Applied Vibration Suppression Using Piezoelectric Materials

Front Cover
Nova Publishers, 2008 - Technology & Engineering - 176 pages
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The aim of this book is to provide insight on the vibration problem in structurally flexible mechanisms, particularly robotic manipulators. The book covers different aspects of flexible structures. It partially includes the fundamental formulations for modelling of a flexible structure actuated with piezoelectric actuators. Mathematical modelling, when possible, as well as experimental techniques for obtaining models of flexible structures are discussed. Additionally, different control techniques adapted for flexible robotic manipulators equipped with piezoelectric actuators and sensors are covered in the book. Depending on the system, linear and non-linear control techniques for stabilising residual vibrations in the system are discussed.
 

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Contents

Introduction and Mathematical Background
1
12 Piezoelectricity
3
121 Constitutive Equations of Piezoelectric Materials
5
13 Beam Theory
7
131 EulerBernoulli Beam
8
132 Beam Equation
10
15 Piezoelectric Sensing
13
16 Piezoelectric Stack
14
53 Mathematical Modeling
96
531 The SubBoundary Conditions
97
532 Piezoelectric Stack Formulation
98
533 Solution of the Partial Differential Equation
99
534 Matrix Model of an Actuated Beam
104
54 Piezoelectric Sensor
106
55 Optimum Parameters of the Actuator
108
551 Numerical Example
111

Piezoelectric Actuator Placement and Control
21
22 Modeling an Actuated Flexible Beam
23
222 Discrete Model of an Actuated Beam
24
23 Optimizing Performance of a Piezoelectric Actuator
25
231 The Relative Thicknesses
29
232 The Relative Youngs Modulus of Elasticity
30
234 Numerical Example
33
24 General Considerations for Controlling a Flexible Beam
35
25 Experimental Results
39
252 ClosedLoop Controller
40
26 Conclusion
44
Flexible link Manipulator
47
32 System Modeling
49
33 Control Design
51
34 Experimental Evaluations
52
341 Software Implementation
54
342 Case Studies
55
35 Conclusion
60
References
62
Friction Compensation
65
42 Friction Modeling
67
421 Stability
68
43 Case Studies
77
44 Conclusion
85
References
86
Piezoelectric Stack Design and Control
89
52 Actuator Design
91
56 Experimental Results
113
561 Frequency Response Function
114
562 ClosedLoop Controller
117
57 Conclusion
118
References
120
Macro Manipulator
123
611 Rigid Body Modeling
125
612 Flexible link Modeling
126
62 Vibration Suppression of the Flexible Parts
133
621 Identification of the Upper Part
134
622 Model Analysis
139
623 Finite Element Analysis
142
63 Control Design
143
631 Selection of the Weighting Functions
146
632 Controller Implementation
148
64 Experimental Results
149
65 Conclusion
152
References
155
Conclusion
159
72 Future Work
160
Dynamic Modeling
161
A2 Solution of Riccati Equation
164
Piezoelectric Stack Actuator
165
Macro Manipulator
171
C2 Automation
172
Index
175
Copyright

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