Stability Analysis of Electrostatically Actuated Resonators With Delayed Feedback Controller

The Stability

In this work we investigate the stability of parallel-plate electrostatic MEMS resonators using a delayed feedback controller. Two case studies are investigated: a capacitive sensor made of cantilever beams with a proof mass at their tip and a clamped-clamped microbeam. Dover-cliff integrity curves and basin-of-attraction analysis are used for the stability assessment of the frequency response of the resonators for several scenarios of positive and negative gain in the controller. It is found that, in the case of a positive gain, a velocity or a displacement feedback controller can be used to effectively enhance the stability of the resonators. This is confirmed by an increase in the area of the safe basin of attraction and in shifting the Dover-cliff curve upward. On the other hand, it is shown that a negative gain can significantly weaken the stability of the resonators. This can be of useful use in MEMS for actuation applications, such as in the case of capacitive switches, to lower the activation voltage of these devices and to ensure their trigger under all initial conditions.

Integrity Analysis of Electrically Actuated Resonators With Delayed Feedback Controller

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4003262 ◽

2011 ◽

Vol 133 (3) ◽

Cited By ~ 19

Author(s):

Fadi Alsaleem ◽

Mohammad I. Younis

Keyword(s):

Microelectromechanical Systems ◽

Initial Conditions ◽

Basin Of Attraction ◽

Capacitive Sensor ◽

Delayed Feedback ◽

Feedback Controller ◽

Positive Gain ◽

The Stability ◽

Integrity Analysis

In this work, we investigate the stability and integrity of parallel-plate microelectromechanical systems resonators using a delayed feedback controller. Two case studies are investigated: a capacitive sensor made of cantilever beams with a proof mass at their tip and a clamped-clamped microbeam. Dover-cliff integrity curves and basin-of-attraction analysis are used for the stability assessment of the frequency response of the resonators for several scenarios of positive and negative gain in the controller. It is found that in the case of a positive gain, a velocity or a displacement feedback controller can be used to effectively enhance the stability of the resonators. This is confirmed by an increase in the area of the basin of attraction of the resonator and in shifting the Dover-cliff curve to higher values. On the other hand, it is shown that a negative gain can significantly weaken the stability and integrity of the resonators. This can be of useful use in MEMS for actuation applications, such as in the case of capacitive switches, to lower the activation voltage of these devices and to ensure their trigger under all initial conditions.

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

Stabilizing the Dynamics of Electrostatic MEMS Resonators Using Delayed Feedback Controller

10.1115/detc2009-86903 ◽

2009 ◽

Author(s):

Fadi M. Alsaleem ◽

Mohammad I. Younis

Keyword(s):

Delayed Feedback ◽

Feedback Controller ◽

Superior Performance ◽

Mems Resonator ◽

Mems Resonators ◽

Electrostatic Mems ◽

Simulation And Experiment ◽

The Stability ◽

Selection Of

We study the effect of delayed feedback controller on the dynamic stability of a MEMS resonator actuated with DC and AC voltages. We show that the delayed feedback controller, with a careful selection of its parameters, can be used to stabilize an originally unstable resonator operating in the escape (dynamic pull-in) frequency band. Also, the controller is shown to enhance the stability of the resonator near pull-in, where it experiences a strong fractal behavior. In both cases, the controller shows superior performance in rejecting disturbances. Experimental and theoretical results are presented to demonstrate the capability of the feedback controller to stabilize the performance of the capacitive resonator. A good agreement between simulation and experiment was achieved.

Stabilization of electrostatic MEMS resonators using a delayed feedback controller

Smart Materials and Structures ◽

10.1088/0964-1726/19/3/035016 ◽

2010 ◽

Vol 19 (3) ◽

pp. 035016 ◽

Cited By ~ 32

Author(s):

Fadi M Alsaleem ◽

Mohammad I Younis

Keyword(s):

Delayed Feedback ◽

Feedback Controller ◽

Mems Resonators ◽

Electrostatic Mems ◽

Delayed Feedback Controller

Volume 13: Nano-Manufacturing Technology; and Micro and Nano Systems, Parts A and B ◽

Analysis of the Orbits of Electrostatic MEMS Resonators

10.1115/imece2008-68042 ◽

2008 ◽

Author(s):

F. Najar ◽

E. M. Abdel-Rahman ◽

A. H. Nayfeh ◽

S. Choura

Keyword(s):

