Encyclopedia of Smart Materials (Vols 1 and 2) - M. Schwartz (2002) Episode 13 pps

P1: GIG/GIG P2: GIG/GIG QC: FCH/UKS T1: FCH PB091-T-DRV January 24, 2002 15:36 TRUSS STRUCTURES WITH PIEZOELECTRIC ACTUATORS AND SENSORS 1081 0 1 2 3 4 5 6 7 8 1.5 1 0.5 0 0.5 1 1.5 x 10 3 xDisp.(m) 0 1 2 3 4 5 6 7 8 1.5 1 0.5 0 0.5 1 1.5 x 10 3 yDisp.(m) Time (s) Figure 19. Displacement of node 24 during H ∞ control (experimental). 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 1 (V) 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 2 (V) 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 3 (V) 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 4 (V) Time (s) Figure 20. Control signals during H ∞ control (experimental). P1: GIG/GIG P2: GIG/GIG QC: FCH/UKS T1: FCH PB091-T-DRV January 24, 2002 15:36 1082 TRUSS STRUCTURES WITH PIEZOELECTRIC ACTUATORS AND SENSORS 0 10 20 30 40 50 60 70 80 90 100 110 100 90 80 70 60 50 40 30 20 10 0 Frequency Tranfer Function Estimate (dB) Figure 21. Frequency response during H ∞ control (experi- mental). Figure 22. Application point for the continuous disturbance. 0 0.1 0.2 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Flexible structures are difficult to control because their dynamics are characterized by a large number of vibra- tional modes. To reduce computational complexity, con- troller design is typically performed using a reduced order model. The H ∞ controller design procedure yields a con- troller that concentrates the control energy on the modes included in the design model. The design procedure ac- counts for sensor noise and disturbances resulting from nonlinearities in the amplifier and piezoelectric actuators. Control input saturation can be avoided by using a high penalty on the control energy during the controller design. The H ∞ controller performance is analyzed using a high- order evaluation model. The simulations showed that the H ∞ controller provides significant increase in damping to the modes included in the design model, but does affect the higher-order excluded modes. This behavior is ideal, as it ensures that the structure will not become unstable through the excitation of higher-order modes. P1: GIG/GIG P2: GIG/GIG QC: FCH/UKS T1: FCH PB091-T-DRV January 24, 2002 15:36 TRUSS STRUCTURES WITH PIEZOELECTRIC ACTUATORS AND SENSORS 1083 0 1 2 3 4 5 6 7 8 2 1 0 1 2 x 10 4 xDisp.(m) 0 1 2 3 4 5 6 7 8 2 1 0 1 2 x 10 4 yDisp.(m) Time (s) Figure 23. Displacement of node 24 during continuous distur- bance test with H ∞ control (experimental). Experimental results with the truss structure have con- firmed the validity of the simulations. Two tests have been performed, an impact test and shaker test. Comparisons between the open loop and the closed loop responses show that the H ∞ controller significantly decreases the vibra- tional mode amplitudes. The controller targets its efforts on the modes retained in the design model. Piezoelectric materials are ideally suited for construct- ing actuators and sensors for vibration suppression in flexible structures. Polyvinylidene fluoride (PVDF) is ide- ally suited for sensor construction. It is lightweight, flexi- ble, and provides a high voltage for a given strain. Piezo- ceramic materials are suited to actuator construction. Piezoceramics are stiff, rugged, and provide relatively 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 1 (V) 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 2 (V) 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 3 (V) 0 1 2 3 4 5 6 7 8 5 0 5 Actuator 4 (V) Time (s) Figure 24. Control signals during continuous dis- turbance test with H ∞ control (experimental). Table 4. Mode Attenuation Mode Attenuation (dB) 113 225 312 429 515 large strains when subjected to an electric field. The pre- dominately linear behavior of the piezoelectric materials, and the simple manner in which they can be integrated into a structure, make them a good choice for actuators and sensors in a vibration suppression control system. ACKNOWLEDGMENTS The authors would like to thank Dr. Steven Yeung, Mr. Howard Reynaud, Dr. George Vukovitch, and Dr.Yan-Ru Hu at the Canadian Space Agency for their technical and financial assistance. This work has been supported by the Canadian Space Agency under contracts 9F009-0-4140, 9F011-0-0924, 9F028-5-5106, and 9F028-6-6162, and the Natural Sciences and Engineering Re- search Council of Canada. BIBLIOGRAPHY 1. J.C. Doyle. IEEE Trans. Autom. Contr. AC-23(4): 756–757 (1978). 