Electrostatic Torsional Micromirror With Enhanced ... - IEEE Xplore

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE/ASME TRANSACTIONS ON MECHATRONICS

1

Electrostatic Torsional Micromirror With Enhanced Tilting Angle Using Active Control Methods Yuan Ma, Member, IEEE, Shariful Islam, and Ya-Jun Pan, Member, IEEE

Abstract—Electrostatic microelectromechanical systems (MEMS)-based torsional micromirrors are a fundamental building block for many optical network applications, such as optical wavelength-selective switches, configurable optical add-drop multiplexers and optical cross-connects. Although the device architecture, materials and fabrication processes determine the micromirrors’ functioning space, one major technical challenge to achieving their full performance potentials is the controllability and stability of the tilting angle. In this paper, an electrostatic micromirror is designed and fabricated using a standard MEMS silicon-oninsulator (SOI) process. Active control approaches including gain scheduling and nonlinear proportional and derivative (PD) control are proposed. Both approaches can improve the performance of the mirror tilting and enhance the robustness of the structures to any stochastic perturbations. Furthermore, the nonlinear PD control can eliminate the micromirror “pull-in” phenomenon, hence significantly expanding the mirror tilt range, and as a result achieving enhanced device performance and functionality. The nonlinear PD control method is experimentally implemented and the results demonstrate the effectiveness of the approach. Index Terms—Closed-loop control, electrostatic, micromirror, nonlinear control torsional.

I. INTRODUCTION SING the fabrication process of the integrated circuit (IC), microelectromechanical systems (MEMS) technology integrates the multiple functions of mechanical, electrical, magnetic, thermal and optics into a single semiconductor substrate. Function integration at the micro-scale across such a variety of disciplines enables the development of systems whose performance, cost and footprint are not achievable with any other technology. The wide deployment of dense wavelength division multiplexing (DWDM) optical network is inevitable with the ever expanding internet and wireless traffic. Conventional optical network components, such as discrete switches, and variable optical attenuators, are becoming increasingly unattractive, expensive, and very often, infeasible to be used for the implementation of a communication system with such high chan-

U

Manuscript received April 30, 2010; revised July 21, 2010; accepted July 31, 2010. Recommended by Technical Editor J. Ueda. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, in part by the Canada Foundation for Innovation, and in part by CMC Microsystems. This work was presented in part at the The 4th IEEE Conference on Automation Science and Engineering, Washington DC, August 23-26, 2008. Y. Ma is with the Department of Electrical and Computer Engineering, Dalhousie University, Halifax, NS B3J 2X4, Canada (e-mail: Yuan.Ma@Dal. Ca). S. Islam and Y.-J. Pan are with the Department of Mechanical Engineering, Dalhousie University, Halifax, NS B3J 2X4, Canada (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMECH.2010.2066283

nel density. For years, MEMS technology has been a critical player for many optical network functions such as wavelength switching, wavelength interleaver, multi-channel optical adddrop multiplexers (OADM) and optical cross-connects etc. with unmatched performance on chromatic dispersion, insertion loss, speed and reliability [1]. Electrostatic actuation is favored for many MEMS applications because of its simplicity of implementation and low power consumption [2], [3]. A widely used structure in optical network components is an electrostatically actuated MEMS torsional micromirror with a planar bottom drive that can steer a light beam in a continuous and controllable fashion. It requires a less stringent micro-fabrication process compared to other actuation methods such as electro-magnetic actuation or vertical comb-drive [4]. The device has a high fill factor, i.e., the ratio of the active reflecting micromirror area to the device area. The large scale integratability and low cost for high volume mass production of MEMS components create significant potentials for the ever expanding optical communication networks. Due to the high fill factor of the electrostatic micromirror, the discrete structure can be easily expanded to high channel count subsystems such as wavelength selective switches without changing the basic device operating principles and its manufacturing process. For applications requiring minimum dynamic cross-talk between optical ports, a second tilt perpendicular to the first rotation axis can be introduced using an internal hinge gimbal [5]. The second tilt steers the light away from the ports that are located in between the two switching start and end ports. The most critical performance parameter of an electrostatic torsional micromirror is its controllable tilting range, which relates directly to the routing range of switching function. An important property (or limitation) of the electrostatic actuators is their “pull-in” angle, beyond which the electrostatic torque overcomes the mechanical torque, and the micromirror snaps abruptly to the activated electrode plane, which results in a loss of the controllability of the tilting angle. This unique complexity of uncertainty and nonlinearity is one of the most challenging aspects of “micro- and nanoscale” mechatronic systems as compared to their “macroscale” versions [6]. In the literature, some approaches have been suggested to increase the controllable travel range of parallel plate actuators, such as adding series capacitor [7] and leveraged bending [8]. These approaches can be adapted to increase the controllable tiling range of torsional electrostatic micromirror. However, all these approaches require either increased actuation voltage, larger device area, or slower switching speed and lower resonant frequencies as tradeoff for the increase of tilting range. The tradeoff has become a common design challenge for

