FRF identification system, FRF identification method and ILC algorithm

Abstract

To provide an FRF identification system for identifying FRF that has solved a problem of significant FRF identification error in partial frequency bands where an input signal spectrum is small and the need for sufficient control design and adjustment in advance to perform highly accurate FRF identification.SOLUTION: An FRF identification system 1 for identifying FRF of an identification target system while repeating a predetermined positioning operation, includes: an FRF estimation algorithm 4 for estimating the FRF of the identification target system; and an ILC algorithm 5 having filters 6 and 7, and calculating feedforward control input by ILC (iterative learning control) aimed at reducing a deviation between a command and detection output, wherein the update of estimation FRF estimated by the FRF estimation algorithm 4 while repeating a predetermined operation and the update of the filters 6 and 7 used in the ILC calculation are performed.SELECTED DRAWING: Figure 1A

Description

[Technical Field]

[0001] The present invention relates to an FRF identification system, an FRF identification method, and an ILC algorithm. [Background technology]

[0002] Identifying an accurate frequency response function (FRF) for a controlled object (plant) is an important control design process for achieving high-speed, high-precision servos. For highly accurate FRF identification, due to the fundamental properties of frequency response analysis based on the discrete Fourier transform (DFT), a method of exciting the plant using disturbance signals such as sine waves is commonly used. However, if the plant is a resonant system, excitation tends to generate drive noise near the resonant mode frequency, and in many cases, disturbance signal excitation is not desirable from the perspective of factors such as the load on the drive mechanism.

[0003] Patent Document 1 describes a frequency response analysis system that calculates a difference value for a force-dimensional input of a plant via a first difference calculator, then calculates a frequency response via a first DFT calculation unit, calculates a difference value for a position-dimensional output of the plant via a second difference calculator, then calculates a frequency response via a second DFT calculation unit, and calculates the plant FRF from the frequency responses of the input and output in a multiplier / divider (see Figures 1C and 2B).This system can identify a desired FRF from a time signal during a specified positioning operation without using a separate disturbance signal for excitation, such as a sine wave. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2018-147149 Summary of the Invention [Problem to be solved by the invention]

[0005] The conventional technology in Patent Document 1 can identify FRFs simply by performing a predetermined operation, but has problems such as significant FRF identification errors occurring in partial frequency bands where the input signal spectrum is small, and the need for sufficient control design and adjustment in advance to perform highly accurate FRF identification. Therefore, the object of the present invention is to provide an FRF identification system that identifies FRFs and solves these problems. [Means for solving the problem]

[0006] The present invention, which solves the above problems, is as follows. (1) An FRF identification system that identifies the FRF of a system to be identified while repeatedly performing a predetermined positioning operation, characterized in that it has an FRF estimation algorithm that estimates the FRF of the system to be identified, and an ILC algorithm that calculates a feedforward control input using ILC (Iterative Learning Control) with the aim of reducing the deviation between a command and a detected output, and updates the estimated FRF estimated by the FRF estimation algorithm while repeating a predetermined operation, and updates the filter used in calculating the ILC. (2) The FRF identification system according to (1) is characterized in that the FRF estimation algorithm calculates an estimated FRF P[hat] and a function W representing the reliability of P[hat] from a DFT (Discrete Fourier Transform) of input and output signals during a predetermined operation. (3) In the FRF estimation algorithm, when new P[hat] and W are calculated, the learning filter L and stabilization filter Q that constitute the filter are updated, and ILC calculation is performed based on the updated L and Q. [Effects of the Invention]

[0007] According to the present invention, it is possible to reduce partial FRF identification errors and significantly reduce the effort and cost involved in advance control design and adjustment. [Brief explanation of the drawings]

