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Beam-stabilized optical switch using a voice-coil motor actuator
Journal of the Franklin Institute 348 (2011) 1–11 www.elsevier.com/locate/jfranklin
Beam-stabilized optical switch using a voice-coil motor actuator Taha Landolsi, Rached Dhaouadi, Oubadah Aldabbas American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates Received 30 December 2007; received in revised form 8 February 2009; accepted 20 February 2009
Abstract This paper presents the design, analysis, and implementation of a beam-stabilized optical switch using a voice-coil motor actuator. A closed-loop control system using a proportional-integralderivative (PID) controller is developed to stabilize the beam at the desired angle to maximize the optical power detected by a photodiode. Experimental results show a good performance with 17 ms switching speed and a maximum overshoot of only 3%. r 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. Keywords: Optical switch; Gaussian laser beam; Vibration control; Voice-coil motor actuator
1. Introduction Laser beam stabilization technology is used in many areas ranging from civil and industrial to military applications. Typical scanning systems, free-space optics communications, semiconductor devices manufacturing, biomedical systems and many other applications require precise mechanical alignment which is often achieved through the use of laser technology because of the coherence and good collimation properties of laser sources. Most of these applications require that the laser beam be switched from one position to another within very small time, called switching time, while sometimes scanning relatively wide angles. Laser stabilization is essential to provide the needed switching performance by simultaneously managing low-frequency, large-angle and high-frequency, small-angle corrections. Optical switches needed for these applications are required to have Corresponding author. Tel.: +971 6 515 2473.
E-mail address: [email protected] (T. Landolsi). 0016-0032/$32.00 r 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfranklin.2009.02.004
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T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
millisecond-range switching time, long-term reliability and good performance repeatability over their expected service time. In addition, they must have relatively simple controller design for them to be economically attractive [1,2]. Micro-electro mechanical systems (MEMS) technology for optical switching was the focus of tremendous research and product development over the past two decades [3–5]. Optical mirrors are typically mounted on MEMS structures which are actuated either electro-statically or electro-magnetically to achieve optical-beam steering in 3D space. Such techniques present several advantages in terms of the integration level and the footprint of the switch as well as in terms of achieving relatively low loss and good switching performance [3]. Electro-static actuation of such systems, however, require relatively high voltages to achieve acceptable switching times for applications such as optical line protection switching which usually requires a switching time below 50 ms. High actuation voltage level increases power consumption, heat dissipation, and long-term reliability of the switch. Recently, some attention has been paid to voice-coil motor (VCM) technology, which is extensively used in fast-access and high-capacity hard disk industry, as a platform for optical switching applications [6]. The advantage of using standard VCM actuator is to provide a low-cost, reliable, and fast-response actuator for the optical switch design. Hard disk drives use a VCM to rotate a thin metal arm in a planer surface. This swing-arm actuator runs with an acceleration greater than 20g. A standard hard disk drive consists of two major mechanical parts: the data storage part which is composed of an aluminum disk with a ferromagnetic coating, and a read-write triangular metal arm. On the opposite side of the metal arm axis sits a tightly wound trapezoidal coil of copper wire, positioned between rare-earth magnets. The coil and the magnet, called a voice-coil actuator, move and control the position of the metal arm. The actuator is contained in a steel case which confines the magnetic field in the coil. Devising high-performance and robust controllers for such actuators has proven to be technically easy and economically attractive [7]. For these reasons the hard drive industry has been adopting the VCM technology for several decades. In this paper, a voice-coil-based optical switch design and control is presented. The intent is to demonstrate a proof-of-concept prototype switch that meets the switching time requirement of such applications as optical line protection switching using off-the-shelf components, and straightforward controller design. The remaining of the paper is organized as follows: The system modeling, experimental setup, and a robust proportionalintegral-derivative (PID) controller design are reported in Section 2. System modeling includes a detailed description of VCM parameters, photodiode and position sensor specifications and mode of operation. In Section 3, the overall experimental setup and the principle of operation of the system is proven. In Section 4, the PID controller design is described. Section 5 concludes the paper with summarizing remarks and a comparison of our proposed optical switch design with other types of switches. 2. System modeling The system block diagram is shown in Fig. 1. It consists of a VCM from an off-the-shelf computer hard disk brand. A protected silver mirror with fused-silica substrate (for high reflectivity at the optical wavelength used in the experimental setup) is mounted on the tip of the arm where the hard disk reading head is typically mounted. A position sensor,
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11 Controller
3
Op-Amp
DAQ Position Sensor
Photocurrent Mirror
Power Amp Voice-coil Motor
Photodiode He-Ne Laser
Fig. 1. Laser stabilization system block diagram.
