation (14) are the function g' i (n) (i = α , β, γ)
It is given by the product of and wasted time. This revealed that the previous guess was correct.

In equations (49), (50), and (51), n
By substituting = 1, the three roots of the standard form of cubic equation (44) become, and by substituting equation (54) into equation (53), the three roots of f(σ) = 0 of cubic equation (14) become From equation (55), f(σ) of cubic equation (14) = 0
The minimum positive real root of is the following equation obtained from the second equation of equation (53).

a = 1.377389L (n = 1)
...(56) Also (49) , (50) ,
In equation (51), by substituting n=5, the three roots of equation (44) in the standard form of the cubic equation become
), f(σ) of cubic equation (14) = 0
From equation (58), the three roots of cubic equation (14) are f(σ)=0
The minimum strain real root of is obtained from the second equation of equation (53),
The following formula is obtained.

a = 1.3608093L (n = 5)
−(59) Minimum distortion real root (33
), (34) and the true minimum distortion real root (56), (
59) Comparing the formulas, it can be seen that they match up to one digit. Moreover, the minimum distortion real root obtained by the quadratic approximation formula is σo=1.
4L has better accuracy than σ0=1.3L. This is the same as in the case of the −th order approximation formula.

As can be seen from the above explanation, the first-order and second-order approximations of the minimum distortion real root of the cubic equation f(σ) = 0 with K and time scale factor σ are the ratio n(=L
/T) and the dead time. Also, the cubic equation f(σ)=O of the time scale factor σ
The true value of the minimum real root of distortion is also the ratio n of dead time and time constant T.
It is expressed as the product of a function of (=L/T) and dead time.

Looking at this from a different perspective, the first-order approximation formula, the second-order approximation formula, and the true value of the minimum distortion real root of the cubic equation f(σ) = O of the time scale factor σ are the ratio of the dead time and the time constant T. n
(=L/T) and the dead time f'jlf is expressed as a function of L.

To summarize what has been explained above, the control parameter determination system 4 determines the parameters of the transfer function Gp(S) of the process 1, the gain K, and time constant T,
Based on the dead time, calculate the time scale factor σ using the approximation formula explained earlier, and use this to calculate (8),
The control parameters of the PID controller 2, proportional gain Kp, integral time TI, and differential time Td are determined by equations (9) and (10). As the approximation formula, the first-order approximation formula (Equation (23) or (24)) or the second-order approximation formula (Equation (31) or (32)) obtained previously is used.

Next, the previously obtained results are evaluated through simulation. It is assumed that the process characteristics are expressed by a quadratic delay + dead time system. in this case.

It is necessary to approximate the second-order lag ten-dead time system by the first-order lag ten dead time system. Here, first, the second-order delay is approximated by a first-order delay ten dead time system, and by adding the remaining dead time system to this, the entire first-order delay ten dead time system is approximated.

The quadratic delay ten dead time system is given by the following equation.

Here, Ts, Tz: time constant, L': dead time (60
) If we take out the second-order lag system from Eq.

In order to match the denominator coefficients of equations (62) and (63) up to the second-order term, T 1+ T z = T + L"
・(64)L12 TxTz=TL'+ ...(6
5) must hold true.

Equation (61) can be transformed as shown in the following equation.

On the other hand, if we expand the −order lag ten dead time system by microrin.

1+T must hold true.

The conventional approximation formula 〇=
1, 37L and − order approximation formula (23), quadratic approximation formula (3
Simulations were performed using equation 4), true value (56), and equation (59). The results are shown in Figures 7 and 8. In Figure 7, n (-L/T) = 1
The case shown in FIG. 8 is the case where n=5. Figure 7,
As can be seen from FIG. 8, the negative approximation equation (23) and the quadratic approximation equation (34) have true values (56).

The response is almost the same as when formula (59) is used. On the other hand, when the conventional approximation formula σ=1.37L is used, the approximation accuracy is poor, and there is a difference in response compared to when the true value is used.

In the embodiment described above, the time scale and the factor σ are determined in the control parameter determination system 4 using an approximation formula (-order approximation formula or quadratic approximation formula), but in other embodiments, the true value The time scale factor σ is obtained from the second equation of equation (53), and this σ is used to perform (8).

The control parameters of the PID controller, the proportional gain Kp, the integral time T1, and the differential time Ta may be determined using equations (9) and (10).

In addition, in the embodiment described above, when determining the approximate expression for the 1-hour scale factor σ, the Tiller expansion approximation expression (Equation (22), Equation (26)) in the vicinity of σ0 of f(σ) is (for example, σo = 1.4 L), and the time scale factor σ was determined by using the approximate value of f(σ) = O as the approximate value that the obtained approximate expression becomes zero.

