JPS62119604A - Method of adjusting automatically control constant of pid controller - Google Patents

Abstract

PURPOSE:To attain automatic adjustment without causing the oscillating state by obtaining control constants of a PID controller generated from the production of a transient deviation. CONSTITUTION:In adjusting the PID control constant in following to the characteristic change in a controlled system 2, the PID control constant is decided by the attenuation constant and the oscillation period of the oscillation generated from the production of a transient deviation. Times tz1, tz2, tz3 when the deviation (e) is zero are obtained at first from observation data ti, ei of the oscillation, an angular frequency omegan and an initial phase difference psin are obtained, an attenuation constant sigman and an amplitude An are obtained by the least square method operation, and the optimum proportional gain Kpt is decided by using a present proportional gain Kpn, an object attenuation e<-at> and a coefficient ap and the optimum integration time Ti and differentiation time Td are decided by using the coefficients.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application This invention is directed to a control system using a proportional, integral, and differential (PID) control system, which follows changes in the characteristics of a controlled object.
The present invention relates to an automatic control constant adjustment method for a PID controller that automatically adjusts PID control constants.

Prior Art In the conventional automatic control constant adjustment method for a PID controller, the PI
Setting the integral time Ti of the D controller to infinity and the differential time Td to zero, only proportional control is performed, the proportional gain Kp is gradually increased to generate an oscillation state, and the proportional gain Kp□ and period Pu in this oscillation state are , proportional gain Kp, integral time Ti + gI minute time Td, Kp = o, a x Kp □ −−−− (1)
Ti20.5 X Pu・・・・・・
・・・・・・・・・・・・(2) Tal: o, 125
It was calculated as X Pu-...-River...-=(3). (Ziegler-Nichols limit sensitivity method) Problems to be solved by the invention However, in this method of adjusting the PID control constant, it is necessary to bring the control system into a firing state for adjustment. Therefore, there was a problem that controllability deteriorated.

The present invention has been made in view of the above points, and an object of the present invention is to adjust the PIDID inter-leg constant movement without causing the control system to be in an oscillating state.

Means for Solving the Problems In order to solve the above-mentioned problems, the present invention determines the PIDID constant from the damping constant and vibration period of the vibration caused by the transient deviation. .

Page 6 Effects In the present invention, the PID control constant can be determined by the method described above, so automatic adjustment can be performed without causing an oscillation state, and there is no deterioration in controllability for adjustment.

Embodiment FIG. 1 is a block diagram showing an embodiment 11HJk of a control system using the method for automatically adjusting control constants of a PID controller according to the present invention.

In the M1 diagram, 1 is the controller from P, 2 is the controlled object, and 3
is a PID leg constant automatic adjustment section, and PID controller 1
The manipulated variable U that is frequently output is input to the controlled object 2, and the output y of the controlled object 2 is inputted to the PID controller 1 as a deviation e which is the difference from the target value r, forming a PID feedback control loop. has been done.

Furthermore, the deviation e is input to the PID control constant automatic adjustment section 3, and the optimal proportional gain Kp and integral time Tl+differential time Td are determined in the PID control constant automatic adjustment section 3,
The control constant of PID controller 1 is automatically adjusted by 6 pages.

Next, an automatic adjustment method of the PID jdilJ control constant automatic adjustment section 3 will be explained.

In Fig. 1, when the target value r changes or the output y changes due to disturbance, a transient deviation e occurs, and the PID control constant of the PID controller 1 is inappropriate for the characteristics of the controlled object 2. In this case, the deviation e does not settle quickly and vibration occurs. This vibration is e (t) = person, 6 fft,
It is expressed as 5in(ωt+ψ)=・−・+・”(4).

Here, θ(t): deviation A: amplitude σ: Attenuation constant t: time ω: Angular frequency ψ: initial phase angle It is.

The amplitude, damping constant σ, and angular frequency ω in this equation (4)
, and the initial phase difference ψ are calculated from observation data.

The angular frequency ω and the initial phase difference ψ are
As shown in the vibration waveform in the figure, the time when the deviation 6(t) becomes 0 is tzI + tZ 2 + tZ 3 and tz3-1
It can be obtained as z1 tZ5-tzl.

Observation data obtained every sampling time Δ (t1+e,), (t, , e, ,)
......(1n, θn), equation (4) becomes θi
=),,6 ”1-sin(ωt1+<i+) −
---(7) becomes. If we fully transform this equation (7), and further take the logarithm of both sides, we get ~ Here,
(11)a=Aoge(A)...
・ ・・・・・・・(12)b−−σ
・・・P・・・・・・・・・・・・(13) If (
9) The formula is: y = i 1)) (i ・・・・・・・・・・・・
...(14).