2. M.J. Balas. IEEE Trans. Autom. Contr. 27(3): 522–535 (1982). 3. J.J. Allen and J.P. Lauffer. J. Dyn. Syst. Meas. Contr. 119: (September 1997). P1: GIG/GIG P2: GIG/GIG QC: FCH/UKS T1: FCH PB091-T-DRV January 24, 2002 15:36 1084 TRUSS STRUCTURES WITH PIEZOELECTRIC ACTUATORS AND SENSORS 4. J.C. Doyle, K. Glover, P.P. Khargonekar, and B.A. Francis. IEEE Trans. Autom. Contr. AC-34(8): 831–847 (1989). 5. B.A. Francis. A Course in H ∞ Control Theory. Lecture Notes in Control and Information Series, Vol. 88. 1987. 6. K. Zhou, J.C. Doyle, and K. Glover. Robust and Optimal Con- trol. Prentice Hall, Englewood Cliffs, NJ, 1995. 7. S.A. Buddie and T.T. Goergiu, ¨ U. ¨ Ozg ¨ uner and M.C. Smith.Int. J. Contr. 58(1): 1–19 (1993). 8. P. Van Woerkom. Control-Theory Adv. Tech. 9(3): 639–669 (1993). 9. T. Bailey and J.E. Hubbard. J. Guid. Contr. Dyn. 8: 605–611 (1985). 10. J.M. Plump, J.E. Hubbard, and T. Bailey. J. Dyn. Syst. Meas. Contr. 109: 133–139 (1987). 11. E.F. Crawley and J. de Luis. AIAA J. 25(10): 1373–1385 (1987). 12. C.K. Lee and F.C. Moon. J. Appl. Mech. 57(6): 434–441 (1990). 13. D.W. Miller, S.A. Collins, and S.P. Peltzman. 31st AIAA/ ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Long Beach, CA, 1990. 14. D.W. Miller and M.C. van Schoor. Proc. 1st Joint US/Japan Conf. on Adaptive Structures, Maui, Hawaii, 1990, pp. 304–331. 15. A.F. Vaz. Modelling Piezoelectric Behaviour for Actuator and Sensor Applications. DSS Contract 9F009-0-4140. Canadian Space Agency, February 1991. 16. A.F. Vaz. Theoretical Development for an Active Vibration Damping Experiment. DSS Contract 9F009-0-4140. Canadian Space Agency, March 1991. 17. A.F. Vaz. Empirical Verification of Interaction Equations for Flexible Structures with Bonded Piezoelectric Films. DSS Con- tract 9F011-1-0924. Canadian Space Agency, September 1991. 18. A.F. Vaz. IEEE Trans. Instrumentation and Measurement, 24(2): (1998). 19. R. Bravo, T. Farr, andA.F. Vaz. Analysis and Testing of Flexible Structure Dynamics. 9F028-6-6162. Canadian Space Agency, December 1997. 20. T. Farr. M.Eng. Thesis. Mechanical Engineering Department. McMaster University, Canada, 1997. 21. A.F. Vaz and T.J. Farr. IEEE Conf. on Instrumentation and Measurement, Ottawa, Ontario, April 21–23, 1997. 22. R. Bravo. Ph.D. Thesis. Mechanical Engineering Department. McMaster University, Canada, 2000. 23. R. Bravo, S. Leatherland, and A.F. Vaz. Final Report on De- sign and Construction of a Truss Structure Testbed. 9F028-8- 2094/001-XSD. Canadian Space Agency, April 1999. 24. W. Weaver and P.R. Johnston. Structural Dynamics by Finite Elements. Prentice Hall, Englewood Cliffs, NJ, 1987. 25. SDRC Corp. I-DEAS Master Series Student Guide. On World Press, 1996. 26. P. Gahinet. Automatica 32(7): 1007–1014 (1996). 27. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali. LMI Control Toolbox for Use with MATLAB. Mathworks, Natick, MA, 1995. 28. Mathworks Inc. Matlab: Language of Technical Computing, Matlab Function Reference. Release 11, Natick, MA, 1999. 29. Mathworks Inc. Simulink: Dynamics System Simulation for Matlab, Using Simulink. Simulink 3, Release 11, Natick, MA, 1999. 30. Quanser Consulting Inc. MultiQ-3 Programming Manual. Hamilton, Ontario, Canada, 1999. 31. D.C. Hanselman. Mastering MATLAB 5: A Comprehensive Tutorial and Reference. Prentice Hall, Englewood Cliffs, NJ, 1998. 32. R. Bravo, A.F. Vaz, S. Leatherland, and M. Dokanish. 1999 CANSMART Workshop, Canadian Space Agency, St. Hubert, Quebec, September 13–14, 1999. P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-V-Drv January 10, 2002 21:38 V VIBRATION CONTROL SEUNG -BOK C HOI Inha University Inchon, Korea INTRODUCTION The insatiable demand for high performance on various dynamic systems quantified by high-speed operation, high control accuracy, and lower energy consumption has triggered vigorous research on vibrational control of distributed flexible structures and discrete systems. Numerous control strategies for conventional electromag- netic actuators have been proposed and implemented to suppress unwanted vibration. However, the successful empirical realization of electromagnetic actuators may be sometimes very difficult under certain conditions due to hardware limitations such as saturation and response speed. This