JP4683255B2 - Frequency characteristic calculation device for motor control device - Google Patents

Frequency characteristic calculation device for motor control device Download PDF

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Publication number
JP4683255B2
JP4683255B2 JP2001248435A JP2001248435A JP4683255B2 JP 4683255 B2 JP4683255 B2 JP 4683255B2 JP 2001248435 A JP2001248435 A JP 2001248435A JP 2001248435 A JP2001248435 A JP 2001248435A JP 4683255 B2 JP4683255 B2 JP 4683255B2
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Prior art keywords
motor
rotation
signal
frequency characteristic
sensor
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JP2003061379A (en
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剛彦 小宮
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Yaskawa Electric Corp
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Yaskawa Electric Corp
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Description

【0001】
【発明の属する技術分野】
本発明は、半導体製造装置や工作機械、産業用ロボット等に用いられて位置決め制御をするモータ制御装置に関するものであり、特にその調整を最適なものとするために、制御対象を含む周波数特性を正しく測定する周波数特性演算装置に関するものである。
【0002】
【従来の技術】
従来、半導体製造装置やロボットなどのサーボ系を有する機械装置は、その性能を向上するため、サーボ系のサーボ特性を向上させる努力が払われてきた。その際、機械を含むサーボ系の周波数特性を知ることが重要であり、様々な方法で計測されている。特に、2軸以上のサーボ系を有するモータ制御装置の場合は、1軸毎の周波数特性を別々に計測し、その結果を総合して全体の特性が把握されていた。また、周波数特性の測定を正確なものとするため、サーボ系で用いるセンサと別に固定台等に振動センサを設け、振動信号を測定するということも行われていた。
【0003】
【発明が解決しようとする課題】
ところが上記のような従来技術では、全軸の周波数特性を計測するには長時間を要するという問題があった。特に、軸間に干渉がある場合は、軸間の組み合わせを考慮する必要があるため、1軸の周波数特性を計測するよりも多くの時間と手間を要し、計測した結果を処理するときにも多大の時間を要すという問題があった。さらに、少数の振動センサを順番に機械全体に配置するような場合は、1軸ごとに計測を繰り返して機械の振動モードや振動の挙動が把握されており、莫大な時間と手間が必要であるという問題があった。本発明はこれらの問題に鑑みてなされたものであり、モータ制御系の周波数特性を容易に計測することができる周波数特性演算装置を提供することを目的とする。
【0004】
【課題を解決するための手段】
上記問題を解決するため、本発明の周波数特性演算装置は、固定台に搭載されて移動可能に支持された可動部と、モータと、そのモータの回転を伝えて前記可動部を移動させる伝達機構と、前記モータの回転を検出して信号Xを出力する回転センサと、前記モータの回転指令Fと前記回転センサの信号Xを受けて前記モータの回転を制御するサーボ装置とを複数備えて複数のサーボ系をなすモータ制御装置において、前記モータの回転指令Fを出力し、前記回転センサの信号Xを入力して所定の式に基づいて周波数特性を演算することを特徴とするものである。
【0005】
また本発明は、固定台に搭載されて移動可能に支持された可動部と、モータと、そのモータの回転を伝えて前記可動部を移動させる伝達機構と、前記モータの回転を検出して信号Xを出力する回転センサと、前記モータの回転指令Fと前記回転センサの信号Xを受けて前記モータの回転を制御するサーボ装置とを複数備えて複数のサーボ系をなすモータ制御装置において、前記サーボ系とは別に1つ以上の振動センサを前記可動部もしくは前記固定台に設け、前記モータの回転指令Fを出力して前記振動センサの信号Xを入力し、所定の式に基づいて周波数特性を演算することを特徴とするものである。
このようになっているので、容易にモータ制御系の周波数特性を計測することができるのである。
【0006】
【発明の実施の形態】
以下、本発明の実施の形態を図にもとづいて説明する。図1は本発明の請求項1に記載の発明に係わる実施例を示す構成図である。図において、1は演算装置であり、2は第1軸のサーボ装置、3は第2軸のサーボ装置、4は第1軸のセンサ、5は第2軸のセンサ、6は第1軸のモータ、7は第2軸のモータ、8は第1軸の伝達機構、9は第2軸の伝達機構、10は第1軸の可動部、11は第2軸の可動部、12は固定台であり、センサ4、5はモータ6、7の回転と振動を検出する。
【0007】
次に動作について図3のフローチャートに沿って説明する。まず、(S1)演算装置1が相関関係のない第1軸の動作指令信号F1と第2軸の動作指令信号F2を生成して、(S2)それぞれ第1軸のサーボ装置2と第2軸のサーボ装置3に送ると、(S3)各サーボ装置2、3が入力した各動作指令信号と等価な制御信号S1、S2を生成して、それぞれ第1軸のモータ6と第2軸のモータ7に出力し、モータ6、7を回転させる。その回転は第1軸の伝達機構8と第2軸の伝達機構9を介して、それぞれ第1軸の可動部10と第2軸の可動部11に伝えられて動作し、固定台12を含む機械系全体に振動が発生する。(S4)そしてセンサ4、5がそれぞれモータ6、7の回転と振動を検出し、(S5)検出された信号X1、X2がサーボ装置2とサーボ装置3を介して演算装置1に入力される。すると(S6)演算装置1は2つの指令S1、S2と2つの入力信号X1、X2を周波数分析し、請求項1に記載の式(1)に基づいて周波数特性を計算する。
