|
|
|
| Stiffness nonlinearity and control of multi-DOF micro-gyroscope under time-delay displacement feedback |
| HAO Shuying1,2, SONG Yuhao1,2, LI Weixiong1,2, ZHANG Qichang3, FENG Jingjing1,2, HAN Jianxin4 |
1.Tianjin Key Laboratory of Advanced Electromechanical System Design and Intelligent Control, Tianjin University of Technology, Tianjin 300384, China;
2.National experimental teaching demonstration center of mechanical and electrical engineering, Tianjin University of Technology, Tianjin 300384, China;
3.Tianjin University, Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin University, Tianjin 300072, China；
4.School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China |
|
|
|
Abstract To reveal influence of displacement feedback term on the dynamic characteristics of a multi-DOF micro-gyroscope nonlinear system and explore control methods for nonlinearity, a class of 4-DOF electrostatically driven micromachined gyroscopes is researched, then the dynamic characteristics of micro-gyroscope controlled system in frequency domain and time domain are analyzed by multi-scale method. The research found that feedback gain can effectively adjust the resonant frequency of the system when the time delay is the whole period or half period; feedback gain mainly affects the amplitude and the resonant frequency remains basically the same when the time delay is one quarter or three quarters of the period; When the feedback control parameters are selected properly, multistable solutions caused by nonlinearity can be eliminated ,then sensitivity stability of the gyroscope is increased, however, improper selection will lead to complex almost periodic motion of the system, which will destroy the sensitivity stability.
|
|
Received: 15 March 2019
Published: 28 July 2020
|
|
|
|
[1] P. Greif, B.Boxenhorn, et al. A vibratory micromechanical gyroscope.AIAA Guidance and Control Conf, 1988,Aug. 15-17:1033-1040.
[2] Tatar E, Mukherjee T, Fedder GK. Nonlinearity tuning and its effects on the performance of a MEMS gyroscope[J]. Transducers-International Conference on Solid-state Sensors, 2015: 1133-1136.
[3] Jeon S H, Lee J Y, Jung H K. Two-mass system with wide bandwidth for SiOG (silicon on glass) vibratory gyroscopes[J]. International Conference on Solid-state Sensors, 2005, 1(1): 539-542.
[4] Han J X, Zhang Q C, Wang W. Static bifurcation and primary resonance analysis of a MEMS resonator actuated by two symmetrical electrodes[J]. Nonlinear Dynamics, 2015, 80(3): 1585-1599.
[5] Shao S, Masri K M, Younis M I. The effect of time-delayed feedback controller on an electrically actuated resonator[J]. Nonlinear Dynamics, 2013, 74(1-2): 257-270.
[6] Yamasue K, Hikihara T. Control of microcantilevers in dynamic force microscope using time delayed feedback[J]. Review of Scientific Instruments, 2006, 77(5): 53703.
[7] Nayfeh A H, Nayfeh N A. Time-delay feedback control of lathe cutting tools[J]. Journal of Vibration and Control, 2011, 18(8): 1106-1115.
[8] Mehta A, Cherian S, Hedden D, et al. Manipulation and controlled amplification of Brownian motion of microcantilever sensors[J]. Applied Physics Letters, 2001, 78(11): 1637-1639.
[9] 李欣业，陈予恕，吴志强. 参数激励Duffing-Van del Pol振子的动力学响应及反馈控制[J]. 应用数学和力学, 2006, 27(12): 1387-1396.
LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang. Response of a parametrically excited duffing-van der pol oscillator with delayed feedback[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1387-1396.
[10] 李欣业，张振民，张华彪. Duffing-van del Pol振子的时滞反馈控制研究[J]. 振动与冲击，2010，29(10): 118-121.
LI Xin-ye, ZHANG Zhen-min, ZHANG Hua-biao. Research on delay feedback control of duffing-van der pol oscillator[J]. Journal of vibration and shock, 2010，29(10): 118-121.
[11] Morrison T M, Rand R H. 2:1 resonance in the delayed nonlinear Mathieu equation[J]. Nonlinear Dynamics, 2007, 50(1-2): 341-352.
[12] Alsaleem F M, Younis M I. Stabilization of electrostatic MEMS resonators using a delayed feedback controller[J]. Smart Materials and Structures, 2010, 19(19): 35016.
[13] 张丽娟. 微陀螺系统非线性动力学及其时滞反馈控制[D]. 河北工业大学, 2011.
ZHANG Li-juan. Nonlinear dynamics and delayed feedback control of micro-gyroscope system[D]. Hebei University of Technology, 2011.
[14] Shehrin S, Jason C V. Active control of effective mass, damping and stiffness of MEMS[C]. Design, Test, Integration and Packaging of MEMS/MOEMS(DTIP), 2013.
[15] Warminski J. Frequency locking in a nonlinear MEMS oscillator driven by harmonic force and time delay[J]. International Journal of Dynamics and Control, 2015, 3(2): 122-136.
[16] Wang W, Lv X, Sun F. Design of micromachined vibratory gyroscope with two degree-of-freedom drive-mode and sense-mode[J]. IEEE Sensors Journal, 2012, 12(7): 2460-2464.
|
|
|
|