Vc
Power V + Amplifier
Kt J⋅s+b
1 L⋅s+R
1 s
θ Position
Kt Back EMF Fig. 2. Voice-coil motor model.
consisting of a potentiometer with a voltage divider, is mounted on the shaft of the VCM rotating arm to monitor its angular position. A red Helium–Neon (He–Ne) laser source and a silicon photodiode detector are fixed on opposite sides from each other so that when proper voltage is applied to the VCM, driven by a power amplifier, the mirror will switch the laser source optical signal to the photodetector. The resulting photocurrent is amplified and fed back to a data acquisition (DAQ) card. This photocurrent along with the signal acquired from the position sensor are used as the feedback signals in the closed-loop controller which drives the VCM to the desired angular position. 2.1. Voice-coil model The VCM can be modeled as a permanent magnet DC motor as shown in Fig. 2. The transfer function between the motor voltage and the coil position can be derived as follows [8]: GðsÞ ¼
yðsÞ Kt ¼ V ðsÞ s½ðLs þ RÞðJs þ bÞ þ K t K b
(1)
where K t is the motor torque constant, K b is the back-emf constant, L is the armature inductance, R is the armature resistance, J is the moment of inertia of the arm, and b is the viscous friction coefficient. This transfer function can be rewritten as GðsÞ ¼
Km sð1 þ t1 sÞð1 þ t2 sÞ
(2)
where K m is the equivalent gain and t1 , t2 are the motor time constants. This nominal linear model is a good approximation of the low-frequency dynamics of the VCM actuator
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2.5
Voltage (Volt)
2
1.5
1
0.5
0
0
0.05
0.1 Current (A)
0.15
0.2
Fig. 3. V –I characteristics of voice-coil with mirror and position sensor.
when the friction effects are neglected. The presence of stiction and nonlinear friction makes the transfer characteristics to be nonlinear. Moreover, many lightly damped modes become visible at high frequencies. The servocontroller for the VCM actuator is often designed using a nominal model. The high-frequency modes are treated as unmodeled dynamics, and are taken care of by ensuring sufficient attenuation of the closed-loop transfer function at the resonant frequencies. An exact model is therefore not required for the high-frequency modes and an estimate of the resonant frequencies is sufficient for this purpose. The internal resistance of the voice-coil was calculated by plotting the voltage–current characteristics curve with the arm locked as shown in Fig. 3. Then the slope of the line is the value of the resistance. Initial operation of the voice-coil needs a voltage supply of 0.874 V and draws a current of 74 mA. The slope of the V –I curve is calculated to be R 11O. 2.2. Position sensor model The position sensor assembly for sensing the arm rotary position includes a rotary potentiometer coupled to the arm. The servo potentiometer is constructed with a precision ball bearing system and long life flush bonded conductive track. The wipers are nickel silver-based for low contact resistance. The position sensor is supplied by a DC voltage V s ¼ 12 V and gives an output voltage V m proportional to the angular position of the voice-coil arm. Because of the limited travel range of the arm, the output voltage from the position sensor varies between 0 and 1 V. Hence, an additional amplification stage with a gain of 5 is used as a middle stage between the sensor and the DAQ card. This results in a measured position voltage V y ¼ 30 y=p. Fig. 4 shows the open-loop step response of the position sensor for a unit-step input voltage. The open-loop response of the system shows a linear acceleration of the arm from rest. The maximum position is reached in less than 150 ms. The maximum output voltage of the position sensor is limited to 5 V which corresponds to an angular position of 30 . The ripples in the plot occur because of the effect of the mechanical stop at the maximum position of the VCM arm.
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
5
6
Amplitude (Volts)
5 4 3 2 1 0
0
100
200 300 Time (ms)
400
500
Fig. 4. Position sensor open-loop step response for a unit step input of 1 V.
2.3. Optical model The optical signal emanating from the laser source is commonly modeled as a Gaussian beam whose intensity varies with the propagation distance z and the radius of the beam r, measured from its center, as follows [9,10]: W0 2 2r2 Iðr; zÞ ¼ I 0 exp 2 (3) W ðzÞ W ðzÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Here I 0 is the maximum beam intensity measured in the center of the beam, r ¼ x2 þ y2 , W 0 is the minimum waist of the beam assumed to occur at the origin ðz ¼ 0Þ and W ðzÞ is the beam waist at distance z. If the Rayleigh range of the beam is noted z0 and the pffiffiffiffiffiffiffiffiffiffiffiffi optical wavelength l, then the beam’s waist is given by W 0 ¼ lz0 =p and W ðzÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi W 0 1 þ ðz=z0 Þ2 . This beam characteristic is illustrated in Fig. 5. This figure clearly shows the diffraction of a Gaussian beam in free-space. As the laser beam propagates, its power remains constant but its intensity decreases with an inverse-square law. This behavior is important to consider in the design of the experimental setup because the power intercepted by the photodetector depends on the area of the detector active surface and on the beam waist at the distance separating the beam minimum waist location, i.e. z ¼ 0, and z the location of the photodetector. A disk of radius r0 on the photodetector plane will intercept a portion of the total beam power PT given by [9] Z r0 1 2r2 Iðr; zÞ2pr dr ¼ 1 exp 2 0 (4) PT 0 W ðzÞ If the photodetector active surface is not large enough (i.e. small r0 ) then a serious beam apodization problem will take place manifested by severely reduced optical power detection. We used a silicon photodiode to measure the incident optical power as a
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W(z) 2W0 W0 0
−z0
z0
z
Fig. 5. Gaussian beam characteristic parameters.