【0008】
センサ出力X1の周波数分析結果X1とセンサ出力X2の周波数分析結果X2には、双方とも指令S1の周波数分析結果FAと指令S2の周波数分析結果FBで加振され、各周波数特性となる伝達要素を経由した結果が含まれる。例えば、センサ出力X1の周波数分析結果X1は、指令S1とセンサ出力X1間の周波数特性H1Aに、指令S1の周波数分析結果FAが掛け合わされた成分と、指令S2とセンサ出力X1間の周波数特性H1Bに、指令S2の周波数分析結果FBが掛け合わされた成分が足し合わされているため、式(3)のように表すことができる。
【0009】
【数3】

Figure 0004683255
ここで、Hは周波数特性、Xはセンサ信号、Fは演算装置1の動作指令信号、センサ信号Xの添字1、2は第1軸と第2軸の何れであるかを示し、動作指令信号Fの添字A、Bは第1軸と第2軸の何れであるかを示している。
【0010】
式(3)に動作指令信号F1の周波数分析結果FAと動作指令信号F2の周波数分析結果FBの複素共役の転置行列を右から掛けた上、動作指令信号F1の周波数分析結果FAと動作指令信号F2の周波数分析結果FBの動作指令信号の要素のみからなる行列の逆行列を右から掛けると、式(1)と等価となり、動作指令信号F1とセンサ信号X1間の周波数特性H1Aと、動作指令信号F2とセンサ信号X2間の周波数特性H2Bと、動作指令信号F1とセンサ信号X2間の周波数特性H2Aと、動作指令信号F2とセンサ信号X1間の周波数特性H1Bを一度に求めることができる。
なお、以上の実施例で示したモータ制御装置では、軸数とセンサの数が何れも2で一致していたが、本発明の趣旨に従えば、これらは一致していなくても良い。
【0011】
次に本発明の第2の実施例を図にもとづいて説明する。図2は請求項2の発明に係わる実施例を示す構成図であり、図1と異なるのは、可動部10、11に振動センサ13、14を取り付けた点である。この振動センサ13、14により可動部10、11の振動が検出されて、その信号が演算装置1に入力される。図2の場合は振動センサ13の信号のみが演算装置1に入力されている。振動センサ以外については、第1実施例の場合と同様の動作をするので説明を省略する。
この実施例の場合は、各軸を同時に動作させ、第1軸と第2軸の動作指令信号F1、F2と、振動センサ1、2の検出信号X1、X2間の周波数特性を分離して求められる。
【0012】
演算装置1が動作指令信号F1、F2を出力するとサーボ装置2、3がモータ6、7を駆動し、それぞれ伝達機構8、9を介して、可動部10、11が同時に動作する。そして固定台12を含む機械系全体に振動が発生し、振動センサ13、14が振動を検出して検出信号X3、X4を演算装置1に出力する。演算装置1は、動作指令信号F1、F2と振動センサ13、14の信号X3、X4を周波数分析し、請求項2に記載の式(2)に基づいて周波数特性を求める。請求項1に記載の式(1)と異なっているのは、Xが振動センサの信号であり、その添字1、2は振動センサの番号を表している。この構成によると、動作指令信号F1と振動センサ13の信号X3間の周波数特性H1Aと、動作指令信号F2と振動センサ14の信号X4間の周波数特性H2Bと、動作指令信号F1と振動センサ14の信号X4間の周波数特性H2Aと、動作指令信号F1と振動センサ13の信号X3間の周波数特性H1Bを一度に求めることができる。
【0013】
なお、第2実施例のモータ制御装置では、振動センサ13、14を2つとした例を示したが、振動センサは2つ以上でも2つ以下でもよく、軸数と振動センサの数が一致していなくても良い。
また、第2実施例のモータ制御装置では、振動センサ13、14は可動部10、11の振動を検出するとしたが、請求項2に記述したように、振動センサ13、14は位置や方向を変えて固定台12の振動を検出してもよく、さらに、振動センサ13、14を可動部10もしくは11と固定台12に別けて配置して振動を検出してもよい。
また、上記2つの実施例では、モータの回転を検出するセンサを用いる例と振動センサを用いる例を分けて記述したが、これら2種類のセンサを混合して使用しても良い。
【0014】
また、上記2つの実施例では、各軸の影響を除去した周波数特性を求めたが、各軸の影響を含めた周波数特性を求める場合には、請求項1の式(1)の演算途中結果、例えば 第1軸の動作指令信号13と第2軸の動作指令信号14の各々のオートパワースペクトルFA・FA *、FB・FB *やクロススペクトルFB・FA *などを別途記録しておけば、式(4)を用いて後で演算処理して求めることができる。
【0015】
【数4】
Figure 0004683255
Figure 0004683255
【0016】
【発明の効果】
以上述べたように、本発明によれば、請求項1または請求項2に記載の構成としたため、多軸構成のモータを同時に動作させ、各軸の加振の影響を分離した周波数特性と、これまで簡単に得られなかった各軸間の周波数特性を計測できる周波数特性演算装置を提供できるという効果がある。
【図面の簡単な説明】
【図1】請求項1記載の発明を用いたモータ制御装置の構成図
【図2】請求項2記載の発明を用いたモータ制御装置の構成図
【図3】周波数特性を求める手順を示すフローチャート
【符号の説明】
1:演算装置
2、3:サーボ装置
4、5:センサ
6、7:モータ
8、9:伝達機構
10、11:可動部
12:固定台
13、14:振動センサ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a motor control device that is used in semiconductor manufacturing devices, machine tools, industrial robots, etc., and performs positioning control, and in particular, in order to optimize the adjustment, the frequency characteristics including the controlled object are provided. The present invention relates to a frequency characteristic calculation device that measures correctly.
