JPS6344177A - Transmission function measuring apparatus - Google Patents

Abstract

PURPOSE:To obtain a correct frequency characteristic, by determining a pulse transmission function to be controlled from a coefficient of an autoregressive moving average (ARMA) model identified. CONSTITUTION:A control value y(t) of a process 1 is picked up with an A/D converter 2 as such sampled at a fixed sampling cycle. An output signal u(k) of an identification signal generating section 3 which generates a simulated white noise or the like to identify dynamic characteristic of the process 1 is held with a D/A converter 4 at the same sampling cycle and the signal u(t) outputted is turned to an input of the process 1. An ARMA model identifying section 5 picks up signals u(k) and y(k) sequentially to identify a coefficient of an ARMA model of the process 1 by identification method. Then, a frequency characteristic computing section 6 computes the frequency characteristic of the process. This enables the computation of a correct gain/phase characteristic from low to high frequency.

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Industrial Application Field) The present invention relates to a transfer function measuring device for determining the dynamic characteristics of a process.

(Prior art) As methods for measuring the transfer function that determines the dynamic characteristics of a process, (a) a method using a servo analyzer, (0) a correlation method,
(c) A method using a combination of an ARMA (autoregressive moving average) model and a least squares method is known.

The method using a servo analyzer involves inputting a sine wave as the process operation signal as an identification signal, and examining the phase difference between the amplitude of the controlled variable and the input waveform when a steady state is reached, using frequency as a parameter.

It measures the frequency characteristics of process gain and phase. This method inputs a sine wave to the controlled object over a long period of time, and is implemented in an open loop, so it is difficult to apply to actual processes. Next, in the correlation method, white noise containing many frequency components is input into the process operation signal as an identification signal, the power spectrum is determined from the correlation function with the controlled variable, and the gain of the controlled object is determined from the power spectrum ratio. and the frequency characteristics of the phase. Compared to the method using a servo analyzer, since it uses an identification signal with many frequency components, it has the advantage that the measurement time is somewhat shorter, but the amount of data to be processed is enormous, and the frequency characteristics of the obtained controlled object are There were also many errors.

Finally, the method based on the combination of the ARMA model and the least squares method is highly useful and has been widely used in recent years as a systematic method that can measure the dynamic characteristics of a controlled object even during closed-loop control if the identification conditions are met. As increasingly used, the resulting ARMA model is equivalent to a pulse transfer function expressed by a constant sample period. Therefore, there is a problem in that the frequency characteristic of the pulse transfer function has an error in the frequency characteristic of the original transfer function due to the influence of side waves as it approaches the relative Beniquist frequency.

(Problems to be Solved by the Invention) The purpose of the present invention is to improve the drawbacks of the transfer function measurement method by combining the ARMA model and the least squares method, and to obtain accurate frequency characteristics from the measured ARMA model. An object of the present invention is to provide a measuring device for the transfer function obtained.

[Structure of the invention] (Means for solving problems) The present invention uses the identified coefficients of the ARMA model.

Dynamic characteristics of a process configured to calculate the pulse transfer function of the controlled object, and then correct the frequency customization from the frequency characteristics of the gain and phase of this pulse transfer function using a correction function that removes sampling data and held effects. This is a device for measuring transfer functions.

(Operation) In order to obtain the frequency characteristics of the pulse transfer function of the controlled object, a method of substituting ejx into the time transition operator Z is widely used, but in this case, this frequency characteristic is different from the frequency characteristic of the original transfer function. It is known to deviate. The reason for this is that the pulse transfer function is defined for hold data for each sampling period, so the sideband spectrum ω
This is due to the fact that the phase appears to be out of phase with the dein due to the influence of From the standpoint of designing a continuous control system, the gain and phase shift due to the 1111j band wave is in a high frequency range, making it difficult to design the limit. Therefore, in the present invention, in order to perform calculations to correct the frequency characteristics of gain and phase using a correction function that removes the effect of this held sampling data, the frequency characteristics can be adjusted from the low frequency region to the high frequency region without error. can be found.

(Example) Hereinafter, the present invention will be described in detail with reference to the drawings. FIG. 1 is a block diagram showing the configuration of a transfer function measuring device according to the present invention. In this figure.

The control my(1) of process 1 is a constant sampling period τ
The suppressed H amount y (
k). Furthermore, the output signal u(k
) is held by the D/A converter 4 at the same sampling period τ, and the output signal u(1) is input to the process 1.

In the ARM A model identification unit 5, the A model MA model y(k)+ as Y(k-1)+ at Y(k'
+-Scream” + (k-n)ny = b, u (k 1 ) + b, u (k z )
+ ,,・・,,,,・,+yu (k″1)...
. . . 1st formula % Formula % Identification is performed using known identification methods such as the least squares method and the maximum likelihood method. Next, the frequency characteristic calculating section 6 is a block that calculates the frequency characteristics of the process.

FIG. 2 details the calculation steps inside this frequency characteristic calculation section. In this figure.

The block 6-1 is a block that constitutes a transfer function in which eTS is substituted for the time transition operator 2 in the pulse transfer function 0, (Z) expressed using the coefficients determined by the ARMA model identification unit 5.

Continuing on, block 6-2 is a block that configures a correction transfer function Δ(s) for removing the influence of sidebands caused by u(k) being sampled and held. The last block 6-3 is a block that calculates 0AIN, PHA, and 9E by changing the angular frequency ω between the radial in and ωrrIIX based on the transfer function formed by the blocks 6-1 and 6-2.

The calculation performance of the frequency characteristic calculation unit 6 using the transfer function Δ(S) corrected to remove sidebands will be shown below.

First, Gp(Σ) in the fourth equation is the transfer function G(5
) is the pulse transfer function identified using the ARSIA model.

. . . Equation 4 FIG. 3 compares the calculation performance of the frequency characteristic calculation section 6. In the same figure, solid line A and curve A represent the fifth
These are the frequency characteristics of the gain (solid line) and phase (dotted line) of the transfer function of the equation, the solid line B and the dotted line B are the frequency characteristics of the pulse transfer function of the fourth equation, and the real @C and dotted line C are the frequency characteristics calculation This is the frequency characteristic calculated by section 6. It can be seen from the figure that the solid line C and the dotted line C match the solid line A and the real IA, respectively, from low frequencies to high frequencies.

〔Effect of the invention〕

As described in detail above, by using a transfer function that is corrected to remove the effect of the hold element from the identified ARM A model, accurate gain and phase characteristics can be calculated from low frequencies to high frequencies.

[Brief explanation of drawings]

Fig. 1 is a block diagram showing the structure of the transfer function measurement lid according to the present invention, Fig. 2 is a calculation block diagram of the most central frequency characteristic calculation section, and Fig. 3 is shown for comparison. It is a frequency characteristic diagram. 5... ARMA model identification section, 6... Frequency characteristic calculation section, 6-2... Correction transfer function block. Agent Patent Attorney Noriyuki Chika Yudo Kikuo Takehana Figure 1 Figure 2

Claims (1)

[Claims] A means for identifying an ARMA (autoregressive moving average) model of a process by inputting a controlled variable (output) and a manipulated variable (input) of a process at a constant sampling period, and an identified AR
Transfer function measurement characterized by comprising means for calculating the frequency characteristics of the gain and phase of the process transfer function from the coefficients of the MA model, the sampling period, and the correction transfer function that corrects to remove the sampling effect. Device.