1083-4435/$26.00 © 2010 IEEE

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2

IEEE/ASME TRANSACTIONS ON MECHATRONICS

devices relying on the electrostatic force for actuation. Without compromising the mechanical or electrical performance, other viable methods to increase the controllable tilting range include modifying the arrangement of the driving electrodes [9] and utilizing active control of the micromirror [10]–[15]. Since modifying the driving electrode configuration usually requires changes made to the fabrication process, many researchers focus on the active control methods to stabilize the electrostatic MEMS and extend their travel range. A charge control method with a switched-capacitor configuration has been proposed in [10]. The modeling and feedback control issues of electrostatically actuated mechanical systems with parallel plates have been studied in [11]–[13]. Passivity based control and Lyapunov methods were applied and the performance was validated through simulations. The work implied that for an electrostatic micromirror device, nonlinear control strategies would be a better solution. A closed-loop control technique using linear voltage control law is developed and experimentally implemented in [14], [15] to overcome the pull-in problem. A voltage slightly larger than the pull-in voltage is first applied when the actuator is at small displacement positions, and the voltage is then linearly reduced as the actuator tilts toward the desired position. The objective of this work is to design effective control schemes to improve the response through achieving a larger tilting angle than the pull-in angle. The response of the micromirror should not have large overshoot and should have short response time which improve the performance of the mirror switching. In this paper, an electrostatic micromirror is designed and fabricated using standard MEMS process. At first, a closed-loop gain scheduling method is applied to the mirror with simulation results. The mirror can track a desired reference angle profile; however, it cannot tilt over the pull-in angle. Hence a nonlinear proportional and derivative (PD) control method is then proposed and experimentally implemented for the 1-degreeof-freedom (DOF) MEMS micromirror device. The proposed nonlinear PD control can improve the performance of the mirror switching with the ability to achieve a larger controllable tilting angle than the pull-in angle, and enhance the robustness of the structure to any stochastic perturbations. As a result, it can significantly improve device performance and functionality. Furthermore, a polysilicon multi-user MEMS process (polyMUMPs) micromirror is designed and tested under the nonlinear PD controller as well. Experimental results demonstrated the effectiveness of the approaches, and are in good agreement with theoretical analysis. The paper is organized as follows. Section II shows the design of electrostatic micromirror while section III formulates the problem. Two control approaches are introduced in section IV, and section V discusses the experimental implementation of the PD controller. Section VI summarizes the contributions of the paper. II. DESIGN OF AN ELECTROSTATIC MICROMIRROR Fig. 1 shows a 3-D optical interferometric profile of an electrostatic torsional mirror fabricated using the micralyne generalized MEMS (MicraGEM) silicon-on-insulator (SOI) process.

Fig. 1.

Optical interferometric profile of an electrostatic torsional micromirror.

Fig. 2.

Cross section of a micromirror showing electrode configuration.