[0008] [Figure 1A]1 is a diagram showing an example of the configuration of an FRF identification system according to one embodiment of the present invention. [Figure 1B] 1B is a diagram showing an example of the configuration of an FRF identification system in which the filters (L, Q) included in the ILC algorithm in FIG. 1A are shown. [Figure 1C] FIG. 1 is a diagram showing an example of the configuration of a conventional FRF identification system. [Figure 2A] FIG. 1 is a flowchart showing an FRF identification system according to one embodiment of the present invention. [Figure 2B] FIG. 1 shows a flowchart of a prior art FRF identification system. [Figure 3] FIG. 1 illustrates an FRF estimation algorithm. [Figure 4] FIG. 1 illustrates an ILC algorithm according to one embodiment of the present invention. [Figure 5] 1 is a diagram showing the time response waveforms of u and y in the FRF identification system 1. FIG. [Figure 6] FIG. 1 is a diagram showing the frequency characteristics of P[hat] in the FRF identification system 1. [Figure 7] FIG. 10 is a diagram showing the frequency characteristics of the identification error of P[hat] in the FRF identification system 1. [Figure 8] FIG. 10 is a diagram showing the frequency characteristics of the DFT U of u in the FRF identification system 1. [Figure 9] FIG. 2 is a diagram showing a method for calculating a function W that indicates the reliability of an estimated FRF, according to one embodiment of the present invention. [Figure 10] 1 is a diagram showing a method for updating a learning filter L according to one embodiment of the present invention. [Figure 11] FIG. 1 is a diagram showing a method for updating a stabilization filter Q according to one embodiment of the present invention. [Figure 12] FIG. 1 is a diagram showing the frequency characteristics of Y and W in the FRF identification system 1. [Figure 13] FIG. 10 is a diagram showing the frequency characteristics of L in the FRF identification system 1. [Figure 14] FIG. 2 is a diagram showing the frequency characteristics of Q in the FRF identification system 1. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, embodiments of the present invention will be described with reference to the drawings. The present invention is not limited to the following embodiments, and changes, modifications, and improvements can be made without departing from the scope of the invention.

[0010] As shown in FIG. 1A, an FRF identification system 1 according to one embodiment of the present invention includes an FRF estimation algorithm 4 that estimates the FRF of a system to be identified (controlled object 3), and an ILC algorithm 5 that includes filters L6 (learning filter) and Q7 (stabilization filter) (see FIG. 1B) described below and calculates a control input for ILC (iterative learning control) aimed at reducing the deviation between a command r corresponding to a predetermined operation and a detected output, and the command r is input to the controlled object 3 via a feedback controller 2.

[0011] FIG. 1B shows the FRF identification system 1 including the learning filter L6, stabilization filter Q7, and memories 8 and 8' that constitute the filters of the ILC algorithm 5.

[0012] As shown in the flowchart of FIG. 2A, the FRF identification system 1 operates. The FRF identification system 1 starts operation (S101) and first initializes the number of positioning operations i (i=1, S102). Next, the servo device performs a predetermined positioning operation based on the ILC (S103), and determines whether i is equal to 1 (S104). If i is equal to 1, the estimated FRF P[hat](ω k ) and its reliability function W(ω k ) is calculated (S105). Then, it is determined whether the FRF identification termination condition is satisfied (S106). If the FRF identification termination condition is satisfied, the operation is terminated (S111). On the other hand, if i is not equal to 1, it is determined whether the ILC termination condition is satisfied (S108). If the ILC termination condition is satisfied, the process proceeds to S105.

[0013] If the FRF identification termination condition is not satisfied in S106, the learning filter L and the stabilization filter Q are updated (S107). Then, the feedforward control input is updated (S109), and i is incremented (S110). Then, the process proceeds to S103. If the ILC termination condition is not satisfied in S108, the process proceeds to S109.

[0014] That is, FRF identification system 1 combines an FRF identification method using positioning input / output signals (prior art, Patent Document 1) with iterative learning control (ILC), and is capable of highly accurate FRF identification even in situations where there is a lot of uncertainty in the plant FRF and sufficient control design and adjustment has not been performed.Furthermore, FRF identification system 1 can identify the plant FRF while repeating a predetermined positioning operation in a servo device, as an FRF identification method that does not require disturbance signal excitation.

[0015] In contrast, the conventional FRF identification system operates as shown in the flowchart of Fig. 2B. The FRF identification system starts its operation (S201), performs a positioning operation only once (S202), and calculates the estimated FRF P[hat](ω k ) is calculated (S203), and the process ends (S204).