[0002]
[Prior art]
Conventionally, efforts have been made to improve the servo characteristics of a servo system in order to improve the performance of a mechanical apparatus having a servo system such as a semiconductor manufacturing apparatus or a robot. At that time, it is important to know the frequency characteristics of the servo system including the machine, and it is measured by various methods. In particular, in the case of a motor control device having two or more servo systems, the frequency characteristics for each axis are measured separately, and the overall characteristics are grasped by summing the results. In addition, in order to accurately measure frequency characteristics, a vibration sensor is provided on a fixed base or the like separately from a sensor used in a servo system, and a vibration signal is measured.
[0003]
[Problems to be solved by the invention]
However, the conventional technology as described above has a problem that it takes a long time to measure the frequency characteristics of all axes. Especially when there is interference between the axes, it is necessary to consider the combination between the axes, so it takes more time and effort than measuring the frequency characteristics of one axis, and when processing the measurement results There was also a problem that it took a lot of time. Furthermore, when a small number of vibration sensors are arranged in order on the entire machine, the measurement is repeated for each axis, and the vibration mode and vibration behavior of the machine are grasped, requiring enormous time and effort. There was a problem. The present invention has been made in view of these problems, and an object of the present invention is to provide a frequency characteristic calculation apparatus that can easily measure the frequency characteristic of a motor control system.
[0004]
[Means for Solving the Problems]
In order to solve the above problem, a frequency characteristic calculation apparatus according to the present invention includes a movable part mounted on a fixed base and supported to be movable, a motor, and a transmission mechanism that transmits the rotation of the motor to move the movable part. A plurality of rotation sensors that detect rotation of the motor and output a signal X; and a plurality of servo devices that control the rotation of the motor in response to the rotation command F of the motor and the signal X of the rotation sensor. In the motor control apparatus that constitutes the servo system, the motor rotation command F is output, the rotation sensor signal X is input, and the frequency characteristic is calculated based on a predetermined formula.
