Effects of delayed time active controller on the vibration of a nonlinear magnetic levitation system to multi excitations

Abstract

In this paper, a time-delayed positive position feedback controller is proposed to reduce the horizontal vibration of a magnetically levitated body subjected to multi force excitations. This controller is coupled to the main system with 1:1 internal resonance. The method of multiple scales perturbation technique is employed to obtain an approximate solution which clarifies the nonlinear behavior for both amplitude and phase of the whole system. The effects of time delay magnitude are investigated to indicate the safe region of operation. Validation curves are involved to compare the approximate solution with the numerical simulation.

Vibration suppression of a nonlinear magnetic levitation system via time delayed nonlinear saturation controller

“…It can be observed from these figures that the relation between the main system amplitude and the excitation force (before control) is a nonlinear relation that produces large system amplitudes for a slight increase in the excitation force. After control at 1 c ω µ as in equation (23) and the whole energy is channeled to the controller due to the saturation phenomenon. In figure (13) after control, when the external force amplitude f reaches approximately 0.24, a Hopf bifurcation appears and the whole system exhibits unstable response.…”

“…Figure (6) demonstrates the frequency response curves for the main system and controller (closed loop case) without any time delay. The main system amplitude before control is represented by the blue curve which is plotted according to equation (22) while it's plotted after control by the dark curve according to equations (23) and (24). In this figure, as 1 σ increases from left to right, we see that the main system amplitude takes the path of the blue curve and behaves in the same way without control until it reaches the point P. At this point, the controller is activated automatically forcing the main system amplitude to exhibit a new behavior and takes the path of the dark curve.…”

“…El-Ganaini et al [23] applied a time-delayed positive position feedback controller to reduce the horizontal vibration of a magnetically levitated body subjected to multi force excitations. This controller was coupled to the main system with 1:1 internal resonance.…”

Nonlinear Vibration-Damping Investigation of a Vertical Cantilever Beam Simulation Aircraft tail via NTDSC Procedure

“…Control issues in loop-delayed systems have received a lot of attention [22]. The effects of time delay were investigated in order to determine the system secure operating zone [23]. The horizontal vibration of a magnetically levitated body subjected to multi-force excitations was reduced using a time-delayed position feedback controller.…”

Analysis of Vibration Control of Nonlinear Beam Using a Time-Delayed PPF Controller

“…ey concluded that time delays could adjust the effective frequency bandwidth of the saturation controller and avoid the occurrence of the controller overload. El-Ganaini et al [15] proposed a time-delayed PPF controller to suppress the horizontal vibration of a magnetically levitated body subjected to multiple force excitations. ey concluded that the amplitudes of the controlled system did not depend only on a certain delay, but on the sum of two delays.…”