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Feedback Driven Fast Piezoelectric Micro-lens Actuator
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 168 (2016) 1492 – 1495
30th Eurosensors Conference, EUROSENSORS 2016
Feedback Driven Fast Piezoelectric Micro-lens Actuator A.Michael*, S.S.Chen, and C.Y.Kwok School of Electrical Engineering and Telecommunication, UNSW AUSTRALIA, Sydney, Kensigton 2052, AUSTRALIA
Abstract This paper studies the dynamic behavior of a piezoelectric micro-lens actuator driven by a feedback system. The feedback system consists of the actuator in the forward path and an optical displacement sensor and a 90o phase shifter multiplied by a gain as feedback elements. The piezo-electric micro-lens actuator is fabricated and characterized for its dynamic performance by varying the feedback gain. The results show that the settling time and quality factor of the actuator are reduced by a factor of more than 100 and 10dB, respectively when the gain is increased from 0 to 0.0134. The micro-lens actuator demonstrated switching time of 2.5ms at a resonance frequency of 750Hz without affecting its static deflection characteristic. This is significantly fast in comparison to other reported switching times for micro-lens actuator. Crown Copyright © 2016Published Published by by Elsevier Elsevier Ltd. © 2016 The Authors. Ltd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference. Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords: Micro-lens actuator, Feedback control, piezo-electric actuator, quality factor
1. Introduction Micro-lens actuator that displaces a micro-lens in an out-of-plane direction is a critical component of a microoptics system for miniaturized camera, confocal microscopy and pico-projector applications. The desired performance requirements for such micro-lens actuators are high resonance frequency, low quality factor and large deflection in order to enable high end functionalities such as fast auto focus or extended optical zooming. Although achieving such a high performance actuator is very challenging due to the natural contradiction among the requirements, progresses have been made employing various actuation mechanisms and structures. Electro-thermal micro-lens actuators that produce large deflection have been reported but their response times were low [1]. Electrostatically driven micro-lens actuators are also common but they do not yield enough energy density to provide large * A.Michael. Tel.: +61-02-93855663; fax: +61-02-93855300. E-mail address: [email protected]
1877-7058 Crown Copyright © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference
doi:10.1016/j.proeng.2016.11.432
A. Michael et al. / Procedia Engineering 168 (2016) 1492 – 1495
1493
deflection or large resonance frequency [2]. Recently, piezo-electrically actuated micro-actuators have shown promising results [3]. However, despite having comparatively large resonance frequency and deflection, the switching time of the actuator was limited by high quality factor of the structure. In this paper, we present the study of micro-lens piezo-electric actuator driven by feedback system to control the quality factor and reduce switching time. 2. Piezoelectric micro-lens actuator The piezoelectric micro-lens actuator employed for the feedback experiment is shown in Fig. 1(a). It consists of eight piezo-electrically driven beams supporting a lens-holding frame on which a silica micro-sphere ball lens of 600µm in diameter and weighing 300µg is mounted as seen from Fig. 1(c). Each piezo-electrically driven beam is a multilayer 800µm long structure made of Pt (0.1µm)/PZT(1.5µm)/ZrO2(0.6µm)/SiO2(1µm)/Si(5µm). The top Pt layer is interdigitated to enable d33 mode of actuation with electrodes of 10µm wide and 5µm spacing. When voltage is applied in the direction polarization, which is along the x direction, the PZT film in each beam expands to produce a downward out-of-plane displacement as illustrated in ANSYS simulation in Fig. 2(a). After poling the fabricated actuator at 120V, the static displacements produced by applied electric fields have been measured and provided in Fig. 2(b).
