JPS63316409A - Support control device of magnetic attraction type - Google Patents
Support control device of magnetic attraction typeInfo
- Publication number
- JPS63316409A JPS63316409A JP15128487A JP15128487A JPS63316409A JP S63316409 A JPS63316409 A JP S63316409A JP 15128487 A JP15128487 A JP 15128487A JP 15128487 A JP15128487 A JP 15128487A JP S63316409 A JPS63316409 A JP S63316409A
- Authority
- JP
- Japan
- Prior art keywords
- magnetic attraction
- support device
- spatial support
- control device
- attraction type
- 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
Links
- 238000006073 displacement reaction Methods 0.000 claims abstract description 22
- 238000000034 method Methods 0.000 abstract 1
- 238000010586 diagram Methods 0.000 description 14
- 230000001133 acceleration Effects 0.000 description 3
- 238000006243 chemical reaction Methods 0.000 description 3
- 230000005484 gravity Effects 0.000 description 2
- 238000007796 conventional method Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000000087 stabilizing effect Effects 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
Classifications
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0444—Details of devices to control the actuation of the electromagnets
Landscapes
- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Mechanical Engineering (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
Abstract
Description
【発明の詳細な説明】
〔産業上の利用分野〕
この発明は、磁気吸引力を用いて被制御体を非接触支持
すると共に、水平方向に移動可能とした磁気吸引型支持
制御装置に関するものである。[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a magnetic attraction type support control device that uses magnetic attraction force to support a controlled object in a non-contact manner and is movable in the horizontal direction. be.
(従来技術とその問題点〕
磁気吸引型支持装置は、静摩擦がゼロのため、精密位置
決め装置等の支持装置として有望な装置であるが、被制
御体の移動距離が大きい場合は、移動することにより2
組の空中支持装置間で干渉したり、空中支持装置の制御
ループのループゲインが変化するという問題があり、安
定化させ、軸受剛性を向上する上で問題となっていた。(Prior art and its problems) Magnetic attraction type support devices have zero static friction, so they are promising devices as support devices for precision positioning devices, etc. However, when the controlled object has a long movement distance, it is difficult to move. By 2
There are problems with interference between pairs of aerial support devices and changes in the loop gain of the control loop of the aerial support devices, which pose problems in stabilizing and improving bearing rigidity.
これらの模様を図を用いて説明すると次の通りである。These patterns are explained below using diagrams.
第11図は従来の磁気吸引型支持装置のモデル図で、例
えば被制御体が軸1である場合、移動方向(水平方向)
に2つのLil気軸受(空中支持装置)を配置し、それ
ぞれ上下に電磁石をもち、磁気吸引力により軸1を非接
触支持している。Figure 11 is a model diagram of a conventional magnetic attraction type support device. For example, when the controlled object is axis 1, the moving direction (horizontal direction)
Two Liqi bearings (aerial support devices) are arranged at the top and bottom, each having an electromagnet at the top and bottom, and supports the shaft 1 in a non-contact manner by magnetic attraction.
2つの軸受は、紙面に垂直な方向にも同様の軸受を備え
ているが、説明を簡単化するのため省略している。Although the two bearings have similar bearings in the direction perpendicular to the plane of the drawing, they are omitted to simplify the explanation.
この図において、21.22は第1及び第2の軸受、そ
の中間点Sとの距離は10.0は軸lの重心位置、Sか
らの右方向の距離はY、21゜22と0の距離はnl、
ff12,21,0.22における袖1o−上方向変位
はX、、X、 X2 、 21゜0.22における軸
1に作用する上方向の力はFl+F、F2、θは軸1の
重心位置Oまわりのふれ角、トルクはTである。In this figure, 21.22 are the first and second bearings, the distance between them and the intermediate point S is 10.0 is the center of gravity of the axis l, and the rightward distance from S is Y, 21°22 and 0. The distance is nl,
The upward displacement of the sleeve 1o at ff12, 21, 0.22 is X,,X, The surrounding deflection angle and torque are T.
