Frequency response function identification system

Abstract

A frequency response function identification system 1 comprises an observer 14 for generating an estimated effective torque u^e on the basis of a torque command value ur and a motor angular displacement θM, and an identifying unit 15 for identifying a frequency response function on the basis of the estimated effective torque u^e and the motor angular displacement θM, wherein: the observer 14 comprises an estimating unit 41 for estimating an estimated motor torque u^ from the torque command value ur, a static friction model 42 for outputting an estimated static frictional force τ^f on the basis of the motor angular displacement θM, and a calculating unit 43 for calculating the estimated effective torque u^e on the basis of the estimated motor torque u^ and the estimated static frictional force τ^f; and the identifying unit 15 uses local frequency modeling to identify the frequency response function from the estimated effective torque u^e and the motor angular displacement θM.

Description

[Technical Field]

[0001] This disclosure relates to a frequency response function identification system. [Background technology]

[0002] Systems for identifying the frequency response functions of plants and the like are known. For example, Patent Document 1 describes a servo analyzer that outputs a broadband signal to the system under test and determines the transfer function (frequency response function) by performing a discrete Fourier transform on the broadband signal and the output signal from another point on the system under test. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 8-94690 [Overview of the project] [Problems that the invention aims to solve]

[0004] In systems such as plants, the effective torque driving the linear elements of the system can fluctuate due to friction occurring within the system. However, the servo analyzer described in Patent Document 1 does not take into account the effects of friction within the system. Therefore, there is a risk that the identification error of the frequency response function will be large.

[0005] This disclosure describes a frequency response function identification system that facilitates the construction of a frequency response function identification system while improving the accuracy of frequency response function identification. [Means for solving the problem]

[0006] A frequency response function identification system relating to one aspect of this disclosure is a system that identifies the frequency response function of an object for analysis from state values ​​obtained when a driving force corresponding to a control value is input to the object for analysis. This frequency response function identification system comprises: a generation unit that generates a pre-processing control value according to the difference between a command value and a state value; an adder that generates a control value by adding an excitation value to the pre-processing control value; an observer that generates an estimated effective driving force, which is an estimated value of the effective driving force obtained by subtracting the static friction force that occurs when the object for analysis is operating from the driving force, based on the control value and the state value; and an identification unit that identifies the frequency response function based on the estimated effective driving force and the state value. The observer comprises: an estimation unit that estimates the estimated driving force, which is an estimated value of the driving force, from the control value; a static friction model that defines the relationship between velocity and static friction force and outputs an estimated static friction force, which is an estimated value of the static friction force, based on the state value; and a calculation unit that calculates the estimated effective driving force based on the estimated driving force and the estimated static friction force. The identification unit uses local frequency modeling to identify the frequency response function from the estimated effective driving force and state values.

[0007] In this frequency response function identification system, the estimated driving force is estimated from the control value, the estimated static friction force is output based on the state value, and the estimated effective driving force is calculated based on the estimated driving force and the estimated static friction force. Then, the frequency response function is identified based on the estimated effective driving force and the state value. Therefore, since the frequency response function is identified considering static friction force, the processing load can be reduced compared to cases where both static and dynamic friction forces are considered. A static friction model is used to estimate the estimated static friction force. Since the static friction model is a model for estimating static friction force, it can be constructed more easily than a model that estimates both dynamic and static friction forces. Static friction is friction that occurs while the object being analyzed is moving, so when identifying the frequency response function in a section where static friction occurs, the position and velocity differ at the start and end points of this section. For this reason, leakage errors may occur in the discrete Fourier transform of the state value, but by adding the excitation value to the pre-processing control value and using the local frequency modeling method, the frequency response function and leakage errors can be separated. As a result, it becomes possible to improve the accuracy of frequency response function identification while facilitating the construction of a frequency response function identification system. [Effects of the Invention]

[0008] According to this disclosure, it is possible to improve the accuracy of frequency response function identification while facilitating the construction of a frequency response function identification system. [Brief explanation of the drawing]