difficulty can be resolved by employing smart material actuators in vibrational control. As is well-known, smart material technology features actuating capability, control capability, and computational capabil- ity (1). Therefore, these inherent capabilities of smart materials can execute specific functions autonomously in response to changing environmental stimuli. Among many smart material candidates, electrorheological(ER) fluids, piezoelectric materials, and shape-memory alloys (SMA) are effectively exploited for vibrational control in various engineering applications. A viable vibrational control algo- rithm can be optimally synthesized by integrating control strategies, and actuating technology, and sensing technol- ogy, as shown in Fig. 1. The design philosophy presented in Fig. 1 contains a very large number of decisions and design parameters for the characteristics of controllers, actuators, and sensors. Furthermore, the designer seeking a global optimal solution for the synthesis of a closed-loop smart structure system must also address other crucial decisions concerning the time delay of a high-voltage/current ampli- fier, the speed of the signal converter, and the microchip hardware of the control software. In this article, two differ- ent flexible smart structures fabricated from ER fluids and piezoelectric materials areintroduced, and vibrationalcon- trol techniques for each smart structure are presented. In addition, vibrational control methodology for a passenger vehicle under various road conditions is given by adopting an ER damper, followed by vibrational control of a flexible robotic manipulator that features piezoceramic actuators. VIBRATIONAL CONTROL OF SMART STRUCTURES ER Fluid-Based Smart Structures Significant progress has been made in developing smart structures that incorporate electrorheological(ER) fluids. Typically, this class of smart structures features an autonomous actuating capability that makes them ideal for vibrational control applications in variable service con- ditions and in unstructured environments. This may be accomplished by controlling the stiffness and energy dis- sipation characteristics of the structures. This, of course, is possible due to the tunability of rheological properties of ER fluids by the intensity of the electric field. The de- velopment of ER fluid-based smart structures was initi- ated by Choi et al. (2). They completed an experimental study of a variety of shear configurations based on sand- wich beam structures. Gandhi et al. (3) suggested using an ER fluid as an actuator to suppress deflections of the flex- ible robotic arm structures by avoiding resonance. In this work, a phenomenological governing equation was derived by assuming that the structures are viscoelastic materials. A passive control scheme for obtaining a desired transient response was developed on the basis of experimentally obtained phenomenological governing equation, in which field-dependent modal properties were used as pseudocon- trol forces (4). Vibrational control logic to minimize the tip deflections of an ER fluid-based cantilever beam struc- tures was illustrated by field-dependent responses in the frequency domain (5). Coulter and Duclos (6) suggested a methodology for replacing a conventional viscoelastic material by an ER fluid. Following the formulation of an analytical model for ER fluid-embedded structures via the conventional sandwich beam theory, they presented a feasibility that the controllability of the complex shear modulus of an ER fluid itself can be used to obtain the desired responses of the structures. Rahn and Joshi (7) de- veloped dynamics for an ER fluid-based on the complex shear modulus of the ER fluid and also theoretically sug- gested a feedback controller for transient vibration con- trol. Oyadiji (8) developed a theoretical equation to predict the field-dependent frequency response by treating the ER fluid layer as a constrained damping layer and verified its validity by experiment. Choi et al. (9) presented a dynamic model for an ER fluid-based smart beam, in which the com- plex shear modulus of the ER fluid itself, measured by a rotary oscillationtest, was taken intoconsideration. To val- idate the methodology, the predicted elastodynamic prop- erties, such as damped natural frequencies and loss fac- tors, were compared with those measured. Gong