JPS62298803A - Automatic adjusting method for control constant of pid controller - Google Patents

Abstract

PURPOSE:To automatically adjust a control system without placing it in an oscillation state by finding the angular frequency and phase angle of vibrations caused owing to transient deviation and determining the control constant of a PID controller. CONSTITUTION:A manipulated variable (u) output by the PID controller 1 is inputted to a controlled system 2, whose output (y) is inputted to the PID controller 1 as deviation which is a difference from a target value (r), thus constituting a feedback control loop. Further, the deviation (e) is inputted to an automatic control constant adjustment part 3. The automatic control constant adjustment part 3 finds the angular frequency and phase angle of oscillations due to the transient deviation from the time when the deviation observed value of the vibrations becomes zero and approximates the vibrations to the smallest square- law method to find the attenuation constant of the vibrations. Then, control constants of the best proportional gain Kp, integration time Tit, and differentiation time Tdt of the PID controller 1 are found from the attenuation constant and angular frequency to make an automatic adjustment.

Description

[Detailed Description of the Invention] 3. Detailed Description of the Invention Industrial Field of Application The present invention follows changes in the characteristics of a controlled object in a feedback control system using proportional, integral, and differential ()) ID) regulators. The present invention relates to a method for automatically adjusting a control constant of a PID adjuster, which automatically adjusts the control constant of the PID adjuster to an optimum value.

Prior Art In the conventional automatic control constant adjustment method for a PID controller, the PI
Proportional control is performed by setting the integral time Ti of the D regulator to infinity and the differential time Td to zero, gradually increasing the proportional gain Kp,
An oscillation state is generated, and from the proportional gain Kp0 and period Pu in this oscillation state, the optimal proportional gain Kpt,
Integral time T41. The differential time Tdt is Kpt=o, exKpo --(1)T,
t=0.5XPu −, −(2)
Tdt=0.125xPu −・・−・(3
) was sought as C Ziegler-Nichol
s (Ziegler-Nichols) limit sensitivity method].

Problems to be Solved by the Invention However, in this automatic adjustment method of control constants, it is necessary to bring the control system into an oscillation state for adjustment, which deteriorates controllability. There were problems. The present invention was made in view of the above problems, and aims to automatically adjust control constants without causing the control system to be in an oscillation state.

Means for Solving the Problems In order to solve the above-mentioned problems, the present invention aims to improve the angular frequency of vibrations and The phase angle is determined, and based on these, the vibration is approximated as a periodic function by the method of least squares, the damping constant of the vibration is determined, and the control constant of the PID controller is determined from these damping constants and the angular frequency.

Function: In the present invention, by determining the control constant using the method described above, 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 of a control system using the method for automatically adjusting control constants of a PID controller according to the present invention.

In FIG. 1, 1 is a PID controller, 2 is a controlled object, and 3 is a PID controller.
is a control constant automatic adjustment section, in which the manipulated variable U output from the PID controller 1 is input to the controlled object 2, and the output y of the controlled object 2 is expressed as the deviation e which is the difference from the target value r.
The signal is input to the D controller 1, and a feedback control loop is configured.

Furthermore, the deviation e is input to the control constant automatic adjustment section 3, and the control constant automatic adjustment section 3 calculates the optimum proportional gain Kp,
, integration time T84. The differential time Tdt is determined and P
The control constant of the ID controller 1 is automatically adjusted.

Next, a method of adjusting the 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 controlled object 2
With respect to the characteristics, if the control constant of the PID regulator 1 is inappropriate, the deviation e will not settle quickly and vibration will occur. This vibration is e=A−exp −8IN(ωt+ψ) ・=−(
4) Expressed as 5''''-.

here, e: deviation A: Amplitude σ: Attenuation constant t: time ω: Angular frequency ψ: phase angle It is.

In order to find the relationship between the damping constant σ and the angular frequency ω and the control constant, a numerical experiment was conducted on vibration generation while changing the target value r.

However, the integral time T and differential time T of the PID controller 1
d was fixed, the characteristics of the controlled object 2 were dead time + first-order delay system, the process gain was 1 time constant T, and the values of dead time were as shown in the table.

A- The vibration waveforms in Experiment 1 are shown in Figures 2(a) to 2(no), and the damping constant σ and angular frequency ω of these vibrations are
The relationship with proportional gain Kp is shown in FIG.

In Figure 3, the proportional gain K has a value of 1.0 on the vertical axis.
is the oscillation proportional gain K, and the value obtained by dividing the proportional gain K by the oscillation proportional gain K and the reduction p
p.

The relationship between the table constant σ and the angular frequency ω for all experiments is shown in FIG.

The regression equation based on the least squares method for the experimental points in Figure 4 is identically expressed as follows.

here, ap: coefficient (ap-10, 590) bp: coefficient (bp=1.596) It is.

Since the damping constant σ and the angular frequency ω have a large influence on controllability, 6 z p-(II7r, which provides the best controllability, is defined as the target damping value θXp, and the damping constant of vibration at the current proportional gain Kpn The relationship between σ and angular frequency 9 and the optimal proportional gain Kpt can be expressed as from equation (6), and by transforming equations (6) and (7), the optimal proportional gain Kpt can be obtained from equation (8). As the value of the target damping value eXp-at, the damping coefficient ξ is
It is known that the square control area is minimum when the value is 0.5 (Automatic Control Handbook Basic Edition 1984), and the relationship between the damping coefficient ξ, the damping constant σ, and the angular frequency ω is as follows. The target attenuation value e x p''-at is expressed as, and if the attenuation coefficient ξ is 0.5, the target attenuation value eXp'-at is expressed as
” becomes 0.163, and at this time, the square control area becomes the minimum.

