JPS6349901A - Control constant setting device for plant control system - Google Patents

Abstract

PURPOSE:To guarantee the stability of a device by calculating a gain margin and a phase margin from the characteristic factors of a reference model indicating required dynamic characteristics of a control system. CONSTITUTION:A plant control system control constant setting device is constituted of a phase margin/gain margin (PM.GM) arithmetic part 1 to be a 1st arithmetic means and a control constant arithmetic part 2 to be a 2nd arithmetic means. The PM.GM arithmetic part 1 inputs the characteristic factors alpha1-alpha3 of the reference model indicating a required response and calculates the phase and gain margins PM, GM of the reference model. The control constant arithmetic part 2 inputs the phase and gain margins PM, GM calculated by the arithmetic part 1, compensating operation format information and a transmission function G(S) of a control system and calculates control constants C0-f1. Since the control constants matched with the set gain and phase margins GM, PM are calculated, a zero point of a controlled system and useless time are automatically considered.

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Industrial Application Field) The present invention relates to a control constant setting device for a plant control system that controls the temperature, flow rate, pressure, etc. of a plant.

(Conventional technology) For example, in a PID control system, the deviation e between the target value signal r(tl and control: 1Ly(tl) (from tl, the operation signal u
(tl is calculated using the arrow PID calculation formula. Here, C0+ 01
*C2 is a control constant, and is an integral gain, a proportional gain, and a differential gain, respectively. In addition, in the I-PD control system,
The operation signal u(tl is obtained by the following I-PD calculation formula. Here, K, fo, and fl are control constants, and are an integral gain, a proportional gain, and a differential gain, respectively.

In a control system, it is usually necessary to appropriately set these control constants according to the dynamic characteristics of the color 11 object. Conventionally,
As a method for setting control constants common to both PID control systems and I-PD control systems, a control system design method based on partial knowledge of the controlled object (written by Toshiyuki Kitamori, Proceedings of the Society of Instrument and Control Engineers, -
101,15+Mu4 August 1971, P549-55
5) is known. This method has the advantage that the control constants of the control device can be determined by a simple arithmetic expression from a transfer function expressed as a denominator series of the controlled object and a reference model representing desirable characteristics of the control system.

However, this method has the disadvantage that it is not necessarily well designed for control systems where the step response waveform of the controlled object is 11 per sheet or has an inverse response, since the design is not based on gain margin and phase margin. Ahhh. Furthermore, there was also the problem that the stability of the control system was not guaranteed when designed control constants were used.

On the other hand, in the case of PID control systems, a design method based on gain margin and phase margin has been known for a long time, but this method requires a trial-and-error method using gate diagrams. Moreover, the method for setting gain margin and phase margin in the control system specifications was not clear, and was done based on experience.

It was impossible to automate the setting of this control constant.

(Problems to be Solved by the Invention) As described above, in the conventional control constant setting method for plant control systems, it is difficult to set control constants according to the desired control system characteristics for all types of compensation operation such as PID and I-PD. Therefore, it was not possible to guarantee the stability of the control system after it was designed.

The present invention improves the drawbacks of the conventional automatic design method of control constants described above.
It is an object of the present invention to provide a control constant calculation unit a for a plant control system that can design control constants according to desired control system characteristics and further guarantee the stability of the designed control system.

[Structure of the Invention] (Means for Solving the Problem) The present invention inputs the characteristic coefficients of a reference model indicating desirable dynamic characteristics of a control system, and calculates the phase margin (PM) from these characteristic coefficients.
: Phase Margin) and gain margin (GM
: Ga1n Margin), the input transfer function of the controlled object, PID, I-
9 compensation operation mode information such as PD, and the phase margin and gain margin calculated by the first calculation means are input, and the phase margin and gain margin of the controlled object match the phase margin and gain margin of the above reference model. The present invention is characterized by comprising a second calculation means for calculating the control constant of the controlled object so as to calculate the control constant of the controlled object.

- (Function) Until now, in process control systems, the phase margin was 16 to 80 degrees.
In the control system, the gain margin was 3 to 9 dB, and the phase margin was 40 to 65 degrees, and the gain margin was 12 to 20 dB, which is a 10% wide tolerance range. The stability of the control system is maintained because it is based on these phase margins and gain margins, but it is not known at the time of design whether the response waveform of the control system has the intended desired response. It was a trial and error process of designing by changing the allowance little by little.

In the present invention, accurate phase margins and gain margins are calculated from characteristic coefficients of a reference model representing desirable characteristics of a control system. In addition, the control constants can be calculated from the given compensation operation mode (PID control system or I-PD control system) and the input transfer function of the controlled object so that the calculated phase margin and gain margin are achieved. The subsequent dynamic characteristics of the control system will be consistent with the characteristics of the set reference model, and stability is also guaranteed. , (Example) The present invention will be described in detail below according to an illustrated example.

FIG. 1 is a diagram showing the configuration of a plant control system control constant setting device according to an embodiment of the present invention.

That is, the present device is composed of a PM-GM calculation section 1, which is a first calculation means, and a control constant calculation section 2, which is a second calculation means.

The PM-GM calculation unit 1 inputs characteristic coefficients αl, α2, and α3 of a reference model indicating a desirable response, and calculates a phase margin PM and a gain margin GM of the reference model. Further, the control constant calculation section 2 calculates the phase margin PM and gain margin GM calculated by the PM-GM calculation section 1,
Compensation operation mode information (information indicating whether the control system is a PID control system or an I-PD control system) and the transfer function G (Sl) of the control system are inputted, and the control constants C8 and C1 are determined.