Fig. 1. (a) Piezo-electric micro-lens actuator; (b) Schematics illustrating constituting layers of the actuator along A-A’;(c) Micro-lens mounted on the lens holding frame
Fig. 2. (a) Simulation result showing downward displacement when driven by voltage in a direction of polarization; (b) Measured deflection characteristics as a function of driving voltages;
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3. Feedback driven micro-lens actuator system The feedback system for the micro-lens actuator has the micro-lens actuator in the forward path, and optical displacement sensor and 90o phase shifter multiplied by a gain in the feedback path. The block diagram of the system and measurement setup is schematically illustrated in Fig. 3. The dynamic characteristics of the micro-lens actuator with and without the feedback path are measured up to 1500Hz at a driving voltage of 10V. The normalized magnitude and phase responses of the actuator with out and with a feedback gain of 0.0134 are plotted in Fig. 3(b) and (c), respectively. The response of the actuator without feedback can be approximated by a second order system with a resonance frequency of 750Hz, a quality factor of 24dB, and a dc gain of 0.065µm/V. With the feedback, the system is still a second order with the same resonance frequency, dc gain but a reduced quality factor. The closed loop quality factor, Q*, can be shown to be related to the feedback gain, G, and the open loop quality factor, Q as in Eq. (1)
1 Q*
1 GADZo Q
(1)
where A is the dc gain, D is a displacement decoder factor, and ωo is the resonance frequency in rad/s. Eq. (1) shows that the quality factor of the micro-lens actuator system is controlled by the feedback gain, G, in the inversely proportional manner. With the gain G = 0.0134, the quality factor is reduced to 9dB, by a factor of 15dB as compared the open loop quality factor.
Fig. 3. (a) Measurement setup and feedback arrangement; Frequency response with and without feedback (b) magnitude (c) phase.
The effect of the feedback system on the switching behavior of the actuator is also studied by applying a 20V square wave excitation signal at 1Hz and varying the feedback gain, G. The time responses of the actuator with feedback at G=0.0134 and without feedback are shown in Fig. 4(b) and (a), respectively. For the open loop system, where the G=0, the actuator takes 260ms to settle down to a position within 1% of the final value. The settling time reduces to 2.5ms when G is increased to 0.0134. The significant decrease in settling time can be attributed to the reduction in the quality factor, which infers an increase in the damping coefficient of the system, as the feedback gain, G, is increased.
Fig. 4. Displacement response for 1Hz and 20V square wave excitation with (a) no feedback; (b) feedback at G=0.0134.
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The transient response of the second order feedback system with the quality factor, Q*, resonance frequency, ωo, and dc gain of A for a unit step excitation in underdamped condition is given by
y (t )
· § ¸ ¨ Zot 2 ¸ ¨ 2Q* § 1 · e A¨1 sin(Zo 1 ¨¨ * ¸¸ t ) ¸u (t ) 2 ¨ © 2Q ¹ ¸ § 1 · ¸ ¨ 1 ¨¨ * ¸¸ ¸ ¨ Q 2 © ¹ ¹ ©
(2)
The settling time, tr, in which the final position is attained within less than 1% of accuracy can be calculated from Eq. (2) and is obtained as
tr |
9.22 GADZo
2
(3)
As can be seen from the above equation, the switching time is inversely proportional to the feedback gain. The switching times and quality factors of the actuator are measured for various feedback gains and plotted in Fig. 5(a) and (b), respectively. For comparison purpose, the calculated values of switching times are also shown in Fig. 5(a) indicating a good agreement.
Fig. 5. (a) switching times; (b) quality factor for various feedback gains.
4. Conclusion We have demonstrated a simple feedback driven piezoelectric micro-lens actuator which shows significant reduction in switching time by two orders of magnitude and similar static deflection characteristic. This is achieved by modifying the damping coefficient of the system through a 90o phase shifter multiplied by a gain in the feedback path. In comparison to previously reported switching times for micro-lens actuators, the attained switching time of 2.5ms is a substantial improvement and paves the way to a faster micro-lens actuation system possible for microoptics applications. References [1] Jain A and Xie H, “Half millimeter range vertically scanning micro-lenses for microscopic focusing applications,” in solid-state Sensors, Actuators and Microsystems workshop, 2006, pp. 74-77. [2] Bargiel S et al, “Electrostatically driven optical Z-axis scanner with thermally bonded glass microlens,” in Procedia of Engineering., vol.5, 2010, pp. 762-65. [3] A.Michael et al, “Piezo-electric micro-lens actuator,” Sensors and Actuators A: Physical,Vol.236, 116-129, 2015.