Natural angular frequency ω. and the current damping constant σ. and angular frequency ω. There is a relationship between the oscillation period Pu and the natural angular frequency ω.

9 ″ is expressed as , and the coefficients in equations (2) and (3) are each a
.

and ad, and by substituting equations (11) and (12) into equations (2) and (3), we obtain the following: From these equations (13) and (14), the optimal integration time T and The differential time Tdt is found.

From these equations (8), (13), and (14), the optimal proportional gain Kp, integral time Tit, and differential time Tdt can be found, but the current attenuation constant σ. and angular frequency ω.

needs to be determined from the observed values of vibration.

When the characteristics of controlled object 2 are linear and no noise is added (4
) The vibration expressed by the equation has a vibration waveform as shown in FIG. 5, and the observed deviation value passes through zero deviation at time 10''''' tz1. tz2. From tz3, the angular frequency ω and phase angle ψ in equation (4) can be determined as follows.

Observation data (t e ), (t2.e2), where the deviation observation value is obtained every sampling time Δ.

1' 1 ... (tn, en), equation (4) becomes e(=As
exp 1*5IN (ωati ten ψ) --(17)
becomes. Here, (i=1.2...n).

Transforming this equation (17), we get the following, and by taking the logarithm of both sides, we get
1) a = nogo(A) --
(22)b −1σ ・Old ・−・
(23), equation (19) is yi=a+l)z, ・・・
...(24).

Here, the angular frequency ω and phase angle ψ are expressed by equation (15) and (
16) Since it is known from equation 16), by the least squares method, (
24) The coefficients a and b of the equation can be found as follows. From the coefficients a and b, the damping constant σ can be obtained as σ−−b···−−(27).

However, in actual observed values of vibration, there are vibration waveforms in which the center of vibration deviates from zero deviation, as shown in Figure 6, when the characteristics of the controlled object 2 are nonlinear, and noise waveforms, as shown in Figure 7. , control constants obtained using the attenuation constants and angular frequencies obtained from these waveforms are inappropriate values, resulting in poor controllability.

In the case of vibration waveforms such as those shown in FIGS. 6 and 7, the error in periodic function approximation for determining the damping constant becomes large.

From this, when the error in periodic function approximation is large, deterioration in controllability can be avoided by not performing automatic adjustment using the control constant determined from the damping constant and the angular frequency.

The procedure for determining these control constants is shown in the flowchart of FIG. In Figure 8, we first show the vibration observation data (ti,
e, ), detect the time tz1, z2' tz3 at which the deviation e passes 13'' through zero deviation,
From these equations (15) and (16), the angular frequency ω
. and phase angle ψ. is obtained, data conversion is performed using equations (2o) and (21), and the attenuation constant σ□ is obtained using the least squares method calculation of equation (26) and equation (27).

If the error in periodic function approximation of vibration by the least squares method is large, the damping constant σ. and the control constant is not determined based on the angular frequency ω. Otherwise, equation (8), (
From equations (13) and (14), the optimal proportional gain Kp
, , determine the integral time Tit and the differential time Tdt.

Effects of the Invention As described above, according to the present invention, the control constant of the 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 This method does not deteriorate controllability, and prevents inappropriate adjustment of control constants due to noise, etc., and is extremely useful in practice.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of a control system using the method of automatically adjusting the control constant of a PID controller according to the present invention;
From Figure 2 (-) to Figure 2 Ul)) are vibration waveform diagrams obtained by changing the proportional gain in Experiment 1, and Figure 3 is from Figure 2 (,) to Figure 2 (I!,) Figure 4 shows the relationship between the vibration damping constant and angular frequency and the proportional gain in all experiments. Figure 6 shows the vibration waveform without adding noise, Figure 6 shows the vibration waveform 11 when the characteristics of the controlled object are nonlinear, Figure 7 shows the noise waveform, and Figure 8 shows the procedure for determining the control constants. It is a flowchart. 1... PID controller, 2... Controlled object, 3...
・Control constant automatic adjustment section. Name of agent: Patent attorney Toshio Nakao and 1 other person No. 1
figure,? Fig. 2 (a) (b) Fig. 2 (C) (d) No. (dry) kP-4, OTj-0, 33Tel-0 (h) Fig. 2 (j) Fig. 2 (do) kp-fJ , 0 η-θ33 Td-0()kP-9,07t" 0337d-Q Fig. 3 01234567B? ↑ Fig. 4 KP KP 1000 Fig. 5 Fig. 6 Fig. 7

Claims (1)

[Claims] Determine the angular frequency and phase angle of the vibration from the time when the observed deviation value of the vibration generated due to the occurrence of a transient deviation passes the zero deviation, and based on the angular frequency and phase angle, calculate the vibration, A periodic function approximation is performed using the method of least squares to determine the damping constant of the vibration, and from the damping constant and the angular frequency, the optimal value of the control constant in the PID controller is determined, automatic adjustment is performed, and the error in the periodic function approximation is determined. A method for automatically adjusting a control constant of a PID controller, characterized in that when the attenuation constant and the angular frequency are large, automatic adjustment is not performed using the control constant determined from the attenuation constant and the angular frequency.