JPH09128006A - Controller with phase compensation function - Google Patents
Controller with phase compensation functionInfo
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- JPH09128006A JPH09128006A JP28229695A JP28229695A JPH09128006A JP H09128006 A JPH09128006 A JP H09128006A JP 28229695 A JP28229695 A JP 28229695A JP 28229695 A JP28229695 A JP 28229695A JP H09128006 A JPH09128006 A JP H09128006A
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- Prior art keywords
- controller
- compensator
- phase
- time constant
- control
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Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は位相補償機能つき制
御装置に関する。さらに詳しくは、整定時間を短くし、
プロセスの安定性を向上させることが可能な位相補償機
能つき制御装置に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control device with a phase compensation function. More specifically, shorten the settling time,
The present invention relates to a control device with a phase compensation function that can improve process stability.
【０００２】[0002]
【従来の技術】従来、プロセスにむだ時間を含む系、た
とえば炉温の制御、圧延機の板厚の制御などにおいてむ
だ時間を含むプロセスの位相補償のためにスミス補償器
が用いられている。従来のスミス補償器を用いた制御装
置の一例のブロック線図を図６に示す。図６において、
１１は、位相補償器であるスミス補償器であり、１３は
制御対象、１４はＰＩコントローラである。2. Description of the Related Art Conventionally, a Smith compensator has been used for phase compensation of a system including a dead time in a system including a dead time in a process, such as control of a furnace temperature and control of a plate thickness of a rolling mill. FIG. 6 shows a block diagram of an example of a control device using a conventional Smith compensator. In FIG.
Reference numeral 11 is a Smith compensator which is a phase compensator, 13 is a control target, and 14 is a PI controller.
【０００３】以下、圧延機の板厚を制御するためにスミ
ス補償器を用いた制御装置について説明する。まず圧延
機の出側に設置した厚み計により、圧延材の出側板厚偏
差を検出する。検出された値は、ＰＩコントローラ１４
に入力され、ＰＩコントローラ１４では、比例演算処
理、積分演算処理、または比例積分演算処理することに
より、制御量を求める。ＰＩコントローラ１４により求
められた前記制御量を位相補償器であるスミス補償器１
１に入力したのち、さらにスミス補償器１１で求められ
た補償信号をＰＩコントローラ１４にフィードバックす
る。板厚偏差があらかじめ設定された板厚偏差設定
「０」となるまで、フィードバックまでの一連の工程が
繰り返される。ところで、スミス補償器１１は、むだ時
間を含む系においては、図６に示されるように制御対象
に応じてあらかじめ推定したむだ時間推定伝達関数ｅ
-Ts、プロセス推定伝達関数Ｇ（ｓ）ｐｓ、およびプロ
セス推定ゲインＫsを構成要素としている。すなわち、
従来のスミス補償器１１は、制御量に対するむだ時間後
の変動を予測し、実測定値Ｙを相殺することによって制
御ゲイン過大による過制御（ハンチングなどの不安定現
象）を防止している。A control device using a Smith compensator for controlling the strip thickness of the rolling mill will be described below. First, the deviation of the strip thickness on the delivery side of the rolled material is detected by a thickness gauge installed on the delivery side of the rolling mill. The detected value is the PI controller 14
And the PI controller 14 obtains the control amount by performing proportional calculation processing, integral calculation processing, or proportional integral calculation processing. The control amount obtained by the PI controller 14 is the Smith compensator 1 which is a phase compensator.
After being input to 1, the compensation signal obtained by the Smith compensator 11 is fed back to the PI controller 14. A series of steps up to feedback are repeated until the plate thickness deviation reaches a preset plate thickness deviation setting "0". By the way, in the system including the dead time, the Smith compensator 11 estimates the dead time estimation transfer function e in advance according to the controlled object as shown in FIG.
-Ts, it is a process estimating the transfer function G (s) ps, and process estimator gain K s components. That is,
The conventional Smith compensator 11 predicts the variation after the dead time with respect to the control amount and cancels the actual measurement value Y to prevent over-control (an unstable phenomenon such as hunting) due to excessive control gain.
【０００４】このスミス補償器を用いた制御装置におい
ては、ＰＩコントローラ１４の伝達関数Ｇ（ｓ）ｃは積
分時定数ＴiとトータルゲインＫoを用いて、次式（１）
で表される。また、制御対象１３のプロセス伝達関数
は、制御対象によって異なる時定数Ｔpを用いて３次遅
れ関数で近似される（次式（２）参照）。In the controller using the Smith compensator, the transfer function G (s) c of the PI controller 14 is calculated by the following equation (1) using the integral time constant T i and the total gain K o.