and Lim (10) experimentallyinvestigated the vibrationalproperties of sandwich beam structures in which an ER fluid layer was partially or fully filled as a constraint damping layer. Yalcintas and Coulter (11) proposed a vibrational model based on thin-plate theory, and the transverse vibration response of a nonhomogeneous ER smart beam was inves- tigated. In addition, the vibrational control capacity of an ER beam was illustrated by emphasizing mode shape con- trol associated with an on and off state of the electric field. On the other hand, Choi and Park (12) controlled vibration of ERsmart beamstructures by using a closed-loop control. The vibrational control technique was empirically realized by activating a field-dependent fuzzy controller. In this article, the field-dependent fuzzy control scheme is introduced after briefly explaining the typical block 1085 P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-V-Drv January 10, 2002 21:38 1086 VIBRATION CONTROL Figure 1. An algorithm for synthesizing a closed-loop smart structure system. Stop No Yes Acceptable performance Control performance and characteristics Control strategies Actuation technologies Sensing technologies Characteristics of desired control performance Start PID control Optimal control Sliding mode control Adaptive control Optimal combination and best performance Control accuracy and fastness Easy implementation and practical feasibility Robustness to unstructured uncertainties Energy consumption and cost effectiveness Electrorheological fluid Magnetorheological fluid Piezoelectric material Shape memory alloy Piezoelectric material Fiber optics Accelerometer Strain gage diagram for vibrational control of ER fluid-based smart structures, shown in Fig. 2. The control system consists of a set of sensors, signal converters, microprocessor, high- voltage amplifier, and control algorithm. Most of the sen- sors currently available such as accelerometers can be adapted to measurethe dynamic responseof ERfluid-based smart structures. The microprocessor which includes A/D (analog–digital) and D/A(digital–analog) signal converters plays a very important role in closed-loop control time. The Figure 2. Schematic diagram for controlling the vibration of an ER fluid-based smart struc- ture. High voltage amplifier Face structure Insulator ER fluid Sensor signals Microprocessor (control algorithm) A/D D/A Input field microprocessor should have at least 12 bits to realize con- trol software and also should take into account a high sam- pling frequency up to 10 kHz. The high-voltage amplifier should have enough power to generate the required ER effect in smart structures. Furthermore, the response time of the high-voltage amplifier to the source input control voltage should befastenough not to delay the controlaction of the feedback controlsystem. Typically, a smart structure consists of two host(face) structures, insulators, and an ER P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-V-Drv January 10, 2002 21:38 VIBRATION CONTROL 1087 0 Excitation frequency Vibration magnitude E = 0 kV/mm E = E 1 kV/mm E = E 2 kV/mm ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 Figure 3. Field-dependent frequency responses of an ER beam structure. fluid layer, as shown in Fig. 2. For the composite laminate, the lay-up angle of the laminates can be selected as a de- sign parameter to investigate the effect of the ER fluid for different stiffnesses. The insulator is a seal to maintain the integrity of the structure and is also used to adjust the vol- ume fraction of the ER fluid relative to the total volume of the structure. For certain elastodynamic purposes, a smart structure can be constructed that consists of multilayers of ER fluids whose rheological properties are different. The elastodynamic properties of an ER fluid-based smart structure vary with the level of the electric field, as shown in Fig. 3. This implies that the natural frequency of each vibrational mode can be adjusted by tailoring the electric field and that, consequently, vibration in real time can be effectively suppressed in the presence of resonant disturbances(excitations). In other words, the desired re- sponse for minimizing the vibrational magnitude can be obtained by selecting the lowest envelope in the frequency range considered. The desired electric field corresponding to the