The diameter of the micromirror is 500 µm with a thickness ˚ ˚ low stress TiW/Au. of 10 µm, and coated with 500 A/2000 A The combination of thick single crystalline silicon and the low stress gold provides a highly reflective surface with a radius of curvature larger than 0.5 m, which is ideal for optical network applications. The mirror is suspended by two serpentine shaped hinges over a cavity etched into the Pyrex substrate. The width of the serpentine shaped hinges is about 1.5 µm after fabrication and the cavity depth is 12 µm. The bottom electrode consists of a group of individual controllable rectangular gold electrodes deposited using lift-off techniques. Fig. 2 shows a cross-section diagram of the micromirror structure. The bottom electrode beneath the left half of the mirror consists of four individual controllable rectangular electrodes. The four electrodes can be configured to provide four different electrode lengths of 100 µm, 150 µm, 200 µm and 250 µm corresponding to pull-in angles of 3.1, 2.1, 1.6 and 1.3 degrees respectively. Longer electrode provides greater electrostatic force with reduced controllable range compared with shorter electrode driving a similar structure. The electrodes beneath the right half of the mirror are grounded to the same potential as the mirror. The maximum torsional angle of the micromirror is defined by the mechanical stop when the mirror touches the bottom of the cavity. For a micromirror with 500 µm diameter and 30 µm anti-stiction fingers, the mechanical stop angle is about 2.45 degrees.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. MA et al.: ELECTROSTATIC TORSIONAL MICROMIRROR WITH ENHANCED TILTING ANGLE USING ACTIVE CONTROL METHODS

Fig. 3.

3

Schematic diagram of the electrostatic torsional micromirror.

The micromirror is designed to have a sufficient high natural resonance frequency to survive the impact testing as specified by Telcordia GR-1221-CORE for passive optical components. The maximum normal and shear stress of the micromirror under 500 g shock on three axis are less than 150 MPa, which gives a 30 times safety margin to the failure strength of silicon.

Fig. 4.

Angle response under open loop control with step input. TABLE I PARAMETERS

III. PROBLEM FORMULATION The schematic diagram of the electrostatic torsional micromirror designed in Section II is shown in Fig. 3. Note that a1 is the distance between the rotation axis to the nearest edge of the bottom electrode; a2 is the distance to the end of the electrode; and a3 is the distance to the end of the movable plate. b is the electrode width; d is the vertical separation distance between the micromirror and the bottom electrodes; and α is the rotational angle. The dynamics of the electrostatic micromirror can be described as follows: Iα ¨ + B α˙ + Kα = f (α) V 2

(1)

where I is the moment of inertia around the rotation axis which is determined by the shape of the mirror; B is the damping coefficient; and K is the stiffness of supporting hinges. V is the actuation voltage and f (α) is a nonlinear function with respect to the state variable α. Assuming small tilting angles and using the definition of Fig. 3, f (α) is of the form [15]: 1 1 ε0 b − f (α) = 2 2α 1 − (βα/αm ax ) 1 − (γα/αm ax ) αm ax − βα +ln . (2) αm ax − γα In this nonlinear function, ε0 is the dielectric constant of the surrounding medium; αm ax = d/a3 is the maximum constrained tilt; β = a2 /a3 and γ = a1 /a3 are constants. For sufficiently low voltages, (1) has two solutions, where only the one with the lower tilting angle is stable. For a certain voltage, only one solution exists and this is the pull-in voltage. Above the pull-in voltage the electrostatic torque is always greater than the mechanical torque and there is no equilibrium that can be reached. Fig. 4 shows the open-loop response of the micromirror with a step input. The parametric values in the simulation are as shown in Table I. K and B are theoretically calculated from the micromirror geometry [16]; and ε0 is the dielectric constant of vacuum. The moment of inertia of the cir-

cular mirror is then represented as I = 14 M a23 , where the mass is M = πρa23 h, ρ is the silicon density and h is the thickness of the mirror. Open-loop control of the micromirror is commonly used in industrial applications due to its low cost, but it requires accurate calibration of the tilting angle as a function of the driving voltage for each mirror, which can be time consuming and labor intensive. Open-loop control is also sensitive to any external perturbations and the settling time is usually longer at a higher deflection angle of the mirror. From Fig. 4 we can see the pull-in angle is around 1.3 degrees and the pull-in voltage is around 30 volts for the chosen electrode length. Open-loop method can only provide reasonable response characteristics under the condition that the desired angle is less than the pull-in angle and pre-shaping of the driving voltage may also be required if the ringing response of the micromirror to a step function actuation becomes a problem to a specific application. Once the input voltage is over the pull-in voltage such as the dashed line in Fig. 4, the mirror cannot sustain a stable position and the desired angle cannot be reached. IV. CONTROL APPROACHES FOR IMPROVING MICROMIRROR TILTING Compared with the open-loop control approach, the feedback closed-loop control with measurable system states offers a stable operation with desired performance, including shorter settling time, insensitivity to perturbations, and larger tilting angle. A. Closed-Loop Gain Scheduling Strategy Gain scheduling is widely used in nonlinear systems which can be linearized around their equilibrium points. It is applicable



to nonlinear systems of the general form x˙ = fs (x, u)