However, in order to improve accuracy, as another example,
The approximate value of σ obtained above is set as σ0 again, and the Tiller expansion approximation formula in the vicinity of σ0 of f(σ) (Equation (22), (2
6), and σ for which the obtained approximate expression becomes zero is f(
The time scale factor σ may be obtained by using an approximate value of σ)=0 and repeating this several times.

In addition, in the embodiment described above, the time scale factor σ is determined using an approximation formula in the control parameter determination system 4, and using this σ, (8), (9),
The explanation has mainly focused on determining the control parameters of the PID controller 2, the proportional gain Kp, the integral time T1, and the differential time Ti using the equation (10). However, the process of finding approximate expressions is also important. The process of finding the approximate expression can be represented by the flow diagram shown in FIG. That is, (1
) Find the approximate shape of the cubic equation f (σ) of the time scale factor σ, (2) Find the region where the cubic equation f (σ) = 00 minimum positive real root exists from the approximate shape of the cubic equation f (σ), (3) Find the approximate Tiller expansion formula for σ0 of the cubic formula f(σ), (4) Substitute the Tiller expansion approximate formula for σ0 in the region where the minimum positive real root obtained in (2) exists in (3). The time scale factor σ is determined from the value of σ at which the obtained approximate expression becomes zero. In the embodiment described above, the region where the minimum positive real root exists is a region where the value of σ is smaller than the value of σ that gives the local minimum value.

As can be seen from Figure 7, when n = 1, the conventional approximation formula σ = 1.37L becomes the true value σ = 1.377389L
When using the approximate formula σ=1.37L, the response rises faster than when using the true value.

Furthermore, as can be seen from Fig. 8, when n=5, the conventional approximation formula 〇=1.37L becomes true value σ=1.360809.
3L, and the rise of the response is slower when using the approximation formula 〇=1.37L than when using the true value. However, in both Figures 7 and 8, the amount of overshoot is determined by the approximate formula α
It can be seen that there is almost no change in both the case of =1.3L and the case of the true value. These results show that by making the time scale factor σ a function of L and increasing or decreasing the coefficient of this function, it is possible to adjust the rise time of the response without changing the amount of overshoot.

A simulation was carried out for the case where the time scale factor σ was increased or decreased as a function of L for a second-order delay ten dead time system. The results are shown in Figure 10,
Shown in Figure 1. FIG. 10 shows the case where n(=L/T)=1, and FIG. 11 shows the case where n=5. Figure 10, 1st
From Figure 1, in both cases of n = 1 and n = 5, by increasing or decreasing the time scale factor σ around the true value, the rise time of the response can be delayed without changing the amount of overshoot. You can adjust it by speeding it up or speeding it up.

For a process that can be approximated by a first-order delay/dead time system,
Since the time scale factor σ cannot be made smaller than the dead time, the time scale factor σ cannot be made smaller than the dead time.
If we adjust the factor σ.

The rise time of the control response can be adjusted to be slower or faster without changing the amount of overshoot.

σ=kL (kz1)...
(68) Alternatively, the following equation can also be used to adjust the rise time.

σ=1.37L-K, L=(1,37-ki)L (0<kt<0.37)(
(When accelerating the rise) ... (69) (F=1.
37L-)cz-L = (1,37-kz)L (0<kz) (when slowing down the rise) ... (70) In addition, (69),
In equation (70), the conventional approximation formula σ = 1.37L was used as the reference for the rise time, but the linear approximation formula for the least positive real root of the cubic equation f(σ) = o, the quadratic An approximate expression or a true value expression may be used.

In the example described above, the transfer function wr(
s), the Kitamori model (αz=0.5°αa=0.1
5. αa=0.03. ...) was mainly explained. However, the transfer function Wr(s) of the reference model is
As shown in FIG. 12, Betteuoorth.

I T A E minimum, Binonomi
There are various models such as a1, and these reference models can also be used. This can be implemented by substituting the coefficient value of each reference model for the coefficient α in equation (11).

〔Effect of the invention〕

According to the present invention, in tuning a PID controller using the partial model matching method, if the process to be controlled can be approximated by a first-order lag and dead time system, the cubic equation f(σ) of the time scale factor σ = The approximate solution of the minimum positive real root of O is expressed as (1) the ratio L of the dead time and the time constant T.
/T and dead time, or (2) find it as the product of the dead time and a function of the ratio n (L/T) of dead time and time constant T, or (3) f (σ
), identify the range of solutions for the minimum positive real root from this rough shape, and find the value of σ at which the Tiller expansion approximation formula for f(σ) becomes zero, or (4) (3) Since the value of σ is repeatedly calculated, the accuracy of the approximate solution is improved, and the error between the control response of the PID controller whose control parameters are adjusted using this approximate solution and the desired control response is reduced.