C2 or +fo*ft is calculated.

Now, for example, a reference model G showing the desired dynamic characteristics of the control system
Suppose that m(S) is expressed as... (3). Note that here, S is a differential operator, and σ is a coefficient related to the rise time of the step response.

The characteristic coefficients α1, α2, α of the reference model are expressed as follows (4
), and step response waveform group 1 when the value of α is varied.

When α=0.0 is set, a response without overshoot is obtained, and when α=0.4, a response with almost no overshoot and the fastest rise is obtained. As α becomes larger than 0.4, the amount of overshoot increases accordingly, and when α=1.0, the amount of overshoot becomes about 10%.

The PM-GM calculation unit 1 has characteristic coefficients α2, α1, . α4 is input.

In the PM-GM calculation unit 1, a phase margin (PM) and a gain margin (GM) are calculated by the following calculations.

In other words, the open loop transfer function Gm (St of the reference model can be expressed as follows from equation (3), and its frequency response can be expressed by setting S=jω...(7) With a radius of 1 The angle ψ between the point P that intersects the circle and the negative real axis
, is the phase margin PM.

Now, if the crossing angular frequency at point P is ω, then the gain is 1 at point P, so from equation (7),...
・The relationship (8) is obtained, and by expanding and rearranging equation (8) by setting x = = (σω, )2, we get 1-x + (2α3-α2') x2 + (2α2α and α32
)x3-α42x4=0 (9). This (9
) Find the maximum positive group xm of X from the formula.

Then, from equation (7) and Figure 3, the phase margin ψM is 9
M = cai-' (α2xrn-α4x-2)
・・・・・・It can be obtained by αq.

Similarly, since the point G where the Grn (j w & vector intersects the negative real axis shown in FIG. 3) defines the gain margin GM, the dyne margin GM can be expressed as: Therefore, PM-GM The calculation unit 1 is
Characteristic coefficients α1, α1. of the input reference model. α3 Next, the control constant calculating section 2 calculates the control constant as follows.

First, let the input transfer function G (Sl) of the controlled object be, where t is the dead time, al (i=0.l, 2...
・) is the coefficient of the denominator polynomial, J (1=0.1 # 2−
) are the coefficients of the numerator polynomial. This frequency response is given by S=jω, G(j 6J) = l G(jω) I ・e−'
”” −・−・・・QJ. Here IG (
jω)1 is a gain characteristic, and 0(ω) is a phase characteristic.

Assuming that the compensation operation form of the controlled object that has just been input is an I-PD control system, the round transfer function T(S) between the deviation e(t) and the control amount y(t) is as follows, and S= 3ω and by substituting equation (6), we obtain the equation. Regarding the vector locus of this -cyclic transfer function T(jω), (2) 9M is obtained from the condition that there is a phase margin ψ at point P, similar to the locus in FIG. However, ω is the crossing angular frequency when passing through point P.

Next, we obtain the condition that the in margin at point G is GM. Here, town is the angular frequency when passing through point G. Then, in the I-P operation, sf*"0 is set, and in the I-FD operation, as f1→, a→, α.

K s fo a when a town that satisfies the 0:00 formula is found
fl is a control constant that satisfies the set gain margin GM and phase margin ψ1.

Next, when the input compensation operation form is a PID control system, the round transfer function T(S) between the deviation e(υ and the controlled variable y(1) is as follows, i), 5=Js. By substituting equation (2), we obtain (a). Similarly, from the condition that there is one phase margin ψ at two points, we obtain.

Also, since the in-margin at point G is GM, we get

Totori 9. co when ω is found that satisfies the formula
l cll c is a control constant that satisfies the set gain margin GM and phase margin ψ.

As described above, the control constant calculation unit 2 calculates the equations (1s, (1', t:tυ) in the case of the I-PD control system, and calculates the equations ? By doing so, it is possible to calculate control constants that match the desired characteristics of the control system.

[Effects of the Invention] As described above, according to the present invention, the gain margin GM and the phase margin ψ are calculated from the characteristic coefficients of the reference model that determines the desired dynamic characteristics of the control system, so that the response waveform image Accurate matching gain and phase margins are computed. Next, the control constants that match the set gain margin and phase margin are determined from the key-in characteristics and phase characteristics of the transfer function of the controlled object, so the zero point and dead time of the controlled object are automatically taken into account. In this way, the scope of application can be greatly expanded compared to the conventional control system design method (described above) based on partial knowledge of the controlled object.

Furthermore, the problem that the stability of the control system cannot be guaranteed with the conventional method is solved because sufficient stability can be left in the gain margin and phase margin, and stability is guaranteed.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing a control constant setting device for a plant control system according to an embodiment of the present invention, FIG. 2 is a response waveform diagram of a reference model, and FIG. 3 is a vector locus of the open-loop transfer function of the reference model. FIG. 1...PM-GM i-military section, 2...Control constant calculation section. Figure 1 Figure 2 Figure 3

Claims (1)

[Claims] a first calculation means for inputting characteristic coefficients of a reference model indicating a desired response of the controlled object and calculating a gain margin and a phase margin of the reference model; and a gain margin and a phase margin calculated by the first calculation means. , input the transfer function of the controlled object and compensation operation form information of the controlled object, and make the gain margin and phase margin of the controlled object match the in margin and phase margin of the calculated reference model. A control constant setting device for a plant control system, comprising: second calculation means for calculating a control constant of the controlled object.