[0009] [Figure 1] Figure 1 is a block diagram showing the configuration of a frequency response function identification system according to one embodiment. [Figure 2] Figure 2 shows an example of the velocity characteristics of a static friction model. [Figure 3] Figure 3 is a diagram illustrating the time interval over which static friction occurs. [Figure 4]Figure 4(a) shows an example of the gain characteristics of the frequency response function of the plant shown in Figure 1. Figure 4(b) shows an example of the phase characteristics of the frequency response function of the plant shown in Figure 1. [Figure 5] Figure 5(a) shows the gain characteristics of the frequency response functions of the examples and comparative examples. Figure 5(b) shows the phase characteristics of the frequency response functions of the examples and comparative examples. [Modes for carrying out the invention]

[0010] A frequency response function identification system according to one embodiment will be described in detail below with reference to the attached drawings. In the description of the drawings, the same reference numerals are used for identical or equivalent elements, and redundant explanations are omitted.

[0011] The configuration of a frequency response function identification system according to one embodiment will be described with reference to Figures 1 to 4(b). Figure 1 is a block diagram showing the configuration of a frequency response function identification system according to one embodiment. Figure 2 is a diagram showing an example of the velocity characteristics of a static friction model. Figure 3 is a diagram for explaining the time interval in which static friction occurs. Figure 4(a) is a diagram showing an example of the gain characteristics of the frequency response function of the plant shown in Figure 1. Figure 4(b) is a diagram showing an example of the phase characteristics of the frequency response function of the plant shown in Figure 1.

[0012] The frequency response function identification system 1 shown in Figure 1 is a system for identifying the frequency response function of the object to be analyzed. In this embodiment, plant 2 is used as an example of the object to be analyzed. A servo motor can be used as an example of plant 2. The frequency response function identification system 1 identifies the motor angular displacement θ M Identify the frequency response function of Plant 2 from the (state value). Motor angular displacement θ M This is obtained when motor torque u (driving force) is input to plant 2. In other words, when motor torque u is input to plant 2, the motor angular displacement θ is produced from plant 2. M The following will be output.

[0013] The plant 2 can be represented by non-linear elements such as frictional force and linear elements such as spring mass. That is, in the frequency response function identification system 1, the effective torque u e (effective driving force) is input, and the linear characteristics (frequency response function P(z)) of the plant 2 that outputs the motor angular displacement θ M are identified. The effective torque u e is obtained by subtracting (subtracting) the static frictional force τ f from the motor torque u. The static frictional force τ f is the frictional force generated when the analysis target is operating. The frequency response function identification system 1 outputs the identified frequency response function (identified frequency response function) outside the frequency response function identification system 1.

[0014] The frequency response function identification system 1 may be configured as a computer system including a processor such as a CPU (Central Processing Unit), a memory such as a RAM (Random Access Memory) and a ROM (Read Only Memory), and a communication device such as a network card. The frequency response function identification system 1 includes a generation unit 11, an adder 12, a servo amplifier 13, an observer 14, and an identification unit 15.

[0015] The generation unit 11 generates a pre-processing torque command value (pre-processing control value) according to the difference Δθ Mr (command value) between the motor angular displacement command value θ M and the motor angular displacement θ M . The motor angular displacement command value θ Mr is the target value of the motor angular displacement θ M . The generation unit 11 receives, for example, the motor angular displacement command value θ Mr from an external control device. The generation unit 11 includes a subtractor 11a and a controller 11b. The subtractor 11a calculates the difference Δθ Mr by subtracting the motor angular displacement θ M from the motor angular displacement command value θ M . The subtractor 11a outputs the difference Δθ M to the controller 11b.

[0016] Controller 11b controls the difference Δθ M The difference Δθ is converted to a pre-processing torque command value. The controller 11b, for example, based on a predetermined control algorithm, M Convert this to the pre-processing torque command value. The pre-processing torque command value is the motor angular displacement θ M The motor angular displacement command value θ Mr Match (difference Δθ) M This is the torque command value to set it to 0. The controller 11b outputs the pre-processing torque command value to the adder 12.

