Twisting Sliding Mode Control of an Electrostatic MEMS Micromirror for a Laser Scanning System
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摘要
In this paper, we present a twisting control scheme with proportional-integral-derivative(PID) sliding surface for a two-axis electrostatic torsional micromirror, and the utilization of the proposed scheme in a laser scanning system. The experimental results of set-point regulation verify that the proposed scheme provides enhanced transient response and positioning performance as compared to traditional sliding mode control.To evaluate the tracking performance of the closed-loop system,triangular waves with different frequencies are used as desired traces. With the proposed scheme the experimental results verified that the closed-loop controlled micromirror follows the given triangular trajectories precisely. A micromirror-based laser scanning system is developed to obtain images. When compared with open-loop control, the experimental results demonstrated that the proposed scheme is able to reduce the distortion of the raster scan, and improve the imaging performance in the presence of cross-coupling effect.
In this paper, we present a twisting control scheme with proportional-integral-derivative(PID) sliding surface for a two-axis electrostatic torsional micromirror, and the utilization of the proposed scheme in a laser scanning system. The experimental results of set-point regulation verify that the proposed scheme provides enhanced transient response and positioning performance as compared to traditional sliding mode control.To evaluate the tracking performance of the closed-loop system,triangular waves with different frequencies are used as desired traces. With the proposed scheme the experimental results verified that the closed-loop controlled micromirror follows the given triangular trajectories precisely. A micromirror-based laser scanning system is developed to obtain images. When compared with open-loop control, the experimental results demonstrated that the proposed scheme is able to reduce the distortion of the raster scan, and improve the imaging performance in the presence of cross-coupling effect.
In this paper, we present a twisting control scheme with proportional-integral-derivative(PID) sliding surface for a two-axis electrostatic torsional micromirror, and the utilization of the proposed scheme in a laser scanning system. The experimental results of set-point regulation verify that the proposed scheme provides enhanced transient response and positioning performance as compared to traditional sliding mode control.To evaluate the tracking performance of the closed-loop system,triangular waves with different frequencies are used as desired traces. With the proposed scheme the experimental results verified that the closed-loop controlled micromirror follows the given triangular trajectories precisely. A micromirror-based laser scanning system is developed to obtain images. When compared with open-loop control, the experimental results demonstrated that the proposed scheme is able to reduce the distortion of the raster scan, and improve the imaging performance in the presence of cross-coupling effect.
引文
[1]A.D.Yakcubjaya,H.U.Urey,D.Brown,T.Montague,and R.Sprague,"Two-axis electromagnetic microscanner for high resolution displays,"J.Microelectromech.Syst.,vol.15,no.4,pp.786-794,Aug.2006.
[2]P.B.Chu,S.S.Lee,and S.Park,"MEMS:the path to large optical crossconnects,"IEEE Commun.Mag.,vol.40,no.3,pp.80-87,Mar.2002.
[3] A.D.Yalcinkaya,O.Ergeneman,and H.Urey,"Polymer magnetic scanners for bar code applications,"Sens.Actuators A:Phys.,vol.135,no.1,pp.236-243,Mar.2007.
[4] J.T.W.Yeow,V.X.D.Yang,A.Chahwan,M.L.Gordon,B.Qi,I.A.Vitkin,B.C.Wison,and A.A.Goldenberg,"Micromachined 2-D scanner for 3-D optical coherence tomography,"Sens.Actuators A:Phys.,vol.117,no.2,pp.331-340,Jan.2005.
[5]Z.X.Xiao,W.Y.Peng,X.T.Wu,and K.R.Farmer,"Pull-in study for round double-gimbaled electrostatic torsion actuators,"J.Microelectromech.Syst.,vol.12,no.1,pp.77-81,Jan.2002.
[6] J.H.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,Dec.2004.
[7] G.C.Zhu,M.Packirisamy,M.Hosseini,and Y.A.Peter,"Modelling and control of an electrostatically actuated torsional micromirror,"J.Micromech.Microeng.,vol.16,no.10,pp.2044-2052,Aug.2006.
[8] Y.Zhao,F.E.H.Tay,G.Y.Zhou,and F.S.Chau,"Fast and precise positioning of electrostatically actuated dual-axis micromirror by multiloop digital control,"Sens.Actuators A:Phys.,vol.132,no.2,pp.42 1-428,Nov.2006.