Photodiode Output (Volt)
0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0
20
40 60 Time (ms)
80
100
Fig. 6. Photodiode open-loop step response.
function of angle of rotation. The photodiode absorbs photons and generates current which is proportional to incident power. This current is a function of incident optical power and the wavelength l. The output voltage across the load resistor is given by: V 0 ¼ RPRL where R is the responsivity of the silicon photodetector at the optical signal wavelength. The photodiode has a small output voltage, but it is acceptable for our purpose. In Fig. 6, the photodiode open-loop response is plotted. The photodiode is placed at 15 from the initial z-axis position. The time taken by the voice-coil arm to reflect the laser beam into the photodiode at that desired position is 40 ms. Therefore, if smaller time is required to reach the photodiode, we need to decrease the deflection angle or reduce the response time of the arm. The maximum voltage reading is 0.51 V. It is shown that there are some small ripples appearing before and after the peak impulse. The corresponding photodiode output voltage of those ripples is 0.25 V. This phenomenon happens because the detector absorbs ambient room light. The bandwidth of the photodiode Df is inversely proportional to the diode capacitance C and the load resistance RL and is given by 2pRL C Df ¼ 1.
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
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3. Experimental setup In the experimental setup shown in Fig. 7, we used a computer hard disk VCM. A silvercoated fused-silica mirror coated with 96% average reflectivity was fixed on the motor’s arm, and a position sensor was mounted on its axis of rotation. For the Gaussian laser source we used a visible Helium–Neon (He–Ne) laser operating at 635 nm wavelength with an output power of about 4.5 mW. To detect the laser signal, a silicon-photodiode with good responsivity between 350 and 1100 nm and with an active area of 13:0 mm2 was used. The VCM, the position sensor, and the photodiode were connected to a personal computer through a DAQ which was used to control the input voltage of the voice-coil and to acquire both position and laser detection signals as shown in Fig. 7. When the optical switch is in the OFF position, corresponding to an 0 V output voltage, the arm of the voice-coil is at its initial (rest) position and the photodiode is not sensing any input (equivalent output voltage equal to 0.25 V). Once the switch is in the ON position (represented as 1 V), the arm of the VCM moves to the desired position where the mirror reflects the laser beam from the source to the photodiode position. At this stage the output of the photodiode is 0.51 V. The voice-coil used in this experiment requires about 100 mA to operate properly, which is a relatively high current. A linear power amplifier (LM12) was used to amplify the current supplied to the voice-coil. The voltage command used here is supplied from the computer through the DAQ. A normal operational amplifier (LM741) is used to amplify the output voltage from the position sensor. With a gain of 5, the amplifier output is set between 0 and 5 V. Output voltages from both the position sensor and the photodiode are fed back to the computer via the DAQ. 4. Controller design We used MATLAB/Simulink environment to acquire data, build the controller and view the output results in real-time. There are two controller approaches to stabilize the laser beam at the desired position. The first method is to control the position of the VCM arm at a fixed angle where the photodetector is located. This can be achieved based on the angular Photodiode
Power Op-amp
Laser source
Position sensor
Mirror
Fig. 7. Photo of the experimental setup showing the hard drive with the mirror and control circuitry.
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position feedback of the servopotentiometer as shown in Fig. 8. The PID controller is designed to have a fast under-damped response with low overshoot and minimum settling time. The gains were also chosen to minimize the steady state error of the system. In Fig. 9, the closed-loop position response is plotted for K p ¼ 2:5, K i ¼ 1:5, and K d ¼ 0:01. From the figure, the system is shown to be relatively fast. Within less than 60 ms, it stabilizes at the desired position (15 ) with 4.3% steady-state error and 33% overshoot. The second method is based on the measured optical power detected by the photodiode. The Simulink model for this approach is shown in Fig. 10. The optical power reference corresponds to the maximum power detected when the laser is perfectly aligned with the photodetector. A linear PID controller was implemented, using fixed step-size simulation with a sampling period 0.1 ms (10 kHz sampling rate), to stabilize the laser so that it maximizes the optical power delivered to the photodiode. In this experiment the maximum power (final value) corresponds to a measured voltage value of 0.48 V. The closed-loop response of the photodetector with gains K p ¼ 1:1, K i ¼ 8:3, and K d ¼ 0:02 when the VCM arm sweeps an angle of 8 is shown in Fig. 11. The settling time of the closed-loop VCM & Position sensor
Position Reference
Step 0 Constant
5/30 S
In1 Out1
PID Add
Gain1
Discrete PID Controller Measured Position 30/5
Gain2 Pos Plot Fig. 8. Simulink block diagram for the position control system.
Position (Degrees)
20
15
10
5
0
0
50
100
150
Time (ms) Fig. 9. Closed-loop position response with the first PID controller design.
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
Optical power reference Step
VCM with mirror and photo-detector In1 Out1
PID
S
0 Constant
9
Gain1
Add
Discrete PID Controller Phot-diode output PTot Plot
Fig. 10. Simulink block diagram for the optical power control system.