(3)

where x ∈ n and u ∈ m are the system states and control input, respectively. For the proposed micromirror system, the linearized model can be described as follows. The equilibrium point family is denoted as s Ks and ueq = xeq = f (s) 0 where s is the scheduling variable. The linearized model around the equilibrium point set is then represented as (the detailed derivation is omitted here due to limited space) ˜˙ = Ae (s)˜ x + Be (s)˜ u x

Fig. 5.

System response through gain scheduling for a time varying reference.

Fig. 6.

System response through gain scheduling for a linear reference.

(4)

˜ = x − xeq (s), u where x ˜ = u − ueq (s) and   0 1 B Ae (s) =  3K + g(s) − − I I   0   Be (s) =  Ksf (s)  . 2 I Note that

βαm ax γαm ax Kε0 b − g(s) = 2 2Isf (s) (αm ax − βs) (αm ax − γs)2

(γ − β)αm ax + . (αm ax − βs)(αm ax − γs)

(5)

In the system (4), design a controller with gains K1 , K2 , K3 , and ˜ − K3 (x1d − s) u ˜ = − [K1 (s) K2 (s)] x such that Ae (s) − Be (s) [K1 (s) K2 (s)] is stable. Note that x1d is the desired angle for the mirror to tilt. Here is one example of assigning K1 and K2 such that

0 1 Ae (s) − Be (s) [K1 (s) K2 (s)] = (6) −5 −5 and K3 = 5 for zero steady state error. Solving (6) for K1 (s) and K2 (s), we have the gains designed as K1 (s) =

5I − 3K + Ig(s) 5I − B K2 (s) = . 2 Ksf (s) 2 Ksf (s)

(7)

The gain scheduled control input is finally represented as u(s) = u ˜(s) + ueq (s) = −K1 (s)(x1 − s) − K2 (s)x2 + − 5(x1d − s).

Ks f (s) (8)

Note that the scheduling variable s can be designed as a desired reference signal such as a smooth nonlinear function, a step input, a smoothed step input or a reference step with linear transient region. s should be used such that the linearized model in the neighbourhood of the equilibrium s is stable. Figs. 5 and 6 show the evolution of the mirror angle when the gain scheduled control is applied. The scheduling signal in Fig. 5 is an arbitrary smooth function, e.g., the scheduling variable s is the dash-dotted line. It shows that the angle follows the desired scheduling variable very well. When a linear slope transient line is applied as in Fig. 6, the performance remains good. The main advantage of the gain scheduling is that the closedloop control system can track a desired reference angle profile, especially when the transient response is relatively important for some applications. There is a limitation of this method: the tilt cannot exceed the pull-in angle since the system around the equilibrium points around the pull-in angle is not stable. The idea of gain scheduling method is from the linearization of nonlinear system in the neighborhood of a range of operating points, which can be represented by a scheduling variable or scheduling variables (e.g. “s” in (4)). Note that the original


Fig. 7.

