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

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.

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.

scholarly journals On the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji chaotic system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jianping Shi ◽  
Liyuan Ruan
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Chaotic System ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Delay Systems ◽  
Feedback Gain ◽  
Stability Of Equilibrium ◽  
Delayed Feedback Controller

Abstract In this paper, we study the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji (BG) chaotic system. Since the current study on Hopf bifurcation for fractional-order delay systems is carried out on the basis of analyses for stability of equilibrium of its linearized approximation system, it is necessary to verify the reasonability of linearized approximation. Through Laplace transformation, we first illustrate the equivalence of stability of equilibrium for a fractional-order delay Bhalekar–Gejji chaotic system and its linearized approximation system under an appropriate prior assumption. This semianalytically verifies the reasonability of linearized approximation from the viewpoint of stability. Then we theoretically explore the relationship between the time delay and Hopf bifurcation of such a system. By introducing the delayed feedback controller into the proposed system, the influence of the feedback gain changes on Hopf bifurcation is also investigated. The obtained results indicate that the stability domain can be effectively controlled by the proposed delayed feedback controller. Moreover, numerical simulations are made to verify the validity of the theoretical results.

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