Initial Conditions ◽

Order Approximation ◽

Differential Quadrature Method ◽

Basin Of Attraction ◽

Mems Resonator ◽

Mems Resonators ◽

Electrostatic Mems ◽

Differential Integral Equation ◽

First Order Approximation ◽

The Basin Of Attraction

We study the dynamic behavior of an electrostatic MEMS resonator using a model that accounts for the system nonlinearities due to mid-plane stretching and electrostatic forcing. The partial-differential-integral equation and associated boundary conditions representing the system dynamics are discretized using the Differential Quadrature Method (DQM) and the Finite Difference Method (FDM) for the space and time derivatives, respectively. The resulting model is analyzed to determine the periodic orbits of the resonator and their stability. Simultaneous resonances are identified for large orbits. Finally, we develop a first-order approximation of the microbeam dynamic response, which reveals an erosion of the basin of attraction of the stable orbits that depends heavily on the amplitude and frequency of the AC excitation. Simulations show that the smoothness of the boundary of the basin of attraction can be lost to be replaced by fractal tongues, which increase the sensitivity of the microbeam response to initial conditions. As a result, the locations of the stable and unstable fixed points are likely to be disturbed.

Volume 7B: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

Investigation of a Delayed Feedback Controller of MEMS Resonators

10.1115/detc2013-12045 ◽

2013 ◽

Author(s):

Karim M. Masri ◽

Mohammad I. Younis ◽

Shuai Shao

Keyword(s):

Microelectromechanical Systems ◽

Electrostatic Force ◽

Time Integration ◽

Basins Of Attraction ◽

Delayed Feedback ◽

Feedback Controller ◽

Mems Resonator ◽

Mems Resonators ◽

Long Time

Controlling mechanical systems is an important branch of mechanical engineering. Several techniques have been used to control Microelectromechanical systems (MEMS) resonators. In this paper, we study the effect of a delayed feedback controller on stabilizing MEMS resonators. A delayed feedback velocity controller is implemented through modifying the parallel plate electrostatic force used to excite the resonator into motion. A nonlinear single degree of freedom model is used to simulate the resonator response. Long time integration is used first. Then, a finite deference technique to capture periodic motion combined with the Floquet theory is used to capture the stable and unstable periodic responses. We show that applying a suitable positive gain can stabilize the MEMS resonator near or inside the instability dynamic pull in band. We also study the stability of the resonator by tracking its basins of attraction while sweeping the controller gain and the frequency of excitations. For positive delayed gains, we notice significant enhancement in the safe area of the basins of attraction.

2017 21st International Conference on System Theory, Control and Computing (ICSTCC) ◽

A delayed feedback controller for active vibration control: A rightmost-characteristic root assignment based approach

10.1109/icstcc.2017.8107073 ◽

2017 ◽

Author(s):

Islam Boussaada ◽

Sami Tliba ◽

Silviu-Iulian Niculescu

Keyword(s):

Vibration Control ◽

Active Vibration Control ◽

Characteristic Root ◽

Delayed Feedback ◽

Feedback Controller ◽

Active Vibration

Sway Reduction on Container Cranes Using Delayed Feedback Controller

Nonlinear Dynamics ◽

10.1023/b:nody.0000013512.43841.55 ◽

2003 ◽

Vol 34 (3/4) ◽

pp. 347-358 ◽

Cited By ~ 94

Author(s):

Ziyad N. Masoud ◽

Ali H. Nayfeh

Keyword(s):

Delayed Feedback ◽

Feedback Controller ◽

Container Cranes ◽

Delayed Feedback Controller

A Study of Noise Impact on the Stability of Electrostatic MEMS

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4048365 ◽

2020 ◽

Vol 15 (11) ◽

Author(s):

Yan Qiao ◽

Wei Xu ◽

Hongxia Zhang ◽

Qin Guo ◽

Eihab Abdel-Rahman

Keyword(s):

Noise Intensity ◽

Initial Conditions ◽

Basins Of Attraction ◽

Low Noise ◽

Intensity Level ◽

Lumped Mass ◽

Mass Model ◽

Restoring Force ◽

Electrostatic Mems ◽

The Stability

Abstract Noise-induced motions are a significant source of uncertainty in the response of micro-electromechanical systems (MEMS). This is particularly the case for electrostatic MEMS where electrical and mechanical sources contribute to noise and can result in sudden and drastic loss of stability. This paper investigates the effects of noise processes on the stability of electrostatic MEMS via a lumped-mass model that accounts for uncertainty in mass, mechanical restoring force, bias voltage, and AC voltage amplitude. We evaluated the stationary probability density function (PDF) of the resonator response and its basins of attraction in the presence noise and compared them to that those obtained under deterministic excitations only. We found that the presence of noise was most significant in the vicinity of resonance. Even low noise intensity levels caused stochastic jumps between co-existing orbits away from bifurcation points. Moderate noise intensity levels were found to destroy the basins of attraction of the larger orbits. Higher noise intensity levels were found to destroy the basins of attraction of smaller orbits, dominate the dynamic response, and occasionally lead to pull-in. The probabilities of pull-in of the resonator under different noise intensity level are calculated, which are sensitive to the initial conditions.