desired response can be expressed as a fuzzy con- trol algorithm (12): if ω i ≤ ω<ω i+1 , then E d = E j . The variable ω denotes the disturbance frequency, and E d is the desired electric field. Note that the variation poten- tial of elastodynamic properties with respect to the applied field may be different upon operating conditions such as the magnitude of excitation when are altered. Therefore, the frequency bandwidth and the corresponding desired field for the control algorithm should be modified. From fuzzy logic, the control field for the case shown in Fig. 3 is determined as follows: if 0 ≤ ω<ω 1 , then E d = E 2 ;if ω 1 ≤ ω<ω 2 , then E d = 0; if ω 2 ≤ ω<ω 3 , then E d = E 1 ;if ω 3 ≤ ω<ω 4 , then E d = E 2 ;ifω 4 ≤ ω<ω 5 , then E d = 0;and if ω 5 ≤ ω<ω 6 , then E d = E 1 . Figure 4 presents the tip de- flection of a cantilevered ER beam in the frequency do- main, which has been experimentally obtained by imple- menting the fuzzy control logic (12). It is evident from this figure that there are effective vibrational suppressions in the neighborhood of the resonant frequencies. However, a small nonzero vibrational magnitude exists across a broad frequency range. This indicates that ER fluids do not provide an actuating force but change the stiffness and the damping propertiesto avoid resonance. To improve vibrational control performance of the fuzzy control logic, 10 20 30 40 50 60 70 80 90 100 110 120 0 1 2 3 4 5 6 7 Vibration magnitude (mm) Frequency (Hz) Uncontrolled Controlled Figure 4. Forced vibrational responses of a cantilevered ER beam. appropriate membership functions for the excitatory mag- nitudes and frequencies can be used to determine the elec- tric fields desired. On the other hand, it is known that an ER fluid contained in adistributed parameter structuralsystem un- der continuous and periodic small deformations remains in the preyield state, which shows viscoelastic properties represented by a complex shear modulus (7,9). The com- plex shear modulus G ∗ f of an ER fluid is expressed by G ∗ f = G s f + iG l f , where i = √ −1. Here, G s f is defined as the storage shear modulus (in-phase), a measure of the en- ergy stored, relating to the stiffness of the structure that contains the ER fluid. G l f is the loss shear modulus (out- of-phase), a measure of the energy dissipated. The shear loss factor is the ratio of the energy lost to the energy stored in a cycle of deformation and denotes the damp- ing characteristic of the ER fluid-embedded smart struc- ture. The complex shear modulus of the ER fluid is nor- mally measured by employing the oscillation mode of an electrorheometer (9). The measured complex shear mod- ulus is integrated with a sixth-order partial differential equation, which is obtainedby adopting conventional sand- wich beam theory (13). Then, the field-dependent elas- todynamic properties of the structure such as the nat- ural frequency are determined through a finite-element model which is governed by [M ]{¨u(t)}+[C(E )]{˙u(t)}+ [K(E )]{u(t)}={f (t)}. The global mass, damping, and stiff- ness matrices are denoted by [M ], [C(E )], and [K(E )], re- spectively. Clearly, both the stiffness matrix [K(E )] and damping matrix [C(E )] are functions of the electric field (E) applied to the ER fluid domain. Thus, these matrices can be tuned as functions of the electric field. The vari- able {u(t)} is a displacement vector, (·) is the time deriva- tive, and { f (t)} represents the external(or disturbance) force vector. By introducing modal coordinates and also adopting mode shape characteristics of the smart struc- ture, the finite-element model can be rewritten in a typi- cal form of state space representation as follows (4): ˙x(t) = Ax(t) + A(E )x(t) + Bf(t). The state vector x(t) represents modal coordinates and the matrix B indicates the in- fluence matrix of the disturbance. A represents the system matrix in the absence of an electric field, and A(E ) denotes the additional system matrix due to the elec- tric field. This implies that the desired response of the P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-V-Drv January 10, 2002 21:38 1088 VIBRATION CONTROL 0.0 0.2 0.4 0.6 0.8 1.0 −2.2 −1.1 0.0 1.1 2.2 Tip deflection (mm) Time (sec) Uncontrolled Controlled Figure 5. Transient vibrational responses of a cantilevered ER beam. structure can be achieved by tuning the