5

Block diagram of the PD controller.

nonlinear system (open-loop system) around the equilibrium points or the scheduling variable should be stable, since the gain scheduled controller is designed based on the stable linearized model. For the micromirror, when the scheduling variable s is approaching the pull-in angle, the system becomes unstable and the controller cannot change this property due to its design concept. Thus, there is no problem to apply the controller for desired tilting angles lower than the pull-in angle, but not beyond it. B. Closed-Loop Nonlinear Proportional and Derivative (PD) Control The proposed nonlinear PD control uses the error signals by comparing the actual system states with their desired setting values. Define x1 = α, x2 = α˙ and u = V . Then the state space representation of (1) is a second order system described as x˙ 1 = x2 (9) B K f (x1 ) 2 u x˙ 2 = − x2 − x1 + I I I where 1 1 0 b f (x1 ) = 2 − 2x1 1 − (βx1 /x1,m ax ) 1 − (γx1 /x1,m ax ) x1,m ax − βx1 +ln x1,m ax − γx1 and x1,m ax is the maximum tilting angle of the micromirror. Fig. 7 shows the block diagram of the nonlinear PD controller. The PD controller is designed as Kx1d + Kp e(t) + Kd e(t) ˙ (10) u = Fn = f (x1 ) where e(t) = x1d − x1 (t) and x1d is the desired angle θd . Kd and Kp are design gains of the nonlinear PD controller and they can be designed and tuned to change the error convergence rate. In addition, the PD gains, Kp and Kd , should be tuned appropriately to meet the requirement of positive square root in (10). The closed-loop error dynamics becomes ˙ + (K + Kp )e(t) = 0. I e¨(t) + (B + Kd )e(t)

(11)

In order to satisfy limt→∞ e(t) = 0, Kd and Kp have to meet the conditions of B + Kd > 0 and K + Kp > 0 respectively. A saturation function is added at the control input of the system to prevent damages to the device due to possible high actuation voltages. Thus, the controller can be expressed as

Fig. 8. System response under nonlinear PD control with K p = 1 × 10 −6 and K d = 0.00169.

usat = sat(u, um ax ), where um ax is the maximum actuation voltage input to the system. Fig. 8 shows the simulation response of the micromirror under nonlinear PD control with a desired target tilting angle of 2.2 degrees, which is larger than the pull-in angle of 1.3 degrees. The gains are tuned as Kp = 1 × 10−6 and Kd = 0.00169 targeting at fast response and minimum overshoot. The angle reaches its steady state after about 0.4 milliseconds. Compared with the open-loop approach in Fig. 4, the response in Fig. 8 is faster and the overshoot is small. The gains can be tuned to reach zero overshoot. The most important advantage is that a tilting angle larger than the pull-in angle can be successfully achieved. C. Discussions on Nonlinear PD Control with Parametric Uncertainties According to the expression of the nonlinear PD control as in (10), if uncertainties exist in some parameters such as angular stiffness K, geometric sizes of the mirror as in Fig. 3 which influence the nonlinear function f (·), then a steady-state error may exist. However, the closed-loop stability is not affected with appropriate gains in the controller. Fig. 9 shows one example of the response when there exists 2% uncertainty in the angular stiffness coefficient K. The steady state error is around 0.045 degrees or around 2% of the desired angle. In Section V, experimental studies are carried out. Note that the real mirror parameters won’t be the same as the parameters designed and used in the controller, e.g. parameter K. However, as shown in Fig. 11 and Fig. 14, with a fine tuning of the controller gains, both mirrors can reach the tilting angles above the pull-in angle limit. V. EXPERIMENTAL IMPLEMENTATION A. Experimental Setup The nonlinear PD controller has been implemented experimentally as shown in Fig. 10. A 12-mm one-dimensional



Fig. 9. System response under nonlinear PD control with 2% uncertainty in the angular stiffness K .

Fig. 11.

Experimental closed-loop response.

Fig. 12. Step response of the micromirror measured by the Micro System Analyzer. Fig. 10.

Experimental setup.

Hamamatsu position sensing detector (PSD) is used to measure the actual tilting angle of the mirror and feed it back to the controller. The PSD is positioned 6.5 cm away from the micromirror, and supplies continuous position data utilizing differential photodiode surface resistance. A red laser with 650 nm wavelength is focused through a convex lens onto the micromirror and reflected perpendicularly onto the PSD surface. The output of the PSD is ±10 V depending on the position of incident light beam on the detector surface. For small deflections of the micromirror, i.e. tan 2θ ≈ 2θ, the output of the PSD is directly proportional to the mirror tilting angle. The resolution of the PSD is 4 µm, which corresponds to about 2 millidegree mirror tilt in the setup. Theoretical measurement error is tan 2θ − 2θ, which corresponds to about 1 % at the maximum stop angle. The measurement error is due to the fact of a straight PSD being used instead of a cylindrical surface with the micromirror at the center of the arc. B. Implementation of the Nonlinear PD Controller The nonlinear PD controller is implemented using LabView with a National Instruments’s NI6040E Data Acquisition (DAQ)

