JP2021135860A - Frequency characteristic estimation device and frequency characteristic estimation method - Google Patents

Abstract

To provide a frequency characteristic estimation device and a frequency characteristic estimation method that are able to estimate a frequency characteristic of a control object in a short time and at a low cost.SOLUTION: A frequency characteristic estimation device 1 includes: an open loop data acquisition unit 211 that acquires at least one pair of input and output responses obtained by input of a predetermined input signal to a control target; and an arithmetic unit 212 that generates input and output signals for the control target relative to a plurality of sinusoidal signals on the basis of an estimated value generation filter for inputting a prescribed input signal and outputting a sinusoidal signal and on the basis of the control target. Further, the arithmetic unit 212 sets a sinusoidal signal, output from the estimated value generation filter, to a predetermined frequency; generates a first output signal obtained by input of input signals of the input and output responses acquired by the open loop data acquisition unit 211, to the estimated value generation filter; generates a second output signal obtained by input of output signals of the input and output responses to the estimated value generation filter; and generates the input and output signals for the control target on the basis of the first output signal and the second output signal.SELECTED DRAWING: Figure 1

Description

The present invention relates to a frequency characteristic estimation device and a frequency characteristic estimation method.

In order to set the structural parameters of the controller and design a control system with good performance, it is necessary to understand the response characteristics of the controlled object. In particular, in order to improve stability and response characteristics, it is necessary to understand the frequency characteristics of the controlled object. The frequency characteristics of the controlled object are estimated by inputting signals of various frequencies to the controlled object and measuring the output signal and the input signal. Further, in order to make it easier to understand the frequency characteristics of the controlled object, a Bode diagram is created from the estimated frequency characteristics (for example, Patent Document 1).

Japanese Unexamined Patent Publication No. 2006-10596

In Patent Document 1, sinusoidal signals of various frequencies are input to a closed loop circuit, frequency characteristics are estimated from the relationship between the output signal and the input signal, and a Bode diagram is created.

In order to accurately estimate the frequency characteristics of the controlled object, it is necessary to perform an input / output response acquisition experiment for sinusoidal signals of various frequencies, so that the time and cost required for identification increase.

The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a frequency characteristic estimation device and a frequency characteristic estimation method capable of estimating the frequency characteristics of a controlled object in a short time and at low cost. ..

In order to achieve the above object, the frequency characteristic estimation device according to the first aspect of the present invention is
An open-loop data acquisition unit that acquires at least one set of input / output responses obtained by inputting a predetermined input signal to the control target, and
An estimation value generation filter that inputs the predetermined input signal and outputs a sine wave signal, and a calculation unit that generates an input / output signal of the control target for a plurality of sine wave signals of different frequencies based on the control target. And with
The calculation unit
The sine wave signal output by the estimated value generation filter is set to a predetermined frequency, and the frequency is set.
The input signal of the input / output response acquired by the open loop data acquisition unit is input to the estimated value generation filter to generate a first output signal.
The output signal of the control target acquired by the open-loop data acquisition unit is input to the estimated value generation filter to generate a second output signal.
The input / output signal to be controlled is generated based on the first output signal and the second output signal.

In addition, the predetermined input signal is
Step input or impulse input,
It may be that.

In the frequency characteristic estimation method according to the second aspect of the present invention,
An open-loop data acquisition process that acquires at least one set of input / output responses obtained by inputting a predetermined input signal to the control target, and
Data generation that generates input / output signals of the control target for a plurality of different frequency sine wave signals based on the estimation value generation filter that inputs the predetermined input signal and outputs the sine wave signal and the control target. Including the process
In the data generation step,
The sine wave signal output by the estimated value generation filter is set to a predetermined frequency, and the frequency is set.
The input signal of the input / output response acquired in the open loop data acquisition step is input to the estimated value generation filter to generate a first output signal.
The output signal of the controlled object acquired in the open-loop data acquisition step is input to the estimated value generation filter to generate a second output signal.
The input / output signal to be controlled is generated based on the first output signal and the second output signal.

