MCE603: Interfacing and Control of Mechatronic Systems

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1 MCE603: Interfacing and Control of Mechatronic Systems Chapter 7: Actuators and Sensors Topic 7d: Piezoelectric Actuators. Reference: Various articles. Cleveland State University Mechanical Engineering Hanz Richter, PhD Piezoelectric Actuator Features MCE603 p.1/16 Extremely high stiffness and light weight. Consequently, high bandwidth. Nanometer and sub-nanometer positioning accuracy possible. Large load capacity (kn range) Drawback: need for expensive driving electronics (high-voltage, high bandwidth amplifiers designed to drive large capacitive loads.) Hysteresis appears when piezo actuators are voltage-driven. Drift and nonlinear sensitivity are also present (Richter, et.al., 1998). Piezoactuators must operate under feedback control MCE603 p.2/16

2 Piezoelectric Actuator Configurations Piezoelectric stack: Several d 33 elements stacked together to amplify the total range of linear motion (up to millimeters with piezoceramics). Piezoelectric tube: Tubes typically fitted with electrodes 90 degrees apart. It is possible to generate 3D motion of the tip. Piezoelectric patches: Thin rectangular plates which expand and contract in a preferred direction according to the d 31 effect. Usually attached to structural members to control bending. Piezoelectric bimorph actuators: An back-to-back arrangement of piezo strips that can bend in two directions. Used in a similar way as piezo patches. In addition, rotary and linear piezomotors are being developed for MEMS applications. MCE603 p.3/16 Piezoelectric Stack Actuator MCE603 p.4/16

3 Dynamic Analysis of the Piezo Stack Use a lumped-parameter approach to determine the stiffness, sensitivity and natural frequency of the piezo stack. Piezoelectric Tube Actuators (Scanners) MCE603 p.5/16 MCE603 p.6/16

4 3D Motion in Tube Scanners The tube can be considered as being made of 4 d 31 strips. Application of electric field in the radial direction results in axial expansion of each strip. If the same voltage is applied to all electrodes, a net expansion occurs only in the axial direction. If different voltages are applied, bending wil occur. It is possible to generate a 3D tip trajectory with appropriate feedback control. The piezo scanner is commonly used in the atomic force microscope. MCE603 p.7/16 Application of Piezo Tube in Nano-machining MCE603 p.8/16

5 Nanocut Machine MCE603 p.9/16 Nanocut Machine MCE603 p.10/16

6 Nonlinear Sensitivity and Creep of Piezo Tube Step Reponses Normalized by Input Value Creep Data Normalized by Input Value Norm. Position Signal, Volts/Volt V 29.87V 50.4V 63.3V 83V 98.8V 119.9V Norm. Position Signal, Volts/Volt V 29.87V 50.4V 63.3V 83V 98.8V 119.9V Time, seconds Time, seconds MCE603 p.11/16 A Rotary Piezomotor Design MCE603 p.12/16

7 Piezoelectrically Actuated Beam y piezoelectric patch x x1 x2 cantilever beam The effect of the piezoelectric patch is commonly taken to be a distributed moment (Fanson and Caughley, 1987) M(t,x) = bd 31 E p (t a + t b )V (t)[u(x x 1 ) u(x x 2 )] where t a and t b are the thicknesses of piezo and beam, E p is the Young s modulus of the piezo, b is the width of piezo and beam (assumed the same) and u(x) is the step function. MCE603 p.13/16 Analysis of Piezo Beam Dynamic modal analysis using the Euler-Bernoulli beam model and experimental verification will be one of the MCE603/703 term projects for this semester. Now we derive only the static tip deflection corresponding to a constant voltage. Take t a = 0.5 mm, t b = 1.5 mm, b = 25 mm, E = 70 GPa, L b = 200 mm, x 1 = 10 mm, x 2 = 30 mm, V = 60 volts. Piezo patch made of PZT 5A. MCE603 p.14/16

8 Self-Sensing Technology Piezoelectric materials work both a a charge generators in response to motion and as a motion generator in response to charge. Can we use a single physical element to realize the functions of sensing and actuation? The answer is YES. The technology has matured significantly since the fundamental work by Inmanb (see paper). Aside from reducing cost and complexity, self-sensing actuation is more energy-efficient and permits collocated control. Collocated control affords enhanced stability properties. One can use velocity feedback to cancel vibrations in a structure and obtain unconditional stability (stability for all values of gain). MCE603 p.15/16 Reference Papers 1. Flint, E.M. and Rogers, C.A., Electro-Dynamic Transduction Equations for Piezoelectric Stack Actuators, ASME Adaptive Structures and Composite Materials: Analysis and Application, MD-V 54, 1994, pp Richter, H., Misawa, E.A. and Lucca, D.A., Characterization of Nonlinearities in a Piezoelectric Positioning Device, Proc IEEE Int. Conf. on Control Applications, Hartford, CT, pp Richter, H. et.al.,modeling Nonlinear Behavior in a Piezoelectric Actuator, Precision Engineering, v.25 N.2, April 2001, pp Dosch, J.J. and Inman, D.J., A Self-Sensing Piezoelectric Actuator for Collocated Control, Journal of Intelligent Materials, Systems and Structures, v3, Jan 1992, pp Sirohi, J. and Chopra, I., Fundamental Understanding of Piezoelectric Strain Sensors, Journal of Intelligent Materials, Systems and Structures, v11, April 2000, pp Wang, B.T. and Wang, C.C., Feasibility Analyisis of Using Piezoceramic Transducers for Cantilever Beam Modal Testing, Smart Materials and Structures, v.6, 1997, pp MCE603 p.16/16