In addition, the approximate solution of the least positive real root of f(σ) = 0 mentioned above is expressed as (5) σ as a function of L/T and L, and σ is increased or decreased by increasing or decreasing the coefficient of this function, or (6) Since σ is expressed as a function of L, and σ is increased or decreased by increasing or decreasing the coefficient of this function, the characteristics of dead time and time constant T are reflected in the control parameters of the PID controller, suppressing changes in the amount of overshoot. The rise time of the response can be adjusted while maintaining a stable control response.

[Brief explanation of drawings]

Fig. 1 is an explanatory diagram of an embodiment of the present invention, Fig. 2 is an explanatory diagram of a conventional technique, and Figs. 3 to 6 are for obtaining an approximate expression for the time school factor σ of the present invention. An explanatory diagram of
FIGS. 7 and 8 are diagrams showing simulation results for explaining the effects of an embodiment of the present invention, and FIG. 9 shows an approximate expression for the time scale factor σ in an embodiment of the present invention. The flow diagram of the process, Figures 10 and 11, are
FIG. 12, a diagram showing simulation results for explaining the effects of another embodiment of the present invention, is an explanatory diagram of transfer functions of various reference models. K...gain, T...time constant, L...dead time. T-Akebono Fraud High School 30 Figure 4 Figure 2 TI? lε(SεC) 80th TI? I (SECI 帛○ Figure TIME (SEcλ Figure 9 High Figure TI HE (SEC)

Claims (6)

[Claims] 1. In a PID controller that controls a controlled object so that the controlled variable matches a target value through proportional, integral, and differential control operations, the characteristics of the controlled object are approximately expressed using a first-order lag + dead time system, and the Using the process gain K, time constant T, and dead time L, the time scale factor σ in the partial model matching method is expressed as the ratio n (=L/T) of the dead time L and the time constant T, and the dead time L. The proportional gain K_p, integral time T_1, and differential time T_ of the PID controller are calculated using the time scale factor σ.
4. A method for adjusting a PID controller, characterized by determining the value of 4. 2. The method for adjusting a PID controller according to claim 1, characterized in that the scale factor σ is obtained as a product of a function of a ratio n (=L/T) of the dead time L and the time constant T and the dead time L. . 3. In a PID controller that controls a controlled object so that the controlled variable matches a target value through proportional, integral, and differential control operations, the characteristics of the controlled object are approximately expressed using a first-order lag + dead time system, and the When calculating the time scale factor σ in the partial model matching method using the process gain K, time constant T, and dead time L as the minimum positive real root of the cubic equation f(σ) = 0, f(σ) Understand the approximate shape of , specify the range of the solution of the minimum positive real root from this approximate shape, and find the value of σ at which the Taylor expansion approximation formula of the cubic formula f(σ) becomes zero in this specified range. A method for adjusting a PID controller, characterized in that a proportional gain K_p, an integral time T_1, and a differential time T_4 of the PID controller are determined using the time scale factor σ. 4. In claim 3, σ such that the Taylor expansion approximation formula of the cubic formula f(σ) becomes zero.
Find the Taylor expansion approximation formula of the cubic formula f(σ) near the value of , find the value of σ at which this approximation formula becomes zero, and repeat this calculation several times to calculate the scale factor σ
is determined, and using the time scale factor σ thus determined, the proportional gain K_p and integral time T_ of the PID controller are determined.
1. A PID controller adjustment method characterized by determining a differential time T_4. 5. In a PID controller that controls a controlled object so that the controlled variable matches a target value through proportional, integral, and differential control operations, the characteristics of the controlled object are approximately expressed using a first-order lag + dead time system, and the The time scale factor σ in the partial model matching method is calculated using the process gain K, time constant T, and dead time L, and the control parameter K_
When determining P, T_1, T_d, express the time scale factor σ as a function of the ratio n (=L/T) of the dead time L and the time constant T and the dead time L, and calculate the coefficient of this function. A PID characterized in that by increasing or decreasing the time scale factor σ, the rise time of the control response is adjusted to be slower or faster.
How to adjust the controller. 6. In claim 5, the time scale factor σ is expressed as a function of the dead time L, and by increasing or decreasing the time scale factor by increasing or decreasing a coefficient of this function, the rise time of the control response can be slowed or accelerated. A method for adjusting a PID controller, characterized in that the PID controller is adjusted by: