JPH0643911A - Model error compensating feedback control method - Google Patents

Model error compensating feedback control method

Info

Publication number
JPH0643911A
JPH0643911A JP23993992A JP23993992A JPH0643911A JP H0643911 A JPH0643911 A JP H0643911A JP 23993992 A JP23993992 A JP 23993992A JP 23993992 A JP23993992 A JP 23993992A JP H0643911 A JPH0643911 A JP H0643911A
Authority
JP
Japan
Prior art keywords
model
origin
feedback control
control system
error
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
JP23993992A
Other languages
Japanese (ja)
Inventor
Keiji Watabe
慶二 渡部
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
Original Assignee
Individual
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Individual filed Critical Individual
Priority to JP23993992A priority Critical patent/JPH0643911A/en
Publication of JPH0643911A publication Critical patent/JPH0643911A/en
Pending legal-status Critical Current

Links

Abstract

PURPOSE:To obtain the feedback control method which can optionally adjust a frequency range wherein low sensitivity is obtained while the stability of a feedback control system without depending upon a model error. CONSTITUTION:The multiplicative model error E(s) between the transfer function matrix, Gp(s) of a controlled system and the transfer function matrix G(s) of a model is represented as G(s)E(s), and the number of unstable poles of Gp(s) and E(s) are equally set to (m). The desired frequency band which is set to low sensitivity is from a direct current to certain high frequency omegao. When the transfer matrix of a compensator 5 which can optionally be set is denoted as P(s)6 and G(s)P<-1>(s) is an expanded model 4, the multaiplicative error is P(s)E(s). Then P(s) 6 is set at omegao from a frequency band 0 so that the vector track of detP(s)E(s) centering on the origin of a complex plane does not rotates on the origin in a Gp(s) 3 stable state or rotates m/2 times counterclockwise on the origin. The expanded model G(s)P<-1>4 using this P(s) is regarded as the controlled system to constitute the feedback control system.

Description

【発明の詳細な説明】Detailed Description of the Invention

【0001】[0001]

【産業上の利用分野】この発明は、制御対象の温度、電
圧、回転数等の被制御量を目標量に近づけるためのフィ
ードバック制御方法に関する。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a feedback control method for bringing a controlled quantity such as a temperature, a voltage and a rotation speed of a controlled object close to a target quantity.

【0002】[0002]

【従来の技術】フィードバック制御系の設計目標は、制
御対象の出力を目標入力に小さな定常偏差で追従させ、
外乱や制御対象の動特性の変動、設計に使用した制御対
象のモデルと対象の間の誤差の出力への影響を小さく抑
え、かつ、制御対象の動特性の変動やモデル誤差に対し
フィードバック制御系の安定性を保持することである。
目標入力追従特性、外乱除去特性をよくし、モデル誤差
の出力への影響を小さくするには、感度関数の値を小さ
くすることであり、モデル誤差に対しフィードバック制
御系の安定性を保持するには、相補感度関数の値を小さ
くすることである。しかし、感度関数と相補感度関数の
和は1あるいは単位行列であり、同時に小さくすること
ができない。そこで周波数上で分割し、低周波成分に対
しては感度関数を小さくし低感度に、高周波成分に対し
ては相補感度を小さくし安定性を確保してきた。従来、
低感度にできる周波数範囲はモデル誤差に依存し、モデ
ル誤差が大きくなると安定性を保ったまま低感度にでき
る範囲がせまくなる。
2. Description of the Related Art The design goal of a feedback control system is to make the output of the controlled object follow the target input with a small steady deviation,
The influence of disturbances and fluctuations in the dynamic characteristics of the controlled object, the error between the model of the controlled object used for design and the object on the output is suppressed to a small level, and a feedback control system is provided for fluctuations in the dynamic characteristics of the controlled object and model errors. To maintain stability.
To improve the target input tracking characteristics and disturbance rejection characteristics and reduce the effect of model error on the output, it is necessary to reduce the value of the sensitivity function, and to maintain the stability of the feedback control system against model error. Is to reduce the value of the complementary sensitivity function. However, the sum of the sensitivity function and the complementary sensitivity function is 1 or a unit matrix and cannot be reduced at the same time. Therefore, by dividing the frequency, the sensitivity function has been reduced to low sensitivity for low frequency components, and the complementary sensitivity has been reduced for high frequency components to ensure stability. Conventionally,
The frequency range in which the sensitivity can be lowered depends on the model error, and when the model error becomes large, the range in which the sensitivity can be lowered while maintaining the stability becomes narrow.