It is represented by Further, the process transfer function of the controlled object 13 is approximated by a third-order lag function using a time constant T p that varies depending on the controlled object (see the following equation (2)).
【０００５】[0005]
【数１】 (Equation 1)
【０００６】[0006]
【発明が解決しようとする課題】前記従来のスミス補償
器を用いた制御装置を、圧延機の板厚制御のようにむだ
時間が大きく、時定数が小さいものに適用するばあいに
は、圧延機の低速領域において板厚精度は向上する反
面、高速領域においては精度はあがらない。また、従来
の制御装置は、既設のＰＩ制御ループ内にスミス補償器
を追加するため、制御定数（トータルゲインＫｏおよび
積分定数）を再調整する必要があるが、オンラインでこ
れらの調整をすることが困難であるという問題があるう
えに、モデル誤差に対する安定性がわるいという問題が
ある。When the control device using the conventional Smith compensator is applied to a rolling mill having a large dead time and a small time constant, such as the thickness control of a rolling mill, the Although the plate thickness accuracy is improved in the low speed region of the machine, the accuracy is not improved in the high speed region. Further, in the conventional control device, since the Smith compensator is added in the existing PI control loop, it is necessary to readjust the control constants (total gain Ko and integral constant), but these adjustments should be made online. However, there is a problem that the stability against model error is poor.
【０００７】また、炉温制御のようにむだ時間が小さ
く、時定数が大きいものに適用するばあいには、式
（１）でむだ時間Ｔが０に近づくことから、ＰＩＤ（比
例微分および積分）制御と同等の制御しか行えず、制御
性がわるいという問題がある。Further, when applied to a furnace temperature control that has a small dead time and a large time constant, since the dead time T approaches 0 in the equation (1), the PID (proportional derivative and integral ) There is a problem that controllability is poor because only control equivalent to control can be performed.
【０００８】本発明はこのような問題を解決し、調整が
容易で、安定性の向上した位相補償機能つき制御装置を
提供することを目的とする。An object of the present invention is to solve the above problems and to provide a control device with a phase compensation function which is easy to adjust and has improved stability.
【０００９】[0009]
【課題を解決するための手段】本発明の位相補償機能つ
き制御装置は、ＰＩコントローラからの制御信号に対し
てあらかじめ推定されているプロセス推定ゲインを位相
補償器に入力し、えられる出力を前記ＰＩコントローラ
にフィードバックし、制御目標値に対して測定値の位相
補償をする位相補償手段と、前記位相補償器に含まれる
安定補償器によって系を安定に補償する安定補償手段と
からなり、前記ＰＩコントローラの伝達関数が安定補償
器時定数と積分時定数との商と、前記プロセス推定ゲイ
ンの逆数との積を含むことを特徴とするむだ時間を有す
るプロセスの制御に用いられる位相補償機能つき制御装
置である。A control device with a phase compensation function according to the present invention inputs a process estimation gain estimated in advance with respect to a control signal from a PI controller to a phase compensator, and outputs the obtained output. It comprises a phase compensating means for feeding back to the PI controller and compensating the phase of the measured value with respect to the control target value, and a stable compensating means for stably compensating the system by the stable compensator included in the phase compensator. Control with phase compensation function used for control of process with dead time, characterized in that transfer function of controller includes product of quotient of stable compensator time constant and integral time constant and reciprocal of process estimation gain It is a device.
【００１０】[0010]
【発明の実施の形態】つぎに図面を参照しながら本発明
の位相補償機能つき制御装置の一実施例を説明する。BEST MODE FOR CARRYING OUT THE INVENTION Next, an embodiment of a control device with a phase compensation function of the present invention will be described with reference to the drawings.
【００１１】図１は本発明の位相補償機能つき制御装置
の一実施例のブロック線図である。図１において、１は
位相補償器であり、２は安定補償器であり、３は制御対
象であり、４はＰＩコントローラである。ここで安定補
償器２は、安定性を確保するために一次遅れ伝達関数で
表し、その伝達関数Ｇ（ｓ）ｈは、安定補償器時定数Ｔ
hを用いて次式（３）で表されており、安定補償時定数
Ｔhを調整することにより、制御系としての安定性を確
保している。FIG. 1 is a block diagram of an embodiment of a control device with a phase compensation function of the present invention. In FIG. 1, 1 is a phase compensator, 2 is a stability compensator, 3 is a control target, and 4 is a PI controller. Here, the stability compensator 2 is represented by a first-order lag transfer function in order to ensure stability, and its transfer function G (s) h is a stability compensator time constant T.