card. Since the DAQ card output is limited to ±10 V, a DC voltage amplifier circuit is added to amplify the input to the micromirror. Fig. 11 shows the system response under the proposed nonlinear PD control. The system can reach a tilting angle of 1.6 degrees, which is larger than the pull-in angle of 1.3 degrees. The micromirror reaches its steady state after about 1.2 milliseconds. The gain of the controller has been tuned to Kp = 1.0 × 10−9 and Kd = 2.5 × 10−12 to minimize the overshoot of the angle and settling time. The damping ratio of the micromirror is measured to be 0.027 using a Polytec Micro System Analyzer (MSA) as shown in Fig. 12 [16]. The velocity response of the micromirror to a step actuation is measured by the Scanning Laser-Doppler Vibrometry method. Experimental data shows a settling time about 10 milliseconds. The contour of the damped motion is fit into an exponentially decay equation and from which the damping ratio is calculated. The first resonant frequency of the micromirror is measured to be 1.95 kHz, which is within ±3% of the designed frequency of 2 kHz. The maximum tilt of the micromirror is constrained by the geometry of the mirror to an angle of 2.45 degrees. A tilting range of 65% of the maximum tilt can be achieved with the nonlinear PD controller. For a stable tilting


Fig. 13.

7

Optical interferometric picture of a PolyMUMPs micromirror. TABLE II PARAMETERS OF POLYMUMPS MICROMIRROR

angle larger than 1.6 degrees, faster DAQ and PSD are required for the dynamic control of the micromirror. C. Testing of the Nonlinear PD Controller with a Polymumps Micromirror In order to test the full functionality of the implemented PD controller without increasing the speed of the DAQ and PSD, a slow response micromirror is designed and fabricated using the polyMUMPs process. An optical interferometric picture of the micromirror is shown in Fig. 13. The parameters of the polyMUMPs micromirror can be found in Table II. Different to the ones in Table I, d, h, and ρ are polyMUMPs process parameters, and K and B are theoretically calculated from the polyMUMPs micromirror geometry [16]. The small electrode gap fabricated with the polyMUMPs process reduces the theoretical pull-in angle of the micromirror to less than 0.7 degrees, and the response time is more than 100 milliseconds due to the squeeze film damping effect [17]. Due to the residual stress from the micro-fabrication process, the fabricated micromirror is concave curved as shown in Fig. 13. This curvature of the micromirror increases the effective gap between the mirror and the bottom electrodes, which leads to a slightly bigger pull-in angle than the simulated value. Experimental measured pull-in angle is around 0.8 degrees, and the maximum geometry constrained tilt of the micromirror is around 1.4 degrees. Fig. 14 shows the system response under the proposed nonlinear PD control for a tilting angle of 1.3 degrees. The gains of the controller have been manually tuned to lower the initial voltage while increasing the response time. From Fig. 14 we can see the system can reach the steady state after about 130 milliseconds with the gains of the controller tuned to Kp = 1.0 × 10−10 and Kd = 1.0 × 10−14 . The tilting profile difference within the first 100 milliseconds of the system response is mainly due to

Fig. 14. System response of the polyMUMPs micromirror under the proposed PD control.