【0003】[0003]

【発明が解決しようとする課題】フィードバック制御系
の安定性を保ったまま低感度にできる周波数範囲を、モ
デル誤差に依存せずに、任意に調整できるフィードバッ
ク制御方法を与えることである。
SUMMARY OF THE INVENTION It is an object of the present invention to provide a feedback control method capable of arbitrarily adjusting the frequency range in which the sensitivity of the feedback control system can be reduced while maintaining the stability of the feedback control system without depending on the model error.

【0004】[0004]

【課題を解決するための手段】制御対象の伝達行列をG
(s)、モデルの伝達行列をG(s)、G(s)と
G(s)の乗法的誤差E(s)を、G(s)=G
(s)E(s)とし、G(s)が安定のとき、E
(s)は安定、G(s)が不安定のとき、G(s)
とE(s)の不安定極の数は等しくm個とする。低感度
にしたい周波数帯域を、直流からある高周波ωまでと
する。設計者が任意に設定できる補償器の伝達行列をP
(s)とし、G(s)P−1(s)を拡大モデルとする
と、乗法的モデル誤差は、G(s)=G(s)P−1
(s)P(s)E(s)より、P(s)E(s)とな
る。G(s)が安定のとき、複素平面の原点を中心と
するdetP(s)E(s)のベトル軌跡が、直流から
周波数ωで、図1に示すように原点の左側に回らない
ようにP(s)を設定する。あるいは、detP(s)
E(s)を小さくする。G(s)が不安定のときは、
原点を中心とするdetP(s)E(s)のベクトル軌
跡が、周波数帯域0からωで、図2に示すように原点
のまわりを反時計方向にm/2回まわるようにP(s)
を設定する。このP(s)を用いた拡大モデルG(s)
−1(s)を制御対象とみなして、フィードバック制
御系を構成する。
A transfer matrix of a controlled object is represented by G
P (s), multiplicative error E models transfer matrix G (s), G P ( s) and G (s) a (s), G P (s ) = G
(S) E (s), and when G P (s) is stable, E
(S) is stable, and when GP (s) is unstable, GP (s)
And the number of unstable poles of E (s) is equal to m. The frequency band for which the sensitivity is desired to be low is set from DC to a certain high frequency ω O. Let P be the transfer matrix of the compensator that the designer can set arbitrarily.
(S) and G (s) P −1 (s) as an expansion model, the multiplicative model error is G P (s) = G (s) P −1.
From (s) P (s) E (s), P (s) E (s) is obtained. When G P (s) is stable, the bettle locus of detP (s) E (s) centered on the origin of the complex plane does not turn to the left side of the origin as shown in FIG. 1 from DC to frequency ω O. So that P (s) is set. Alternatively, detP (s)
Reduce E (s). When G P (s) is unstable,
The vector locus of detP (s) E (s) centered on the origin is in the frequency band 0 to ω O , and P (s) is rotated counterclockwise m / 2 times around the origin as shown in FIG. )
To set. Enlarged model G (s) using this P (s)
A feedback control system is configured by regarding P −1 (s) as a control target.

【0005】制御対象G(s)とモデルG(s)の乗
法的モデル誤差E(s)が、G(s)=E(s)G
(s)のときは、P−1(s)G(s)を拡大モデルと
する。乗法的モデル誤差は、G(s)=E(s)P
(s)P−1(s)G(s)より、E(s)P(s)と
なる。G(s)安定の場合、複素平面の原点を中心と
するdetE(s)P(s)のベクトル軌跡が直流から
周波数ωで、図1に示すように原点の左側に回らない
ようにP(s)を設定する。あるいは、detE(s)
P(s)を小さくする。G(s)が不安定のときは、
原点を中心とするdetE(s)P(s)のベクトル軌
跡が、周波数帯域0からωで、図2に示すように原点
のまわりを反時計方向にm/2回まわるようにP(s)
を設定する。このP(s)を用いた拡大モデルP
−1(s)G(s)を制御対象とみなして、フィードバ
ック制御系を構成する。
The multiplicative model error E (s) between the controlled object G P (s) and the model G (s) is G P (s) = E (s) G
In the case of (s), P −1 (s) G (s) is used as the expansion model. The multiplicative model error is G P (s) = E (s) P
From (s) P −1 (s) G (s), E (s) P (s) is obtained. When G P (s) is stable, the vector locus of detE (s) P (s) centered on the origin of the complex plane is from DC to frequency ω O , and should not turn to the left of the origin as shown in FIG. Set P (s). Alternatively, detE (s)
Reduce P (s). When G P (s) is unstable,
The vector locus of detE (s) P (s) centered on the origin is in the frequency band 0 to ω O , and P (s) is rotated counterclockwise m / 2 times around the origin as shown in FIG. )
To set. Expansion model P using this P (s)
−1 (s) G (s) is regarded as a control target, and a feedback control system is configured.

