撓性結構之主動振動控制

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王得安(De-An Wang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

撓性結構之主動振動控制
(Active Vibration Control of Flexible Structures)

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摘要(中)

在撓性結構之研究與設計中，結構振動為一重要的研究主題。本
論文將探討受外力激振之撓性結構的主動振動控制，控制目標為全域
降低結構振動。在本文中將以獨立模態控制法為架構，利用離散式感
測器與制動器進行控制。在模態控制法中，需要知道各個模態的模態
座標及模態速度，以便進行控制法則的設計與控制系統的實現。在此
將利用模態濾波的技術求得相關的模態座標及模態速度。由於有外擾
的存在，若只採用狀態回授控制，則無法有效抑制結構振動。本文將
引入模態空間外力抵消的概念，以降低外擾的影響。為了能實現模態
空間外力相消，本研究將使用三種不同的模態外力估測器，並發展三
種不同的控制方法來實現主動式振動控制。第一種方法採用模態空間
前饋及回饋控制抑制結構振動。在此方法中，外力估測器是利用逆動
態技術來設計。控制法則則是用擴增型最佳控制理論求得，此理論乃
是將外擾當成一個增生的狀態變數進行求解。第二種方法是採用Hoo
控制技術來設計控制系統。在此，利用模型誤差補償器當成模態外力
估測器，估測未知、任意的外擾，以達成模態外力抵消的構想。但在
外力相消之後，仍有些許的殘留外力存在，因此設計了Hoo控制器，
以確保外力壓抑的效果。最後，一個新的數位式變結構控制方法將應用於撓性結構主動振動控制。變結構控制對外擾和系統參數誤差具有
強健性。此數位式變結構控制器內含一個外力估測器，可以估測未知
的外擾。如此便不需要外擾上界以設計變結構控制器，大大提高了變
結構控制的實用性。本論文將著重於外力估測器性能的探討以及三種
控制方法對結構振動改善的情形。

摘要(英)

Mechanical vibration is an important topic in the study and design of
exible structures.
This dissertation studies the active vibration control of a
exible structure
subjected to arbitrary, unmeasurable disturbance forces. The control objective is to
reduce the structure vibration globally. The concept of independent modal space
control is adopted. Here, discrete sensors and actuators are used. The modal lters
are chosen as the state estimator to obtain the modal coordinates and modal velocities
for the modal space control. Because of the existence of the disturbance forces,
the vibration control only with the state feedback control law can not suppress the
vibration well. The method of disturbance forces cancellation is then added in the
control loop. In order to implement the disturbance forces cancellation, the unknown
disturbance modal forces must be observed. Three di erent kinds of control
algorithms are developed, in the dissertation, for the active vibration control. All
of them involve the suitable disturbance force observers to observe the disturbance
modal forces. The observed disturbance modal forces then are included in the control
loops to cancel out the undesired excitation. The rst method employs the modal
space feedforward and feedback control loops to suppress the structure vibration. A
disturbance force observer, based on the inverse dynamics technique, is established.
The control gains are derived from the extended optimal control algorithm, where
the disturbance modal forces are treated as exogenous state variables. Second, the
author applies the H1 control to the structure vibration attenuation. The model
error compensator is employed to observe the unknown disturbance modal forces forthe direct cancellation. After the implementation of the disturbance modal forces
cancellation, there are still some residual disturbance modal forces which excite the
structure. The disturbance attenuation problem is concerned in the design of the
state feedback control law. For ensuring the in
uence of the residual disturbance
modal forces is reduced to an acceptable level, the robust static H1 state feedback
controller is designed here. In the last, the author studies the application of using
the discrete-time variable structure control method to reduce the vibration of the
exible structure. A discrete-time variable structure controller with a disturbance
force observer is adopted here due to its distinguished robustness property of insensitiveness
to parameters uncertainties and external disturbances. The included
disturbance force observer can observe the unknown disturbance modal forces, which
are used in the discrete-time variable structure control law to cancel out the excitations.
The upperbound limitations of the unknown disturbances in the variable
structure control, therefore, are no longer needed. The performances of estimating
the disturbance modal forces and the vibration reduction of the
exible structure of
the three control laws are discussed.

論文目次

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1 Introduction 1
1.1 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Equation of Motion of the Flexible Structure 10
2.1 Boundary-Value Problem of a Beam . . . . . . . . . . . . . . . . . . . 10
2.2 The Eigenvalue Problem of a Cantilever Beam . . . . . . . . . . . . . 14
2.3 Response of the Beam . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Dimensionless System Description . . . . . . . . . . . . . . . . . . . . 17
3 Independent Modal Space Control 20
3.1 Independent Modal Space Control . . . . . . . . . . . . . . . . . . . . 21
3.2 Point Actuators Forces . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Modal Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Observation Spillover and Control Spillover . . . . . . . . . . . . . . . 25
3.5 Dimensionless System Description . . . . . . . . . . . . . . . . . . . . 26
3.5.1 Continuous-Time System . . . . . . . . . . . . . . . . . . . . . 26
3.5.2 Discrete-Time System . . . . . . . . . . . . . . . . . . . . . . 28
4 Control Law Design 30
4.1 Nearly Optimal Control Law with a Disturbance Force Observer . . . 30
4.1.1 Disturbance Force Observer . . . . . . . . . . . . . . . . . . . 31
4.1.2 Nearly Optimal Control Law Design . . . . . . . . . . . . . . 33
4.2 H1-Based Control Law with a Model Error Compensator . . . . . . . 37
4.2.1 H1 Control Law Design . . . . . . . . . . . . . . . . . . . . . 38
4.2.2 Model Error Compensator . . . . . . . . . . . . . . . . . . . . 40
4.3 Discrete-Time Variable Structure Controller Design . . . . . . . . . . 44
4.3.1 Optimal Switching Function Design . . . . . . . . . . . . . . . 46
4.3.2 Discrete-Time Variable Structure Control Law with a Disturbance
Force Observer . . . . . . . . . . . . . . . . . . . . . . . 49
5 Numerical Results and Discussions 52
5.1 Nearly Optimal Control with a Disturbance Force Observer . . . . . . 52
5.1.1 Observation Spillover E ect Discussion . . . . . . . . . . . . . 53
5.1.2 Estimated States by Using Modal Filters . . . . . . . . . . . . 55
5.1.3 Disturbance Force Observer . . . . . . . . . . . . . . . . . . . 56
5.1.4 Modal Space Control . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 H1-Based Controller with a Model Error Compensator . . . . . . . . 60
5.2.1 Estimated States by Using Modal Filters . . . . . . . . . . . . 60
5.2.2 Modal Space Vibration Control with H1 Controller and MEC 61
5.3 Discrete-Time Variable Structure Control . . . . . . . . . . . . . . . . 65
5.3.1 Estimated States by Using Modal Filters . . . . . . . . . . . . 665.3.2 Modal Space Vibration Control by the Discrete-Time Variable
Structure Control Method . . . . . . . . . . . . . . . . . . . . 66
5.4 The Comparisons of the Three Control Methods . . . . . . . . . . . . 70
6 Conclusions 72
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2 Recommendations for Future Investigation . . . . . . . . . . . . . . . 74
Bibliography 75
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Publication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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指導教授

黃以玫(Yii-Mei Huang)

審核日期

2002-1-17

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