the fact that the parameters such as damping coefficient, stiffness of mirror hinges, and controller gains for the fabricated polyMUMPs chip are different from the theoretical values used in the simulation. Small ringing noise has been found on the experimental data with a frequency of 60 Hz. This is due to the coupled AC noise in the voltage amplifier used, which can be eliminated with a better voltage amplifier. Nevertheless, experimental data clearly shows that the pull-in is eliminated for the full tilting range of the micromirror. Any angle below the maximum geometry constrained angle can be reached. D. Alternative Angle Feedback Approaches Although it has been proven that the pull-in effect can be eliminated with the proposed nonlinear PD controller, low-cost angle feedback approach still represents a challenge to implementing high channel-count optical switching devices or cross-connects. Two alternative approaches commonly used for angle monitoring are piezoresistive rotation angle sensor [18] that requires a piezoresistive material incorporated in the rotation hinges of the micromirror structures, and capacitive phase-angle sensor [19] that has to be built with complicated capacitance detection circuits. Since the objective of this work is to see if pull-in can be eliminated with active control methods, external PSDs are used to monitor the mirror angle without modifying the current mirror structures. This can be expensive to implement in practical applications. Part of the reflected beams from each micromirror surface needs to be steered, and assembly of photodetectors is required. VI. CONCLUSION An optical electrostatic micromirror has been designed and fabricated using the standard MEMS fabrication process. Active closed-loop control methods including a gain scheduling control and a nonlinear PD control are used to improve the tilting angle of the micromirror. Compared to the open-loop response, the micromirror can track a desired reference angle profile with minimum overshoot and shorter response time using the gain scheduling strategy. The nonlinear PD control can overcome the angle snapping of electrostatic actuation and achieve stable



torsional micromirror tilting beyond the pull-in angle. Experimental results of the implemented PD controller demonstrated the effectiveness of the proposed control algorithm. REFERENCES [1] T. Ducellier, J. Bismuth, S. F. Roux, A. Gillet, C. Merchant, M. Miller, M. Mala, Y. Ma, L. Tay, J. Sibille, J. Alavanja, A. Deren, M. Cugalj, D. Ivancevic, V. Dhuler, E. Hill, A. Cowen, B. Shen, and R. Wood, “The MWS 1x4: A high performance wavelength switching building block,” in Proc. 28th Eur. Conf. Opt. Commun., Copenhagen, Denmark, 2002, pp. 1–2. [2] Y. F. Li and R. Horowitz, “Mechatronics of electrostatic microactuators for computer disk drive dual-stage servo systems,” IEEE/ASME Trans. Mechatronics, vol. 6, no. 2, pp. 111–121, Jun. 2001. [3] D. A. Horsley, R. Horowitz, and A. P. Pisano, “Microfabricated electrostatic actuators for hard disk drives,” IEEE/ASME Trans. Mechatronics, vol. 3, no. 3, pp. 175–183, Sep. 1998. [4] R. Sulima and S. Wiak, “Modelling of vertical electrostatic comb-drive for scanning micromirrors,” Int. J. Comput. Math. Electr. Electron. Eng., vol. 27, no. 4, pp. 780–787, 2008. [5] M. Mala, J. M. Miller, G. McKinnon, and Y. Ma, “Piano MEMS micromirror,” U.S. Patent 6 934 439, Aug. 23, 2005. [6] N. Jalili, P. X. Liu, G. Alici, and A. Ferreira, “Guest Editorial: Introduction to the focused section on mechatronics for MEMS and NEMS,” IEEE/ASME Trans. Mechatronics, vol. 14, no. 4, pp. 397–404, Aug. 2009. [7] E. K. Chan and R. W. Dutton, “Electrostatic micromechanical actuator with extended range of travel,” J. Microelectromech. Syst., vol. 9, no. 3, pp. 321–328, 2000. [8] E. S. Hung and S. D. Senturia, “Extending the travel range of analogtuned electrostatic actuators,” J. Microelectromech. Syst., vol. 8, no. 4, pp. 497–505, 1999. [9] Y. Ma, G. McKinnon, and J. M. Miller, “Sunken electrode configuration for MEMS micromirror,” U.S. Patent 7 302 131, Nov. 27, 2007. [10] R. Nadal-Guardia, A. Dehe, R. Aigner, and L. M. Castaner, “Current drive methods to extend the range of travel of electrostatic microactuators beyond the voltage pull-in point,” J. Microelectromech. Syst., vol. 11, no. 3, pp. 255–263, 2002. [11] D. H. S. Maithripala, B. D. Kawade, J. M. Berg, and W. P. Dayawansa, “A general modelling and control framework for electrostatically actuated mechanical systems,” Int. J. Robust, Nonlinear Control, vol. 15, pp. 839– 857, 2005. [12] D. H. S. Maithripala, J. M. Berg, and W. P. Dayawansa, “Control of an electrostatic microelectromechanical system using static and dynamic output feedback,” Trans. ASME, J. Dyn. Syst., Meas., Control, vol. 127, pp. 444–450, 2005. [13] G. Zhu, J. Levine, and L. Praly, “Improving the performance of an electrostatically actuated MEMS by nonlinear control,” in Proc. 44th IEEE Conf. Decis., Control, Eur. Control Conf., Seville, Spain, 2005, pp. 7534–7539. [14] J. Chen, W. Weingar, A. Azarov, and R. C. Giles, “Tilt-Angle stabilization of electrostatically actuated micromechanical mirrors,” in Proc. Nanotech. Conf., San Francisco, CA, 2003, pp. 424–427. [15] J. Chen, W. Weingartner, A. Azarov, and R. C. Giles, “Tilt-Angle stabilization of electrostatically actuated micromechanical mirrors beyond the pull-in point,” J. Microelectromech. Syst., vol. 13, no. 6, pp. 988–997, 2004. [16] Md. S. Islam, “Electrostatic torsional micromirror and its active control,” M.Sc. Thesis, Dept. Mech. Eng., Dalhousie Univ., Halifax, NS, Canada, Oct. 2009, pp. 22–25, 60–62. [17] M. Bao and H. Yang, “Squeeze film air damping in MEMS,” Sens. Actuators A, vol. 136, no. 1, pp. 3–27, 2007. [18] M. Sasaki, M. Tabata, T. Haga, and K. Hane, “Piezoresistive rotation angle sensor integrated in micromirror,” Jpn. J. Appl. Phys., vol. 45, no. 4B, pp. 3789–3793, 2006. [19] A. Kuijpers, D. Lierop, R. Sanders, J. Tangenberg, H. Moddejonge, J. Eikenbroek, T. Lammerink, and R. Wiegerink, “Towards embedded control for resonant scanning MEMS micromirror,” Proc. Eur. XXIII Conf., Procedia Chem., 2009, vol. 1, pp. 1307–1310.