It is expressed by the following equation (3) using h , and the stability as a control system is secured by adjusting the stability compensation time constant T h .
【００１２】[0012]
【数２】 (Equation 2)
【００１３】位相補償器１は、プロセス推定伝達関数Ｇ
（ｓ）Ｐｓ（図１では、プロセス伝達関数Ｇ（ｓ）ｐｓ
とむだ時間推定伝達関数ｅ-Tsの積で表わす）、安定補
償器２の伝達関数Ｇ（ｓ）ｈ、およびプロセス推定ゲイ
ンＫsを構成要素としている。The phase compensator 1 has a process estimation transfer function G
(S) Ps (process transfer function G (s) ps in FIG. 1)
It is represented by the product of the dead time estimation transfer function e −Ts ), the transfer function G (s) h of the stable compensator 2, and the process estimation gain K s .
【００１４】本発明の位相補償機能つき制御装置を、む
だ時間が大きく、かつ、時定数が小さいプロセス、たと
えば圧延機の板厚の制御などに用いるばあいの制御方法
をつぎに説明する。A control method when the control device with a phase compensation function of the present invention is used for a process having a long dead time and a small time constant, for example, control of the strip thickness of a rolling mill, will be described below.
【００１５】まず、板厚計で板厚を検出し（検出工程は
図示せず）、検出された値が図１のＰＩコントローラ４
に入力される。板厚を検出する際には、むだ時間の計算
に用いるための板の速度を計るための板速計でトラッキ
ングする。入力された値に基づいて、ＰＩコントローラ
４では比例演算処理、積分演算処理、または比例積分演
算処理を行う。演算処理が行われたのちに、位相補償器
１（安定補償器２を含む）に入力してえられた出力をＰ
Ｉコントローラ４にフィードバックする。これら一連の
動作を所望の板厚になるまで繰り返す。First, the plate thickness is detected by a plate thickness meter (the detection process is not shown), and the detected value is the PI controller 4 shown in FIG.
Is input to When detecting the plate thickness, tracking is performed by a plate speed meter for measuring the speed of the plate used for calculating the dead time. Based on the input value, the PI controller 4 performs a proportional calculation process, an integral calculation process, or a proportional-integral calculation process. After the arithmetic processing is performed, the output obtained by inputting to the phase compensator 1 (including the stability compensator 2) is P
Feedback to the I controller 4. These series of operations are repeated until the desired plate thickness is reached.
【００１６】前記ＰＩコントローラ４と位相補償器１か
らなる閉ループ以降に外乱ΔＧがあるばあいには、実測
定値Ｙに外乱ΔＧ分の変動が検出されることになり、制
御量に対するむだ時間後の変動の予測値との相殺に誤差
を生じる。その誤差を発生したままＰＩコントローラ４
にフィードバックする。これら一連の動作を所望の板厚
になるまで繰り返す。If there is a disturbance ΔG after the closed loop consisting of the PI controller 4 and the phase compensator 1, a fluctuation of the actual measurement value Y corresponding to the disturbance ΔG will be detected. There is an error in offsetting the predicted value of the fluctuation. PI controller 4 with the error generated
Feedback to These series of operations are repeated until the desired plate thickness is reached.
【００１７】ここで、位相補償器１（安定補償器２を含
む）からの補償信号との協調をとるために、ＰＩコント
ローラ４の伝達関数Ｇ（ｓ）ｃは、プロセス推定ゲイン
Ｋs、積分時定数Ｔiおよび安定補償器時定数Ｔhを用い
て、次式（４）のように一義的に定められる。Here, in order to coordinate with the compensation signal from the phase compensator 1 (including the stability compensator 2), the transfer function G (s) c of the PI controller 4 is calculated by the process estimation gain K s and the integral. Using the time constant T i and the stability compensator time constant T h , it is uniquely determined as in the following equation (4).