[9] T.Juneau,K.Unterkofler,T.Seliverstov,S.Zhang,and M.July,"Dualaxis optical mirror positioning using a nonlinear closed-loop controller,"in Proc.12th Int.Con.f.Solid-State Sensors,Actuators and Microsystems,Boston,MA,USA,2003,pp.560-563.
[10]Y.J.Pan,Y.Ma,and S.Islam,"Electrostatic torsional micromirror:its active control and applications in optical network,"in Proc.IEEE Int.Conf.Automation Science and Engineering,Arlington,VA,USA,2008,pp.151-156.
[11] Y.Ma,S.Islam,and Y.J.Pan,"Electrostatic torsional micromirror with enhanced tilting angle using active control methods,"IEEE/ASME Trans.Mechatron.,vol.16,no.6,pp.994-1001,Dec.2011.
[12] P.B.Chu,I.Brener,C.Pu,S.S.Lee,J.1.Dadap,S.Park,K.Bergman,N.H.Bonadeo,T.Chau,M.Chou,R.A.Doran,R.Gibson,R.Harel,J.J.Johnson,C.D.Lee,D.R.Peale,B.Tang,D.T.K.Tong,M.J.Tsai,Q.Wu,W.Zhong,E.L.Goldstein,L.Y.Lin,and J.A.Walker,"Design and nonlinear servo control of MEMS mirrors and their performance in a large port-count optical switch,"J.Microelectromech.Syst.,vol.14,no.2,pp.261-273,Apr.2005.
[13]C.G.Agudelo,M.Packirisamy,G.C.Zhu,and L.Saydy,"Nonlinear control of an electrostatic micromirror beyond pull-in with experimental validation,"J. Microelectromech.Syst.,vol.18,no.4,pp.914-923,Aug.2009.
[14] C.G.Agudelo,G.Zhu,M.Packirisamy,and L.Saydy,"Flatness-based control of an electrostatic torsional micro-minor with voltage feedback,"in Proc.50th IEEE Midwest Sy mp.Circuits and Systems,.Montreal,Que.,Canada,2007,pp.654-657.
[15] C.G.Agudelo,G.Zhu,and L.Saydy,"Nonlinear closed-loop control of an electrostatic torsional micro-mirror by means of differential actuation,"in Proc.50th IEEE Midwest Symp.Circuits and Systems,Montreal,Que.,Canada,2007,pp.658-661.
[16] W.Sun,J.T.W.Yeow,and Z.Sun,"Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking,"IET Control Theory Appl.,vol.6,no.1,pp.111-119,Jan.2012.
[17] K.M.Liao,Y.C.Wang,C.H.Yeh,and R.S.Chen,"Closed-loop adaptive control for torsional micromirrors,"in Proc.Volume 5346,MOEMS and Miniaturized SystemsⅣ,San Jose,California,USA,2004,pp.184-192.
[18]N.Yazdi,H.Sane,T.D.Kudrle,and C.H.Mastrangelo,"Robust slidingmode control of electrostatic torsional micromirrors beyond the pullin limit,"in Proc.12th Int.Conf.Solid-State Sensors,Actuators,and Microsystems,Boston,MA,USA,2003,pp.1450-1453.
[19]H.S.Sane,N.Yazdi,and C.H.Mastrangelo,"Application of sliding mode control to electrostatically actuated two-axis gimbaled micromirrors",in Proc.American Control Conf.,Denver,CO,USA,2003,pp.3726-3731.
[20]H.S.Sane,N.Yazdi,and C.H.Mastrangelo,"Modified sliding mode control and its application to electrostatically controlled dual-axis micromirrors,"in Proc.American Control Conf.,Boston,MA,USA,2004,pp.1934-1939.
[21]Y.Zhao,F.E.H.Tay,F.S.Chau,and G.Y.Zhou,"Stabilization of dual-axis micromirrors beyond the pull-in point by integral sliding mode control,"J.Micromech.Microeng.,vol.16,no.7,pp.1242-1250,May2006.