Yuan Ma (M’06) received the B.Sc., and M.Eng. degrees from Southeast University, China, in 1991 and 1994 respectively, and the M.Sc. and Ph.D. degrees in electrical and computer engineering from the University of Alberta, Edmonton, AB, Canada, in 1997 and 2002 respectively. From November 2000 to June 2006, she worked as a Research Scientist in the Exploratory Research group of JDS Uniphase, Ottawa, ON, Canada. In July 2006, she joined the Electrical and Computer Engineering Department, Dalhousie University, Halifax, NS, Canada, as a University Faculty Award recipient. Her research interests include micro-sensors and actuators, mechatronic system design and analysis, photonics, and MEMS device industrial applications.

Shariful Islam was born in Jessore, Bangladesh, in 1977. He received the B.Sc. degree in mechanical engineering from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in 2001, and the M.A.Sc. degree in mechanical engineering from Dalhousie University, Halifax, NS, Canada, in 2009. Currently, he is working towards the Ph.D. degree at Dalhousie University. His research interests include microsystems, controls, and robotics.

Ya-Jun Pan (M’03) received the B.E. degree in mechanical engineering from Yanshan University, China, in 1996, the M.E. degree in mechanical engineering from Zhejiang University, China, in 1999, and the Ph.D degree in electrical and computer engineering from the National University of Singapore, in 2003. After receiving the Ph.D. degree, she was a Postdoctoral Fellow of the CNRS in the Laboratoire d’Automatique de Grenoble, France, from 2003 to 2004. In 2004, she held a postdoctoral position in the Department of Electrical and Computer Engineering at the University of Alberta, Canada. Since January 2005, she has been with the Faculty of the Mechanical Engineering Department at Dalhousie University, Halifax, NS, Canada, and where she is currently an Associate Professor. Her research interests are in the fields of nonlinear systems and control, networked control systems, intelligent transportation control systems, and tele-robotics. She is currently an Associate Editor of the Journal of the Franklin Institute and the International Journal of Information and Systems Sciences. She is a member of the American Society of Mechanical Engineers and a Registered Professional Engineer in the Province of Nova Scotia, Canada.