Tracking control of an electrostatic torsional micromirror beyond the pull-in limit with enhanced performance

In this paper, we will study the output-error-constrained tracking control problem of an electrostatic torsional micromirror beyond the pull-in limit. We will first show that this problem can be formulated as a robust output regulation problem and it further boils down to a robust regulation problem with output-constrained by adaptive internal model design, the solution of which would in turn lead to the solution of the original problem. Then we design a regulation controller for such a regulation problem by using the barrier Lyapunov function technique. Our adaptive control law ensures the electrostatic torsional micromirror with a enhanced tracking performance in the sense that the moveable micromirror can achieve the sinusoidal wave scanning of any frequency up to a full gap operation without contacts of the fixed bottom electrode, and furthermore, the estimated sinusoidal wave frequency converges to its real value.

[1]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[2]  Brian C Wilson,et al.  Design, Fabrication, and Characteristics of a MEMS Micromirror With Sidewall Electrodes , 2010, Journal of Microelectromechanical Systems.

[3]  Guchuan Zhu,et al.  Nonlinear Control of an Electrostatic Micromirror Beyond Pull-In With Experimental Validation , 2009, Journal of Microelectromechanical Systems.

[4]  Francis Eng Hock Tay,et al.  Barrier Lyapunov Functions for the control of output-constrained nonlinear systems , 2009, Autom..

[5]  Jie Huang,et al.  Parameter convergence and minimal internal model with an adaptive output regulation problem , 2009, Autom..

[6]  Jim Euchner.  Design , 2014, Catalysis from A to Z.

[7]  W. Wonham,et al.  Probing signals for model reference identification , 1977 .

[8]  Keng Peng Tee,et al.  Adaptive Control of Electrostatic Microactuators With Bidirectional Drive , 2009, IEEE Transactions on Control Systems Technology.

[9]  J. S-C,et al.  Probing Signals for Model Reference Identification , 1977 .

[10]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[11]  Jie Huang,et al.  A general framework for tackling the output regulation problem , 2004, IEEE Transactions on Automatic Control.

[12]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[13]  Zhong-Ping Jiang,et al.  Integrator backstepping design for motion systems with velocity constraint , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[14]  Guchuan Zhu,et al.  Flatness-Based Control of Electrostatically Actuated MEMS With Application to Adaptive Optics: A Simulation Study , 2006, Journal of Microelectromechanical Systems.

[15]  V. O. Nikiforov,et al.  Adaptive Non-linear Tracking with Complete Compensation of Unknown Disturbances , 1998, Eur. J. Control.

[16]  Jordan M. Berg,et al.  Passivity-Based Stabilization of a 1-DOF Electrostatic MEMS Model With a Parasitic Capacitance , 2009, IEEE Transactions on Control Systems Technology.

[17]  Jinghong Chen,et al.  Tilt-angle stabilization of electrostatically actuated micromechanical mirrors beyond the pull-in point , 2004, Journal of Microelectromechanical Systems.

[18]  John T.W. Yeow,et al.  Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking , 2012 .

[19]  Ali H. Nayfeh,et al.  Input-shaping control of nonlinear MEMS , 2008 .

[20]  Ya-Jun Pan,et al.  Electrostatic Torsional Micromirror With Enhanced Tilting Angle Using Active Control Methods , 2011, IEEE/ASME Transactions on Mechatronics.