このモデルを力学的に表わして解(とF I + F
2+X、、X2の間には第12図に示すよ−)な関係
がある。Express this model dynamically and find the solution (and F I + F
There is a relationship between 2+X and X2 as shown in FIG.
こ−で軸1の質量をm、軸1のOまわりの損性モーメン
トをJ、 y=Y/1.とずれば、第12図における伝
達関数az、a+z+ az+、azzは夫々次式で
表わされる。Here, the mass of shaft 1 is m, the loss moment around O of shaft 1 is J, and y=Y/1. Then, the transfer functions az, a+z+ az+, azz in FIG. 12 are respectively expressed by the following equations.
この発明は上記の問題点を解決するため、4つの関数発
生器と、4つの乗算器と、2つの加算器から成る関数演
算器を設け、この関fi演算器に、水平移動方向の変位
信号と2つの位相補償器の信号を与えて第1.第2の軸
受の力指令信号を関数演算により求め、その力指令信号
を第1.第2の軸受、即ち空中支持装置に与えるように
したものである。In order to solve the above problems, this invention provides a function calculator consisting of four function generators, four multipliers, and two adders, and a displacement signal in the horizontal movement direction is provided in the function calculator. and the signals of the two phase compensators are applied to the first . The force command signal of the second bearing is obtained by functional calculation, and the force command signal of the second bearing is applied to the first bearing. It is intended to be applied to a second bearing, that is, an air support device.
〔作 用]
上記のような手段を採ると、水平方向に被制御体が水平
に移動しても空中支持装置間の制御ループが干渉せず、
また空中支持装置毎のループゲインも変化せず。安定化
及び高剛性化が可能となるのである。[Function] By adopting the above measures, even if the controlled object moves horizontally, the control loops between the aerial support devices will not interfere.
Also, the loop gain for each aerial support device does not change. This makes it possible to achieve stability and high rigidity.
第1図はこの発明の実施例のモデル図、第2図は関数演
算器を含む実施例装置のブロック図で、1は第1及び第
2の軸受21,22により非接触支持され、水平方向に
移動可能となっている軸又はf多動テーブルである。な
お、この図面では紙面に垂直な方向の変位を拘束する軸
受は図示していない。Fig. 1 is a model diagram of an embodiment of the present invention, and Fig. 2 is a block diagram of an embodiment device including a functional calculator. It is an axis or f-hyperactive table that can be moved to Note that this drawing does not show a bearing that restrains displacement in a direction perpendicular to the plane of the paper.
3は軸lの移動方向の変位を検出する水平方向変位セン
サ、4はその出力信号変換器である。3 is a horizontal displacement sensor for detecting displacement in the moving direction of the axis l, and 4 is its output signal converter.
Gは軸1の重心であり、Sは第1及び第2の軸受21,
22の中間位置の点、2゜は3点と第1又は第2の軸受
間の距離、Yは3点からGまでの右方向き変位である。G is the center of gravity of the shaft 1, S is the first and second bearing 21,
22 is the intermediate position point, 2° is the distance between the 3rd point and the first or second bearing, and Y is the rightward displacement from the 3rd point to G.
水平方向変位センサ3と同変換器4によって検出される
Yに比例する信号はy (=Y/ffo )である。The signal proportional to Y detected by the horizontal displacement sensor 3 and the converter 4 is y (=Y/ffo).
このモデルの力学的関係をブロック図にすると第12図
になるのは前述している。As mentioned above, the mechanical relationship of this model is shown in a block diagram in FIG. 12.
第1及び第2の磁気軸受21.22は、軸1の上下方向
変位を検出する変位センサと、位相補償器と、磁気吸引
力の線形補償器と、パワーアンプとより成っているが図
示していない。The first and second magnetic bearings 21 and 22 consist of a displacement sensor that detects the vertical displacement of the shaft 1, a phase compensator, a linear compensator for magnetic attraction, and a power amplifier, but these are not shown in the figure. Not yet.
