Piezoelectric Transducers for Vibration Control And Damping

by Moheimani, S. O. Reza; Fleming, Andrew J.

• ISBN13: 9781846283314
• ISBN10: 1846283310
• Format: Hardcover
• Copyright: 2006-07-30
• Publisher: Springer Verlag

Summary

Flexible mechanical systems experience undesirable vibration in response to environmental and operational forces. The very existence of vibrations can limit the accuracy of sensitive instruments or cause significant errors in applications where high-precision positioning is essential so in many situations control of vibrations is a necessity. Piezoelectric transducers have been used in countless applications as sensors, actuators, or both. When traditional passive vibration control techniques fail to meet requirements, piezoelectric transducers in conjunction with feedback controllers can be used effectively to suppress vibrations. Piezoelectric Transducers for Vibration Control and Damping presents recent developments in vibration control systems that employ embedded piezoelectric sensors and actuators. In particular, it covers various ways in which active vibration control systems can be designed for piezoelectric laminated structures, paying distinct attention to how such control systems can be implemented in real time. The text contains numerous examples and experimental results obtained from laboratory-scale apparatus, with details of how similar setups can be built. Features and topics: An overview of piezoelectricity. Modelling of flexible structures with embedded piezoelectric sensors and actuators. Feedback control of structural vibration using PPF and resonant controllers. A comprehensive treatment of piezoelectric shunt damping systems using systems-theoretic tools. A paradigm for designing active high-performance piezoelectric shunts. Innovative techniques to deal with the problem of hysteresis in piezoelectric transducers. Instrumentation for piezoelectric sensors and actuators. Applications in atomic force and scanning tunneling microscopy. An essential text and reference for graduates, researchers, and professionals working in mechanical engineering, aerospace engineering and mechatronics disciplines, this book will be a specially useful resource for scientists and engineers engaged in vibration control research.

Author Biography

Reza Moheimani's background is in robust control and its applications to real world systems. In particular, over the past seven years he has concentrated on applications of advanced control techniques in vibration control of flexible structures with embedded piezoelectric sensors and actuators. He has published in this area extensively with (to date) 54 refereed journal papers, has served as a Guest Editor for special issues of journals devoted to this topic and is an Associate Editor on IEEE Transactions on Control Systems Technology, Control Engineering Practice and International Journal of Control, Automation and Systems. He regularly reviews articles for 13 journals in control and mechatronics, including all the most important control journals. He has been very successful in attracting research funding in this field. Doctor Mohiemani has published two previous books, editing Lecture Notes in Control and Information Sciences Vol. 268 for Springer and Spatial Control of Vibration for World Scientific.Doctor Moheimani teaches regularly in the undergraduate signal processing and control programs at Newcastle, has supervised several Ph.D. and Masters students to postgraduate qualifications and postdoctoral researchers from as far afield as Uppsala and Los Angeles. Doctor Moheimani has regularly been a member of program committees for international conferences including the IFAC World Congress in Prague (July 2005). He is a senior member of the IEEE and serves on the IFAC Technical Committees for Mechatronics and Robust Control. Previous to his current appointment at the University of Newcastle, he worked at the Australian Defense Force Academy in Canberra.Andrew Fleming completed his Ph.D. in the field of Dynamics and Control of Smart Structures in 2003. His expertise lies in the analysis, design, and implementation of control systems for structural vibration control, acoustic noise control, and nano/micro-positioning systems. He is a technical reviewer for various journals including Automatica and the ASME Journal of Sound and Vibration. He is beginning to appear on the stage of international conferences, organising and chairing a session on Micro- and Nano-positioning at CDC/ECC in December 2005. He is a member of IEEE and SPIE.The authors are the holders of three patents connected with vibrational damping apparatus.