0.65
Photodiode Output (Volt)
0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25
0
10
20
30 Time (ms)
40
50
60
Fig. 11. Closed-loop photodiode response with the second PID controller design.
response is about 21 ms and the maximum overshoot is 3%. The response shows two sharp notches before the laser stabilizes. This phenomenon could be due to the physical structure of the photodiode and the unmodeled dynamics of resonant frequencies due to the low stiffness of the moving-coil arm coupling. Table 1 compares the switching time achieved by several optical MEMS switching techniques and the VCM-based switch presented in this paper. In practice, the switching speed is defined as the time required from the moment when a command is given to the switch to the moment when more than 90% of the final value (maximum optical power) is delivered to the photodiode [2]. For our switch, 90% of optical power was delivered to photodiode within less than 17 ms. Such a result takes into account the delays incurred in the DAQ and PC such as signal propagation delay, A/D conversion time, and computer processing delay. Such delays are expected to be very small and do not introduce sizeable measurement errors. From a switching application perspective, the switching speed achieved by our VCM-based switch is adequate for protection switching in optical
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Table 1 Comparison of the switching time for the VCM-based system and other optical switching technologies. Type of switch
Switching time
Silicon-on-insulator polymeric waveguides MEMS switch [11] Silica-on-silicon LETI MEMS switch [12] 2D MEMS waveguide X-bar switch [13] Our VCM-based switch
p200 ns o1 ms 3 ms 17 ms
networks [3,1] and many X-ray beam applications [6]. Better performance could be achieved if the voice-coil was operated in a vacuum enclosure to reduce the air friction that causes the relatively high switching time. In addition, reducing the size of the mirror will reduce the total system inertia and hence improve the system response time. While the table shows that our proposed technique switching performance is lower than the other techniques, it clearly indicates that the order or magnitude of our switching time is still acceptable for such applications as optical line protection switching. Our solution is, however, more advantageous in terms of power consumption simplicity of the controller design because of the reduced drive voltage required to actuate the switch. 5. Conclusions In this paper, an optical switch was developed and implemented using a VCM actuator. We investigated the adaptation of a VCM from a standard computer hard-disk drive to provide a fast and accurate electromechanical actuator for laser beam switching. A voltage-controlled VCM was designed to control the mirror position in order to maximize the reflected optical power detected by a photodiode located at a precise angular position. The laser beam stabilization system is shown to give a very fast and accurate control of the optical switch which is adequate for several industrial applications including optical line protection switching. For our design to be more economically attractive, medium to large scale integration of the discrete system components should be considered. Future work will focus on improving the switch design by decreasing both the switching time and the maximum overshoot percentage. This could be achieved by reducing the mirror size and weight to reduce the air friction effects, using better VCM with higher coupling stiffness, and implementing an adaptive nonlinear PID controller. References [1] X. Ma, G.-S. Kuo, Optical switching technology comparison: optical MEMS vs. other technologies, IEEE Communications Magazine 41 (11) (2003) S16–S23. [2] P. De Dobbelaere, K. Falta, L. Fan, S. Gloeckner, S. Patra, Digital MEMS for optical switching, IEEE Communications Magazine 40 (3) (2002) 88–95. [3] X. Zheng, V. Kaman, Y. Shifu, X. Yuanjian, O. Jerphagnon, K. Adrian, R.C. Anderson, H.N. Poulsen, L. Bin, J.R. Sechrist, C. Pusarla, R. Helkey, D.J. Blumenthal, J.E. Bowers, Three-dimensional MEMS photonic cross-connect switch design and performance, IEEE Journal of Selected Topics in Quantum Electronics 9 (2) (2003) 571–578. [4] T.P. Kurzweg, A.S. Morris III, Macro-modeling of systems including free-space optical MEMS, in: Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems (MSM2000), San Diego, CA, March 27–29, 2000, pp. 146–149.
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[5] T.P. Kurzweg, S.P. Levitan, J.A. Martinez, P.J. Marchand, D.M. Chiarulli, Modeling and simulating optical MEM switches, in: Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Kauai, Hawaii, August 2000, pp. 47–48. [6] L.P. Maguire, S. Szilagyi, R.E. Scholtena, High performance laser shutter using a hard disk drive voice-coil actuator, Review of Scientific Instruments 75 (9) (2004) 3077–3079. [7] R. Oboe, F. Marcassa, G. Maiocchi, Hard disk drive with voltage-driven voice coil motor and model-based control, IEEE Transactions on Magnetics 41 (2) (2005). [8] R.C. Dorf, R.H. Bishop, Modern Control Systems, Pearson Prentice-Hall, 2005. [9] B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, Wiley, New York, 1991. [10] A.E. Siegman, Lasers, University Science Books, 1986. [11] T. Bakke, C.P. Tigges, C.T. Sullivan, 1 2 MOEMS switch based on silicon-on-insulator and polymeric waveguides, IEEE Electronics Letters 38 (4) (2002) 177–178. [12] E. Ollier, Optical MEMS devices based on moving waveguides, IEEE Journal of Selected Topics in Quantum Electronics 8 (1) (2002) 155–162. [13] N. Iyer, C.H. Mastrangelo, S. Akkaraju, C. Brophy, A two-dimensional optical cross-connect with integrated waveguides and surface micromachined crossbar switches, Elsevier Journal of Sensors and Actuators A109 (2004) 231–241.