こ−でいう磁気吸引力の線形補償器とは、特開昭59−
113315号公報、同59−112605号公報、同
59−205026号公報に示されているもので、力指
令[。This linear compensator for magnetic attraction is described in Japanese Patent Application Laid-open No. 1983-
The force command [.
と2つの電磁石の合力Fが比例関係(F=Kfs)とな
るように構成された補償器である。This is a compensator configured so that the resultant force F of the two electromagnets is in a proportional relationship (F=Kfs).
第2図において、61.62は夫々第1及び第2の軸受
21,22の位相補償器、71〜74は関数発生器、7
6〜79は乗算器、81.82は加算器、91.92は
前記磁気吸引力の線形補償器とパワーアンプと軸受21
,22の電磁石から成るアクチュエータである。In FIG. 2, 61 and 62 are phase compensators for the first and second bearings 21 and 22, respectively, 71 to 74 are function generators, and 7
6 to 79 are multipliers, 81.82 is an adder, 91.92 is a linear compensator for the magnetic attraction force, a power amplifier, and a bearing 21.
, 22 electromagnets.
ΔXl+Δx2は軸受21,22の上下方向変位の指令
値との偏差、yは変換器4の出力信号、f−+、 ff
s1は位相補償器61.62の出力信号、fil+ f
$2はアクチュエータ91.92の入力信号、F、、F
、はアクチュエータ91.92が軸1に作用する上向き
の力である。ΔXl+Δx2 is the deviation from the command value of the vertical displacement of the bearings 21 and 22, y is the output signal of the converter 4, f-+, ff
s1 is the output signal of the phase compensator 61.62, fil+f
$2 is the input signal of actuator 91.92, F,,F
, is the upward force exerted by the actuators 91,92 on the shaft 1.
上記関数発生器71〜74の演算内容はであり、例えば
J =0.0122 tm=0.41. io =0.
1の場合を図示すると第4図、第5図のようになる。The calculation contents of the function generators 71 to 74 are as follows, for example, J = 0.0122 tm = 0.41. io=0.
Case 1 is illustrated in FIGS. 4 and 5.
以上のよいうな構成とすることにより、第2図と第12
図で示される全体系は第7図で示されるブロック図に等
価となり、2つの軸受間で非干渉系を構成することがで
きるのである・。By having the above-mentioned configuration, it is possible to
The overall system shown in the figure is equivalent to the block diagram shown in Fig. 7, and a non-interference system can be constructed between the two bearings.
この第7図において、変換后の等価な伝達関数101、
102はKとなる。また加速度から変位への伝達関数1
1L112はラプラス演算子Sを用いると□となる。In this FIG. 7, an equivalent transfer function 101 after conversion,
102 becomes K. Also, the transfer function 1 from acceleration to displacement
1L112 becomes □ using the Laplace operator S.
第2図中、破線で示した本発明のポイントとなる部分の
具体的内容は、第3図の構成でもよい。The specific content of the key points of the present invention indicated by broken lines in FIG. 2 may be the structure shown in FIG. 3.
この場合関数発生2575の内容は第6図に示すものと
なる。ullち
また、第9図または、第10図の構成でもよい。In this case, the contents of function generation 2575 are as shown in FIG. Alternatively, the configuration shown in FIG. 9 or FIG. 10 may be used.
同図中、121.122はA/Dコンバータ、131i
32はCP U、 141.142はROM、152
、152はD / Aコンバータである。In the same figure, 121.122 is an A/D converter, 131i
32 is CPU, 141.142 is ROM, 152
, 152 is a D/A converter.
第9図の場合、A/Dコンバーター21がf31fsz
、 yの信号をとり込みデジタル変換し、l/C,。In the case of Fig. 9, the A/D converter 21 is f31fsz
, y signal is taken in and converted to digital, l/C,.
1/Cg 、bzl/Cr 、b+z/Czの計算式に
従って演算し、f’sl + f’5g + f″55
.f″、2をアナログ量として出力する。そして加算器
81.82によりf31’+fst”を得る。Calculate according to the formulas of 1/Cg, bzl/Cr, b+z/Cz, and calculate f'sl + f'5g + f''55
.. f'', 2 is output as an analog quantity. Then, f31'+fst'' is obtained by adders 81 and 82.
