The Impact of the Nonlinear Integral Positive Position Feedback (NIPPF) Controller on the Forced and Self-Excited Nonlinear Beam Flutter Phenomenon
Abstract
:1. Introduction
2. Scientific Type
2.1. Uncontrolled System Dynamics
2.2. System Dynamics with NIPPF Control
3. Analytical Investigations
3.1. Perturbation Analysis
- (i)
- PR:
- (ii)
- IR:
3.2. Periodic Solutions
3.3. Fixed-Point Solution
3.4. Determining Stability by Linearizing the System
4. Results and Discussion
4.1. System Performance with and without NIPPF Control
4.2. Occurrence Rejoinder Curvatures (ORC)
5. Comparison
5.1. Comparison between Time History before and after the Controller
5.2. Comparison between Perturbation Solution and Numerical Simulation
5.3. Comparison with Previous Work
6. Conclusions
- The Nonlinear Integral Positive Position Feedback (NIPPF) controller effectively mitigates high-amplitude atmospheres inside nonlinear structures.
- The PR and IR case and is one of the worst vibrating reverberation cases.
- The breadth of the exciting structure declined around 99.8% after employing the NIPPF reaction supervisor associated with its rate deprived of the regulator.
- The efficiency of the NIPPF reaction supervisor, signified as Ea, influences approximately 482.5, showcasing its high effectiveness in supervising the structure’s performance.
- The comeback or performance of the measured structure deepens with the increase in the peripheral excitement force, .
- The rejoinder of the focal structure diminished with the growth of the natural frequency .
- Increasing the NIPPF parameter shifts the curves to the right, which can improve the performance of the NIPPF controller, particularly in mitigating high-amplitude vibrations within the nonlinear system, which is beneficial to the operation of the NIPPF controller.
- For the NIPPF parameter, the amplitude of the measured system decreases very sluggishly.
- The smallest possible amplitudes of the vibrating suspended cable happen when
- The frequency response curves and the Runge–Kutta fourth-order method yield consistent results, validating the analysis in both the frequency and time domains.
- The closed-loop response of the relative displacement, using the NIPPF controller, exhibits a peak overshoot, which is a characteristic of the system’s transient behavior.
- The modified NIPPF controller effectively controls the relative displacement of the suspension system. This is evident in the improved closed-loop performance, characterized by minimized peak overshoot and settling time.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Dislodgment, speed, and acceleration of the preliminary vein of the system, correspondingly. | |
Structure rheostat manipulating movement, speed, and acceleration of the controller. | |
Dimensionless movement, velocity of the controller. | |
Dimensionless control signal gain. | |
Dimensionless feedback signal gain. | |
Dimensionless linear parameter of the controller. | |
System and control damping coefficients, respectively. | |
The inherent order and patterns observed in both the system and its control strategy. | |
The strength and rate of external forces acting on a system. | |
Nonlinear coefficients of the focal structure. | |
External excitation frequency. | |
Detuning parameter. | |
Slight variation parameter. |
Abbreviations
MTST | Multiple time scales technique. |
NIPPF | Nonlinear integral positive position feedback (PPF + IRC). |
PR | Primary resonance. |
FREs | Frequency response equations. |
IR | Internal resonance. |
Appendix A
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Time | Approximate Solution beforeNIPPF | Numerical Solution beforeNIPPF |
---|---|---|
62.8 | −1.9 | −1.9 |
883.883 | −1.9 | −1.9 |
49.6 | 1.9 | 1.9 |
833.416 | 1.9 | 1.9 |
Time | Approximate Solution after NIPPF | Numerical Solution after NIPPF |
62.8 | −0.004 | −0.004 |
883.883 | −0.004 | −0.004 |
49.6 | 0.004 | 0.004 |
833.416 | 0.004 | 0.004 |
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Alluhydan, K.; Amer, Y.A.; EL-Sayed, A.T.; EL-Sayed, M.A. The Impact of the Nonlinear Integral Positive Position Feedback (NIPPF) Controller on the Forced and Self-Excited Nonlinear Beam Flutter Phenomenon. Symmetry 2024, 16, 1143. https://doi.org/10.3390/sym16091143
Alluhydan K, Amer YA, EL-Sayed AT, EL-Sayed MA. The Impact of the Nonlinear Integral Positive Position Feedback (NIPPF) Controller on the Forced and Self-Excited Nonlinear Beam Flutter Phenomenon. Symmetry. 2024; 16(9):1143. https://doi.org/10.3390/sym16091143
Chicago/Turabian StyleAlluhydan, Khalid, Yasser A. Amer, Ashraf Taha EL-Sayed, and Marwa Abdelaziz EL-Sayed. 2024. "The Impact of the Nonlinear Integral Positive Position Feedback (NIPPF) Controller on the Forced and Self-Excited Nonlinear Beam Flutter Phenomenon" Symmetry 16, no. 9: 1143. https://doi.org/10.3390/sym16091143