Effect of negative velocity feedback control on the vibration of a nonlinear dynamical system

In this paper, a system of nonlinear, second-order differential equations describing the oscillations of a cantilever beam has been considered and solved. A proportional derivative (PD) and negative derivative feedback (NDF) controllers are applied for reducing the vibrations. MSPT as one of the per...

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Bibliographic Details
Published in:International journal of dynamics and control 2023-12, Vol.11 (6), p.2842-2855
Main Authors: Abd El-Salam, M. N., Amer, Y. A., Darwesh, F. O.
Format: Article
Language:English
Subjects:
Approximation
Cantilever beams
Complexity
Control
Control and Systems Theory
Control systems
Controllers
Differential equations
Dynamical Systems
Engineering
Feedback control
Frequency response
Perturbation methods
Proportional derivative
Resonance
Vibration
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Summary:In this paper, a system of nonlinear, second-order differential equations describing the oscillations of a cantilever beam has been considered and solved. A proportional derivative (PD) and negative derivative feedback (NDF) controllers are applied for reducing the vibrations. MSPT as one of the perturbation techniques is used to get solutions for the system of first approximation with applying NDF controller and second approximation with applying PD controller. The worst resonance case is the primary resonance case for PD controller and the simultaneous [primary and internal] resonance case for NDF controller. Frequency response curves are obtained and the stability of the steady-state solution is studied near the selected resonance case. Effect of the parameters on the response curves are examined. A comparison between the two proposed controllers are explained numerically.
ISSN:2195-268X
2195-2698
DOI:10.1007/s40435-023-01138-0