The effect of time-delayed feedback controller on an electrically actuated resonator
- 477 Downloads
This paper presents a study of the effect of a time-delayed feedback controller on the dynamics of a Microelectromechanical systems (MEMS) capacitor actuated as a resonator by DC and AC voltage loads. A linearization analysis is conducted to determine the stability chart of the linearized system equations as a function of the time delay period and the controller gain. Then the method of multiple-scales is applied to determine the response and stability of the system for small vibration amplitude and voltage loads. It is shown that negative time-delay feedback control gain can lead to unstable responses, even if AC voltage is relatively small compared to the DC voltage. On the other hand, positive time delay can considerably strengthen the system stability even in fractal domains. We also show how the controller can be used to control damping in MEMS, increasing or decreasing, by tuning the gain amplitude and delay period. Agreements among the results of a shooting technique, long-time integration, basin of attraction analysis with the perturbation method are achieved.
KeywordsDelayed system Control MEMS Electrostatic force Multiple scales
The authors are thankful to Professor Ali Nayfeh for fruitful discussions on modeling time-delayed systems using perturbation methods. This research has been supported in part by the National Science Foundation (through grant #0846775).
- 2.Balachandran, B., Kalmár-Nagy, T., Gilsinn, D.: Delay Differential Equations: Recent Advances and New Directions. Springer, New York (2009) Google Scholar
- 22.El-Bassiouny, A.F.: Fundamental and subharmonic resonances of harmonically oscillation with time delay state feedback. Shock Vib. 13, 65–83 (2006) Google Scholar
- 23.El-Bassiouny, A.F.: Vibration control of a cantilever beam with time delay state feedback. Z. Naturforsch. A, J. Phys. Sci. 61, 629–640 (2006) Google Scholar
- 24.El-Bassiouny, A.F., El-Kholy, S.: Resonances of a nonlinear single-degree-of-freedom system with time delay in linear feedback control. Z. Naturforsch. A, J. Phys. Sci. 65, 357–368 (2010) Google Scholar
- 29.Hamdi, M., Belhaq, M.: Control of Bistability in a Delayed Duffing Oscillator. Adv. Acoust. Vib. 2012, 872498 (2012) Google Scholar