field-dependent A(E ). In transient vibrational control without an exter- nal disturbance, the desired eigenvalues of the system, which directlyindicate the desired natural frequencies and damping ratios of the system, can be obtained by adjusting the intensity of the electric field in the matrix A(E). One of the effective control algorithms for achieving this goal is a so-called pseudostate feedback controller proposed by Choi et al. (4). In this method, the state equation is modi- fied to fit a PD (proportional-derivative) controller in which the proportional gain is related to the field-dependent nat- ural frequency, and the derivative gain is related to the field-dependent damping ratio. In addition, we can easily shift the desired eigenvalues of the system to avoid reso- nant phenomena by employing this control algorithm. Fig- ure 5 presents the transient vibrational control response of a cantilevered ER beam (4). The first mode eigenvalues of the structure are calculated from −1.7313 ± i91.167 in the absence of an electric field. However, the desired eigen- values of −11.44 ± i122.114 are achieved by employing ap- propriate control parameter, which indicate the intensity of the electric field. An ER beam structure for vibrational control can eas- ily be extended to an ER plate structure. In the vibrational control of flexible plate structures, the significance of mode shape control is no less important than vibrational magni- tude control. When we consider large flexible structures such as aircraft wings and helicopter blades, the mode shape is directly related to lift distribution and stabil- ity due to internal and external disturbances and other aeroelastic problems in a stringent environment. There- fore, much research on the mode shape control of plate structures have been undertaken by using smart mate- rial actuators (14). Choi et al. (15) proposed an ER plate and investigated its field-dependent mode shapes. Figure 6 presents the measured mode shape of an ER plate which has clamped-clamped boundary conditions(15).Itis clearly observed that the magnitude of each mode shape is effi- ciently suppressed by applying a control electric field. Note that we can also control the mode shape in part of the plate structure (15) by partitioningthe ERplate andapplying an electric field to the specific portion. By doing this, we may alter the twist/camber of an airfoil in the aircraft wing, which in turn controls the lift distribution, to produce de- sirable performance by real-time control. Uncontrolled 0.4 0 0.2 0 0.2 0.4 1.2 × 10 −1 Z 0 Controlled 0.4 0 0.2 X(m) X(m) 0 0.2 Y(m) Y(m) 0.4 8.9 × 10 −2 Z 0 (a) Mode (1,1) 0.4 0 0.2 0 0.2 0.4 2.4 Z 0 0.4 0 0.2 0 0.2 Y(m) Y(m) X(m) X(m) 0.4 2.4 × 10 −2 × 10 −2 Controlled Uncontrolled Z 0 (b) Mode (2,2) Figure 6. Measured mode shapes of an ER plate. Smart Structures That Feature Piezoelectric Actuators and Sensors So far, many natural and synthetic materials that exhibit piezoelectric properties have been proposed and devel- oped. Natural materials include quartz, ammonium phos- phate, paraffin, and bone; synthetic materials include lead zironate titanate (PZT), barium titanate, lead niobate, lithium sulfate, and polyvinylidene fluoride (PVDF). Among these materials, PZT and PVDF are the most pop- ular and commercially available. Both classes of materials are available in a broad range of properties suited to vibra- tional control applications as actuators or sensors. One of the salient properties of a piezoelectric material is that it responds very fast to voltage, and hence has a wide control P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-V-Drv January 10, 2002 21:38 VIBRATION CONTROL 1089 bandwidth. In addition, we can fabricate simple, compact, low-power devices that feature a set of piezoelectric actu- ators or/and sensors. Applications that use piezoelectric materials include vibrational control of flexible structures such as beams, plates, and shells; noise control of cabins; positional controlof structural systemssuch as flexible ma- nipulators; vibrational control of discrete systems such as engine mounts; ultrasonic motors; and various type of sen- sors, including accelerometers, strain gauges, and sound pressure gauges. The successful development of a tech- nology that incorporates piezoelectric materials involves several issues. When we fabricate