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TECHNICAL PAPERS

[+] Author and Article Information
Helen M. Georgiou

J. Dyn. Sys., Meas., Control 128(3), 558-567 (Oct 11, 2005) (10 pages) doi:10.1115/1.2234486 History: Received March 19, 2004; Revised October 11, 2005

## Abstract

In most piezoelectric applications, including precision motion control, pressure regulation in micropumps, and force control in microactuators, there is a need to develop a model that accounts for hysteresis and describes both the electrical and mechanical properties of piezoceramics, along with the electromechanical coupling between the two domains. A model that characterizes hysteresis and the coupled electromechanical effect of the sensing and actuating signals is presented. The model presented characterizes the electromechanical properties of a piezoceramic actuator when subject to variable mechanical load disturbance conditions. The model is tested under a range of voltage excitations at frequencies up to $111Hz$ and is shown to offer high accuracy.

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## Figures

Figure 10

Voltage applied across capacitive and resistive components in the model versus piezoelectric force for a PZT stack actuator excited by an applied voltage, which is used to obtain a value for TVlin

Figure 12

Results for the electromechanical model with the PZT actuator excited at 12Hz and mechanical load disturbance at 21, 51, and 111Hz for (a), (b), and (c), respectively. Results for the model with the PZT actuator excited at 21, 51, and 111Hz and the mechanical load disturbance at 12Hz are shown in (d), (e), and (f). Measured, simulated, and error data are given by dashed (---), solid (—), and dotted (….) lines, respectively.

Figure 13

(a) Single massless-block spring element used to build the Maxwell model. (b) Static and dynamic conditions of force and displacement for a single massless-block spring element, where the horizontal lines represent the dynamic state and the sloping lines represent the static state

Figure 1

Linear relationship between charge and displacement exhibited by a piezoelectric ceramic stack actuator; with no mechanical load or disturbance applied to the stack

Figure 2

(a) Nonlinear charge-to-voltage curve for a piezoceramic actuator. (b) Hysteretic behavior relating voltage to displacement in a piezoelectric stack actuator. [Note: (a) and (b) are plotted with no mechanical load or disturbance applied to the stack actuator]

Figure 11

Excitation force versus displacement for a PZT stack actuator used to acquire M

Figure 14

(a) Input applied force to the n element massless-block spring system. (b) Output displacement of the n element massless-block spring system. For both figures, points a and e, and c and g represent the minimum and maximum values, respectively

Figure 15

Fabricated rising curve for hysteresis behavior of elastic-plastic deformation of a material, used to characterize the Maxwell model. The asterisk is used to show the location of the initial settling point

Figure 16

(a) 100V peak-to-peak 12Hz sinusoidal voltage used to excite the PZT actuator. (b) Initial rising curve for PZT stack actuator used to characterize parameters for Maxwell model, with no dynamic mechanical load applied to the PZT stack actuator

Figure 3

Decrease in capacitance due to an applied mechanical load when modeling a PZT actuator as a capacitor in parallel with a resistor, where the solid and dashed lines represent the capacitance of the actuator in the no load and applied load (blocked actuator) conditions, respectively

Figure 4

Generalized Maxwell slip model for the mechanical analogy, comprised of n massless-block spring elements connected in parallel

Figure 5

(a) Simulated and measured charge data using the Maxwell slip model for 8cycles of a 100V peak-to-peak 12Hz sinusoidal voltage used to excite the PZT actuator, as well as error. (b) Measured and simulated voltage to charge hysteresis curve for a PZT stack. Measured, simulated, and error data are given by dashed (---), solid (—), and dotted (….) lines, respectively. No dynamic mechanical load is applied to the stack actuator

Figure 6

Measured and simulated voltage to charge hysteresis curve for one cycle of a 100V peak-to-peak 12Hz sinusoidal excitation voltage applied to a PZT stack. Measured and simulated data are given by dashed (---) and solid (—) lines, respectively. No dynamic mechanical load disturbance is applied to the PZT stack actuator.

Figure 7

(a) Simulated and measured charge data, as well as error, using the Maxwell slip model with a 12Hz decreasing magnitude sinusoidal voltage excitation used to excite a PZT actuator. (b) Measured and simulated voltage to charge hysteresis curve for a PZT stack. Measured, simulated, and error data are given by dashed (---), solid (—), and dotted (…) lines, respectively. No dynamic mechanical disturbance is applied to the stack actuator

Figure 8

Complete electromechanical model for a PZT stack actuator with voltage input V applied across the stack and resultant output displacement y experienced by the stack

Figure 9

Displacement versus piezoelectric charge for a PZT stack actuator excited by a mechanical load disturbance, which is used to determine Ty

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