Influence of Time Delay on Controlling the Non-Linear Oscillations of a Rotating Blade

Abstract

Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.

Rotor Active Magnetic Bearings System Control via a Tuned Nonlinear Saturation Oscillator

“…This mechanism is called tuning mechanism discussed before in Refs. [6,[8][9][10]24], or in other words if is tuned at one half of the rotor speed Ω (Ω = 2 ). This can be implemented by providing the NSC control unit with the measured rotor speed Ω from a shaft encoder device shown in Fig.…”

“…This time-delayed NSC was quadratically coupled to the main system, then the time delays effects on the system behavior and stability were studied. Kandil et al [9,10] applied the NSC to the first mode only of a thin-walled rotating beam due to the strong coupling between the first and second modes. They adopted the multiple scales method for extracting the steady-state equations so as to describe the system behavior under the action of NSC.…”

Fringe Projection Profilometry for Three-Dimensional Measurement of Aerospace Blades

“…It shares parameters between multiple output Gaussian distributions during training and measures the similarity between input samples in a new embedding space to reduce bias and improve overall prediction accuracy [16]. For actively controlling non-linear blade vibrations, a rotating blade's non-linear oscillations are reduced via a time-delayed, non-linear saturation controller (NSC) [17].…”

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1 : 1 : 1 Simultaneous Resonance

“…Te research indicated that the softening nonlinearity of the studied rotating beam with thermal barrier coatings was enhanced according to the rise of temperature. Hamed and Kandil [25] focused on the timedelay efects of the saturation phenomenon that existed in the control of a vibratory rotating beam. Tey gave timedelay criteria for a safe system operation in order to exhibit a stable bounded beam's behavior.…”