Beam-stabilized optical switch using a voice-coil motor actuator Taha Landolsi, Rached Dhaouadi, Oubadah Aldabbas American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates Received 30 December 2007; received in revised form 8 February 2009; accepted 20 February 2009
Abstract This paper presents the design, analysis, and implementation of a beam-stabilized optical switch using a voice-coil motor actuator. A closed-loop control system using a proportional-integralderivative (PID) controller is developed to stabilize the beam at the desired angle to maximize the optical power detected by a photodiode. Experimental results show a good performance with 17 ms switching speed and a maximum overshoot of only 3%. r 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. Keywords: Optical switch; Gaussian laser beam; Vibration control; Voice-coil motor actuator
1. Introduction Laser beam stabilization technology is used in many areas ranging from civil and industrial to military applications. Typical scanning systems, free-space optics communications, semiconductor devices manufacturing, biomedical systems and many other applications require precise mechanical alignment which is often achieved through the use of laser technology because of the coherence and good collimation properties of laser sources. Most of these applications require that the laser beam be switched from one position to another within very small time, called switching time, while sometimes scanning relatively wide angles. Laser stabilization is essential to provide the needed switching performance by simultaneously managing low-frequency, large-angle and high-frequency, small-angle corrections. Optical switches needed for these applications are required to have Corresponding author. Tel.: +971 6 515 2473.
E-mail address: [email protected] (T. Landolsi). 0016-0032/$32.00 r 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfranklin.2009.02.004
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T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
millisecond-range switching time, long-term reliability and good performance repeatability over their expected service time. In addition, they must have relatively simple controller design for them to be economically attractive [1,2]. Micro-electro mechanical systems (MEMS) technology for optical switching was the focus of tremendous research and product development over the past two decades [3–5]. Optical mirrors are typically mounted on MEMS structures which are actuated either electro-statically or electro-magnetically to achieve optical-beam steering in 3D space. Such techniques present several advantages in terms of the integration level and the footprint of the switch as well as in terms of achieving relatively low loss and good switching performance [3]. Electro-static actuation of such systems, however, require relatively high voltages to achieve acceptable switching times for applications such as optical line protection switching which usually requires a switching time below 50 ms. High actuation voltage level increases power consumption, heat dissipation, and long-term reliability of the switch. Recently, some attention has been paid to voice-coil motor (VCM) technology, which is extensively used in fast-access and high-capacity hard disk industry, as a platform for optical switching applications [6]. The advantage of using standard VCM actuator is to provide a low-cost, reliable, and fast-response actuator for the optical switch design. Hard disk drives use a VCM to rotate a thin metal arm in a planer surface. This swing-arm actuator runs with an acceleration greater than 20g. A standard hard disk drive consists of two major mechanical parts: the data storage part which is composed of an aluminum disk with a ferromagnetic coating, and a read-write triangular metal arm. On the opposite side of the metal arm axis sits a tightly wound trapezoidal coil of copper wire, positioned between rare-earth magnets. The coil and the magnet, called a voice-coil actuator, move and control the position of the metal arm. The actuator is contained in a steel case which confines the magnetic field in the coil. Devising high-performance and robust controllers for such actuators has proven to be technically easy and economically attractive [7]. For these reasons the hard drive industry has been adopting the VCM technology for several decades. In this paper, a voice-coil-based optical switch design and control is presented. The intent is to demonstrate a proof-of-concept prototype switch that meets the switching time requirement of such applications as optical line protection switching using off-the-shelf components, and straightforward controller design. The remaining of the paper is organized as follows: The system modeling, experimental setup, and a robust proportionalintegral-derivative (PID) controller design are reported in Section 2. System modeling includes a detailed description of VCM parameters, photodiode and position sensor specifications and mode of operation. In Section 3, the overall experimental setup and the principle of operation of the system is proven. In Section 4, the PID controller design is described. Section 5 concludes the paper with summarizing remarks and a comparison of our proposed optical switch design with other types of switches. 2. System modeling The system block diagram is shown in Fig. 1. It consists of a VCM from an off-the-shelf computer hard disk brand. A protected silver mirror with fused-silica substrate (for high reflectivity at the optical wavelength used in the experimental setup) is mounted on the tip of the arm where the hard disk reading head is typically mounted. A position sensor,
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11 Controller
3
Op-Amp
DAQ Position Sensor
Photocurrent Mirror
Power Amp Voice-coil Motor
Photodiode He-Ne Laser
Fig. 1. Laser stabilization system block diagram.