[0005]
According to another aspect of the present invention, there is provided a movable part mounted on a fixed base and supported so as to be movable, a motor, a transmission mechanism for transmitting the rotation of the motor to move the movable part, and detecting the rotation of the motor to obtain a signal. In a motor control device comprising a plurality of rotation sensors that output X, and a plurality of servo devices that control rotation of the motor in response to a rotation command F of the motor and a signal X of the rotation sensor, and form a plurality of servo systems, In addition to the servo system, one or more vibration sensors are provided on the movable part or the fixed base, the rotation command F of the motor is output, the signal X of the vibration sensor is input, and the frequency characteristics are based on a predetermined formula Is calculated.
Thus, the frequency characteristic of the motor control system can be easily measured.
[0006]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing an embodiment according to the first aspect of the present invention. In the figure, 1 is an arithmetic unit, 2 is a first axis servo apparatus, 3 is a second axis servo apparatus, 4 is a first axis sensor, 5 is a second axis sensor, and 6 is a first axis sensor. Motor 7, second axis motor 8, first axis transmission mechanism 9, second axis transmission mechanism 10, first axis movable part 11, second axis movable part 12, fixed base The sensors 4 and 5 detect the rotation and vibration of the motors 6 and 7.
[0007]
Next, the operation will be described with reference to the flowchart of FIG. First, (S1) the computing device 1 generates an uncorrelated first-axis motion command signal F1 and a second-axis motion command signal F2, and (S2) the first-axis servo device 2 and second-axis, respectively. (S3) The control signals S1 and S2 equivalent to the operation command signals inputted by the servo devices 2 and 3 are generated, and the first axis motor 6 and the second axis motor are respectively generated. 7 and the motors 6 and 7 are rotated. The rotation is transmitted to the first-axis movable unit 10 and the second-axis movable unit 11 via the first-axis transmission mechanism 8 and the second-axis transmission mechanism 9, respectively, and includes the fixed base 12. Vibration occurs in the entire mechanical system. (S4) The sensors 4 and 5 detect the rotation and vibration of the motors 6 and 7, respectively. (S5) The detected signals X1 and X2 are input to the arithmetic device 1 via the servo device 2 and the servo device 3. . Then (S6) the arithmetic unit 1 performs frequency analysis on the two commands S1 and S2 and the two input signals X1 and X2, and calculates a frequency characteristic based on the equation (1) described in claim 1.
[0008]
The frequency analysis results X 2 frequency analysis results X 1 and the sensor output X2 of the sensor output X1, is vibrated in both the frequency analysis result of the frequency analysis result F A and instruction S2 command S1 F B, and the frequency characteristic The result via the transfer element is included. For example, the frequency analysis result X 1 of the sensor output X1 is obtained by multiplying the frequency characteristic H 1A between the command S1 and the sensor output X1 by the frequency analysis result F A of the command S1, and between the command S2 and the sensor output X1. Since the component obtained by multiplying the frequency characteristic H 1B by the frequency analysis result F B of the command S2 is added, it can be expressed as in Expression (3).
[0009]
[Equation 3]
Figure 0004683255
Here, H is a frequency characteristic, X is a sensor signal, F is an operation command signal of the arithmetic unit 1, subscripts 1 and 2 of the sensor signal X indicate which of the first axis and the second axis, and the operation command signal Subscripts A and B of F indicate whether the axis is the first axis or the second axis.
[0010]
Equation (3) on which multiplied by the complex conjugate transposed matrix of the operation command signal F1 of the frequency analysis result F B frequency analysis result F A and the operation command signal F2 from the right, and the frequency analysis result F A of the operation command signal F1 multiplying the inverse matrix of consisting only matrix elements of the operation command signal of the frequency analysis result F B of the operation command signal F2 from the right becomes equivalent to equation (1), operation command signal F1 and the frequency characteristic H between the sensor signals X1 1A , frequency characteristic H 2B between operation command signal F2 and sensor signal X2, frequency characteristic H 2A between operation command signal F1 and sensor signal X2, and frequency characteristic H 1B between operation command signal F2 and sensor signal X1 You can ask for it at once.
