Vibration and Energy Optimization in Offshore Wind Towers via Time-Delayed Nonlinear Integral Positive Position Feedback Control

Articles in Press

Document Type : Research Paper

Authors
T.S. Amer 1
M.K. Abohamer 2
T.A. Bahnasy 2
I.S. Hamada 1
A.M. Farag 1
1 Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2 Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta 31734, Egypt
10.22055/jacm.2026.48900.5585
Abstract
The main scope of this research is to analyze the control of energy transmission and oscillation effectiveness in mathematical applications, specifically represented by the first bending mode of offshore wind turbine towers, using a superposition of excitations. Due to the generation of overlapping multi-resonance obstacles and ignorance of feedback delays in most conventional passive and active devices, the time-delayed nonlinear integral positive position feedback (TD-NIPPF) controller is employed to prevent the turbine structure from harmful oscillations and regulate energy transmission of the wind turbine, particularly at resonance states. The model’s governing equation (GE) has been approximated to 2nd order using the multiple-scales approach (MSA), and the approximated outcomes are compatible with those acquired numerically through the 4th order Runge-Kutta method (RK-4). Moreover, modulation equations are extracted through the solvability conditions after inserting the resonant states. Additionally, Wolfram Mathematica and MATLAB are implemented to graphically construct the frequency response curves and time response diagrams of the acquired solutions in the presence and without the TD-NIPPF controller. Additionally, the parameter effects are graphically illustrated for the most significant factors on the wind structure. Bifurcation diagrams, Largest Lyapunov exponent (LLE), Poincaré maps, and phase portraits are plotted to illustrate the system's various dynamic behaviors. Lastly, stability examinations and steady-state solutions will be discussed via resonance curves. Moreover, the numerical findings demonstrated that the TD-NIPPF strategy effectively diminished tower distortion response across a wide spectrum of operating conditions, while ensuring stability within time delays and surpassing standard linear control setups in multi-excitation resonance scenarios.
Keywords
Offshore wind turbine structure
Energy flow
Time-delayed nonlinear integral positive position feedback control
Perturbation strategy
Stability
bifurcation
Poincaré
maps
Phase portrait
Large Lyapunov Exponent
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Available Online from 07 May 2026