Vc
Power V + Amplifier
Kt J⋅s+b
1 L⋅s+R
1 s
θ Position
Kt Back EMF Fig. 2. Voice-coil motor model.
consisting of a potentiometer with a voltage divider, is mounted on the shaft of the VCM rotating arm to monitor its angular position. A red Helium–Neon (He–Ne) laser source and a silicon photodiode detector are fixed on opposite sides from each other so that when proper voltage is applied to the VCM, driven by a power amplifier, the mirror will switch the laser source optical signal to the photodetector. The resulting photocurrent is amplified and fed back to a data acquisition (DAQ) card. This photocurrent along with the signal acquired from the position sensor are used as the feedback signals in the closed-loop controller which drives the VCM to the desired angular position. 2.1. Voice-coil model The VCM can be modeled as a permanent magnet DC motor as shown in Fig. 2. The transfer function between the motor voltage and the coil position can be derived as follows [8]: GðsÞ ¼
yðsÞ Kt ¼ V ðsÞ s½ðLs þ RÞðJs þ bÞ þ K t K b
(1)
where K t is the motor torque constant, K b is the back-emf constant, L is the armature inductance, R is the armature resistance, J is the moment of inertia of the arm, and b is the viscous friction coefficient. This transfer function can be rewritten as GðsÞ ¼
Km sð1 þ t1 sÞð1 þ t2 sÞ
(2)
where K m is the equivalent gain and t1 , t2 are the motor time constants. This nominal linear model is a good approximation of the low-frequency dynamics of the VCM actuator
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T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
2.5
Voltage (Volt)
2
1.5
1
0.5
0
0
0.05
0.1 Current (A)
0.15
0.2
Fig. 3. V –I characteristics of voice-coil with mirror and position sensor.
when the friction effects are neglected. The presence of stiction and nonlinear friction makes the transfer characteristics to be nonlinear. Moreover, many lightly damped modes become visible at high frequencies. The servocontroller for the VCM actuator is often designed using a nominal model. The high-frequency modes are treated as unmodeled dynamics, and are taken care of by ensuring sufficient attenuation of the closed-loop transfer function at the resonant frequencies. An exact model is therefore not required for the high-frequency modes and an estimate of the resonant frequencies is sufficient for this purpose. The internal resistance of the voice-coil was calculated by plotting the voltage–current characteristics curve with the arm locked as shown in Fig. 3. Then the slope of the line is the value of the resistance. Initial operation of the voice-coil needs a voltage supply of 0.874 V and draws a current of 74 mA. The slope of the V –I curve is calculated to be R 11O. 2.2. Position sensor model The position sensor assembly for sensing the arm rotary position includes a rotary potentiometer coupled to the arm. The servo potentiometer is constructed with a precision ball bearing system and long life flush bonded conductive track. The wipers are nickel silver-based for low contact resistance. The position sensor is supplied by a DC voltage V s ¼ 12 V and gives an output voltage V m proportional to the angular position of the voice-coil arm. Because of the limited travel range of the arm, the output voltage from the position sensor varies between 0 and 1 V. Hence, an additional amplification stage with a gain of 5 is used as a middle stage between the sensor and the DAQ card. This results in a measured position voltage V y ¼ 30 y=p. Fig. 4 shows the open-loop step response of the position sensor for a unit-step input voltage. The open-loop response of the system shows a linear acceleration of the arm from rest. The maximum position is reached in less than 150 ms. The maximum output voltage of the position sensor is limited to 5 V which corresponds to an angular position of 30 . The ripples in the plot occur because of the effect of the mechanical stop at the maximum position of the VCM arm.
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
5
6
Amplitude (Volts)
5 4 3 2 1 0
0
100
200 300 Time (ms)
400
500
Fig. 4. Position sensor open-loop step response for a unit step input of 1 V.
2.3. Optical model The optical signal emanating from the laser source is commonly modeled as a Gaussian beam whose intensity varies with the propagation distance z and the radius of the beam r, measured from its center, as follows [9,10]: W0 2 2r2 Iðr; zÞ ¼ I 0 exp 2 (3) W ðzÞ W ðzÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Here I 0 is the maximum beam intensity measured in the center of the beam, r ¼ x2 þ y2 , W 0 is the minimum waist of the beam assumed to occur at the origin ðz ¼ 0Þ and W ðzÞ is the beam waist at distance z. If the Rayleigh range of the beam is noted z0 and the pffiffiffiffiffiffiffiffiffiffiffiffi optical wavelength l, then the beam’s waist is given by W 0 ¼ lz0 =p and W ðzÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi W 0 1 þ ðz=z0 Þ2 . This beam characteristic is illustrated in Fig. 5. This figure clearly shows the diffraction of a Gaussian beam in free-space. As the laser beam propagates, its power remains constant but its intensity decreases with an inverse-square law. This behavior is important to consider in the design of the experimental setup because the power intercepted by the photodetector depends on the area of the detector active surface and on the beam waist at the distance separating the beam minimum waist location, i.e. z ¼ 0, and z the location of the photodetector. A disk of radius r0 on the photodetector plane will intercept a portion of the total beam power PT given by [9] Z r0 1 2r2 Iðr; zÞ2pr dr ¼ 1 exp 2 0 (4) PT 0 W ðzÞ If the photodetector active surface is not large enough (i.e. small r0 ) then a serious beam apodization problem will take place manifested by severely reduced optical power detection. We used a silicon photodiode to measure the incident optical power as a
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W(z) 2W0 W0 0
−z0
z0
z
Fig. 5. Gaussian beam characteristic parameters.