Here, the angular frequency ω and the initial phase difference ψ are expressed by equation (5),
Since the equation (6) is already known, the amplitude A1 and the attenuation constant can be found by finding the coefficient '+'r of the equation (14) using the least squares method.

The sum of squares S of the difference between equation (14) and data (t, ei) is S, The normal equation of is, From this, the coefficients a and b are
8) Calculate as 1o b/.

For these a and b, the amplitude A and the attenuation constant σ are A == 6a River...
・(20)σ=-b ・・・・・・・
... can be obtained as (21).

In order to find the relationship between the damping constant σ, the angular frequency ω, and the control constant, the controlled object 2 is assumed to be a (dead time + first-order lag) system, and the integral time Ti of the PID controller 1 is set.

and the derivative time 'r, fixed at 12, the ratio II/! An experiment was conducted by changing the I gain and changing the target value r to generate all the vibrations.

However, the transfer function G p (s) of the controlled object is set here as follows: K: process gain L: dead time 11 Bege T2 time constant. Moreover, the target value r is r=1.1 (time t(1,1(S)) −(23)
r=1. o (time t≧1.1 (S) )−・(2
4).

Here, the values of the process gain and 1 dead time 51 time constant T were as shown in Table 1.

The vibration response results for Table 1 CASIi:1 are shown in Figure 3, and according to the results in Figure 3, the damping constant σ and the angular frequency ω,
FIG. 4 is a plot of the relationship between the proportional gain Kp and the proportional gain that generates vibration where the values of the reference damping constant σB and the reference angular frequency ωB are as follows. The relationship between the value obtained by completely dividing the proportional gain, the damping constant σ, and the angular frequency ω is plotted for all 0ASHs in the fifth graph.
It is a diagram. The regression equation based on the least squares method for the measurement points in FIG. 6 becomes identical.

Here, ap: coefficient ap knee 0.590b = coefficient bp=1.596.

Since the damping constant σ and the angular frequency ω have a large influence on controllability, the damping constant −g has the best controllability.

σ, and at the angular frequency ω. ω is the target attenuation value θ−a
Define t as the oscillating current damping constant σ. , angular frequency ωn, and proportional gain K p n, the optimal proportional gain Kp on page 13 can be expressed as Equation (25), and by transforming Equations (26) and (27), The optimal proportional gain Xpt is determined by equation (28).

As the target damping value e aZO value, the damping coefficient ξ is 142
．． It is known that the square control area (ISK) is minimum when the value is 0.5 (Automatic Control Handbook Motoiso Edition 1)
984 L damping coefficient ξ, damping constant σ, and angular frequency ω
The relationship is expressed as (29)2k Substituting it into the left side of equation (27) and setting the damping coefficient ξ to 0.5, we get θ−aZ
If the value of is i0.163, then the square control area (XSX)
is the minimum.

The natural angular frequency ωU is obtained as ω1ygo+a' (31), and this natural angular frequency ω. and the period Pu in the modified method is ωU, and the coefficients in the limit sensitivity method are ai and 2
L6, and substituting equations (32) and (31) into equation (2), and similarly substituting equations (32) and (31) into equation (3), yields, and these equations (33), The optimal integration time Ti and differential time Td are determined by the equation (34).

The procedure of these calculations is shown in the flowchart of FIG.

In Fig. 6, first, from the vibration observation data (ti+6i), the time tZj+tZ 21 tZ when the deviation e becomes O
3, find υ, (angular frequency 0)n, and initial phase difference ψn using equation (@) and equation (6), and further, (
18) and (19), the most/no 12 east method operation, and (
2o) The damping constant σ is determined by equation (21). , and amplitude A
Determine the optimal proportional gain Kpt using equation (28) using 1 for the current proportional gain and the target attenuation value e-aj/coefficient n ap, and then determine the optimal loading time Ti, and the differential time Td, coefficients a1° and a
It is determined by equations (33) and (34) using d.

Effects of the Invention As described above, according to the present invention, the limiting constant of a PID controller can be automatically adjusted by extremely simple calculations, and furthermore, since the automatic adjustment can be performed without causing an oscillation state, the adjustment process can be simplified. It is extremely useful as it does not cause deterioration of the lateral limbs.