【００１８】[0018]
【数３】 (Equation 3)
【００１９】すなわち、ＰＩコントローラ４の伝達関数
Ｇ（ｓ）ｃが、安定補償時定数Ｔhを積分時定数Ｔiで除
した商（Ｔh／Ｔi）とプロセス推定ゲインＫsの逆数
（１／Ｋs）との積を含んでいる。That is, the transfer function G (s) c of the PI controller 4 is calculated by dividing the stability compensation time constant T h by the integration time constant T i (T h / T i ) and the reciprocal of the process estimation gain K s ( 1 / K s ).
【００２０】ただし、プロセス推定ゲインＫsを一例で
説明すると、モータの端子電圧（入力）とモータの回転
数出力との関係のようなゲインをあらかじめ計算する
か、または実設備で測定して制御装置内で設定してい
る。However, the process estimation gain K s will be described by way of example. The gain such as the relationship between the terminal voltage (input) of the motor and the output of the rotation speed of the motor is calculated in advance or is measured and controlled in actual equipment. It is set in the device.
【００２１】また、圧延機の板厚の制御または炉温制御
に本発明の安定補償器を用いるばあい、前述の安定補償
器時定数Ｔhは、（１／２）Ｔi＜Ｔh＜２Ｔiの範囲程度
に設定されている。When the stability compensator of the present invention is used for controlling the plate thickness of the rolling mill or the furnace temperature, the above-mentioned stability compensator time constant T h is (1/2) T i <T h < It is set in the range of 2T i .
【００２２】式（３）、および式（４）に基づくと、図
１は図２のように変形することが可能である。すなわ
ち、図２は図１の等価ブロック線図である。Based on the equations (3) and (4), FIG. 1 can be modified as shown in FIG. That is, FIG. 2 is an equivalent block diagram of FIG.
【００２３】図２のように変形できるので、等価的にオ
ープンループの制御とすることができる。このため、従
来のスミス法に比べて調整が容易である。しかも、等価
的にオープンループの制御であるため、スミス補償器の
閉ループ系と比べて位相遅れ量がスミス法より少なくな
り、よりプロセスが安定である。Since it can be modified as shown in FIG. 2, it is possible to equivalently perform open loop control. Therefore, the adjustment is easier as compared with the conventional Smith method. Moreover, since the control is equivalently an open loop control, the phase delay amount is smaller than that of the Smith method as compared with the closed loop system of the Smith compensator, and the process is more stable.
【００２４】図３にＫ＝Ｋs＝０．５、ｔ＝Ｔ＝１、Ｔi
＝０．１、Ｔh＝０．２としたばあいにおいて、モデル
推定誤差がないばあいの応答曲線を、従来のスミス補償
器を用いたばあいの応答曲線と比較して示す。図３の曲
線Ａは本発明の制御装置を用いたばあいの応答曲線であ
り、曲線Ｂは従来のスミス補償器を用いたばあいの応答
曲線である。縦軸と横軸はそれぞれステップ量と時間を
示している。図３に示されるように、スミス補償器を用
いたばあいに整定時間が２．２秒程度であったものが、
本発明の制御装置を用いたばあいには、整定時間が１．
８秒程度に短縮された。すなわち、整定時間が約２０％
程度改善され、より安定になっていることがわかる。In FIG. 3, K = Ks = 0.5, t = T = 1, T i
= 0.1 and T h = 0.2, the response curve without the model estimation error is shown in comparison with the response curve with the conventional Smith compensator. Curve A in FIG. 3 is a response curve when the controller of the present invention is used, and curve B is a response curve when a conventional Smith compensator is used. The vertical axis and the horizontal axis represent the step amount and time, respectively. As shown in FIG. 3, when the Smith compensator was used, the settling time was about 2.2 seconds.
When the control device of the present invention is used, the settling time is 1.
It was shortened to about 8 seconds. That is, the settling time is about 20%
It can be seen that the degree has been improved and is more stable.
【００２５】図４は、Ｋ＝Ｋs＝０．５、ｔ＝Ｔ＝１、
Ｔi＝０．１、Ｔh＝０．２とし、モデル推定誤差が発生
したばあいの応答曲線を従来のスミス補償器を用いたば
あいの応答曲線と比較して示す。縦軸と横軸はそれぞれ
ステップ量と時間を示している。図３で適用した推定定
数と比較して、推定定数を２０％増加させている。図３
のばあいと同様に、曲線Ａは本発明の制御装置を用いた
ばあいの応答曲線であり、曲線Ｂは従来のスミス補償器
を用いたばあいの応答曲線である。図４に示されるよう
に、スミス補償器を用いたばあいには振れ幅も大きく発
散気味であるのに対して、本発明の制御装置を用いたば
あいには振れ幅も小さく収束傾向であり安定性がよくな
ったことがわかる。In FIG. 4, K = Ks = 0.5, t = T = 1,
With T i = 0.1 and T h = 0.2, the response curve when a model estimation error occurs is shown in comparison with the response curve when a conventional Smith compensator is used. The vertical axis and the horizontal axis represent the step amount and time, respectively. The estimated constant is increased by 20% compared to the estimated constant applied in FIG. FIG.