Photodiode Output (Volt)
0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0
20
40 60 Time (ms)
80
100
Fig. 6. Photodiode open-loop step response.
function of angle of rotation. The photodiode absorbs photons and generates current which is proportional to incident power. This current is a function of incident optical power and the wavelength l. The output voltage across the load resistor is given by: V 0 ¼ RPRL where R is the responsivity of the silicon photodetector at the optical signal wavelength. The photodiode has a small output voltage, but it is acceptable for our purpose. In Fig. 6, the photodiode open-loop response is plotted. The photodiode is placed at 15 from the initial z-axis position. The time taken by the voice-coil arm to reflect the laser beam into the photodiode at that desired position is 40 ms. Therefore, if smaller time is required to reach the photodiode, we need to decrease the deflection angle or reduce the response time of the arm. The maximum voltage reading is 0.51 V. It is shown that there are some small ripples appearing before and after the peak impulse. The corresponding photodiode output voltage of those ripples is 0.25 V. This phenomenon happens because the detector absorbs ambient room light. The bandwidth of the photodiode Df is inversely proportional to the diode capacitance C and the load resistance RL and is given by 2pRL C Df ¼ 1.
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
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3. Experimental setup In the experimental setup shown in Fig. 7, we used a computer hard disk VCM. A silvercoated fused-silica mirror coated with 96% average reflectivity was fixed on the motor’s arm, and a position sensor was mounted on its axis of rotation. For the Gaussian laser source we used a visible Helium–Neon (He–Ne) laser operating at 635 nm wavelength with an output power of about 4.5 mW. To detect the laser signal, a silicon-photodiode with good responsivity between 350 and 1100 nm and with an active area of 13:0 mm2 was used. The VCM, the position sensor, and the photodiode were connected to a personal computer through a DAQ which was used to control the input voltage of the voice-coil and to acquire both position and laser detection signals as shown in Fig. 7. When the optical switch is in the OFF position, corresponding to an 0 V output voltage, the arm of the voice-coil is at its initial (rest) position and the photodiode is not sensing any input (equivalent output voltage equal to 0.25 V). Once the switch is in the ON position (represented as 1 V), the arm of the VCM moves to the desired position where the mirror reflects the laser beam from the source to the photodiode position. At this stage the output of the photodiode is 0.51 V. The voice-coil used in this experiment requires about 100 mA to operate properly, which is a relatively high current. A linear power amplifier (LM12) was used to amplify the current supplied to the voice-coil. The voltage command used here is supplied from the computer through the DAQ. A normal operational amplifier (LM741) is used to amplify the output voltage from the position sensor. With a gain of 5, the amplifier output is set between 0 and 5 V. Output voltages from both the position sensor and the photodiode are fed back to the computer via the DAQ. 4. Controller design We used MATLAB/Simulink environment to acquire data, build the controller and view the output results in real-time. There are two controller approaches to stabilize the laser beam at the desired position. The first method is to control the position of the VCM arm at a fixed angle where the photodetector is located. This can be achieved based on the angular Photodiode
Power Op-amp
Laser source
Position sensor
Mirror
Fig. 7. Photo of the experimental setup showing the hard drive with the mirror and control circuitry.
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position feedback of the servopotentiometer as shown in Fig. 8. The PID controller is designed to have a fast under-damped response with low overshoot and minimum settling time. The gains were also chosen to minimize the steady state error of the system. In Fig. 9, the closed-loop position response is plotted for K p ¼ 2:5, K i ¼ 1:5, and K d ¼ 0:01. From the figure, the system is shown to be relatively fast. Within less than 60 ms, it stabilizes at the desired position (15 ) with 4.3% steady-state error and 33% overshoot. The second method is based on the measured optical power detected by the photodiode. The Simulink model for this approach is shown in Fig. 10. The optical power reference corresponds to the maximum power detected when the laser is perfectly aligned with the photodetector. A linear PID controller was implemented, using fixed step-size simulation with a sampling period 0.1 ms (10 kHz sampling rate), to stabilize the laser so that it maximizes the optical power delivered to the photodiode. In this experiment the maximum power (final value) corresponds to a measured voltage value of 0.48 V. The closed-loop response of the photodetector with gains K p ¼ 1:1, K i ¼ 8:3, and K d ¼ 0:02 when the VCM arm sweeps an angle of 8 is shown in Fig. 11. The settling time of the closed-loop VCM & Position sensor
Position Reference
Step 0 Constant
5/30 S
In1 Out1
PID Add
Gain1
Discrete PID Controller Measured Position 30/5
Gain2 Pos Plot Fig. 8. Simulink block diagram for the position control system.
Position (Degrees)
20
15
10
5
0
0
50
100
150
Time (ms) Fig. 9. Closed-loop position response with the first PID controller design.
T. Landolsi et al. / Journal of the Franklin Institute 348 (2011) 1–11
Optical power reference Step
VCM with mirror and photo-detector In1 Out1
PID
S
0 Constant
9
Gain1
Add
Discrete PID Controller Phot-diode output PTot Plot
Fig. 10. Simulink block diagram for the optical power control system.