[0017] The adder 12 adds the excitation value v to the pre-processing torque command value. u By adding this, the torque command value u r Generates the (control value). Excitation value v u is the value of the excitation signal. The excitation signal has a frequency spectrum coarse enough to allow identification of the frequency response function described later. In other words, the frequency spectrum of the excitation signal is, in equation (2) described later, the frequency response function P(ω k ) and leakage error term T(ω k ) has a coarseness that allows for separation of the two. Examples of excitation signals include random noise or a multisine time signal. Torque command value u r and motor angular displacement θ M A frequency-shaped excitation signal may be used to prevent the torque from becoming excessively large. This frequency shaping may be performed in either the time domain or the frequency domain. The adder 12 processes the torque command value u r The signal is output to the servo amplifier 13 and the observer 14.

[0018] The servo amplifier 13 controls the torque command value u r The motor torque u corresponding to the torque command value is output to plant 2. The servo amplifier 13 outputs the torque command value u based on a predetermined control algorithm. r This is converted to motor torque u. The transfer function Ga(z) is the torque command value u rThis represents the control algorithm that converts the motor torque u as a transfer function. The servo system is composed of a generator 11, an adder 12, a servo amplifier 13, and a plant 2.

[0019] Observer 14 receives the torque command value u r and motor angular displacement θ M Based on this, the estimated effective torque u^ e Generates (estimated effective driving force). Estimated effective torque u^ e The effective torque u e This is an estimate of "u^ e In the notation ", the "^" is located to the upper right of the "u", but in "u^ e The symbol "^" written between the observer 14 and the identification unit 15 in Figure 1 has the same meaning. The same applies to other "^" notations. In this specification, the symbol "^" means an estimated value except for the frequency response function, and means an identified value for the frequency response function. The observer 14 includes an estimation unit 41, a static friction model 42, and a calculation unit 43.

[0020] The estimation unit 41 calculates the torque command value u r The estimated motor torque u^(estimated driving force) is estimated from this. The estimated motor torque u^ is the estimated value of the motor torque u. The estimation unit 41 uses the transfer function G^a(z) to estimate the torque command value u r This is converted into an estimated motor torque u^. The transfer function G^a(z) is obtained by modeling the servo amplifier 13 using a known method. Note that if the changes in the gain and phase of the servo amplifier are negligibly small in the frequency band in which the frequency response function is identified, the transfer function Ga(z) can be considered as 1, so the transfer function G^a(z) may be set to 1. The estimation unit 41 outputs the estimated motor torque u^ to the calculation unit 43.

[0021] The static friction model 42 is based on the motor angular displacement θ. M Based on this, the estimated static friction force τ^ f Outputs the estimated static friction force τ^ f is the static friction force τ fThis is an estimate. The static friction model 42 is a static friction force τ f A model capable of reproducing the speed characteristics of a motor, where the motor angular velocity v and static friction force τ are used. f This is a model that defines the relationship. As the static friction model 42, the LuGre model and the GMS model, which can represent both static and dynamic friction characteristics, may be used.

[0022] Here, the velocity characteristics of the static friction model 42 will be explained with reference to Figure 2. The horizontal axis of Figure 2 represents the motor angular velocity v, and the vertical axis of Figure 2 represents the estimated static friction force τ^ f This indicates.

[0023] In the region where the absolute value of the motor angular velocity v is greater than or equal to a small angular velocity Δv, the estimated static friction force τ^ is as shown in equation (1). f This is a linear function of the motor angular velocity v with a slope equal to the viscous friction coefficient Dv, and the Coulomb friction force τ. fc It is expressed as the sum with the steady term due to . In the region where the absolute value of the motor angular velocity v is less than the small angular velocity Δv, the estimated static friction force τ^ is as shown in equation (1). f It can be expressed as a linear function of the motor angular velocity v having a proportionality constant greater than the viscous friction coefficient Dv.