【0006】または、離散時間化してG(s)をG’
(Z−1)等にして、連続時間系と同様に拡大モデルを
求め、それを制御対象とみなしてフィードバック制御系
を構成する。
Alternatively, G (s) is converted into G's by discrete time.
(Z −1 ) and so on, an expanded model is obtained in the same manner as in the continuous time system, and the expanded model is regarded as a control target to form a feedback control system.

【0007】[0007]

【作用】モデルG(s)を制御対象とみなして構成した
(s)に対するフィードバック制御系の感度関数を
S(s)、相補感度関数をT(s)=I−S(s)とす
る。また、G(s)=G(s)E(s)=G(s)
[I+δ(s)]とする。フィードバック系の安定性
は、ナイキストの安定判別法から、複素平面の原点を中
心としたdet[I+T(s)δ(s)]のベクトル軌
跡が、G(s)が安定ならば原点の右側を通るとき、
(s)が不安定のときは原点の周りを反時計方向に
m/2回まわるとき、そのときに限ってフィードバック
制御系は安定であ。直流から高周波ωまでS(s)→
0とすると、S(s)+T(s)=Iなので、T(s)
→Iになり、δ(s)が大きいとナイキストの安定条件
が満たせなくなる。従来は、安定化するためT(s)を
小さく、S(s)を大きくせざるを得なかった。これに
対し、本発明では、拡大モデルG(s)P−1(s)、
あるいはP−1(s)G(s)を制御対象とみなしてフ
ィードバック制御系を構成するのでつぎのようになる。
The sensitivity function of the feedback control system with respect to G P (s) constructed by considering the model G (s) as a control object is S (s), and the complementary sensitivity function is T (s) = IS (s). To do. Also, G P (s) = G (s) E (s) = G (s)
[I + δ (s)]. The stability of the feedback system is determined from the stability determination method of Nyquist by the vector locus of det [I + T (s) δ (s)] centered on the origin of the complex plane, and if G P (s) is stable, it is on the right side of the origin. When passing through
When G P (s) is unstable, the feedback control system is stable only when turning around the origin in the counterclockwise direction m / 2 times. From DC to high frequency ω O S (s) →
If 0, S (s) + T (s) = I, so T (s)
→ I, and if δ (s) is large, the Nyquist stability condition cannot be satisfied. In the past, in order to stabilize, T (s) had to be small and S (s) had to be large. On the other hand, in the present invention, the expansion model G (s) P −1 (s),
Alternatively, since P −1 (s) G (s) is regarded as the control target and the feedback control system is configured, the following is performed.