Similar to the case, curve A is the response curve when using the controller of the present invention and curve B is the response curve when using the conventional Smith compensator. As shown in FIG. 4, when the Smith compensator is used, the swing width is large and tends to diverge, whereas when the controller of the present invention is used, the swing width is small and tends to converge. It can be seen that the stability has improved.
【００２６】本発明の位相補償機能つき制御装置を、た
とえば炉温の制御のようにむだ時間が小さく、時定数の
大きいものに用いるばあいにも図１の制御系が用いられ
る。このばあいにも、等価的にオープンループの制御で
あるため、位相遅れ量が通常のＰＩ制御より少なくな
り、制御性が向上する。The control system of FIG. 1 is also used when the controller with phase compensation function of the present invention is used for a furnace having a small dead time and a large time constant, such as a furnace temperature control. In this case as well, since the control is equivalently an open loop control, the amount of phase delay is smaller than that of the normal PI control, and the controllability is improved.
【００２７】図５にＫ＝Ｋs＝０．５、ｔ＝Ｔ＝１、Ｔi
＝１０、Ｔh＝２２としたばあいのステップ応答曲線
を、従来のスミス補償器を用いたばあいの応答曲線と比
較して示す。縦軸と横軸はそれぞれステップ量と時間を
示している。図５の曲線Ａは本発明の制御装置を用いた
ばあいの応答曲線であり、曲線Ｂは従来のスミス補償器
を用いたばあいの応答曲線である。図５に示されるよう
に、整定時間が約２０％程度改善されて制御性が向上し
ていることがわかる。In FIG. 5, K = Ks = 0.5, t = T = 1, T i
= 10 and T h = 22, the step response curve is shown in comparison with the response curve using the conventional Smith compensator. The vertical axis and the horizontal axis represent the step amount and time, respectively. Curve A in FIG. 5 is a response curve when the controller of the present invention is used, and curve B is a response curve when a conventional Smith compensator is used. As shown in FIG. 5, it is understood that the settling time is improved by about 20% and the controllability is improved.
【００２８】[0028]
【発明の効果】本発明によれば、制御装置を等価的にオ
ープンループと考えることができるので、むだ時間が大
きく、時定数が小さいものに本発明の位相補償機能つき
制御装置を用いれば、制御定数の調整が容易で、モデル
誤差のあるものに対しても安定性がよい。According to the present invention, since the control device can be considered as an open loop equivalently, if the control device with the phase compensation function of the present invention is used for a device having a large dead time and a small time constant, The control constants are easy to adjust and the stability is good even for those with model errors.
【００２９】むだ時間が小さく、時定数が大きいものに
本発明の位相補償機能つき制御装置を用いれば、制御性
が向上する。If the controller with a phase compensation function of the present invention is used for a device having a small dead time and a large time constant, the controllability is improved.
【図１】本発明の一実施例にかかわる位相補償機能つき
制御装置を示すブロック線図である。FIG. 1 is a block diagram showing a control device with a phase compensation function according to an embodiment of the present invention.
【図２】図１の位相補償機能つき制御装置の等価的なブ
ロック線図である。FIG. 2 is an equivalent block diagram of the control device with the phase compensation function of FIG.
【図３】モデル推定誤差がないばあいに、本発明の一実
施例にかかわる位相補償機能つき制御装置を圧延機の板
厚の制御に用いるばあいの応答曲線と従来のスミス補償
器を用いるばあいの応答曲線を比較して示す図である。FIG. 3 shows a response curve when a controller with a phase compensation function according to an embodiment of the present invention is used to control the strip thickness of a rolling mill and a conventional Smith compensator when there is no model estimation error. It is a figure which compares and shows the response curve of Ai.