[Brief explanation of drawings]

Fig. 1 is a basic diagram showing an embodiment of a control system using the automatic control constant adjustment method for a PID controller of the present invention, Fig. 2 is a vibration waveform diagram, and Fig. 3 is a diagram showing an example of a control system using the automatic control constant adjustment method of a PID controller according to the present invention. Figure 4 is a plot diagram showing the relationship between the proportional gain, damping constant, and angular frequency in the case of Figure 3. Figure 5 is a response diagram of an example of vibration measured with reference damping constant and reference angular frequency. FIG. 6 is a plot diagram showing the relationship between the value obtained by dividing the proportional gain by the proportional gain that generates , the damping constant, and the angular frequency. FIG. 6 is a flowchart showing the procedure for calculating the limiting constant. 1... PID controller, 2... Controlled object, 3... PID control constant automatic adjustment unit. Name of agent: Patent attorney Toshio Nakao and 1 other person
1 Figure 2 Lee - Exit p Upper S] T (S) Figure 3 Ball 51 Figure 3 f, T1 Figure (S) Figure 3 T (+ Figure (δ) @ 3 Figure (δ) and p -70 Hole-〇33 Tct-0 Ding (S) Figure 3 T (s+ Figure 4, Kp6 Figure 5 e t, AsEf Above! 0 Figure 6 Procedural Amendments June 20, 1985) 1985 Patent Application No. 260158 2. Name of the invention: Method for automatically adjusting control constants for PID controllers. 3. Person who makes amendments. Relationship with the case/patent application. Address: 1006 Kadoma, Kadoma City, Osaka. Name (582). ) Matsushita Electric Industrial Co., Ltd. 2, No. 6, Contents of the amendment (1) The following sentence is inserted next to "Determined." on page 16, line 11 of the specification. [Here, ( ), and the angular frequency ω by equation (6). When calculating the initial phase difference ψ, based on the observation data obtained at every sampling time Δ, the time when the deviation e(1) becomes 0 is '21' Z21 To find t23,
There are cases where the time 'z, 1 z ''z2.tz3 can only be determined as an approximate value.Therefore, vibration is generated and the damping constant σ of the vibration is set to an angular frequency ω different from the true angular frequency ω. Figure 7 shows the results of estimating σ at the angular frequency of ω'-2×ω for the vibration of true ω211.66 and σ2.051, and σ The estimated value of σ8 = 1,988.The solid line in the figure represents the true vibration, and the broken line represents the estimated vibration.Figure 8 shows that for the same vibration, ω' = o, sxω As a result of estimation at the angular frequency of The result of estimation at the frequency was σo-0,518. Figure 10 shows that for the same vibration, the result of estimation at the angular frequency of ω' = Q, sxω was σo = 0, 533. As such, the method for estimating the damping constant of vibration according to the present invention allows the damping constant to be estimated with sufficient accuracy even if the true angular frequency of vibration is not used.'' (2) Page 17, line 8 of the same. 7, 8, 9, and 10 show the damping constant σ at an angular frequency ω' that is different from the angular frequency ω of the true vibration.
FIG. ”. (3) Add drawings 7, 8, 9, and 10 as shown in the attached sheet.

Claims (5)

[Claims] (1) In the PID feedback control loop consisting of the PID regulator and the process to be controlled, the control constant of the PID regulator is determined from the damping constant and angular frequency of vibrations caused by transient deviations. A method for automatically adjusting control constants for a PID controller. (2) A method for automatically adjusting a control constant of a PID controller according to claim 1, in which a damping constant is obtained by approximating vibration observation data to a sine wave using the least squares method. (3) The value obtained by dividing the proportional gain K_p by the proportional gain K_p_o that generates the vibration of the reference damping constant σ_B and the reference angular frequency ω_B, the damping constant σ, and the angular frequency ω
The identity regression equation e^-^(^σ^/^ω)^π=a_p+b_p(K_
p/K_p_o), the current proportional gain K_p_n, the current attenuation constant σ_n, the current angular frequency ω_n, and the target attenuation value e^-^(a_t), the optimal proportional gain K_p is determined.
_t, K_p_t/K_p_o={{[e^-^(a_t)-
a_p]/{e^-^[^(σ_n)^/^(ω_n)
^]^π-a_p}}(K_p_n/K_p_o) PI according to claim 1
Method for automatically adjusting control constants of D controller. (4) From the current damping constant σ_n, angular frequency ω_n, and coefficient a_i, determine the optimal integration time T_i with a_i=0.
5, Ti=a_i{2π/[√(ω_n^2+σ_n^2)
} } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } } ” ” ” ” ” ” ” . (5) From the current damping constant σ_n, angular frequency ω_n, and coefficient a_d, determine the optimal differentiation time T_d with a_d=0.
125, T_d=a_d{2π/[√(ω_h^2+σ_n^2
)]} The method for automatically adjusting a control constant of a PID controller according to claim 1, wherein the control constant is determined as follows.