In addition, the predetermined input signal is
Step input or impulse input,
It may be that.

According to the frequency characteristic estimation device and the frequency characteristic estimation method of the present invention, a plurality of frequency responses can be generated based on at least one set of input / output responses, so that the frequency characteristics to be controlled can be controlled in a short time and at low cost. Can be estimated.

It is a block diagram of the frequency characteristic estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the flow of frequency characteristic estimation which concerns on embodiment. It is a block diagram which shows an example of open loop data. It is a figure which shows the transmission characteristic when a control object and an estimate value generation filter are connected, (A) is a block diagram when the output of an estimate value generation filter is input to a control object, (B) is a control object. It is a block diagram when the output of is input to the estimation value generation filter. It is a graph which shows the example of the step response which is open-loop data. It is a Bode diagram which shows the example of the estimated frequency characteristic.

Hereinafter, the frequency characteristic estimation device 1 according to the embodiment of the present invention will be described with reference to the drawings.

The frequency characteristic estimation device 1 is, for example, a computer device, and includes a control unit 21, a storage unit 22, a display unit 23, and an input unit 24, as shown in the block diagram of FIG.

The control unit 21 is composed of a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), a crystal oscillator, and the like, and controls the operation of the frequency characteristic estimation device 1 and acquires it from the outside. The frequency characteristic of the control target 52 is estimated based on the input / output response of the control target 52. The control unit 21 realizes each function of the control unit 21 shown in FIG. 1 by reading various operation programs and data stored in the ROM of the control unit 21, the storage unit 22, etc. into the RAM and operating the CPU. .. As a result, the control unit 21 operates as the open loop data acquisition unit 211, the calculation unit 212, and the board diagram creation unit 213.

As shown in FIG. 1, the open-loop data acquisition unit 211 is selectively connected to the control system 30 including the control target 52, the external storage device 31, the database 32 via the network, and the like via the input / output interface. The open loop data of the control target 52 is acquired. The acquired open-loop data is input / output response data when a predetermined input signal is input to the control target 52. The predetermined input signal input to the control target 52 is a step input, an impulse input, or the like.

The calculation unit 212 generates frequency responses of a plurality of frequencies based on the open-loop data acquired by the open-loop data acquisition unit 211 and the estimated value generation filter 51. The estimated value generation filter 51 is a filter having a characteristic of inputting an input signal used in open-loop data and outputting a sine wave signal. The detailed configuration of the estimated value generation filter 51 will be described later.

The Bode diagram creation unit 213 creates a Bode diagram representing the frequency characteristics of the control target 52 based on the frequency response generated by the calculation unit 212.

The storage unit 22 is a non-volatile memory such as a hard disk or a flash memory, and stores an estimated value generation filter 51 corresponding to an input signal of open loop data, a generated frequency response, a Bode diagram, and the like.

The display unit 23 is a display device provided in the frequency characteristic estimation device 1 which is a computer device, and is, for example, a liquid crystal panel. The display unit 23 displays the open loop data acquired by the open loop data acquisition unit 211, the board diagram created by the board diagram creation unit 213, and the like.

The input unit 24 is an input device for inputting an open-loop data acquisition instruction, a set frequency for calculating a frequency response, and the like. The input unit 24 is a keyboard, mouse, or the like provided in the frequency characteristic estimation device 1.

Subsequently, the frequency characteristic estimation method using the frequency characteristic estimation device 1 will be specifically described with reference to the flowchart of FIG. In the present embodiment, a case where the step response of the control object 52 acquired in advance as open loop data is acquired from the external storage device 31 and the frequency characteristic of the control object 52 is estimated will be described as an example.

As shown in FIG. 2, as an open-loop data acquisition step, input / output data related to the step response of the control target 52 is acquired (step S11). As shown in FIG. 3, the open-loop data acquired in this step S11 _{gives an input U 0 (s) which is a step input to the actual control target 52, and outputs Y 0} (s) from the control target 52. Input / output data obtained by measurement. The step input according to the present embodiment is a unit step input.