ScienceDirect Procedia Engineering 168 (2016) 1492 – 1495
30th Eurosensors Conference, EUROSENSORS 2016
Feedback Driven Fast Piezoelectric Micro-lens Actuator A.Michael*, S.S.Chen, and C.Y.Kwok School of Electrical Engineering and Telecommunication, UNSW AUSTRALIA, Sydney, Kensigton 2052, AUSTRALIA
Abstract This paper studies the dynamic behavior of a piezoelectric micro-lens actuator driven by a feedback system. The feedback system consists of the actuator in the forward path and an optical displacement sensor and a 90o phase shifter multiplied by a gain as feedback elements. The piezo-electric micro-lens actuator is fabricated and characterized for its dynamic performance by varying the feedback gain. The results show that the settling time and quality factor of the actuator are reduced by a factor of more than 100 and 10dB, respectively when the gain is increased from 0 to 0.0134. The micro-lens actuator demonstrated switching time of 2.5ms at a resonance frequency of 750Hz without affecting its static deflection characteristic. This is significantly fast in comparison to other reported switching times for micro-lens actuator. Crown Copyright © 2016Published Published by by Elsevier Elsevier Ltd. © 2016 The Authors. Ltd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference. Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords: Micro-lens actuator, Feedback control, piezo-electric actuator, quality factor
1. Introduction Micro-lens actuator that displaces a micro-lens in an out-of-plane direction is a critical component of a microoptics system for miniaturized camera, confocal microscopy and pico-projector applications. The desired performance requirements for such micro-lens actuators are high resonance frequency, low quality factor and large deflection in order to enable high end functionalities such as fast auto focus or extended optical zooming. Although achieving such a high performance actuator is very challenging due to the natural contradiction among the requirements, progresses have been made employing various actuation mechanisms and structures. Electro-thermal micro-lens actuators that produce large deflection have been reported but their response times were low [1]. Electrostatically driven micro-lens actuators are also common but they do not yield enough energy density to provide large * A.Michael. Tel.: +61-02-93855663; fax: +61-02-93855300. E-mail address: [email protected]
1877-7058 Crown Copyright © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference
doi:10.1016/j.proeng.2016.11.432
A. Michael et al. / Procedia Engineering 168 (2016) 1492 – 1495
1493
deflection or large resonance frequency [2]. Recently, piezo-electrically actuated micro-actuators have shown promising results [3]. However, despite having comparatively large resonance frequency and deflection, the switching time of the actuator was limited by high quality factor of the structure. In this paper, we present the study of micro-lens piezo-electric actuator driven by feedback system to control the quality factor and reduce switching time. 2. Piezoelectric micro-lens actuator The piezoelectric micro-lens actuator employed for the feedback experiment is shown in Fig. 1(a). It consists of eight piezo-electrically driven beams supporting a lens-holding frame on which a silica micro-sphere ball lens of 600µm in diameter and weighing 300µg is mounted as seen from Fig. 1(c). Each piezo-electrically driven beam is a multilayer 800µm long structure made of Pt (0.1µm)/PZT(1.5µm)/ZrO2(0.6µm)/SiO2(1µm)/Si(5µm). The top Pt layer is interdigitated to enable d33 mode of actuation with electrodes of 10µm wide and 5µm spacing. When voltage is applied in the direction polarization, which is along the x direction, the PZT film in each beam expands to produce a downward out-of-plane displacement as illustrated in ANSYS simulation in Fig. 2(a). After poling the fabricated actuator at 120V, the static displacements produced by applied electric fields have been measured and provided in Fig. 2(b).