[0016] (FRF estimation algorithm) In the FRF estimation algorithm shown in Figure 3, the symbols are as follows: (t): Input signal for the i-th positioning iteration (t={0, 1, …, N-1}), y <1> (t): Output signal for the i-th positioning iteration (t={0, 1, …, N-1}), u f (t):u (t) to F DIF The time signal (t={0,1,…,N-1}) obtained by passing through f (t):y (t) to F DIF The time signal (t={0,1,…,N-1}) obtained by passing through U f (k):u f DFT of (t)(k={1,2,…,N}), Y f (k):y f DFT of (t) (k={1,2,…,N}), N: data length of input / output signal, ω k : Discrete frequency ω corresponding to DFT index k k =2πk / NT S , F DIF : A pre-filter, the differencer (F DIF (z)=1-z -1 )), T s :Sampling period.

[0017] In addition to the FRF estimation algorithm shown in FIG. 3, the following embodiment may be used: The pre-filter may be a filter having a characteristic of cutting off low frequencies, other than a differentiator. 、y However, if there is no frequency leakage due to DFT, it is not necessary to use a pre-filter. 、y To reduce FRF estimation errors due to noise and transient response components in the P[hat] calculation formula, known FRF smoothing processes may be used. For example, the Spectral Analysis method, LPM method, and LRM method (Reference 1: J. Schoukens et al., "Nonparametric Data-Driven Modeling of Linear Systems," IEEE Control System Magazine, August, pp. 49-88, 2018.). In addition, signals other than input and output signals (e.g., r and u in the P identification problem) may be used. F ) may also be used to calculate P[hat]. [Example]

[0018] (Control object) As an example of a precision servo device to which the present invention is applied, a galvano scanner is used as a control target, and a motor torque current command u is input to the galvano scanner, and a motor angular displacement y is calculated. o The s-domain transfer function up to is defined by Equation (1).

[0019]

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[0020] (Positioning control system) The block diagram of the positioning control system used for FRF identification is shown in Figure 1B(1A). In Figure 1B, P is the plant represented by equation (1), C is the feedback controller, r is the displacement command, and y :Encoder(quantization width q m =1.46×10 -6 rad), v : noise due to quantization, etc., u : control input, u F : Feedforward control input, e : Control deviation. The index i={1,2,…} in the superscript symbol <·> represents the number of positionings. When i=1, the feedforward control input by the ILC is u F <1> = 0, which is the equivalent condition to FRF identification by conventional technology. r is the predetermined stroke of 6.579 × 10 -3 rad and a command of 1.2 ms arrival time is given. Assuming that the true plant FRF is unknown, feedback controller C is designed to have a low gain, prioritizing stability. u calculated by positioning simulation <1> , y <1> The time response waveforms of are shown by the solid lines in Figures 5(a) and (b). It can be seen that when i=1, the response to the command r is slow. In this way, the present invention achieves highly accurate identification of the plant FRF even in situations where sufficient control design and tuning has not been performed.

[0021] (Challenges in FRF identification) In order to identify the FRF while suppressing leakage errors in DFT from the input and output signals during point-to-point positioning operation, we use the method described in Reference 2 (Tanaka et al.: "Plant Frequency Response Function Estimation Method Considering the Effect of Quantization of Position Detection Values", Institute of Electrical Engineers of Japan, Mechatronics Control Research Meeting, MEC-20-037, pp. 87-92, 2020). This method is based on the ETFE method (1) and uses a sampling period of T s = 20 μs, data length N = 1000, discrete-time signal u 、y The FRF P[hat] is estimated using the following formula: (ω k ) is obtained.

