A Survey On Modelling And Control Of Electrostatically Actuated Torsional MEMS Micromirror

As one of the typical micro-opto-electro-mechanical system(MOEMS),with its small size,light weight,low cost,low power consumption,simple structure and easy large-scale integration and other characteristics,electrostatic torsion micromirror is playing an increasing important role in the optical communication,projection display,laser radar,micro optics platform and biomedical fields.However,the issues,that the residual vibration in the open loop response of micromirror,the damping effects dominated by squeeze-film phenomenon in the micro scale air film,the nonlinear characteristics induced by multi energy field coupling,and the parametric uncertainties in the fabrication of MEMS devices have made the micromirror system with slow response speed,small torsional angle,low sensitivity & resolution,and poor robust performance,those are the key issues for restraining the further application of micromirror.Therefore,aimed to analyse the air damping,active suppress the residual vibration,overcome the pull-in limit,and realize the robust control for system with parameters uncertain,this paper studied the modelling and control of MEMS micromirror.Due to the characteristics of micro structure,the influence of air damping on the dynamic performance of MEMS devices is significant.In the second-order system model of torsional MEMS micromirror,determining the air damping coefficient which is dominated by air damping is the main factor affecting the dynamic characteristics of the device.The finite element method,which is used to analyze the air damping of MEMS devices,is not only time-consuming,but also not suitable for the development of control system.In this paper,in order to analysis and calculation the air damping,double sine series method is used for solving the Reynolds equation governing the movement of the air,the analytical models of the damping coefficient and the elastic coefficient of the air damping are deduced,and the numerical simulation shows that the model is accurate in the calculation of the air film damping of the MEMS device with fully open boundaries.This similarity methods using simple boundary condition have ignored the border effect,however,when the air venting gap is narrow,or the air venting channel is affected by gimbals' frame,sidewall or other structures,the influence of the boundary effect on the air film damping should not be ignored.To solve the problem of boundary effect on air damping in the complex structure MEMS devices,first,the issue is abstracted as a solving problem of the two order partial differential equation with inhomogeneous boundary conditions,second,the Green's function is adopted to solve the nonlinear Reynolds equation with inhomogeneous boundary conditions,finally,combined with the analysis of the air flow pressure boundary conditions,the damping model considering the boundary effect is presented.In the absence of the multifield coupling analysis of computational fluid dynamics(CFD)software,the accuracy of damping coefficient can be improved by 22.29% and 21.37%.The model also reveals the influence of the boundary effect on damping force and elastic force and the relationship between the boundary effect and the micro structure of micromirror.Simulation results show that the air venting gap has a great effect on the air damping,and the smaller the venting gap,the greater the boundary effect.In order to improve the electrostatic actuation efficiency of the MEMS micromirror,the micromirror is usually designed to work under the under damping condition.The dynamic responses of these under-damped second-order systems are always accompanied by an obvious residual vibration which increases the setting time and therefore reduces the effective bandwidth of actuators.For these devices,how to circumvent the excessive residual vibration in order to achieve a more accurate positioning and faster switching is an important research topic.It is an effective method that Input-shaping technique to suppress residual vibration in mechanical systems,however,the known nonlinearity issues of the electrostatically actuated torsional MEMS micromirror is the main obstacle to the application of the traditional shaping techniques based on linear theories.In this paper,based on the analysis of the static behavior and dynamic response of the electrostatically actuated torsional micromirrors,an active contron method which is called Multistep-shaping control is presented.Compared with other control methods,the proposed multistep-shaping control can yield a good enough performance without extra sensors and actuators.Simulation results show that,without changing the system structure,the maximum amplitudes of residual vibration of the mirror response are reduced by 31.97% and 70.63%,and the settling times are decreased by 56.2% and 74.8% respectively.The inherent Pull-in effect in electrostatic actuation MEMS devices greatly limits the torsional angle range of the micromirror.Closed loop control technology is an effective way to overcome the pull-in phenomenon.In this paper,based on the analysis of the influence of parametric uncertainties in nonlinear proportional-derivative control system,a new combined closed loop feedback control scheme is proposed.This method,combining nonlinear PD control and sliding mode control(SMC),not only inherits the virtue of a good dynamic performance from the nonlinear PD control,but also further improves the robustness with SMC for such MEMS mirrors.Furthermore,this method can be convenient when tuning design gains of the controller to obtain a faster error convergence rate.Numerical simulation results show that with this combined control scheme the torsional angle of the micromirrors is increased by 46.7% and 33.3%,and the stability time is also decreased by 52.5% and 40.5% respectively.This control system also has a good robust performance for up to 50% parametric uncertainties.The proposed air damping model with boundary effect of the MEMS micromirror device,the improvement of input-shaping technology actively suppress residual vibration of the nonlinear system,the research work of the closed-loop control system with high robustness,which all provide a theoretical basis for the development of the next generation high performance digital micromirror.