第10図の場合は、A/Dコンバータ122がfil
+ f!if +yの信号をとり込み、デジタル変換し
、
の演算をした後アナログ変換し、fslZ fst”を
出力する。こうすればいずれも第2図破線部の機能をも
つので、前記非干渉化ができるのである。In the case of FIG. 10, the A/D converter 122
+ f! Take in the signal of if +y, convert it to digital, perform the calculation, convert it to analog, and output "fslZ fst".In this way, both have the functions indicated by the broken line in Figure 2, so the above-mentioned non-interference can be achieved. It is.
なお、前記(2)式中のC+ Ic! +b1z 、b
ulはその系で決まるyの関数であるが、実用上装置を
簡単化する場合干渉型を省略することもでき、その場合
b1□、b21は共にOとなる。In addition, C+ Ic! in the above formula (2)! +b1z, b
ul is a function of y determined by the system, but in order to simplify the device in practice, the interference type can be omitted, in which case both b1□ and b21 become O.
また、C,、CZを近似式(折れ線近似)とすることも
できる。Moreover, C,, CZ can also be approximated (broken line approximation).
更に実施例では2つのアクチュエータ91゜92に線形
補償器を含むと説明したが、これを含まない従来の方法
であってもよいのは勿論である。Further, in the embodiment, it has been explained that the two actuators 91 and 92 include linear compensators, but it goes without saying that a conventional method that does not include this may also be used.
〔発明の効果]
以上のように、可動部が水平方向に移動しても各軸受間
の制御ループが干渉することがなく、ループゲインも変
わらないので、極めて安定した浮上系を構成することが
でき、軸受剛性も高くでき、精密位置決め用の支持装置
として供することが可能となる。[Effect of the invention] As described above, even if the movable part moves in the horizontal direction, the control loops between the bearings do not interfere and the loop gain does not change, so it is possible to construct an extremely stable floating system. The bearing rigidity can also be increased, and it can be used as a support device for precision positioning.
第1図は実施例装置のモデル図、第2図は制御回路のブ
ロック図、第3図は異なる実施例における制御回路のブ
ロック図、第4図〜第6図は夫々関数演算式のグラフ、
第7図は制御系のブロック図、第8図は他の実施例にお
ける制御回路のブロック図、第9図及び第1O図は夫々
他の異なる実施例の構成を示すブロック図、第11図は
従来装置のモデル図、第12図は各部の力学的関係を示
す解析図である。
l・・・軸又は移動テーブル
21・・・第1の軸受
22・・・第2の軸受
3・・・水平方向変位センサ
61.62・・・位相補償器
71〜74・・・関数発生器
8182・・・加算器
9L92・・・アクチュエータ
76〜79・・・乗算器
101、102・・・変換層の伝達関数111、112
・・・加速度→変位の伝達関数121 、122・・・
A/Dコンバータ+3L132・・・CPIJ
141.142・・・ROM
151.152・・・D/Aコンノ1−夕畦τ4図、一
つ2L
第 6 図
第 8 図
・、 1 図
第2図
■・・・軸又は移動テーブル
21・・・第1の軸受
22・・・第2の軸受
3・・・水平方向変位センサ
4・・・出力信号変換器
61.62・・・位相補償器
7″1〜74・・・関数発生器
81.82・・・加算器
91.92・・・アクチュエータ
76〜79・・・乗算器
4 7 z
第 11 図
第 12 図
101.102・・・変換片の伝達関数111、112
・・・加速度→変位の伝達関数。Fig. 1 is a model diagram of the embodiment device, Fig. 2 is a block diagram of the control circuit, Fig. 3 is a block diagram of the control circuit in a different embodiment, Figs. 4 to 6 are graphs of functional calculation formulas, respectively.