smart structures that use piezoelectric actuators and sensors, we must consider, the fabrication method(surfacebonding or embedding), the curing temperature when embedding, insulation between piezoelectric layers, and the harness of electric wires. The important issues to considered in modeling piezoelectric- based smart structures include structural dynamics, ac- tuator dynamics, sensor dynamics, the bonding effect, the hysteresis phenomenon, the optimal location of actuators and sensors, and the number of actuators and sensors. The control technique for vibrational control of piezoelectric-based smart structures is very similar to that of a conventional vibrational control system, except that it uses a voltage amplifier, as shown in Fig. 7. The re- sponse time of the voltage amplifier, which normally has an amplification factor of 200, should be fast enough so that it does not deteriorate the dynamic bandwidth of the piezoactuators. The microprocessor that has A/D(analogto digital) and D/A(digital to analog) signal converters needs to have at least a 12-bit memory, and also needs to ac- count for high sampling frequency up to 10 kHz. Most of the currently available control algorithms for piezoactua- tors are realized in an active manner. Therefore, a wide range of control techniques has been proposed for using piezoelectric material to control the vibration of flexible structures actively. Bailey and Hubbard (16) applied a piezofilm as an active vibrational damper for distributed Microprocessor (control scheme) Voltage amplifier A/D D/A Host structure Piezosensor Piezoactuator Sensor signal Input voltage x y z Figure 7. Schematic diagram for vibrational con- trol of a smart structure that features a piezoactu- ator and a sensor. structural systems. Simulations and experimental inves- tigations of transient vibrational control of a cantilever beam were conducted.Theyderived two typesofcontrollers based on Lyapunov stability: a constant-amplitude con- troller (CAC) and a constant-gain controller (CGC). Favor- able vibrational suppression was achieved by implement- ing these two controllers. It has been also shown that the CAC is more effective than the CGC for the same maxi- mum voltage. However, when the CAC is employed, unde- sirable residual vibration is generated in the settled phase due to the excessive supply of control voltages from the in- evitable time delay of the hardware system. Baz and Poh (17) proposed a modified independent modal space control method to suppress actively the unwanted vibration of a flexible beam structure that features piezoelectric actu- ators. The effects of the bonding layer material and the actuator location on the vibrational control performance were evaluated by numerical simulation. Tzou and Gadre (18) derived a physical model for vibrational control, in which a piezofilm slab was sandwiched between two other plates. The effectiveness of active vibrational control has been demonstrated by implementing CGC. Tzou (19) also applied a piezofilm for vibrational control of arbitrarily shaped shells. Control performance of the distributed sys- tems was successfully evaluated through computer simu- lations by using the CAC and the CGC. Baz et al. (20) in- tegrated the independent modal space control method and the positive position feedback method. Vibrational control performance was enhanced by argumenting the so-called time sharing strategy, and its effectiveness was validated by showing multimode controllability by a single piezoelec- tric actuator. On the other hand, Choi et al. (21) proposed a multistep constant-amplitude controller (MCAC) to re- duce undesirable chattering in the settled phase. They ex- perimentally demonstrated the effectiveness of the MCAC by comparing the vibrational control response of the CAC. Choi and Kim (22) also proposed a new type of discrete- time, fuzzy, sliding mode controller to reduce unwanted [...]... Figure 18 Vibrational magnitudes of a two-link flexible manipulator BIBLIOGRAPHY 1 M.V Gandhi and B.S Thompson, Smart Materials and Structures Chapman & Hall, London, 19 92 2 S.B Choi, B.S Thompson, and M.V Gandhi, Proc Damping ’89 Conf., West Palm Beach, FL, Feb 19 88, 1, pp CAC .1 CAC .14 3 M.V Gandhi, B.S Thompson, S.B Choi, and S Shakir, 10 H Gong and M.K Lim, J Intelligent Mater Syst 4 01 413 (19 97) 11 ... Yalcintas and J.P Coulter, Smart Mater Struct 14 3 (19 98) 12 S.B Choi and Y.K Park, J Sound Vib 17 2(3): 428–4 13 D.J Mead and S Markus, J Sound Vib 10 (2): 16 3 1 14 H.S Tzou and G.L Anderson, Intelligent Structura Kluwer Academic, London, 19 92 15 S.B Choi, Y.K Park, and S.B Jung, J Aircraft 36(2 (19 99) 16 T Bailey and J.E Hubbard, Jr., J Guidance, Control 8(5): 605– 611 (19 85) 17 A Baz and S Poh, J Sound Vib 12 6 (2): ... 