[22]A.Levant,"Sliding order and sliding accuracy in sliding mode control,"Int.J.Control,vol.58,no.6,pp.1247-1263,Dec.1993.
[23]G.Bartolini,A.Posano,E.Punta,and E.Usai,"A survey of applications of second-order sliding mode control to mechanical systems,"Int.J.Control,vol.76,no.9-10,pp.875-892,Jun.2003.
[24]M.Rafiq,S.Rehman,F.Rehman,Q.R.Butt,and I.Awan,"A second order sliding mode control design of a switched reluctance motor using super twisting algorithm,"Simul. Model. Pract.Theory,vol.25,pp.106-117,Jun.2012.
[25]J.X.Liu,S.Laghrouche,M.Harmouche,and M.Wack,"Adaptivegain second-order sliding mode observer design for switching power converters,"Control Eng.Pract.,vol.30,pp.124-131,Sep.2013.
[26]J.X.Liu,S.Laghrouche,and M.Wack,"Observer-based higher order sliding mode control of power factor in three-phase AC/DC converter for hybrid electric vehicle applications,"Int.J.Control,vol.87,no.6,pp.1117-1130,Mar.2014.
[27]S.Laghrouche,J.X.Liu,F.S.Ahmed,M.Harmouche,and M.Wack,"Adaptive second-order sliding mode observer-based fault reconstruction for PEM fuel cell air-feed system,"IEEE Trans.Control Syst.Technol.,vol.23,no.3,pp.1098-1109,May 2015.
[28]Y.H.Bai,J.T.W.Yeow,and B.C.Wilson,"Design,fabrication,and characteristics of a MEMS micromirror with sidewall electrodes,"J.Microelectromech.Syst.,vol.19,no.3,pp.619-631,Jun.2010.
[29]Y.H.Bai,J.T.W.Yeow,and B.C.Wilson,"A characteristic study of micromirror with sidewall electrodes,"Int.J.Optomechatroni.,vol.1,no.3,pp.231-258,Sep.2007.
[30]Y.H.Bai,J.T.W.Yeow,P.Constantinou,S.Damaskinos,and B.C.Wilson,"A 2-D micromachined SOI MEMS mirror with sidewall electrodes for biomedical imaging,"IEEE/ASME Trans.Mechatron.,vol.15,no.4,pp.501-510,Aug.2010.
[31]H.Toshiyoshi,W.Piyawattanametha,C.T.Chan,and M.C.Wu,"Linearization of electrostatically actuated surface micromachined 2-D optical scanner,"J.Microelectromech.Syst.,vol.10,no.2,pp.205-214,Jun.2001.
[32]A.Levant,"Principles of 2-sliding mode design,"Automatica,vol.43,no.4,pp.576-586,Apr.2007.
[33]A.Polyakov and A.Poznyak,"Lyapunov function design for finite-time convergence analysis of'twisting'and'super-twisting'second order sliding mode controllers,"in Proc.Int.Workshop on Variable Structure Systems,Antalya,Turkey,2008,pp.153-158.
[34]A.Polyakov and A.Poznyak,"Lyapunov function design for finite-time convergence analysis:'twisting'controller for second-order sliding mode realization,"Automatica,vol.45,no.2,pp.444-448,Feb.2009.
[35]R.Santiesteban,L.Fridman,and J.A.Moreno,"Finite-time convergence analysis for'twisting'controller via a strict Lyapunov function,"in Proc.11th Int.Workshop on Variable Structure Systems,Mexico City,Mexico,2010,pp.1-6.
[2]P.B.Chu,S.S.Lee,and S.Park,"MEMS:the path to large optical crossconnects,"IEEE Commun.Mag.,vol.40,no.3,pp.80-87,Mar.2002.
[3] A.D.Yalcinkaya,O.Ergeneman,and H.Urey,"Polymer magnetic scanners for bar code applications,"Sens.Actuators A:Phys.,vol.135,no.1,pp.236-243,Mar.2007.
[4] J.T.W.Yeow,V.X.D.Yang,A.Chahwan,M.L.Gordon,B.Qi,I.A.Vitkin,B.C.Wison,and A.A.Goldenberg,"Micromachined 2-D scanner for 3-D optical coherence tomography,"Sens.Actuators A:Phys.,vol.117,no.2,pp.331-340,Jan.2005.