FIG. 7 is a block diagram of the control system, FIG. 8 is a block diagram of a control circuit in another embodiment, FIG. 9 and FIG. 1O are block diagrams showing the configuration of other different embodiments, and FIG. FIG. 12, a model diagram of a conventional device, is an analytical diagram showing the mechanical relationship of each part. l...Axle or moving table 21...First bearing 22...Second bearing 3...Horizontal displacement sensor 61.62...Phase compensators 71-74...Function generator 8182... Adder 9L92... Actuators 76 to 79... Multipliers 101, 102... Transfer functions 111, 112 of conversion layer
...Acceleration → displacement transfer function 121, 122...
A/D converter +3L132...CPIJ 141.142...ROM 151.152...D/A converter 1-Yune τ4 Figure, one 2L Figure 6 Figure 8..., 1 Figure 2 ■ ... shaft or moving table 21 ... first bearing 22 ... second bearing 3 ... horizontal displacement sensor 4 ... output signal converter 61, 62 ... phase compensator 7'' 1 to 74... Function generator 81.82... Adder 91.92... Actuator 76 to 79... Multiplier 4 7 z Fig. 11 Fig. 12 Fig. 101.102... Conversion piece Transfer functions 111, 112
...Acceleration → displacement transfer function.
Claims (1)
向には移動可能とした磁気吸引型支持装置において、2
組の空中支持装置と、水平方向変位センサを設け、前記
第1の空中支持装置の位相・補償器の出力信号f_s_
1と、第2の空中支持装置の位相補償器の出力信号f_
s_2と、水平方向変位センサの変位信号yとを用いて
、関数演算し、第1の空中支持装置の力指令信号f_s
_1^*と第2の空中支持装置の力指令信号f_s_2
^*を得ることを特徴とする磁気吸引型支持制御装置。 2)前記関数演算は次式 f_s_1^*=f_s_1/C_1+f_s_2b_
1_2/C_2f_s_2^*f_s_1b_2_1/
C_1+f_s_2/C_2によって行い、C_1、C
_2、b_1_2、b_2_1は水平方向変位yの関数
である特許請求の範囲第1項記載の磁気吸引型支持制御
装置。 3)前記関数演算を4つの関数発生器と、4つの乗算器
と、2つの加算器からなる関数演算器によって行うこと
を特徴とする特許請求の範囲第1項記載の磁気吸引型支
持制御装置。 4)前記演算をA/D変換器、CPU、D/A変換器を
含むデジタル式の演算器で行なうことを特徴とする特許
請求の範囲第1項記載の磁気吸引型支持制御装置。[Claims] 1) A magnetic attraction type support device that supports a controlled object in a non-contact manner using magnetic attraction force and is movable in the horizontal direction, comprising: 2
a set of air support devices and a horizontal displacement sensor, the output signal f_s_ of the phase compensator of the first air support device;
1 and the output signal f_ of the phase compensator of the second aerial support device.
s_2 and the displacement signal y of the horizontal displacement sensor, a function is calculated, and the force command signal f_s of the first aerial support device is
_1^* and the force command signal f_s_2 of the second aerial support device
A magnetic attraction type support control device characterized by obtaining ^*. 2) The above function operation is the following formula f_s_1^*=f_s_1/C_1+f_s_2b_
1_2/C_2f_s_2^*f_s_1b_2_1/
Performed by C_1+f_s_2/C_2, C_1, C
2. The magnetic attraction type support control device according to claim 1, wherein _2, b_1_2, and b_2_1 are functions of horizontal displacement y. 3) The magnetic attraction type support control device according to claim 1, wherein the function operation is performed by a function operation unit consisting of four function generators, four multipliers, and two adders. . 4) The magnetic attraction type support control device according to claim 1, wherein the calculation is performed by a digital arithmetic unit including an A/D converter, a CPU, and a D/A converter.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP15128487A JPS63316409A (en) | 1987-06-19 | 1987-06-19 | Support control device of magnetic attraction type |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP15128487A JPS63316409A (en) | 1987-06-19 | 1987-06-19 | Support control device of magnetic attraction type |
Publications (1)
Publication Number | Publication Date |
---|---|
JPS63316409A true JPS63316409A (en) | 1988-12-23 |
Family
ID=15515320
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP15128487A Pending JPS63316409A (en) | 1987-06-19 | 1987-06-19 | Support control device of magnetic attraction type |
Country Status (1)
Country | Link |
---|---|