【0008】拡大モデルG(s)P−1(s)を制御対
象とみなしたフィードバック制御系では、G(s)=
G(s)E(s)=G(s)P−1(s)P(s)E
(s)=G(s)P−1(s)[I+η(s)]と展開
できる。G(s)が安定のとき、周波数帯域0からω
で、T(s)→Iより、det[I+T(s)η
(s)]≒det[I+η(s)]=detP(s)E
(s)となり、図1に示すように原点の右側にある。周
波数ωを越えた高周波ではT(s)η(s)+0、d
et[I+T(s)η(s)]→1となる。これより全
周波数にわたるベクトル軌跡は、図3のように原点を回
らず閉ループ系は安定である。また、detP(s)E
(s)を小さくしたときは、E(s)が大きくともde
t[I+T(s)η(s)]のベクトル軌跡は原点のち
かくにあり、T(s)が小さくなると原点の右側にいく
ので、原点をまわることがない。G(s)が不安定の
ときは、周波数帯域0からωで、de[I+T(s)
η(s)]≒detP(s)E(s)のベクトル軌跡
は、図2に示されるように原点の周りを反時計方向にm
/2回まわる。固波数ωを越えた高周波ではT(s)
δ(s)→0、det[I+T(s)η(s)]→1と
なるから、全周波数にわたるdet[I+T(s)η
(s)]の原点を中心としたベクトル軌跡は、図4に示
すように原点の周りを反時計方向にm/2回まわり、閉
ループ系は安定である。したがって、乗法的誤差E
(s)に制限されずに、安定性を保ったまま周波数帯0
からωまで低感度にできる。
In the feedback control system in which the expanded model G (s) P −1 (s) is regarded as the control target, G P (s) =
G (s) E (s) = G (s) P −1 (s) P (s) E
It can be expanded to (s) = G (s) P −1 (s) [I + η (s)]. When G P (s) is stable, from frequency band 0 to ω
At O , from T (s) → I, det [I + T (s) η
(S)] ≈det [I + η (s)] = detP (s) E
(S), which is on the right side of the origin as shown in FIG. At a high frequency exceeding the frequency ω O , T (s) η (s) +0, d
et [I + T (s) η (s)] → 1. As a result, the vector locus over all frequencies does not go around the origin as shown in FIG. 3, and the closed loop system is stable. Also, detP (s) E
When (s) is reduced, even if E (s) is large, de
The vector locus of t [I + T (s) η (s)] is near the origin, and when T (s) becomes small, it goes to the right side of the origin, and therefore does not go around the origin. When G P (s) is unstable, in the frequency band 0 to ω O , de [I + T (s)
The vector locus of η (s)] ≈detP (s) E (s) is m counterclockwise around the origin as shown in FIG.
/ Turn twice. At high frequencies above the solid wave number ω O , T (s)
Since δ (s) → 0 and det [I + T (s) η (s)] → 1 are satisfied, det [I + T (s) η over all frequencies.
The vector locus centered on the origin of (s)] rotates counterclockwise around the origin m / 2 times as shown in FIG. 4, and the closed loop system is stable. Therefore, the multiplicative error E
Not limited to (s), frequency band 0 with stability maintained
The sensitivity can be reduced from ω to ω O.

【0009】拡大モデルP−1(s)G(s)を制御対
象とみなしたフィードバック制御系では、G(s)=
E(s)G(s)=E(s)P(s)P−1(s)G
(s)=[I+η(s)]P−1(s)G(s)とな
る。G(s)が安定のとき、周波数が帯域0からω
で、T(s)→Iより、det[I+η(s)T
(s)]≒det[I+η(s)]=detE(s)P
(s)となり、図1に示すように原点の右側にある。周
波数ωを越えた高周波ではη(s)T(s)→0、d
et[I+η(s)T(s)]→lとなる。これより全
周波数にわたるベクトル軌跡は、図3のように原点を回
らず閉ループ系は安定である。G(s)が不安定のと
き、周波数帯域0からωがT→Iよりdet[I+η
(s)T(s)]≒detE(s)P(s)のベクトル
軌跡は、図2に示されるように原点の周りを反時計方向
にm/2回まわる。周波数ωを越えた高周波ではη
(s)T(s)→0、det[I+η(s)T(s)]
→1となるから、全周波数にわたるdet[I+η
(s)T(s)]の原点を中心としたベクトル軌跡は、
図4に示すように原点の周りを反時計方向にm/2回ま
わり、閉ループ系は安定である。かくして、モデル誤差
の大きさに左右されずに、希望周波数帯域での低感度と
閉ループ系の安定性を同時に得ることができる。
In the feedback control system in which the expanded model P −1 (s) G (s) is regarded as the control target, G P (s) =
E (s) G (s) = E (s) P (s) P −1 (s) G
(S) = [I + η (s)] P −1 (s) G (s). When G P (s) is stable, the frequency is from band 0 to ω O
Then, from T (s) → I, det [I + η (s) T
(S)] ≈det [I + η (s)] = detE (s) P
(S), which is on the right side of the origin as shown in FIG. At high frequencies above the frequency ω O , η (s) T (s) → 0, d
et [I + η (s) T (s)] → l. As a result, the vector locus over all frequencies does not go around the origin as shown in FIG. 3, and the closed loop system is stable. When G P (s) is unstable, from frequency band 0 to ω O, from T → I, det [I + η
The vector locus of (s) T (s)] ≈detE (s) P (s) turns counterclockwise around the origin m / 2 times as shown in FIG. At high frequencies above the frequency ω O η
(S) T (s) → 0, det [I + η (s) T (s)]
→ becomes 1, so det [I + η over all frequencies
The vector locus centering on the origin of (s) T (s)] is
As shown in FIG. 4, it rotates around the origin counterclockwise m / 2 times, and the closed loop system is stable. Thus, the low sensitivity and the stability of the closed loop system in the desired frequency band can be obtained at the same time without being influenced by the magnitude of the model error.