Further, the open loop data according to the present embodiment is acquired in advance as experimental data and stored in the external storage device 31, and the open loop data acquisition unit 211 is connected to the external storage device 31 to store the open loop data. By reading, open loop data is acquired.

Subsequently, as a data generation step, input / output data of the control target 52 for a sine wave signal having a plurality of frequencies is generated based on the open loop data acquired in step S11.

Here, a method of generating a frequency response in the data generation step will be described. As shown in FIG. 4A, the system 50 includes a control target 52, which is a target for estimating frequency characteristics, and an estimated value generation filter 51. The estimated value generation filter 51 is defined as a filter having a transmission characteristic of inputting a predetermined input signal which is an input signal of open loop data and outputting a sine wave signal.

As shown in the following equation, the estimated value generation filter 51 according to the present embodiment has a transmission characteristic X (s) of inputting a unit step signal and outputting a sine wave signal.
X (s) = ωs / (s ² + ω ² ) ・ ・ ・ (1)

FIG. 4A is a block diagram of the system 50 in which the control target 52 is connected to the output side of the estimated value generation filter 51, and FIG. 4B is a control target 52 connected to the input side of the estimated value generation filter 51. It is a block diagram of the system 50'to which the above is connected. Since the overall transmission characteristics of the above two block diagrams are equivalent, the same signal is output for the same signal input.

The frequency response to be generated in the data generation step is the relationship between the input U (s) and the output Y (s) of the control target 52 shown in FIG. 4 (A). That is, the frequency response of the controlled object 52 is generated by giving sinusoidal signals of various frequencies as the input U (s) and generating the output Y (s) for them.

Specifically, since the transmission characteristics of the estimated value generation filter 51 are as shown in Equation (1), the input U ₀ (s), which is a unit step input, is adjusted by adjusting the frequency characteristic parameter ω of the estimated value generation filter 51. ), Sine wave signals of various frequencies can be generated and input to the control target 52.

Further, since the transmission characteristics of the system 50 of FIG. 4 (A) and the system 50'of FIG. 4 (B) are equivalent, the transmission characteristics of the estimated value generation filter 51 of FIG. 4 (A) and FIG. 4 (B) If the transmission characteristics of the estimated value generation filter 51 are equivalent, the outputs Y (s) of the systems 50 and 50'for the _{equivalent inputs U 0 (s) are equivalent.}

Since the input / output relationship of the control target 52 in the system 50'in FIG. 4B can be replaced with the open loop data acquired in step S11, an estimated value generation filter in which the frequency characteristic parameter ω is set to a predetermined frequency. _{By inputting the output Y 0} (s) of the acquired open loop data to 51, the output Y (s) can be calculated offline.

Since the calculated output Y (s) is equivalent to the output Y (s) of the system 50 of FIG. 4 (A) as described above, the calculated output Y (s) is the U (s) that can be calculated as the output of the estimated value generation filter 51. , The input / output data of the control target 52, that is, the frequency response can be obtained from the calculated relationship with Y (s). As described above, based on the open loop data acquired as experimental data and the characteristics of the estimated value generation filter 51, the frequency response of the controlled object 52 at various frequencies is generated by the offline frequency characteristic estimation device 1. The frequency characteristics of the controlled object 52 can be estimated.

Returning to the flowchart of FIG. 2, in the data generation step, first, the transmission characteristic of the estimated value generation filter 51 is determined (step S12). The estimated value generation filter 51 outputs a sine wave signal from the unit step input, and has the transmission characteristic of the equation (1).

As shown in the equation (1) and FIG. 4 (A), the estimated value generation filter 51 has a transmission characteristic of canceling a predetermined input signal (unit step signal) in the open loop data and generating a sinusoidal signal. .. When a predetermined input signal is not set in advance, the estimated value generation filter stored in the storage unit 22 is used as the estimated value generation filter 51 corresponding to the input signal of the open loop data acquired by the open loop data acquisition unit 211. 51 may be read and used by the calculation unit 212.