0.65
Photodiode Output (Volt)
0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25
0
10
20
30 Time (ms)
40
50
60
Fig. 11. Closed-loop photodiode response with the second PID controller design.
response is about 21 ms and the maximum overshoot is 3%. The response shows two sharp notches before the laser stabilizes. This phenomenon could be due to the physical structure of the photodiode and the unmodeled dynamics of resonant frequencies due to the low stiffness of the moving-coil arm coupling. Table 1 compares the switching time achieved by several optical MEMS switching techniques and the VCM-based switch presented in this paper. In practice, the switching speed is defined as the time required from the moment when a command is given to the switch to the moment when more than 90% of the final value (maximum optical power) is delivered to the photodiode [2]. For our switch, 90% of optical power was delivered to photodiode within less than 17 ms. Such a result takes into account the delays incurred in the DAQ and PC such as signal propagation delay, A/D conversion time, and computer processing delay. Such delays are expected to be very small and do not introduce sizeable measurement errors. From a switching application perspective, the switching speed achieved by our VCM-based switch is adequate for protection switching in optical
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Table 1 Comparison of the switching time for the VCM-based system and other optical switching technologies. Type of switch
Switching time
Silicon-on-insulator polymeric waveguides MEMS switch [11] Silica-on-silicon LETI MEMS switch [12] 2D MEMS waveguide X-bar switch [13] Our VCM-based switch
p200 ns o1 ms 3 ms 17 ms
networks [3,1] and many X-ray beam applications [6]. Better performance could be achieved if the voice-coil was operated in a vacuum enclosure to reduce the air friction that causes the relatively high switching time. In addition, reducing the size of the mirror will reduce the total system inertia and hence improve the system response time. While the table shows that our proposed technique switching performance is lower than the other techniques, it clearly indicates that the order or magnitude of our switching time is still acceptable for such applications as optical line protection switching. Our solution is, however, more advantageous in terms of power consumption simplicity of the controller design because of the reduced drive voltage required to actuate the switch. 5. Conclusions In this paper, an optical switch was developed and implemented using a VCM actuator. We investigated the adaptation of a VCM from a standard computer hard-disk drive to provide a fast and accurate electromechanical actuator for laser beam switching. A voltage-controlled VCM was designed to control the mirror position in order to maximize the reflected optical power detected by a photodiode located at a precise angular position. The laser beam stabilization system is shown to give a very fast and accurate control of the optical switch which is adequate for several industrial applications including optical line protection switching. For our design to be more economically attractive, medium to large scale integration of the discrete system components should be considered. Future work will focus on improving the switch design by decreasing both the switching time and the maximum overshoot percentage. This could be achieved by reducing the mirror size and weight to reduce the air friction effects, using better VCM with higher coupling stiffness, and implementing an adaptive nonlinear PID controller. References [1] X. Ma, G.-S. Kuo, Optical switching technology comparison: optical MEMS vs. other technologies, IEEE Communications Magazine 41 (11) (2003) S16–S23. [2] P. De Dobbelaere, K. Falta, L. Fan, S. Gloeckner, S. Patra, Digital MEMS for optical switching, IEEE Communications Magazine 40 (3) (2002) 88–95. [3] X. Zheng, V. Kaman, Y. Shifu, X. Yuanjian, O. Jerphagnon, K. Adrian, R.C. Anderson, H.N. Poulsen, L. Bin, J.R. Sechrist, C. Pusarla, R. Helkey, D.J. Blumenthal, J.E. Bowers, Three-dimensional MEMS photonic cross-connect switch design and performance, IEEE Journal of Selected Topics in Quantum Electronics 9 (2) (2003) 571–578. [4] T.P. Kurzweg, A.S. Morris III, Macro-modeling of systems including free-space optical MEMS, in: Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems (MSM2000), San Diego, CA, March 27–29, 2000, pp. 146–149.
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[5] T.P. Kurzweg, S.P. Levitan, J.A. Martinez, P.J. Marchand, D.M. Chiarulli, Modeling and simulating optical MEM switches, in: Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Kauai, Hawaii, August 2000, pp. 47–48. [6] L.P. Maguire, S. Szilagyi, R.E. Scholtena, High performance laser shutter using a hard disk drive voice-coil actuator, Review of Scientific Instruments 75 (9) (2004) 3077–3079. [7] R. Oboe, F. Marcassa, G. Maiocchi, Hard disk drive with voltage-driven voice coil motor and model-based control, IEEE Transactions on Magnetics 41 (2) (2005). [8] R.C. Dorf, R.H. Bishop, Modern Control Systems, Pearson Prentice-Hall, 2005. [9] B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, Wiley, New York, 1991. [10] A.E. Siegman, Lasers, University Science Books, 1986. [11] T. Bakke, C.P. Tigges, C.T. Sullivan, 1 2 MOEMS switch based on silicon-on-insulator and polymeric waveguides, IEEE Electronics Letters 38 (4) (2002) 177–178. [12] E. Ollier, Optical MEMS devices based on moving waveguides, IEEE Journal of Selected Topics in Quantum Electronics 8 (1) (2002) 155–162. [13] N. Iyer, C.H. Mastrangelo, S. Akkaraju, C. Brophy, A two-dimensional optical cross-connect with integrated waveguides and surface micromachined crossbar switches, Elsevier Journal of Sensors and Actuators A109 (2004) 231–241.