Table of Contents

1 Introduction	1	(8)
1.1 Piezoelectric Transducers	1	(1)
1.2 Vibration Control	2	(1)
1.3 Piezoelectric Shunt Damping	3	(2)
1.4 Hysteresis	5	(1)
1.5 Applications	6	(3)
2 Fundamentals of Piezoelectricity	9	(28)
2.1 Introduction	9	(1)
2.2 History of Piezoelectricity	10	(1)
2.3 Piezoelectric Ceramics	11	(2)
2.4 Piezoelectric Constitutive Equations	13	(5)
2.5 Piezoelectric Coefficients	18	(4)
2.5.1 Piezoelectric Constant dig	18	(1)
2.5.2 Piezoelectric Constant gij	19	(1)
2.5.3 Elastic Compliance Sij	20	(1)
2.5.4 Dielectric Coefficient, eij	20	(1)
2.5.5 Piezoelectric Coupling Coefficient kij	20	(2)
2.6 Piezoelectric Sensor	22	(1)
2.7 Piezoelectric Actuator	23	(3)
2.8 Piezoelectric 2D Actuation	26	(3)
2.9 Dynamics of a Piezoelectric Laminate Beam	29	(4)
2.10 Active and Macro Fiber Composite Transducers	33	(4)
3 Feedback Control of Structural Vibration	37	(36)
3.1 Introduction	37	(1)
3.2 Structural Properties of Resonant Systems	38	(2)
3.3 Modeling and System Identification	40	(3)
3.3.1 Analytic Modeling	40	(1)
3.3.2 Finite Element Analysis	41	(1)
3.3.3 System Identification	41	(2)
3.4 Velocity Feedback	43	(2)
3.5 Resonant Controllers	45	(3)
3.6 Positive Position Feedback	48	(4)
3.7 Experimental Implementation of PPF Control on an Active Structure	52	(14)
3.7.1 Experimental Setup	52	(2)
3.7.2 System Identification	54	(3)
3.7.3 PPF Controller Design	57	(9)
3.8 Self-sensing Techniques	66	(7)
4 Piezoelectric Shunt Damping	73	(20)
4.1 Introduction	73	(1)
4.2 Passive Shunt Damping	74	(10)
4.2.1 Passivity Defined	74	(2)
4.2.2 Linear Techniques	76	(1)
4.2.3 Resonant Single-mode Shunt Circuits	76	(2)
4.2.4 Resonant Multi-mode Shunt Circuits	78	(5)
4.2.5 Non-linear Techniques	83	(1)
4.3 Active Shunt Damping	84	(1)
4.4 Implementation of Resonant Shunt Circuits	85	(4)
4.4.1 Virtual Circuits	85	(1)
4.4.2 Synthetic Admittance	86	(3)
4.5 Experiment al Demonstration	89	(4)
5 Feedback Structure of Piezoelectric Shunt Damping Systems	93	(26)
5.1 Introduction	93	(1)
5.2 Feedback Interpretations	94	(3)
5.3 Feedback Structure of Passive Shunts	97	(3)
5.4 Reduction of Inductance Requirements by Adding a Parallel Capacitor	100	(3)
5.5 Resonant, Shunts	103	(3)
5.6 Properties of Resonant Shunts	106	(1)
5.7 Experimental Implementation of Resonant Shunts	107	(9)
5.8 Hybrid Control	116	(3)
6 Instrumentation	119	(26)
6.1 Introduction	119	(1)
6.2 Strain Voltage Measurement	119	(3)
6.3 Voltage Amplifiers	122	(3)
6.3.1 Linear Amplifiers	122	(2)
6.3.2 Switched-mode Implementation	124	(1)
6.4 Current Amplifiers	125	(2)
6.5 Charge Amplifiers	127	(3)
6.6 Synthetic Admittance	130	(1)
6.7 Switched-mode Synthetic Admittance	131	(6)
6.7.1 Device Operation	132	(1)
6.7.2 Boost Configuration	132	(1)
6.7.3 Efficiency	133	(1)