【図４】モデル推定誤差が発生したばあいに、本発明の
一実施例にかかわる位相補償機能つき制御装置を圧延機
の板厚の制御に用いるばあいの応答曲線と従来のスミス
補償器を用いるばあいの応答曲線を比較して示す図であ
る。FIG. 4 is a graph showing a case where a controller having a phase compensation function according to an embodiment of the present invention is used to control the strip thickness of a rolling mill when a model estimation error occurs, and a response curve and a conventional Smith compensator are used. It is a figure which compares and shows the response curve of the case.
【図５】本発明の一実施例にかかわる位相補償機能つき
制御装置を炉温の制御に用いるばあいの応答曲線と従来
のスミス補償器を用いるばあいの応答曲線を比較して示
す図である。FIG. 5 is a diagram showing a comparison between a response curve when a control device with a phase compensation function according to an embodiment of the present invention is used for controlling furnace temperature and a response curve when a conventional Smith compensator is used.
【図６】従来のスミス補償器を用いた制御装置のブロッ
ク線図である。FIG. 6 is a block diagram of a control device using a conventional Smith compensator.
１ 位相補償器 ２ 安定補償器 ３ 制御対象 ４ ＰＩコントローラ 1 Phase compensator 2 Stability compensator 3 Control target 4 PI controller
Claims (1)
てあらかじめ推定されているプロセス推定ゲインを位相
補償器に入力し、えられる出力を前記ＰＩコントローラ
にフィードバックし、制御目標に対して測定値の位相補
償をする位相補償手段と、前記位相補償器に含まれる安
定補償器によって系を安定に補償する安定補償手段とか
らなり、前記ＰＩコントローラの伝達関数が、安定補償
器時定数を積分時定数で除した商と前記プロセス推定ゲ
インの逆数との積を含むことを特徴とするむだ時間を有
するプロセスの制御に用いられる位相補償機能つき制御
装置。1. A process estimation gain pre-estimated for a control signal from a PI controller is input to a phase compensator, and an obtained output is fed back to the PI controller to obtain a phase of a measured value with respect to a control target. Comprising a phase compensating means for compensating and a stable compensating means for stably compensating the system by a stable compensator included in the phase compensator, and the transfer function of the PI controller uses the stable compensator time constant as an integral time constant. A controller with a phase compensation function used for controlling a process having a dead time, characterized by including a product of a quotient obtained by division and a reciprocal of the process estimation gain.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP28229695A JP3267841B2 (en) | 1995-10-30 | 1995-10-30 | Controller with phase compensation function |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP28229695A JP3267841B2 (en) | 1995-10-30 | 1995-10-30 | Controller with phase compensation function |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH09128006A true JPH09128006A (en) | 1997-05-16 |
| JP3267841B2 JP3267841B2 (en) | 2002-03-25 |
Family
ID=17650583
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP28229695A Expired - Fee Related JP3267841B2 (en) | 1995-10-30 | 1995-10-30 | Controller with phase compensation function |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP3267841B2 (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6259223B1 (en) | 1997-08-13 | 2001-07-10 | Saab Ab | Method and apparatus for phase compensation in a vehicle control system |
| US20100237819A1 (en) * | 2009-03-18 | 2010-09-23 | Nikon Corporation | Control Systems and Methods for Compensating for Effects of a Stage Motor |
| CN111299330A (en) * | 2018-12-12 | 2020-06-19 | 东芝三菱电机产业系统株式会社 | Mathematical model calculation device and control device for rolling production line |
-
1995
- 1995-10-30 JP JP28229695A patent/JP3267841B2/en not_active Expired - Fee Related
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6259223B1 (en) | 1997-08-13 | 2001-07-10 | Saab Ab | Method and apparatus for phase compensation in a vehicle control system |
| US20100237819A1 (en) * | 2009-03-18 | 2010-09-23 | Nikon Corporation | Control Systems and Methods for Compensating for Effects of a Stage Motor |
| US8853988B2 (en) * | 2009-03-18 | 2014-10-07 | Nikon Corporation | Control systems and methods for compensating for effects of a stage motor |
| CN111299330A (en) * | 2018-12-12 | 2020-06-19 | 东芝三菱电机产业系统株式会社 | Mathematical model calculation device and control device for rolling production line |
| CN111299330B (en) * | 2018-12-12 | 2022-03-22 | 东芝三菱电机产业系统株式会社 | Mathematical model calculation device and control device for rolling production line |
Also Published As
| Publication number | Publication date |
|---|---|
| JP3267841B2 (en) | 2002-03-25 |
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