In the motor control apparatus shown in the above embodiment, the number of axes and the number of sensors are both equal to 2, but they may not be consistent according to the gist of the present invention.
[0011]
Next, a second embodiment of the present invention will be described with reference to the drawings. FIG. 2 is a block diagram showing an embodiment according to the second aspect of the invention. The difference from FIG. 1 is that the vibration sensors 13 and 14 are attached to the movable parts 10 and 11, respectively. Vibrations of the movable parts 10 and 11 are detected by the vibration sensors 13 and 14, and the signals are input to the arithmetic device 1. In the case of FIG. 2, only the signal from the vibration sensor 13 is input to the arithmetic unit 1. Except for the vibration sensor, the operation is the same as in the case of the first embodiment, and the description thereof is omitted.
In the case of this embodiment, each axis is operated simultaneously, and the frequency characteristics between the first axis and second axis operation command signals F1 and F2 and the detection signals X1 and X2 of the vibration sensors 1 and 2 are obtained separately. It is done.
[0012]
When the arithmetic device 1 outputs the operation command signals F1 and F2, the servo devices 2 and 3 drive the motors 6 and 7, and the movable parts 10 and 11 operate simultaneously via the transmission mechanisms 8 and 9, respectively. Then, vibration is generated in the entire mechanical system including the fixed base 12, and the vibration sensors 13 and 14 detect the vibration and output detection signals X3 and X4 to the arithmetic unit 1. The arithmetic device 1 performs frequency analysis on the operation command signals F1 and F2 and the signals X3 and X4 of the vibration sensors 13 and 14, and obtains frequency characteristics based on the equation (2) according to claim 2. What is different from the formula (1) described in claim 1 is that X is a signal of the vibration sensor, and subscripts 1 and 2 represent the number of the vibration sensor. According to this configuration, the frequency characteristic H 1A between the operation command signal F1 and the signal X3 of the vibration sensor 13, the frequency characteristic H 2B between the operation command signal F2 and the signal X4 of the vibration sensor 14, the operation command signal F1 and the vibration sensor. The frequency characteristic H 2A between the 14 signals X4 and the frequency characteristic H 1B between the operation command signal F1 and the signal X3 of the vibration sensor 13 can be obtained at a time.
[0013]
In the motor control device of the second embodiment, an example in which two vibration sensors 13 and 14 are provided has been described. However, the number of vibration sensors may be two or more, and the number of axes and the number of vibration sensors match. It does not have to be.
In the motor control device of the second embodiment, the vibration sensors 13 and 14 detect the vibrations of the movable parts 10 and 11, but as described in claim 2, the vibration sensors 13 and 14 have positions and directions. Alternatively, the vibration of the fixed base 12 may be detected, and the vibration sensors 13 and 14 may be arranged separately from the movable portion 10 or 11 and the fixed base 12 to detect the vibration.
In the above two embodiments, the example using the sensor for detecting the rotation of the motor and the example using the vibration sensor are described separately. However, these two types of sensors may be used in combination.
[0014]
In the above two embodiments, the frequency characteristic from which the influence of each axis is removed is obtained. However, when the frequency characteristic including the influence of each axis is obtained, the intermediate result of the expression (1) of claim 1 is obtained. For example, the auto power spectrum F A · F A * , F B · F B * , cross spectrum F B · F A *, etc. of the first axis motion command signal 13 and the second axis motion command signal 14 are separately provided. If it is recorded, it can be calculated later using equation (4).
[0015]
[Expression 4]
Figure 0004683255
Figure 0004683255
[0016]
【The invention's effect】
As described above, according to the present invention, since it is configured as described in claim 1 or claim 2, the multi-axis motor is operated at the same time, and the frequency characteristics obtained by separating the influence of vibration of each axis, There is an effect that it is possible to provide a frequency characteristic calculation device capable of measuring the frequency characteristic between the axes, which has not been easily obtained so far.
