Comparison between passive and active control of a non-linear dynamical system

Abstract

Vibrations and dynamic chaos should be controlled in structures and machines. The wing of the airplane should be free from vibrations or it should be kept minimum. To do so, two main strategies are used. They are passive and active control methods. In this paper we present a mathematical study of passive and active control in some non-linear differential equations describing the vibration of the wing. Firstly, non-linear differential equation representing the wing system subjected to multi-excitation force is considered and solved using the method of multiple scale perturbation. Secondly, a tuned mass absorber (TMA) is applied to the system at simultaneous primary resonance. Thirdly, the same system is considered with 1:2 internal resonance active control absorber. The approximate solution is derived up to the fourth order approximation, the stability of the system is investigated applying both frequency response equations and phase plane methods. Previous work regarding the wing vibration dealt only with a linear system describing its vibration. Some recommendations are given by the end of the work.

Mix active control feedback of a continuously rotating shaft's nonlinear oscillations through simultaneous resonance

“…(6) The response of the main system decreased with increasing the negative linear velocity coefficient 1,3 G . (7) . The amplitude shift to right of the negative linear acceleration feedback…”

“…In turn, the actuators deliver the opposing force to the primary structure. This control method enables greater absorption and broadband applications [7][8][9][10][11]. Different types of controllers, such as the linear velocity and acceleration feedback control, the cubic velocity feedback control, the non-linear saturation controller (NSC), and the positive position feedback (PPF) controller, were used to suppress the vibrations of any system generated by an external force [12][13][14][15].…”

Study of Stability and Vibration Reduction in Multi-Tool Ultrasonic Machining under Simultaneous Primary and Internal Resonance

“…Asfar, Eissa, El-Bassiouny and Shitikova [5][6][7][8][9][10][11][12][13][14][15][16] showed how effective is the passive vibration control reduction at resonance. Eissa, El-Bassiouny and Jaensch [17][18][19][20][21][22][23] showed how effective is the active control in vibration reduction at resonance at different modes of vibration. They demonstrated the advantages of active control over the passive one.…”