6.7.4 Practical Advantages and Considerations	134	(2)
6.7.5 Experimental Application	136	(1)
6.8 Signal Processing	137	(8)
6.8.1 Impedance Transformations	139	(1)
6.8.2 Admittance Transformations	140	(2)
6.8.3 Example: Digital Synthesis	142	(1)
6.8.4 Example: Analog Synthesis	142	(3)
7 Multi-port Shunts	145	(20)
7.1 Introduction	145	(1)
7.2 Multi-port Piezoelectric Shunt	146	(3)
7.3 Stability of the Shunted System	149	(3)
7.4 Multivariable Shunts	152	(2)
7.5 Decentralized Shunts	154	(1)
7.6 Experimental Results	155	(10)
7.6.1 Experimental Setup	155	(2)
7.6.2 System Identification	157	(2)
7.6.3 Implementation of a Multi-port Synthetic Admittance	159	(1)
7.6.4 Implementing the Admittance Transfer Function	160	(1)
7.6.5 Results	160	(5)
8 Adaptive Shunt Damping	165	(12)
8.1 Introduction	165	(1)
8.2 Adaptation Law	166	(4)
8.2.1 Adaptive Single-mode RL Shunt	166	(2)
8.2.2 Adaptive Resonant Multi-mode Shunts	168	(2)
8.3 Experiments	170	(7)
8.3.1 Implementation	170	(1)
8.3.2 Test Structure	170	(2)
8.3.3 Two-mode Damping	172	(1)
8.3.4 Four-mode Damping	173	(4)
9 Negative Capacitor Shunt Impedances	177	(10)
9.1 Introduction	177	(1)
9.2 Negative Capacitor Shunt Controllers	178	(2)
9.3 Implementation	180	(1)
9.3.1 Negative Impedance Converter	180	(1)
9.3.2 Synthetic Admittance	181	(1)
9.4 Experimental Application	181	(6)
9.4.1 Control of a Plate Structure	181	(2)
9.4.2 Control of a Beam Structure	183	(4)
10 Optimal Shunt Synthesis	187	(16)
10.1 Introduction	187	(1)
10.2 Abstracted Model of Shunted Systems	188	(2)
10.3 Experimental Apparatus	190	(2)
10.4 Instrumentation Electronics	192	(1)
10.5 Active S-impedance Shunt Design	193	(10)
10.5.1 Modeling and Parameter Identification	193	(3)
10.5.2 Hinfinity S-impedance Design	196	(7)
11 Dealing with Hysteresis	203	(26)
11.1 Introduction	203	(1)
11.2 Hysteresis	204	(2)
11.3 Charge Control versus Voltage Control	206	(5)
11.4 Resonant Controllers for Charge-driven Piezoelectric Actuators	211	(1)
11.5 Experimental Implementation of a Multivariable Resonant Controller	212	(10)
11.5.1 The Hysteresis Effect	213	(2)
11.5.2 State-space Model of the Composite System	215	(1)
11.5.3 Structure of the State-space Model	216	(1)
11.5.4 System Identification	217	(3)
11.5.5 Controller Design	220	(2)
11.6 Experimental Results	222	(1)
11.7 Some Observations	223	(6)
12 Nanopositioning	229	(28)
12.1 Introduction	229	(1)
12.2 Scanning Probe Microscopes	229	(4)
12.3 Piezoelectric Tube Scanners	233	(4)
12.4 Shunt Circuit Modeling	237	(8)
12.4.1 Open-loop	237	(2)
12.4.2 Shunt Damping	239	(6)
12.5 Implementation	245	(2)
12.5.1 Grounded-load Charge Amplifier	245	(2)
12.6 Experimental Results	247	(10)
12.6.1 Tube Dynamics	248	(1)
12.6.2 Amplifier Performance	249	(1)
12.6.3 Shunt Damping Performance	250	(7)
References	257	(12)
Index	269