JP (1) | JPS63316409A (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5247219A (en) * | 1991-06-27 | 1993-09-21 | Matsushita Electric Industrial Co., Ltd. | Control apparatus of magnetic bearing |
US5671058A (en) * | 1994-03-07 | 1997-09-23 | Kabushiki Kaisha Toshiba | Device for supporting linearly moving a movable member and a controlling system for the device |
CN109688447A (en) * | 2018-12-29 | 2019-04-26 | 联想(北京)有限公司 | A kind of processing method, device and equipment |
-
1987
- 1987-06-19 JP JP15128487A patent/JPS63316409A/en active Pending
Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5247219A (en) * | 1991-06-27 | 1993-09-21 | Matsushita Electric Industrial Co., Ltd. | Control apparatus of magnetic bearing |
US5671058A (en) * | 1994-03-07 | 1997-09-23 | Kabushiki Kaisha Toshiba | Device for supporting linearly moving a movable member and a controlling system for the device |
EP0869340A2 (en) * | 1994-03-07 | 1998-10-07 | Kabushiki Kaisha Toshiba | A device for supporting and linearly moving a movable member |
EP0869340A3 (en) * | 1994-03-07 | 1998-11-25 | Kabushiki Kaisha Toshiba | A device for supporting and linearly moving a movable member |
CN109688447A (en) * | 2018-12-29 | 2019-04-26 | 联想(北京)有限公司 | A kind of processing method, device and equipment |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
KR0154513B1 (en) | Positioning device | |
CN112432634B (en) | Harmonic vibration force suppression method based on multi-synchronous rotation coordinate transformation | |
JPS5846413A (en) | Electric servomechanism | |
Laroche et al. | A Preliminary Study for H Control of Parallel Cable-Driven Manipulators | |
Kuo et al. | Modeling and control of a six-axis precision motion control stage | |
Hung et al. | Nonlinear control of a magnetic bearing system | |
Lai et al. | Control of an underactuated three-link passive–active–active manipulator based on three stages and stability analysis | |
Liu et al. | Design and analysis of a high-payload manipulator based on a cable-driven serial-parallel mechanism | |
WO2024037394A1 (en) | Gantry machine tool moving beam cross coupling control method | |
TWI494725B (en) | Control device, control method and compensating method of position command | |
CN105320057A (en) | Synchronous movement control method of double vibration tables on the basis of coordinate-transformation matrix | |
CN114291295A (en) | Satellite double-axis attitude measurement and control integrated method for single-magnetic suspension control sensitive gyroscope | |
JPS63316409A (en) | Support control device of magnetic attraction type | |
Hoque et al. | Development of an active vibration isolation system using linearized zero-power control with weight support springs | |
CN108279551A (en) | Photoetching machine motion platform and its micromotion platform and control method | |
Lahres et al. | Crane automation by decoupling control of a double pendulum using two translational actuators | |
Chen et al. | Conceptual design and trajectory planning of a precision repetitive-scanning stage with separated drive unit for energy saving | |
CN113670288A (en) | Magnetic suspension rotor harmonic vibration suppression method based on multi-rate quasi-resonant controller | |
CN105676597B (en) | A kind of mask platform balance weight closes the anti-drift motion control method of barycenter | |
Sinha | Dynamics of magnetically suspended vehicles | |
Mohamed et al. | Real-time implementation of a robust H∞ controller for a 2-DOF magnetic micro-levitation positioner | |
JPS5580855A (en) | Rotary arm type positioning mechanism | |
Zhang et al. | Transportation for 4-DOF Tower Cranes: A Periodic Sliding Mode Control Approach | |
Moallem | Control and design of flexible-link manipulators | |
Fan et al. | Passivity and underactuated modeling-based load energy coupling control for three-dimensional overhead crane systems |