Fig. 1. (a) Piezo-electric micro-lens actuator; (b) Schematics illustrating constituting layers of the actuator along A-A’;(c) Micro-lens mounted on the lens holding frame
Fig. 2. (a) Simulation result showing downward displacement when driven by voltage in a direction of polarization; (b) Measured deflection characteristics as a function of driving voltages;
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A. Michael et al. / Procedia Engineering 168 (2016) 1492 – 1495
3. Feedback driven micro-lens actuator system The feedback system for the micro-lens actuator has the micro-lens actuator in the forward path, and optical displacement sensor and 90o phase shifter multiplied by a gain in the feedback path. The block diagram of the system and measurement setup is schematically illustrated in Fig. 3. The dynamic characteristics of the micro-lens actuator with and without the feedback path are measured up to 1500Hz at a driving voltage of 10V. The normalized magnitude and phase responses of the actuator with out and with a feedback gain of 0.0134 are plotted in Fig. 3(b) and (c), respectively. The response of the actuator without feedback can be approximated by a second order system with a resonance frequency of 750Hz, a quality factor of 24dB, and a dc gain of 0.065µm/V. With the feedback, the system is still a second order with the same resonance frequency, dc gain but a reduced quality factor. The closed loop quality factor, Q*, can be shown to be related to the feedback gain, G, and the open loop quality factor, Q as in Eq. (1)
1 Q*
1 GADZo Q
(1)
where A is the dc gain, D is a displacement decoder factor, and ωo is the resonance frequency in rad/s. Eq. (1) shows that the quality factor of the micro-lens actuator system is controlled by the feedback gain, G, in the inversely proportional manner. With the gain G = 0.0134, the quality factor is reduced to 9dB, by a factor of 15dB as compared the open loop quality factor.
Fig. 3. (a) Measurement setup and feedback arrangement; Frequency response with and without feedback (b) magnitude (c) phase.
The effect of the feedback system on the switching behavior of the actuator is also studied by applying a 20V square wave excitation signal at 1Hz and varying the feedback gain, G. The time responses of the actuator with feedback at G=0.0134 and without feedback are shown in Fig. 4(b) and (a), respectively. For the open loop system, where the G=0, the actuator takes 260ms to settle down to a position within 1% of the final value. The settling time reduces to 2.5ms when G is increased to 0.0134. The significant decrease in settling time can be attributed to the reduction in the quality factor, which infers an increase in the damping coefficient of the system, as the feedback gain, G, is increased.
Fig. 4. Displacement response for 1Hz and 20V square wave excitation with (a) no feedback; (b) feedback at G=0.0134.
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A. Michael et al. / Procedia Engineering 168 (2016) 1492 – 1495
The transient response of the second order feedback system with the quality factor, Q*, resonance frequency, ωo, and dc gain of A for a unit step excitation in underdamped condition is given by
y (t )
· § ¸ ¨ Zot 2 ¸ ¨ 2Q* § 1 · e A¨1 sin(Zo 1 ¨¨ * ¸¸ t ) ¸u (t ) 2 ¨ © 2Q ¹ ¸ § 1 · ¸ ¨ 1 ¨¨ * ¸¸ ¸ ¨ Q 2 © ¹ ¹ ©
(2)
The settling time, tr, in which the final position is attained within less than 1% of accuracy can be calculated from Eq. (2) and is obtained as
tr |
9.22 GADZo
2
(3)
As can be seen from the above equation, the switching time is inversely proportional to the feedback gain. The switching times and quality factors of the actuator are measured for various feedback gains and plotted in Fig. 5(a) and (b), respectively. For comparison purpose, the calculated values of switching times are also shown in Fig. 5(a) indicating a good agreement.
Fig. 5. (a) switching times; (b) quality factor for various feedback gains.
4. Conclusion We have demonstrated a simple feedback driven piezoelectric micro-lens actuator which shows significant reduction in switching time by two orders of magnitude and similar static deflection characteristic. This is achieved by modifying the damping coefficient of the system through a 90o phase shifter multiplied by a gain in the feedback path. In comparison to previously reported switching times for micro-lens actuators, the attained switching time of 2.5ms is a substantial improvement and paves the way to a faster micro-lens actuation system possible for microoptics applications. References [1] Jain A and Xie H, “Half millimeter range vertically scanning micro-lenses for microscopic focusing applications,” in solid-state Sensors, Actuators and Microsystems workshop, 2006, pp. 74-77. [2] Bargiel S et al, “Electrostatically driven optical Z-axis scanner with thermally bonded glass microlens,” in Procedia of Engineering., vol.5, 2010, pp. 762-65. [3] A.Michael et al, “Piezo-electric micro-lens actuator,” Sensors and Actuators A: Physical,Vol.236, 116-129, 2015.