【0010】サンプリング周波数を高くとると、離散時
間系でも、連続時間系をほぼ同様のことが言える。
When the sampling frequency is high, the same applies to the continuous time system even in the discrete time system.

【0011】[0011]

【実施例】モータの角度制御システムのブロック線図を
図5に示す。3は制御対象、4は拡大モデル、5は補償
器、6は前置補償器である。7は目標入力、8は制御対
象の入力、9は出力である。制御対象と拡大モデルが等
しいときの目標入力rから出力yまでの伝達関数はG
(s)であり、任意に設定できる。感度関数はS(s)
=Q(s)G(s)であり、直流からωまで低感度に
なるようにQ(s)を決める。ロバスト安定性は、1+
T(s)η(s)のベクトル軌跡が原点を回らないこと
であり、これを満たすように、直流からωでP(s)
E(s)のベクトル軌跡が図1のように第1、4象限に
留るように、位相進み要素をもちいてP(s)を決め
る。図5の系を離散時間化し、実際の制御系は図6とな
る。図6の11の制御器は、図5の11の部分であり、
図7の流れ図で制御入力uの計算をおこなう。応答例を
図8に示す。点線の12がモデルの応答で、13の実線
が制御系の応答であり、かなり一致している。これは、
モデル誤差があるにも関わらず安定で、所定の低感度特
性を有していることを示している。
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT A block diagram of a motor angle control system is shown in FIG. 3 is a controlled object, 4 is an expansion model, 5 is a compensator, and 6 is a predistorter. Reference numeral 7 is a target input, 8 is an input of a controlled object, and 9 is an output. The transfer function from the target input r to the output y when the controlled object and the expansion model are equal is G
(S), which can be set arbitrarily. Sensitivity function is S (s)
= Q (s) G (s), and Q (s) is determined so as to have low sensitivity from DC to ω O. 1+ for robust stability
T (s) eta vector locus of (s) is that does not turn the origin, so as to satisfy this DC from omega O with P (s)
P (s) is determined using the phase advance element so that the vector locus of E (s) remains in the first and fourth quadrants as shown in FIG. The system of FIG. 5 is converted into discrete time, and the actual control system is shown in FIG. The controller 11 of FIG. 6 is the part 11 of FIG.
The control input u is calculated using the flow chart of FIG. An example response is shown in FIG. The dotted line 12 is the model response, and the solid line 13 is the control system response, which are in good agreement. this is,
It is shown that it is stable in spite of the model error and has a predetermined low sensitivity characteristic.

【0012】制御対象G(s)=G(s)E(s)に
対し、直流から周波数ωで、detE(s)P(s)
のベクトル軌跡が、E(s)安定のときは、図1に示す
ように原点の左側に回らないように、G(s)が不安
定のときは、図2に示すように原点のまわりを反時計方
向にm/2回まわるようにP(s)を決める。このP
(s)を用いた拡大モデルG(s)P−1(s)を制御
対象とみなして、図9の制御系を構成する。感度は、Q
(s)で設定できる。
For the controlled object G P (s) = G (s) E (s), from DC to frequency ω O , detE (s) P (s)
When the vector locus of E is stable in E (s), it does not rotate to the left side of the origin as shown in FIG. 1. When G P (s) is unstable, as shown in FIG. P (s) is determined so as to turn counterclockwise m / 2 times. This P
The enlarged model G (s) P −1 (s) using (s) is regarded as a control target, and the control system of FIG. 9 is configured. The sensitivity is Q
It can be set with (s).