For example, when the input signal of the open loop data acquired by the open loop data acquisition unit 211 is a unit impulse signal, the calculation unit 212 stores an estimated value corresponding to the impulse input stored in the storage unit 22 in advance. The generation filter 51 is read and used. The transmission characteristic of the estimated value generation filter 51 in this case is X (s) = ω / (s ² + ω ² ).

Subsequently, in step S13, the frequency characteristics of the estimated value generation filter 51 are set. Specifically, the frequency characteristic parameter ω of the equation (1) for determining the frequency of the sine wave output from the estimated value generation filter 51 is set to a predetermined value, for example, 0.01 rad / sec.

_{The input U 0} (s) of the open loop data acquired in step S11 is input to the estimated value generation filter 51 in which the frequency characteristic parameter ω is set, and the first output signal ^ U (s) is generated (step S14). ). Since the transmission characteristic of the estimated value generation filter 51 is set to output a sine wave signal from the step input, the first output signal ^ U (s) becomes a sine wave signal.

_{Further, the output Y 0} (s) of the open loop data acquired in step S11 is input to the estimated value generation filter 51 in which the frequency characteristic parameter ω is set, and the second output signal ^ Y (s) is calculated ( Step S15).

As shown in FIGS. 4A and 4B, the first output signal ^ U (s) of the system 50 and the second output signal ^ Y (s) of the system 50'calculated in steps S14 and S15 are It corresponds to the input and output of the control target 52. The calculation unit 212 generates a frequency response from the relationship between the first output signal ^ U (s) and the second output signal ^ Y (s) corresponding to the input / output signals of the control target 52, and generates a frequency response of the control target 52. The gain and phase are calculated and stored in the storage unit 22 (step S16).

Hereinafter, the generation of the frequency response of the control target 52 is repeated, and the data necessary for grasping the frequency characteristics of the control target 52 is acquired. More specifically, until the frequency characteristic parameter ω of the estimated value generation filter 51 reaches a preset upper limit value, for example, 100 rad / sec (NO in step S17), a predetermined step size, for example, ω is 10 ⁿ ≤ ω. In the case of <10 ^{n + 1} [rad / s] (n: integer), ω is ^{increased by 10 n} [rad / s] (step S18), and steps S14 to S16 are repeated.

When the frequency characteristic parameter ω of the estimated value generation filter 51 reaches a preset upper limit value, for example, 100 rad / sec (YES in step S17), sufficient data is acquired to grasp the frequency characteristic of the controlled object 52. It is judged that the frequency response has been generated, the generation of the frequency response is finished, and the process proceeds to the next process.

The Bode diagram creation unit 213 reads the gain and phase calculated at each frequency from the storage unit 22 and creates a Bode diagram (step S19). Further, the board diagram creating unit 213 displays the created board diagram on the display unit 23 and stores the created board diagram in the storage unit 22, and the frequency characteristic estimation process is completed.

As described above, according to the frequency characteristic estimation device and the frequency characteristic estimation method according to the present embodiment, the offline frequency characteristic estimation device 1 has various characteristics based on the open loop data which is a set of input / output responses. Since the frequency response at the frequency can be generated and the frequency characteristic of the control target 52 can be estimated, the frequency characteristic of the control target 52 can be estimated in a short time and at low cost.

Further, in the frequency characteristic estimation method according to the present embodiment, various frequency responses are generated by numerical calculation based on a set of input / output responses to estimate the frequency characteristics. Therefore, the transfer characteristics of the control target 52, That is, even if the order of the transfer function is unknown, it is possible to easily create a Bode diagram and estimate the frequency characteristics.

In the present embodiment, the open-loop data is a set of input / output responses, but the present invention is not limited to this, and the frequency characteristics may be estimated based on two or more sets of input / output responses. In this case, the frequency characteristic estimation device 1 may estimate the frequency characteristics of the control target 52 for each set of input / output responses, and display them side by side on the display unit 23. Further, the calculation unit 212 may estimate the average value of the estimated frequency characteristics as the frequency characteristics of the control target 52.