[0024]

number

[0025] The static friction model 42 is, for example, the motor angular displacement θ M The motor angular velocity v is calculated by differentiating the function, and the estimated static friction force τ^ at the calculated motor angular velocity v is calculated. f Outputs.

[0026] The calculation unit 43 calculates the estimated motor torque u^ and the estimated static friction force τ^. f Based on this, the estimated effective torque u^ e The calculation unit 43 calculates the estimated static friction force τ^ from the estimated motor torque u^. The calculation unit 43 is composed of, for example, a subtractor. f By subtracting this, the estimated effective torque u^e The calculation unit 43 calculates the estimated effective torque u^ e The output is sent to the identification unit 15.

[0027] The identification unit 15 estimates the effective torque u^ e and motor angular displacement θ M Based on this, the frequency response function is identified and the identified frequency response function is output. Dynamic friction occurs in the small displacement region immediately after the sign of the motor angular velocity v is reversed, so as shown in Figure 3, the identification unit 15 identifies the time interval Ta, which is the section in which no dynamic friction force occurs, as the motor angular displacement θ M The estimated effective torque u^ obtained in the time interval Ta is determined from this, and then determined from this. e and motor angular displacement θ M The frequency response function is identified using the following. The horizontal axis of Figure 3 shows time (in seconds). The vertical axis of Figure 3 shows the torque command value u from top to bottom. r (Unit: Nm), motor angular displacement θ M The values ​​shown are (in rad) and motor angular velocity v (in rad / s). Time interval Ta is the interval in which the sign of the motor angular velocity v does not reverse and only static friction force is generated. Motor angular displacement θ in time interval Ta M The transition is accompanied by a transient response from the start to the end of the time interval Ta. Unless the sign of the motor angular velocity v reverses, the motor angular displacement θ remains constant. M There are no constraints on the transient response waveform. The identification unit 15 estimates the effective torque u^ in the time interval Ta' (for example, the time interval from 0 to 4s in Figure 3) in which the sign of the motor angular velocity v reverses if the time interval in which the sign of the motor angular velocity v does not reverse is sufficiently long. e and motor angular displacement θ M The frequency response function may also be identified using this method.

[0028] Estimated effective torque u^ in time interval Ta e and motor angular displacement θ M When identifying the frequency response function based on the discrete Fourier transform of , an identification error called leakage error occurs. To eliminate this leakage error, the identification unit 15 uses the local frequency modeling method to estimate the effective torque u^ e and motor angular displacement θ MThe frequency response function is identified from this. Examples of local frequency modeling methods include Local Rational Modeling and Local Polynomial Modeling.

[0029] Here, with reference to Figures 4(a) and 4(b), we will explain the identification theory of frequency response functions using local frequency modeling. The horizontal axis in Figures 4(a) and 4(b) represents frequency. The vertical axis in Figure 4(a) represents gain, and the vertical axis in Figure 4(b) represents phase. Here, Local Rational Modeling is used as the local frequency modeling method. We will explain by defining input u as the input to the linear characteristics of Plant 2, and output y as the output from the linear characteristics of Plant 2. The input u is the estimated effective torque u^ e This corresponds to the motor angular displacement θ. M It corresponds to this.

[0030] The output Y(k) is given by the input U(k) and the frequency response function P(ω) of plant 2. k ), and leakage error term T(ω k It is expressed by equation (2) using ). The output Y(k) is the discrete Fourier transform of the output y at frequency k. The input U(k) is the discrete Fourier transform of the input u at frequency k. Angular frequency ω k This is the angular frequency corresponding to frequency k in the Discrete Fourier Transform.

[0031]

number

[0032] As shown in equation (2), the frequency response function P(ω k ) and leakage error term T(ω k ) is the common denominator polynomial D(ω k ) can be represented as terms having different molecular polynomials. As shown in Figures 4(a) and 4(b), the frequency response function P(ω k ) and leakage error term T(ω k ) is frequency (kN w ) from frequency (k+Nw Assume that it is smooth within the local frequency window up to. Window size N w is a positive integer value. Window size N w Within the local frequency window of, the frequency response function P(ω k ) and the leakage error term T(ω k ) are each modeled as rational functions of frequency r, and Equation (3) is obtained. θ Pq (k), θ Tq (k), and θ Dq (k) are coefficient parameters. q is an integer value from 0 to R. R is the polynomial degree.