【0013】制御対象G(s)=G(s)E(s)に
対し、直流から周波数ωで、detE(s)P(s)
のベクトル軌跡が、E(s)安定のときは、図1に示す
ように原点の左側に回らないように、G(s)が不安
定のときは、図2に示すように原点のまわりを反時計方
向にm/2回まわるようにP(s)を決める。このP
(s)を用いた拡大モデルG(s)P−1(s)をG
(s)P−1(s)=C(sI−A)−1Bと展開し、
これを制御対象とみなして、図10の制御系を構成す
る。図10の14はオブザーバで、kはA−KCを安定
にする行列であり、15はフィードバック行列で、Fは
A−BFを安定にする行列である。直流からωで低感
度になるようにQ(s)を決める。
For the controlled object G P (s) = G (s) E (s), from DC to frequency ω O , detE (s) P (s)
When the vector locus of E is stable in E (s), it does not rotate to the left side of the origin as shown in FIG. 1. When G P (s) is unstable, as shown in FIG. P (s) is determined so as to turn counterclockwise m / 2 times. This P
The enlarged model G (s) P −1 (s) using (s) is G
(S) P −1 (s) = C (sI−A) −1 B, and
Considering this as a control target, the control system of FIG. 10 is configured. In FIG. 10, 14 is an observer, k is a matrix that stabilizes A-KC, 15 is a feedback matrix, and F is a matrix that stabilizes A-BF. Determine Q (s) so that the sensitivity is low at ω O from DC.

【0014】[0014]

【発明の効果】制御対象の動特性が正確に掴みにくくモ
デリング誤差が大きい対象や、動作中に制御対象の動特
性が大きく変動する場合でも、誤差の大きさに左右され
ず、安定性を保ったまま直流から希望周波数まで低感度
にすることができるので、モデル誤差や外乱の影響を抑
え、目標入力に小さな定常偏差で追従させることができ
る。
[Effects of the Invention] Even if the dynamic characteristics of the controlled object are difficult to grasp accurately and the modeling error is large, or the dynamic characteristics of the controlled object fluctuate greatly during operation, stability is maintained without being influenced by the magnitude of the error. Since it is possible to reduce the sensitivity from the direct current to the desired frequency as it is, it is possible to suppress the influence of model error and disturbance and to follow the target input with a small steady deviation.

【図面の簡単な説明】[Brief description of drawings]

【図1】モデル誤差が安定の場合のdetP(s)E
(s)またはdetE(s)P(s)の周波数0ω
でのベクトル軌跡を示す。
FIG. 1 is detP (s) E when the model error is stable.
3 shows a vector locus of (s) or detE (s) P (s) up to the frequency 0ω O.

【図2】モデル誤差が不安定の場合のdetP(s)E
(s)またはdetE(s)P(s)の直流から周波数
ωまでのベクトル軌跡である。
FIG. 2 is detP (s) E when the model error is unstable.
(S) or detE (s) P (s) is a vector locus from direct current to frequency ω O.

【図3】モデル誤差が安定の場合のdet[I+T
(s)η(s)]あるいはdet[I+η(s)T
(s)]の周波数0からωまでのベクトル軌跡であ
る。
FIG. 3 shows det [I + T when the model error is stable.
(S) η (s)] or det [I + η (s) T
(S)] is a vector locus from frequency 0 to ω O.

【図4】モデル誤差が不安定の場合の、det[I+T
(s)δ(s)]あるいはdet[I+η(s)T
(s)]の周波数0からωまでのベクトル軌跡であ
る。
FIG. 4 shows det [I + T when the model error is unstable.
(S) δ (s)] or det [I + η (s) T
(S)] is a vector locus from frequency 0 to ω O.

【図5】モータの角度制御システムのブロック線図であ
る。
FIG. 5 is a block diagram of a motor angle control system.

【図6】制御系の構成図である。FIG. 6 is a configuration diagram of a control system.

【図7】図6の系の11の制御器のアルゴリズムの流れ
図である。
7 is a flow diagram of an algorithm for 11 controllers of the system of FIG.

【図8】図6の系のステップ応答例である。8 is an example step response of the system of FIG.

【図9】フィードバック制御系の別の構成FIG. 9 is another configuration of the feedback control system.

【図10】オブザーバを用いた状態フィードバック制御
FIG. 10 is a state feedback control system using an observer.