[5]Z.X.Xiao,W.Y.Peng,X.T.Wu,and K.R.Farmer,"Pull-in study for round double-gimbaled electrostatic torsion actuators,"J.Microelectromech.Syst.,vol.12,no.1,pp.77-81,Jan.2002.
[6] J.H.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,Dec.2004.
[7] G.C.Zhu,M.Packirisamy,M.Hosseini,and Y.A.Peter,"Modelling and control of an electrostatically actuated torsional micromirror,"J.Micromech.Microeng.,vol.16,no.10,pp.2044-2052,Aug.2006.
[8] Y.Zhao,F.E.H.Tay,G.Y.Zhou,and F.S.Chau,"Fast and precise positioning of electrostatically actuated dual-axis micromirror by multiloop digital control,"Sens.Actuators A:Phys.,vol.132,no.2,pp.42 1-428,Nov.2006.
[9] T.Juneau,K.Unterkofler,T.Seliverstov,S.Zhang,and M.July,"Dualaxis optical mirror positioning using a nonlinear closed-loop controller,"in Proc.12th Int.Con.f.Solid-State Sensors,Actuators and Microsystems,Boston,MA,USA,2003,pp.560-563.
[10]Y.J.Pan,Y.Ma,and S.Islam,"Electrostatic torsional micromirror:its active control and applications in optical network,"in Proc.IEEE Int.Conf.Automation Science and Engineering,Arlington,VA,USA,2008,pp.151-156.
[11] Y.Ma,S.Islam,and Y.J.Pan,"Electrostatic torsional micromirror with enhanced tilting angle using active control methods,"IEEE/ASME Trans.Mechatron.,vol.16,no.6,pp.994-1001,Dec.2011.
[12] P.B.Chu,I.Brener,C.Pu,S.S.Lee,J.1.Dadap,S.Park,K.Bergman,N.H.Bonadeo,T.Chau,M.Chou,R.A.Doran,R.Gibson,R.Harel,J.J.Johnson,C.D.Lee,D.R.Peale,B.Tang,D.T.K.Tong,M.J.Tsai,Q.Wu,W.Zhong,E.L.Goldstein,L.Y.Lin,and J.A.Walker,"Design and nonlinear servo control of MEMS mirrors and their performance in a large port-count optical switch,"J.Microelectromech.Syst.,vol.14,no.2,pp.261-273,Apr.2005.
[13]C.G.Agudelo,M.Packirisamy,G.C.Zhu,and L.Saydy,"Nonlinear control of an electrostatic micromirror beyond pull-in with experimental validation,"J. Microelectromech.Syst.,vol.18,no.4,pp.914-923,Aug.2009.
[14] C.G.Agudelo,G.Zhu,M.Packirisamy,and L.Saydy,"Flatness-based control of an electrostatic torsional micro-minor with voltage feedback,"in Proc.50th IEEE Midwest Sy mp.Circuits and Systems,.Montreal,Que.,Canada,2007,pp.654-657.
[15] C.G.Agudelo,G.Zhu,and L.Saydy,"Nonlinear closed-loop control of an electrostatic torsional micro-mirror by means of differential actuation,"in Proc.50th IEEE Midwest Symp.Circuits and Systems,Montreal,Que.,Canada,2007,pp.658-661.
[16] W.Sun,J.T.W.Yeow,and Z.Sun,"Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking,"IET Control Theory Appl.,vol.6,no.1,pp.111-119,Jan.2012.
[17] K.M.Liao,Y.C.Wang,C.H.Yeh,and R.S.Chen,"Closed-loop adaptive control for torsional micromirrors,"in Proc.Volume 5346,MOEMS and Miniaturized SystemsⅣ,San Jose,California,USA,2004,pp.184-192.
[18]N.Yazdi,H.Sane,T.D.Kudrle,and C.H.Mastrangelo,"Robust slidingmode control of electrostatic torsional micromirrors beyond the pullin limit,"in Proc.12th Int.Conf.Solid-State Sensors,Actuators,and Microsystems,Boston,MA,USA,2003,pp.1450-1453.