[0033]

Equation

[0034] The rational function model P~ k of the frequency response function P(ω k+r (r, θ Pq (k), θ Dq (k)) is represented by Equation (4). For example, in the notation "P~ k+r ", the "~" is located above the right of "P", but "P~ k+r (r, θ Pq (k), θ Dq (k))" has the same meaning as the left side of Equation (4). The same applies to other notations of "~". In this specification, the symbol "~" means a model.

[0035]

Equation

[0036] The rational function model T~ k of the leakage error term T(ω k+r (r, θ Tq (k), θ Dq (k)) is represented by Equation (5). Since the frequency response function P(ω k ) and the leakage error term T(ω k ) have a common denominator polynomial D(ω k ), the rational function model P~ k+r(r,θ Pq (k), θ Dq (k)) and rational function model T~ k+r (r,θ Tq (k), θ Dq (k)) shares a common denominator polynomial, but each has a different numerator polynomial.

[0037]

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[0038] Next, the identification unit 15 performs the following within the local frequency window. Y~ k+r but Y(k+r) and To achieve this, we find the solution θ^(k) for the parameter θ(k) that minimizes equation (6) using the least squares method. The parameter θ(k) is expressed by equation (7). Note that the necessary condition for the above optimization problem to be solvable is 2N w +1 ≥ 3R + 2.

[0039]

number

[0040]

number

[0041] The identification unit 15 finds the solution θ^(k) for the parameter θ(k) that minimizes equation (6) over all frequencies k={0,1,…,N-1} (where N is the data length of the discrete Fourier transform). Then, the identification unit 15 uses equation (8) to find the identified frequency response function P^(ω) at each frequency. k ) obtain.

[0042]

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[0043] Next, the effects of the frequency response function identification system 1 will be explained with reference to Figures 5(a) and 5(b). Figure 5(a) shows the gain characteristics of the frequency response functions of the examples and comparative examples. Figure 5(b) shows the phase characteristics of the frequency response functions of the examples and comparative examples. The horizontal axis in Figures 5(a) and 5(b) represents frequency (unit: Hz). The vertical axis in Figure 5(a) represents gain (unit: dB), and the vertical axis in Figure 5(b) represents phase (unit: deg).

[0044] The frequency response function of the embodiment is the estimated effective torque u^ when the time interval Ta is set to the interval of 0.25 to 3.5 s in Figure 3, as determined by the frequency response function identification system 1. e and motor angular displacement θ M This is the frequency response function identified using [the specified method]. The frequency response function of the comparative example is the motor angular displacement command value θ in Figure 1. Mr This is the frequency response function identified when the sign of the motor angular velocity v frequently reverses in the same time interval Ta of 0.25 to 3.5 s as in the example, with the (command value) set to zero. As shown in Figures 5(a) and 5(b), the frequency response function of the comparative example does not reproduce the frequency response function under analysis at frequencies below 10 Hz. On the other hand, the frequency response function of the example perfectly matches the frequency response function under analysis.

[0045] In the frequency response function identification system 1 described above, the torque command value u r From this, the estimated motor torque u^ is estimated, and the motor angular displacement θ M Based on this, the estimated static friction force τ^ f The following is output: estimated motor torque u^ and estimated static friction force τ^ f Based on this, the estimated effective torque u^ e The following is calculated. And the estimated effective torque u^ e and motor angular displacement θ M Based on this, the frequency response function is identified. Therefore, since the frequency response function is identified considering static friction, the processing load can be reduced compared to the case where both static and dynamic friction are considered.