[0022]

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[0023] Figure 5(a) and (b) solid line u <1> , y <1> P[hat] estimated based on equation (2) <1> (ω k ) is shown by the dashed line in Figure 6, and the FRF identification error (P[hat] <1> (ω k )―P(ω k )) / P(ω k ) in Figure 7 (solid line (P[hat] <1> ) P[hat] <1> (ω k ) is the true FRF P(ω) shown by the solid line in the frequency domain up to about 1 kHz. k ) can be identified with high accuracy, but in the higher frequency ranges there are some identification errors that make it difficult to distinguish the vibration modes. This phenomenon is caused by the noise v (Reference 2: Tanaka et al., "Plant Frequency Response Function Estimation Method Considering the Effect of Quantization of Position Detection Values," Institute of Electrical Engineers of Japan, Mechatronics Control Research Meeting, MEC-20-037, pp. 87-92, 2020). In the FRF calculation formula (2), v is calculated as in formula (3). DFT V The effect of (k) is DFT U This is because (k) becomes apparent in small frequency bands.

[0024]

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[0025] The solid line in Figure 5(a) indicates <1> DFT U <1> The gain characteristic of (k) is shown by the solid line in Figure 8. <1> It can be seen that the frequencies where (k) is small coincide with the frequency bands where significant identification errors occur in Figures 6 and 7. To address such identification errors, a method is known that utilizes the smoothness of the FRF to interpolate the FRF for that frequency band (References 1 and 2), but accurate interpolation becomes difficult when there is error over a wide frequency band, as in this case. Therefore, to perform highly accurate FRF identification using positioning input / output signals, an FRF identification method is required that can suppress identification errors at partial frequencies where the input signal spectrum becomes small.

[0026] (FRF identification method based on iterative positioning operations) In the FRF identification method according to one embodiment of the present invention, a predetermined positioning operation is repeated based on the ILC, and the u obtained by the ILC is first 、y Using P[hat](ω k ) is estimated. Then, P[hat](ω k ), it is characterized by highly accurate FRF identification even in a state where sufficient control design and tuning has not been performed. The area 9 enclosed by the dashed line in Figure 1B is where FRF identification is performed. The identification algorithm consists of the following three steps.

[0027] (Step 1) Positioning operation based on ILC) As shown in Figure 1A, a given positioning operation is repeatedly performed using a control system that generates feedforward control inputs using an ILC. During this process, the ILC calculates the feedforward control input for the next positioning operation according to the update rule in equation (4-1) (Reference 3: D.A. Bristow et al., "A survey of iterative learning control," IEEE Contr. Syst. Mag., June, pp. 96-114, 2006).

[0028]

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[0029] In equation (4-1), L is the learning filter, Q is the stabilization filter, and e : is the control deviation, and u F <1> = 0. The calculation of equation (4-1) is performed in the frequency domain as in equation (4-2), and the calculation result is subjected to an inverse discrete Fourier transform to obtain u F <i+1> In equation (4-2), F D -1 [X]: Inverse Discrete Fourier Transform (IDFT) of complex vector X, U F (k):u F DFT of (t), E (k):e (t) DFT, L(ω k ): Discrete-time Fourier transform (DTFT) of the training filter, Q(ω k ): The DTFT of the stabilized filter. e To obtain high convergence of k ) and the DTFT C(ω k ) and have the following characteristics (Reference 3):

[0030]

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[0031] On the other hand, Q is a filter that is designed taking into consideration the stability of the ILC. To make the ILC function over a wide frequency band, ideally Q(ω k )=1.

[0032] In this specification, L and Q are updated by Step 2 and Step 3 described later every H times the ILC performs iterative learning. The gain of (k) is increased over a wide frequency range.

[0033] (Step 2) FRF estimation) In Step 1, when the timing of ILC repetition H times is expressed as j={H, 2H, . . .}, the time signal u at i=j is 、y Based on equation (2), P[hat](ω k ) is calculated. On the other hand, the quantization noise v <j>< / j> The frequency Ω at which the effect of r is defined as follows (Reference 2):

[0034]

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[0035] Ω r P[hat](ω k ) is a function W(ω k ) is calculated as follows (see FIG. 9):

[0036]

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[0037] (Step 3) Update L and Q) In order to perform high-performance ILC using equation (5) in as wide a frequency range as possible, we return to Step 1 and perform positioning operation before calculating P[hat](ω k ), W(ω k ) to update L and Q as in equations (8-1) and (9) (see Figures 10 and 11).