[Brief description of the drawings]
FIG. 1 is a block diagram of a motor control device using the invention according to claim 1. FIG. 2 is a block diagram of a motor control device using the invention according to claim 2. FIG. 3 is a flowchart showing a procedure for obtaining frequency characteristics. [Explanation of symbols]
1: arithmetic device 2, 3: servo device 4, 5: sensor 6, 7: motor 8, 9: transmission mechanism 10, 11: movable part 12: fixed base 13, 14: vibration sensor

Claims (2)

固定台に搭載されて移動可能に支持された可動部と、モータと、そのモータの回転を伝えて前記可動部を移動させる伝達機構と、前記モータの回転を検出して信号Xを出力する回転センサと、前記モータの回転指令Fと前記回転センサの信号Xを受けて前記モータの回転を制御するサーボ装置とを複数備えて複数のサーボ系をなすモータ制御装置において、
前記モータの回転指令Fを出力し、前記回転センサの信号Xを入力して次式に基づいて周波数特性を演算することを特徴とするモータ制御装置の周波数特性演算装置。
Figure 0004683255
Figure 0004683255
ここで、Hは周波数特性、Xは回転センサの信号、Fはモータの回転指令であり、
*は複素共役、−1は逆行列、添字1〜nは回転センサにつけた番号、添字A〜Mは各サーボ系に入力するモータの回転指令につけた番号である。
A movable part mounted on a fixed base and supported movably, a motor, a transmission mechanism for transmitting the rotation of the motor to move the movable part, and a rotation for detecting the rotation of the motor and outputting a signal X In a motor control device comprising a plurality of sensors, a servo device that receives the rotation command F of the motor and a signal X of the rotation sensor and controls the rotation of the motor to form a plurality of servo systems,
A frequency characteristic calculation device for a motor control device, wherein the motor rotation command F is output, a signal X of the rotation sensor is input, and a frequency characteristic is calculated based on the following equation.
Figure 0004683255
Figure 0004683255
Here, H is a frequency characteristic, X is a rotation sensor signal, F is a motor rotation command,
* Is a complex conjugate, -1 is an inverse matrix, subscripts 1 to n are numbers attached to the rotation sensor, and subscripts A to M are numbers attached to motor rotation commands input to each servo system.
固定台に搭載されて移動可能に支持された可動部と、モータと、そのモータの回転を伝えて前記可動部を移動させる伝達機構と、前記モータの回転を検出して信号を出力する回転センサと、前記モータの回転指令Fと前記回転センサの信号を受けて前記モータの回転を制御するサーボ装置とを複数備えて複数のサーボ系をなすモータ制御装置において、
前記サーボ系とは別に1つ以上の振動センサを前記可動部もしくは前記固定台に設け、前記モータの回転指令Fを出力して前記振動センサの信号Xを入力し、次式に基づいて周波数特性を演算することを特徴とするモータ制御装置の周波数特性演算装置。
Figure 0004683255
Figure 0004683255
ここで、Hは周波数特性、Xは振動センサの信号、Fはモータの回転指令であり、*は複素共役、−1は逆行列、添字1〜nは振動センサにつけた番号、添字A〜Mは各サーボ系に入力するモータの回転指令につけた番号である。
A movable part mounted on a fixed base and supported movably, a motor, a transmission mechanism for transmitting the rotation of the motor to move the movable part, and a rotation sensor for detecting the rotation of the motor and outputting a signal And a motor control device comprising a plurality of servo devices that receive a rotation command F of the motor and a signal from the rotation sensor and control the rotation of the motor to form a plurality of servo systems,
In addition to the servo system, one or more vibration sensors are provided on the movable part or the fixed base, the rotation command F of the motor is output, and the signal X of the vibration sensor is input. A frequency characteristic calculation device for a motor control device, characterized by:
Figure 0004683255
Figure 0004683255
Here, H is a frequency characteristic, X is a vibration sensor signal, F is a motor rotation command, * is a complex conjugate, -1 is an inverse matrix, subscripts 1 to n are numbers assigned to the vibration sensors, and subscripts A to M Is the number given to the motor rotation command input to each servo system.
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JPS62126402A (en) * 1985-11-27 1987-06-08 Omron Tateisi Electronics Co Xy stage control device
JPH07325628A (en) * 1994-05-31 1995-12-12 Canon Inc Method and device for modeling of 6-degree-of-freedom rigid body vibration system
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JPS61135375A (en) * 1984-12-04 1986-06-23 Meidensha Electric Mfg Co Ltd Pwm type power rectifier
JPS62126402A (en) * 1985-11-27 1987-06-08 Omron Tateisi Electronics Co Xy stage control device
JPH07325628A (en) * 1994-05-31 1995-12-12 Canon Inc Method and device for modeling of 6-degree-of-freedom rigid body vibration system
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