Further, the transmission characteristic of the estimated value generation filter 51 according to the present embodiment is set to X (s) = ωs / (s ² + ω ² ), but the present invention is not limited to this, and any characteristic that can generate a frequency response is used. good. ^{For example, X (s) = s 2} / (s ² + ω ² ), which is a transmission characteristic representing a cosine function, may be set.

Hereinafter, a numerical example in the case of estimation using the frequency characteristic estimation method according to the present embodiment will be described. In this example, the transfer characteristic G (s) of the control target 52 is estimated by computer simulation as the transfer characteristic represented by the following transfer function.

また、サンプリング周波数Ｔ_ｓは０．０１秒とした。

The sampling frequency T _s was set to 0.01 seconds.

_{The input U 0} (t) and the output Y ₀ (t), which are open-loop data when the unit step input U ₀ (s) is input to the control target 52, are as shown in FIG. Further, the method of the present invention, by changing the frequency characteristic parameter ω estimate generating filter 51 from 10 ^-2 rad / sec up to 10 ² rad / sec, the Bode diagram created based on the generated frequency response It is shown in FIG. FIG. 6 also shows a Bode diagram of the control target 52 created on a computer for comparison.

As shown in FIG. 6, the gain characteristic is in the range of 30 rad / sec or less and the phase characteristic is in the range of 20 rad / sec or less, which is in good agreement with the result of the computer simulation (gain characteristic ± 10 dB or less, phase characteristic ± 10 deg or less). It can be seen that good estimation results have been obtained.

According to the present invention, even in a system that is difficult to identify, that is, a non-minimum phase system, an oscillating system having two resonance peaks, and a relative order of 3, as in the above numerical example. It is possible to easily estimate the frequency characteristics.

The present invention is suitable for estimating the frequency characteristics of a control system whose structure to be controlled is unknown. In particular, it is suitable for process control systems in which it takes time to acquire input / output responses and it is difficult to acquire operation data.

1 Frequency characteristic estimation device, 21 control unit, 211 open loop data acquisition unit, 212 calculation unit, 213 board diagram creation unit, 22 storage unit, 23 display unit, 24 input unit, 30 control system, 31 external storage device, 32 Database, 50, 50'system, 51 estimate generation filter, 52 controlled object

Claims (4)

An open-loop data acquisition unit that acquires at least one set of input / output responses obtained by inputting a predetermined input signal to the control target, and
An estimation value generation filter that inputs the predetermined input signal and outputs a sine wave signal, and a calculation unit that generates an input / output signal of the control target for a plurality of sine wave signals of different frequencies based on the control target. And with
The calculation unit
The sine wave signal output by the estimated value generation filter is set to a predetermined frequency, and the frequency is set.
The input signal of the input / output response acquired by the open loop data acquisition unit is input to the estimated value generation filter to generate a first output signal.
The output signal of the control target acquired by the open-loop data acquisition unit is input to the estimated value generation filter to generate a second output signal.
An input / output signal to be controlled is generated based on the first output signal and the second output signal.
Frequency characteristic estimator. The predetermined input signal is
Step input or impulse input,
The frequency characteristic estimation device according to claim 1. An open-loop data acquisition process that acquires at least one set of input / output responses obtained by inputting a predetermined input signal to the control target, and
Data generation that generates input / output signals of the control target for a plurality of different frequency sine wave signals based on the estimation value generation filter that inputs the predetermined input signal and outputs the sine wave signal and the control target. Including the process
In the data generation step,
The sine wave signal output by the estimated value generation filter is set to a predetermined frequency, and the frequency is set.
The input signal of the input / output response acquired in the open loop data acquisition step is input to the estimated value generation filter to generate a first output signal.
The output signal of the controlled object acquired in the open-loop data acquisition step is input to the estimated value generation filter to generate a second output signal.
An input / output signal to be controlled is generated based on the first output signal and the second output signal.
Frequency characteristic estimation method. The predetermined input signal is
Step input or impulse input,
The frequency characteristic estimation method according to claim 3.

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