[0038]

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[0039]

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[0040] Also, before the update, <i-h>< / i-h> A new candidate for L L may be updated by weighting (0≦α≦1) and averaging. In that case, equation (8-2) is applied.

[0041] As a termination condition of this algorithm, for example, when the estimated FRF is updated M times, the above Steps 1 to 3 are repeated until i=MH, and finally, the P[hat](ω k ) is the identified FRF.

[0042] (Simulation evaluation of FRF identification method) The FRF P[hat](ω k ) is shown in Figure 6 with a dashed line (P[hat] <3> ) In this FRF identification algorithm, the initial L and Q are <0> is a non-model-based low-gain filter that takes into account the stability of the ILC (Reference 3), and Q <0> gave a low-pass filter with a very low cutoff frequency of 2π×100 rad / s. When i=1, which is equivalent to the case where FRF identification is performed using the conventional technology (Patent Document 1) as a comparative example, the estimated FRF P[hat] <1> (ω k ) has a clear identification error above about 1 kHz. In contrast, the estimated FRF P[hat] at i=3 <3> (ω k ) significantly reduces the identification error after about 1 kHz, and the true FRF P(ω k ) can be identified up to the high frequency range. Looking at the FRF identification error shown in Figure 7, the dotted line (P[hat] <3> The FRF identified by the inventive technology shown by the solid line (P[hat] <1> The identification error is reduced over a wider frequency range than that of the conventional technology shown in Fig. 5. The input / output signal u when i = 3 is shown by the solid line in Fig. 5. <3> , y <3> Focusing on u <1> , y <1> This is why the U shown by the dotted line in Fig. 8 is a response that is more rapid than <3> The gain of (k) increases over a wide frequency band, which confirms that it contributes to reducing identification errors caused by noise.

[0043] Fig. 12(a) shows the difference value y f DFT of Y f (ω k ), and Fig. 12(b) shows the function W (ω k ) is the frequency characteristic of Y f The threshold XE [hat] is shown by the horizontal dashed line. q The estimated FRF P[hat] at frequencies above (ω k ) is judged to have high reliability, and W (ω k )=1. At this time, X=5, E[hat] q =q m T s It is given as √(N / 6).

[0044] Figures 13 and 14 show the filter L updated by the i-th positioning operation. 、Q It can be seen that both filters are updated based on equations (8-1) and (9) each time positioning is repeated.

[0045] In this paper, we invent a plant FRF identification method based on iterative positioning operations that combines an FRF identification method using positioning input / output signals (prior art, Patent Document 1) with ILC (Reference Document 3), and verify its effectiveness through simulation. [Industrial Applicability]

[0046] The present invention can be used to automate and streamline control design at manufacturers that handle servo technology for industrial robots, machine tools, and the like. [Explanation of symbols]

[0047] 1: FRF Identification System (Example 1) 2: Feedback controller 3: Control target 4: FRF estimation algorithm 5: ILC algorithm 6: Learning filter 7: Stabilization filter 8, 8´: Memory 9: Location where FRF identification is performed

Claims

1. 1. An FRF identification system that identifies the FRF of a system to be identified while repeatedly performing a predetermined positioning operation, the system includes an FRF estimation algorithm that estimates the FRF of the system to be identified, and an ILC algorithm that has a filter and calculates a feedforward control input by ILC (iterative learning control) aimed at reducing the deviation between a command and a detection output, the FRF identification system updating an estimated FRF estimated by the FRF estimation algorithm while repeating a predetermined operation and updating the filter used in calculating the ILC, wherein the FRF estimation algorithm calculates an estimated FRF P[hat] and a function W representing the reliability of P[hat] from input / output signals during the predetermined operation, and when new P[hat] and W are calculated in the FRF estimation algorithm, a learning filter L and a stabilization filter Q that constitute the filter are updated, and an ILC calculation is performed based on the updated L and Q.

2. An FRF identification system as described in claim 1, wherein the input / output signals are DFT (Discrete Fourier Transform).

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