JPS638901A - Automatic adjusting method for control constant of pid controller - Google Patents

Abstract

PURPOSE:To make an automatic adjustment without causing an oscillation state and to prevent deterioration in controllability due to the adjustment from being caused by decreasing a proportional gain by a constant rate when the period of vibration caused due to transient deviation is shorter than the constant rate of an integral time set in a PID controller. CONSTITUTION:If a command (r) varies or an output (y) varies owing to disturbance, transient deviation (e) is generated and if the control constant of the PID controller 1 is improper to the characteristics of a controlled system 2, the deviation (e) does not settle speedily and vibration occurs. In this case, when the period (p) is a constant rate and less shorter than the integral time set in the PID controller, the proportional gain Kp is decreased by the constant rate to improve the controllability. Further, similar operation is repeated until the period (p) becomes the constant rate longer than the integration time and thus the period (p) is made the constant rate larger than the integration time, thereby finding the best proportional gain Kpt.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application This invention relates to a feedback control system using a proportional, integral, and derivative (PID) regulator. The present invention relates to a method for automatically adjusting control constants of a PID controller, which automatically adjusts the control constant 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 T 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 Kpδ and period Pu in this oscillation state, the optimal proportional gain Kpt,
Integral time Tit, differential time "dt" are KP, ==0.6 X Kpδ...
...(1) T 1t=o, ts x P u----
--(2)'rd, = 0.125 X Pu・-・
・I was looking for (3). (Ziegler-Nic
hols (Ziegra-Nichols) marginal sensitivity method].

Problems to be Solved by the Invention However, in this method of automatically adjusting control constants, it is necessary to bring the control system into an oscillation state for adjustment, which has the problem of poor controllability.

The present invention has been made in view of this problem, and an object of the present invention is to automatically adjust control constants without causing the control system to enter an oscillation state.

Means for Solving the Problems In order to solve the above problems, the present invention solves the problems described above.When the period of vibration caused by a transient deviation is short and is less than a certain ratio of the integration time set in the PID controller. , decreases the proportional gain by a constant ratio.

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 regulator, 2 is a controlled object 3 is a control constant automatic adjustment section, and the manipulated variable U output from the PID regulator 1 is input to the controlled object 2, and the controlled object 3 is a control constant automatic adjustment section. The output y of 2 is expressed as the deviation e, which is the difference from the target value r, as PI
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, where the proportional gain Kp is determined and the control constant of the PID regulator 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 5IN(ωt÷ψ) -----
−・(4)

Here, e: deviation, A: amplitude, σ: attenuation constant, t: time, ω: angular frequency, ψ: phase angle.

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 is fixed, the characteristics of the controlled object 2 are dead time ÷ first-order delay system, and the values of the process gain and one time constant T1 dead time are as shown in the table below.

The vibration waveforms in Experiment 1 are shown in FIG. 2, and the relationship between the damping constant σ and angular frequency ω of these vibrations and the proportional gain Kp is shown in FIG.

In Fig. 3, the proportional gain K whose value on the vertical axis is 1.0 is defined as the oscillation proportional gain Kpδ, and the proportional gain Kp
FIG. 4 shows the relationship between the value obtained by dividing the period p by the oscillation proportional gain Kpδ, the damping constant σ and the angular frequency ω, and the value obtained by dividing the period p by the integration time Ti for all experiments.

Regarding the attenuation constant σ and the angular frequency ω in FIG. 4, it can be seen that the experimental points exist almost on one straight line. The regression equation based on the least squares method for this experimental point is as follows.

Here, ap: coefficient (a p 20 -690) bp=coefficient (b
p = 1.596).

The relationship between the damping constant σ, the angular frequency ω, and the damping coefficient is as follows.
It is known that when the damping coefficient ζ is 0.5, the square control area becomes the minimum (automatic control C/minimum), and the corresponding horizontal axis Kp/Kpδ becomes 0.472.

On the other hand, the relationship between the value obtained by dividing the period p by the integration time T in Fig. 4 and the horizontal axis Kp/Kpδ shows that for all experiments, when the proportional gain Kp is larger than the appropriate value, the period p is the integration time It is shown that it becomes smaller with respect to Ti.

The controlled object 2 generally has a limited input/output width. For example, pulp, which is one of the process equipment, has a nonlinear input/output characteristic as shown in Figure 5, and the controlled object 2 has such nonlinear characteristics. In this case, the imaging width is limited, and the characteristic diagram in Fig. 4 becomes -Lπ characteristic diagram as shown in Fig. 6, and the value of @Xp'' on the vertical axis is 1.0.
Above that, there will be no change.

From the above, when the period p is shorter than the predetermined ratio compared to the integration time T set in the PID controller, the controllability is improved by reducing the proportional gain K by a predetermined ratio.

Furthermore, the same operation is repeated until the period p becomes longer than the integral time T by a certain ratio, and the period p becomes the integral time TL.
If the ratio exceeds a certain ratio of
The optimal proportional gain Kpt can be found as follows.

The natural angular frequency ω8 is obtained as ω,==fi (8), and the relationship between this natural angular frequency ω8 and the period pu in the limit sensitivity method is as follows. Let the coefficients in a and ad
and substituting equations (8) and (9) into equation (2), we get
Similarly, by substituting equations (8) and (9) into equation (3), the following equations are obtained, and the optimal integration time Tit and differential time "dt" are determined by these equations (10) and (11).

Effects of the Invention As described above, according to the present invention, the control constant of the PID regulator can be determined from the vibration waveform, and furthermore, it can be automatically adjusted without causing an oscillation state, so that the controllability for adjustment is improved. It does not cause any deterioration and is extremely useful in practice.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing an example 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 obtained by varying the proportional gain in Experiment 1; Figure 3 is a characteristic diagram showing the relationship between the vibration damping constant and angular frequency in Figure 2 and the proportional gain, and Figure 4 is the relationship between the value obtained by dividing the proportional gain by the oscillation proportional gain, the damping constant and angular frequency, and the period. Figure 6 shows the input/output characteristics of the valve, and Figure 6 shows the oscillation proportional gain when the controlled object has nonlinear characteristics. FIG. 4 is a characteristic diagram showing the relationship between the value obtained by dividing the period by the integral time, the relationship between the attenuation constant and the angular frequency, and the relationship between the value obtained by dividing the period by the integral time. 1...PID controller, 2...Controlled object, 3...Par/control constant automatic adjustment section. Name of agent: Patent attorney Toshio Nakao and 1 other person No. 1
figure,? Figure 2 (b) KP-θ, 5 7j-0,317-djθ Tsuta 2 Figure (S Cd) IL ri' Figure 2 (f) Figure 2 (h) +151 Figure 12 TIS f5J Figure 2 ( K) ISJ Figure 3 Figure 4 1' 1.1 11.4 It 11.1
10 1.2 /, #l≦Figure 5

Claims (1)

[Claims] A PID controller is provided that outputs the amount of deviation of the controlled object based on the deviation between the output of the controlled object and the target value, and the period of vibration that occurs due to the occurrence of a transient deviation is an integral time set in the PID controller. If it is shorter than a certain ratio of the integral time, reduce the proportional gain by a certain ratio to the proportional gain set in the PID controller, and repeat the same operation until the period of the vibration becomes longer than a certain ratio of the integration time. . A method for automatically adjusting a control constant of a PID adjuster, which calculates a control constant of the PID adjuster from a damping constant and an angular frequency of the vibration when the period of the vibration exceeds a certain ratio of the integration time.