12 6 (2): 327–343 (1 18 H.S Tzou and M Gadre, J Sound Vib 13 6(3): 477–4 19 H.S Tzou, ASME J Dynamic Syst Meas Control 499 (19 91) 20 A Baz, S Poh, and J Fedor, ASME J Dynamic S Control 11 4 (1) : 96 10 3 (19 92) 21 S.B Choi, C.C Cheong, and S.H Kim, J Intellig Syst Struc 6(5): 430–435 (19 95) 22 S.B Choi and M.S Kim, J Guidance Control Dyna 857–864 (19 97) 23 S.M Yang and G.S Lee, ASME J Dynamic Syst Me 11 9 (1) :... measure the strain and accele Piezoelectric coefficients (10 12 m/V) 12 2 12 2 285 d 31 d32 d33 d24 −200 −200 580 0 −295 −295 569 560 − − 2 418 2 418 3333 7600 17 17 16 Piezoelectric stress constants (C/m2 ) −6.5 −6.5 23.3 17 .0 e 31 e32 e33 e23 Electric permittivity 11 /γ0 γ22 /γ0 γ33 /γ0 Mass density (kg/m3 ) 14 80 14 80 13 00 7600 16 95 16 95 16 95 7500 3250 3250 3250 7350 Note: γ0 = 8.85 × 10 12 farad/m, electric... Active Control of Sound and Vibration 19 93, pp 10 0 10 9 68 C.R Fuller J Sound Vib 10 9: 14 1 15 6 (19 86) 69 J Pan, C.H Hansen, and D.A Bies J Acous Soc Am 87: 2098– 210 8 (19 90) 70 C.G Mollo and R.J Bernhard J Vib Acous 11 2: 230–236 (19 90) 71 K.A Cunefare and G.H Koopmann J Acous Soc Am 90: 365–373 (19 91) 72 A.R.D Curtis, P.A Nelson, and S.J Elliott J Acous Soc Am 88: 2265–2268 (19 90) 73 K.H Baek and S.J Elliott... 357–374 (19 99) 50 A L’Esp´ rance, M Bouchard, and B Paillard Can e Mining, Light Metal Sec Metall Soc 90 (10 12): 94 51 W.G Culbreth, E.W Hendricks, and R.J Hansen Soc Am 83: 13 06 13 10 (19 88) 52 R.L Clark, J Pan, and C.H Hansen J Vib Acous 876 (19 92) 53 M.J Brennan, S.J Elliott, and R.J Pinnington In P Conf on Motion and Vibration Control, 19 92, pp 6 54 S.J Elliott, T.J Sutton, M.J Brennan, and R.J Pin... BIBLIOGRAPHY 1 C.R Fuller and A.H von Flotow IEEE Cont Sys Mag 15 (6): 9 19 (19 95) 2 R.R Leitch IEEE Proc 13 4(6): 525–546 (19 87) 3 P.A Nelson and S.J Elliott Active Control of Sound Academic Press, San Deogo, CA, 19 92 4 U.O Akpan, O Beslin, D.P Brennan, P Masson, T.S Koko, S Renault, and N Sponagle CanSmart-99, Workshop, St.-Hubert, Quebec, 19 99 5 J.C Simonich J Aircraft 33(6): 11 74 11 80 (19 96) 6 S.S Rao and. .. M Sonar Appl Mech Rev 47(4): 11 3 12 3 (19 94) 7 V Giurgiutiu, C.A Rogers, and Z Chaudhry J Intell Mater Sys Struct 7: 656–667 (19 96) 8 L Bowen, R Gentilman, D Fiore, H Pham, W Serwatke, C Near, and B Pazol Ferroelectr 18 7: 10 9 12 0 (19 96) 16 A Grewal, D.G Zimcik, and B Leigh CanSmar on Smart Materials and Structures, CSA, St.-Hube Canada, 19 98 17 D.L Sutliff, Z Hu, F.G Pla, and L.J Heidelberg AIAA/CEAS... Romstadt, M.B Lizell, and T.R W SAE Technical Paper Series 950586, Detroit, MI, 1 30 F Gordaninejad, A Ray, and H Wang, ASME J V 11 9: 527–5 31 (19 97) 31 N.D Sims, R Stanway, and S.B Beck, J Intellig Syst Struct 8: 426–433 (19 97) 32 D.J Peel, R Stanway, and W.A Bullough, Proc SP Struct Mater San Diego, 19 98, pp 416 –427 33 S.B Choi, Y.T Choi, E.G Chang, S.J Han, and Mechatronics 8 (2): 14 3 16 1 (19 98) 34... Hsueh and Y.J Lee Trans ASME 11 6 (1) : 43– 43 T Kakinouchi, T Asano, K Tanida, and N Takaha Eng J 10 4(3): 46–52 (19 92) 44 C.R Fuller, S.J Elliott, and P.A Nelson Active Co bration Academic Press, New York, 19 96 45 S Douglas and J Olkin Proc Recent Advances on trol, 19 93 46 C.L Morfey J Sound Vib 1: 60–87 (19 64) 47 A Bihhadi and Y Gervais Acta-Acoustica 2: 343– 48 S Laugesen J Sound Vib 19 5 (1) : 33–56 (19 96) . 605– 611 (19 85). 10 . J .M. Plump, J.E. Hubbard, and T. Bailey. J. Dyn. Syst. Meas. Contr. 10 9: 13 3 13 9 (19 87). 11 . E.F. Crawley and J. de Luis. AIAA J. 25 (10 ): 13 73 13 85 (19 87). 12 . C.K. Lee and. 8: 4 01 413 (19 97). 11 . M. Yalcintas and J.P. Coulter, Smart Mater. Struct. 7 (1) : 12 8– 14 3 (19 98). 12 . S.B. Choi and Y.K. Park, J. Sound Vib. 17 2(3): 428–432 (19 94). 13 . D.J. Mead and S. Markus,. Vib. 13 6(3): 477–490 (19 90). 19 . H.S. Tzou, ASME J. Dynamic Syst. Meas. Control 11 3: 494– 499 (19 91) . 20. A. Baz, S. Poh, and J. Fedor, ASME J. Dynamic Syst. Meas. Control 11 4 (1) : 96 10 3 (19 92). 21.