Integrity Analysis of Electrically Actuated Resonators With Delayed Feedback Controller

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Fadi Alsaleem ◽  
Mohammad I. Younis
Keyword(s):  
Microelectromechanical Systems ◽  
Initial Conditions ◽  
Basin Of Attraction ◽  
Capacitive Sensor ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Positive Gain ◽  
Delayed Feedback Controller ◽  
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.

Stability Analysis of Electrostatically Actuated Resonators With Delayed Feedback Controller

2010 ◽  
Author(s):  
Fadi Alsaleem ◽  
Mohammad I. Younis
Keyword(s):  
Initial Conditions ◽  
Basin Of Attraction ◽  
Capacitive Sensor ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Electrostatic Mems ◽  
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.

Investigation of a Delayed Feedback Controller of MEMS Resonators

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 ◽  
Delayed Feedback Controller ◽  
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.

Stabilizing the Dynamics of Electrostatic MEMS Resonators Using Delayed Feedback Controller

2009 ◽  
Author(s):  
Fadi M. Alsaleem ◽  
Mohammad I. Younis
Keyword(s):  
Delayed Feedback ◽  
Feedback Controller ◽  
Superior Performance ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Electrostatic Mems ◽  
Delayed Feedback Controller ◽  
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.

Numerical Simulation of Nonlocal Delayed Feedback Controller for Simple Bioreactors

Informatica ◽  
2018 ◽  
Vol 29 (2) ◽  
pp. 233-249 ◽  
Author(s):  
Raimondas Čiegis ◽  
Olga Suboč ◽  
Remigijus Čiegis
Keyword(s):  
Numerical Simulation ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Delayed Feedback Controller

Nonlinear analysis of electrostatic micro-electro-mechanical systems resonators subject to delayed proportional–derivative controller

2020 ◽  
pp. 107754632092562 ◽  
Author(s):  
Ulrich Gaël Ngouabo ◽  
Peguy Roussel Nwagoum Tuwa ◽  
Samuel Noubissie ◽  
Paul Woafo
Keyword(s):  
Time Delay ◽  
Nonlinear Analysis ◽  
Initial Conditions ◽  
Basin Of Attraction ◽  
Mechanical Systems ◽  
Micro Electro Mechanical Systems ◽  
Regular Motion ◽  
The Stability ◽  
Proportional Derivative Controller ◽  
Delay Dependent

The present study deals with the nonlinear analysis of electrostatic micro-electro-mechanical systems resonators with two symmetric electrodes and subjected to delayed proportional–derivative controller. After a brief description of the model, the stability analysis of the linearized system is presented to depict the stability charts in the parameter space of proportional gain and time delay. The bifurcation diagram is used to confirm the existence of the delay-dependent and delay-independent regions and to analyze the effect of proportional–derivative gains and time delay on the dynamics of the system. Using Melnikov’s theorem, the criterion for the appearance of horseshoe chaos from homoclinic and heteroclinic bifurcations is presented. Melnikov’s predictions are confirmed by using the numerical simulations based on the basin of attraction of initial conditions. It is found that the increase in proportional gain contributes to increase the region of regular motion in both bifurcations. However, the increase in derivative gain contributes rather to reduce the region of regular motion for homoclinic bifurcation, although it increases rather this region in the case of heteroclinic bifurcation. Moreover, it is also observed, depending on proportional–derivative gains, the existence of a critical value of the delay where before it, the region of regular motion increases and after it, decreases rather.

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