[0046] Estimated static friction force τ^ f The static friction model 42 is used to calculate the static friction force τ. f Since this is a model for estimating the excitation value v, it can be constructed more easily compared to models that estimate both dynamic and static friction. Static friction is friction that occurs while plant 2 is operating, so when identifying the frequency response function in the time interval Ta in which static friction occurs, the position and velocity are different at the start and end of this interval. For this reason, leakage errors may occur in the frequency response function identified based on the discrete Fourier transform, but the pre-processing torque command value and the excitation value v u The torque command value u obtained by adding it r and motor angular displacement θ M and Furthermore, by using local frequency modeling, the frequency response function and leakage error can be separated. As a result, it becomes possible to improve the accuracy of frequency response function identification while simplifying the construction of the frequency response function identification system 1.

[0047] In plant 2, where a large frictional force is generated, the excitation value v u By increasing the excitation value v, it is also possible to identify the frequency response function while suppressing the effect of friction. However, u Increasing this value can cause Plant 2 to vibrate significantly, so this method may not be applicable in some cases. In contrast, the frequency response function identification system 1 uses the estimated motor torque u^ to determine the estimated static friction force τ^ f The estimated effective torque u^ obtained by subtracting u^ e Since this is used, the influence of frictional force in identifying the frequency response function can be reduced. kill .

[0048] In the frequency response function identification system 1, the frequency response function is identified with high accuracy, making it possible to design a controller that achieves high-performance servo control. The frequency response function can be identified even when the servo system is in operation and performing positioning operations. Therefore, it is possible to adjust the controller frequently even while the servo system is in operation, or to diagnose abnormalities in the operating servo system.

[0049] Although one embodiment of the present disclosure has been described in detail above, the frequency response function identification system according to the present disclosure is not limited to the above embodiment.

[0050] The static friction model 42 calculates the static friction force τ in a partial region where the absolute value of the motor angular velocity v is greater than or equal to a small angular velocity Δv. f It is sufficient to reproduce the speed characteristics; for example, in the region where the absolute value of the motor angular velocity v is less than a small angular velocity Δv, it is not necessary to reproduce the above speed characteristics. Similarly, it is not necessary to reproduce the above speed characteristics up to the region where the absolute value of the motor angular velocity v is greater than the operating angular velocity at the time of frequency response function identification.

[0051] The object of analysis (plant 2) is not limited to a servo motor. If a servo motor is not used, an operating device that converts command values ​​into drive values ​​is used instead of the servo amplifier 13. The object of analysis can be any device that outputs a state value when a driving force is input. The state value can be position, velocity, or acceleration. If the state value is position, the static friction model 42 may convert the state value to velocity by differentiating it, or the velocity may be estimated by an observer. Similarly, if the state value is acceleration, the static friction model 42 may convert the state value to velocity by integrating it, or the velocity may be estimated by an observer. [Explanation of Symbols]

[0052] 1...Frequency response function identification system, 2...Plant (object of analysis), 11...Generator, 11a...Subtractor, 11b...Controller, 12...Adder, 13...Servo amplifier, 14...Observer, 15...Identification unit, 41...Estimation unit, 42...Static friction model, 43...Calculation unit.

Claims

[Claim 1] A frequency response function identification system that identifies the frequency response function of an object to be analyzed from state values ​​obtained by inputting a driving force corresponding to a control value to the object to be analyzed, A generation unit that generates a pre-processing control value according to the difference between the command value and the state value, An adder that generates the control value by adding the excitation value to the control value before processing, An observer that generates an estimated effective driving force, which is an estimated value of the effective driving force obtained by subtracting the static friction force that occurs when the object being analyzed is operating from the driving force, based on the control value and the state value, An identification unit identifies the frequency response function based on the estimated effective driving force and the state value, Equipped with, The aforementioned observer, An estimation unit that estimates the estimated driving force, which is an estimated value of the driving force, from the control value, A static friction model that defines the relationship between velocity and the static friction force, wherein the static friction model outputs an estimated static friction force, which is an estimated value of the static friction force, based on the state value, A calculation unit that calculates the estimated effective driving force based on the estimated driving force and the estimated static friction force, Equipped with, The identification unit is a frequency response function identification system that identifies the frequency response function from the estimated effective driving force and the state value using a local frequency modeling method.

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