【符号の説明】[Explanation of symbols]

1 detP(s)E(s)あるいはdetE(s)
P(s)の周波数0ωまでのベクトル軌跡 2 det[I+T(s)η(s)]またはdet
[I+η(s)T(s)]の周波数0からωまでのベ
クトル軌跡 3 制御対象 4 拡大モデル 5 補償器 6 前置補償器 7 目標入力 8 制御入力 9 出力 10 制御器の全体 11 制御器 12 モデルの応答 13 制御系の応答 14 オブザーバ 15 フィードバック行列 16 出力行列 17 補償器
1 detP (s) E (s) or detE (s)
Vector locus of P (s) up to frequency 0ω O 2 det [I + T (s) η (s)] or det
Vector locus of [I + η (s) T (s)] from frequency 0 to ω O 3 Control object 4 Enlarged model 5 Compensator 6 Precompensator 7 Target input 8 Control input 9 Output 10 Overall controller 11 Controller 12 model response 13 control system response 14 observer 15 feedback matrix 16 output matrix 17 compensator

Claims (1)

【特許請求の範囲】[Claims] 【請求項1】 制御対象に対しモデルを拡大し、制御対
象と拡大モデルの間の乗法的誤差ε(s)の行列式のベ
クトル軌跡を、低感度にしたい周波数範囲で、ε(s)
が安定のときは原点を回らないように、ε(s)がm個
の不安定極を持つときは、原点の周りを反時計方向にm
/2回まわるように拡大モデルを選び、拡大モデルを制
御対象とみなしてフィードバック制御系を構成すること
を特徴とするモデル誤差補償フィードバック制御方法。
1. A model is expanded with respect to a controlled object, and a vector locus of a determinant of a multiplicative error ε (s) between the controlled object and the expanded model is ε (s) in a frequency range where low sensitivity is desired.
When ε (s) has m unstable poles, so as not to go around the origin when is stable, m around the origin in the counterclockwise direction.
A model error-compensating feedback control method characterized in that an enlarged model is selected so as to rotate twice, and the enlarged model is regarded as a control target to configure a feedback control system.
JP23993992A 1992-07-24 1992-07-24 Model error compensating feedback control method Pending JPH0643911A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP23993992A JPH0643911A (en) 1992-07-24 1992-07-24 Model error compensating feedback control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP23993992A JPH0643911A (en) 1992-07-24 1992-07-24 Model error compensating feedback control method

Publications (1)

Publication Number Publication Date
JPH0643911A true JPH0643911A (en) 1994-02-18

Family

ID=17052072

Family Applications (1)

Application Number Title Priority Date Filing Date
JP23993992A Pending JPH0643911A (en) 1992-07-24 1992-07-24 Model error compensating feedback control method

Country Status (1)

Country Link
JP (1) JPH0643911A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5950055A (en) * 1997-04-18 1999-09-07 Ricoh Company, Ltd. Powder pump and image forming apparatus having the powder pump and method therefor

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5950055A (en) * 1997-04-18 1999-09-07 Ricoh Company, Ltd. Powder pump and image forming apparatus having the powder pump and method therefor

Similar Documents

Publication Publication Date Title
Cao et al. Design and analysis of a novel L1 adaptive controller, Part II: Guaranteed transient performance
Cao et al. Practical prescribed time tracking control over infinite time interval involving mismatched uncertainties and non-vanishing disturbances
JP6485644B2 (en) Method and motor drive for controlling the angular speed of an induction motor
Oliveira et al. Controlling the speed of a three-phase induction motor using a simplified indirect adaptive sliding mode scheme
Ramos et al. Spatial observer-based repetitive controller: An active disturbance rejection approach
Liu et al. Linear inverted pendulum control based on improved ADRC
JPS59142603A (en) Control system of high gain feedback
JPS61248104A (en) Manipulator controlling device
JPH06138906A (en) Digital-servo control system
JPH06343284A (en) Method and apparatus for repetitively controlling ac servomotor
JPH0643911A (en) Model error compensating feedback control method
Lu et al. Command filtering-based neural network control for fractional-order PMSM with input saturation
WO2019087554A1 (en) Feedback control method and motor control device
JP2929567B2 (en) Digital modulation method
CN115720061A (en) Fuzzy self-adaptive backstepping control method of electromechanical servo system based on finite time
WO2022030346A1 (en) Control assistance device, control system, and control assistance method
Quang et al. Neural Network PID Controller for PMSM Drives
JP4726346B2 (en) Servo motor control device
CN108494304B (en) quasi-PI disturbance perception control method for three-phase permanent magnet synchronous motor
CN111796509A (en) Gyro self-stabilization control method
JPH0834396A (en) Automatic steering gear for ship
Zohrei et al. Robust Backstepping Control Based on Neural Network Stochastic Constrained for Three Axes Inertial Stable Platform
JP2663386B2 (en) Variable structure PI controller
Ananthan Advanced Control Strategies for Rotary Double Inverted Pendulum
Ranger et al. Improved backstepping-based adaptive PID control