[19]H.S.Sane,N.Yazdi,and C.H.Mastrangelo,"Application of sliding mode control to electrostatically actuated two-axis gimbaled micromirrors",in Proc.American Control Conf.,Denver,CO,USA,2003,pp.3726-3731.
[20]H.S.Sane,N.Yazdi,and C.H.Mastrangelo,"Modified sliding mode control and its application to electrostatically controlled dual-axis micromirrors,"in Proc.American Control Conf.,Boston,MA,USA,2004,pp.1934-1939.
[21]Y.Zhao,F.E.H.Tay,F.S.Chau,and G.Y.Zhou,"Stabilization of dual-axis micromirrors beyond the pull-in point by integral sliding mode control,"J.Micromech.Microeng.,vol.16,no.7,pp.1242-1250,May2006.
[22]A.Levant,"Sliding order and sliding accuracy in sliding mode control,"Int.J.Control,vol.58,no.6,pp.1247-1263,Dec.1993.
[23]G.Bartolini,A.Posano,E.Punta,and E.Usai,"A survey of applications of second-order sliding mode control to mechanical systems,"Int.J.Control,vol.76,no.9-10,pp.875-892,Jun.2003.
[24]M.Rafiq,S.Rehman,F.Rehman,Q.R.Butt,and I.Awan,"A second order sliding mode control design of a switched reluctance motor using super twisting algorithm,"Simul. Model. Pract.Theory,vol.25,pp.106-117,Jun.2012.
[25]J.X.Liu,S.Laghrouche,M.Harmouche,and M.Wack,"Adaptivegain second-order sliding mode observer design for switching power converters,"Control Eng.Pract.,vol.30,pp.124-131,Sep.2013.
[26]J.X.Liu,S.Laghrouche,and M.Wack,"Observer-based higher order sliding mode control of power factor in three-phase AC/DC converter for hybrid electric vehicle applications,"Int.J.Control,vol.87,no.6,pp.1117-1130,Mar.2014.
[27]S.Laghrouche,J.X.Liu,F.S.Ahmed,M.Harmouche,and M.Wack,"Adaptive second-order sliding mode observer-based fault reconstruction for PEM fuel cell air-feed system,"IEEE Trans.Control Syst.Technol.,vol.23,no.3,pp.1098-1109,May 2015.
[28]Y.H.Bai,J.T.W.Yeow,and B.C.Wilson,"Design,fabrication,and characteristics of a MEMS micromirror with sidewall electrodes,"J.Microelectromech.Syst.,vol.19,no.3,pp.619-631,Jun.2010.
[29]Y.H.Bai,J.T.W.Yeow,and B.C.Wilson,"A characteristic study of micromirror with sidewall electrodes,"Int.J.Optomechatroni.,vol.1,no.3,pp.231-258,Sep.2007.
[30]Y.H.Bai,J.T.W.Yeow,P.Constantinou,S.Damaskinos,and B.C.Wilson,"A 2-D micromachined SOI MEMS mirror with sidewall electrodes for biomedical imaging,"IEEE/ASME Trans.Mechatron.,vol.15,no.4,pp.501-510,Aug.2010.
[31]H.Toshiyoshi,W.Piyawattanametha,C.T.Chan,and M.C.Wu,"Linearization of electrostatically actuated surface micromachined 2-D optical scanner,"J.Microelectromech.Syst.,vol.10,no.2,pp.205-214,Jun.2001.
[32]A.Levant,"Principles of 2-sliding mode design,"Automatica,vol.43,no.4,pp.576-586,Apr.2007.
[33]A.Polyakov and A.Poznyak,"Lyapunov function design for finite-time convergence analysis of'twisting'and'super-twisting'second order sliding mode controllers,"in Proc.Int.Workshop on Variable Structure Systems,Antalya,Turkey,2008,pp.153-158.
[34]A.Polyakov and A.Poznyak,"Lyapunov function design for finite-time convergence analysis:'twisting'controller for second-order sliding mode realization,"Automatica,vol.45,no.2,pp.444-448,Feb.2009.
[35]R.Santiesteban,L.Fridman,and J.A.Moreno,"Finite-time convergence analysis for'twisting'controller via a strict Lyapunov function,"in Proc.11th Int.Workshop on Variable Structure Systems,Mexico City,Mexico,2010,pp.1-6.