Suppress the vibration of a nonlinear dynamical system subjected to external force using a positive position feedback control. | ||
| Al-Azhar Bulletin of Science | ||
| Article 2, Volume 2021, Issue 9, September 2021, Pages 1-16 PDF (1.4 M) | ||
| Document Type: Review Article | ||
| DOI: 10.21608/absb.2020.46646.1090 | ||
| Authors | ||
| Fagr Osama* 1; Yaser Amer2; Kamal raslan3 | ||
| 1Department of Basic Science, Higher Technological Institute, Tenth of Ramadan City, Egypt. | ||
| 2a Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt | ||
| 3Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Egypt | ||
| Abstract | ||
| Vibration suppression using a positive position feedback (PPF) control for a nonlinear dynamical system which subjected to an external force is studied. The proposed model is the vertical dynamic excitation of structures induced by a single pedestrian walking along a straight path on flat and relatively stiff surfaces. The multiple scale perturbation technique was applied to derive the first order approximate solution of the system. The response equation and the stability criteria for the system were derived near the simultaneous primary and internal resonance cases. MATLAB 14.0 have been used for the numerical studying to show the time history of the main system with and without PPF controller. Also, the effect of the system parameters on the response system have been studied. A comparison between the approximate and numerical solutions is illustrated and it show a good agreement between them. It is found that (PPF) controller is very suitable for small natural frequency dynamical systems subjected to primary resonance excitations. | ||
| Keywords | ||
| Positive position feedback controller; multiple scale perturbation method; response equation; primary resonance case; external force | ||
| References | ||
|
[1] Jun L. Positive Position Feedback Control for High-Amplitude Vibration of a Flexible Beam to a Principal Resonance Excitation. Shock and Vibration. 2010; 17:187-203.
[2] Wang Y, Inman DJ. Comparison of Control Laws for Vibration Suppression Based on Energy Consumption. Journal of Intelligent Material Systems and Structures. 2011; 22:795-809.
[3] Cazzulani G, Resta F, Ripamonti F. The Active Modal Tuned Mass Damper (AMTMD ) for Vibration Suppression in Flexible Structures.
[4] Orszulik R, Shan J. Multi-mode adaptive positive position feedback: An experimental study. In: Proceedings of the 2011 American Control Conference.; 2011:3315-3319. doi:10.1109/ACC.2011.5991454
[5] Shin C, Hong C, Jeong WB. Active vibration control of clamped beams using positive position feedback controllers with moment pair. Journal of Mechanical Science and Technology. 2012;26(3):731-740. doi:10.1007/s12206-011-1233-y
[6] Mitura A, Warminski J, Bochenski M. Optimal control methods for vertical and horizontal beam dynamics. In: ; 2012.
[7] El-Ganaini WAA, Saeed NA, Eissa M. Positive position feedback (PPF) controller for suppression of nonlinear system vibration. Nonlinear Dynamics. 2013; 72:517-537.
[8] Jung W, Noh I, Kang D. The vibration controller design using positive position feedback control. In: 2013 13th International Conference on Control, Automation and Systems (ICCAS 2013). ; 2013:1721-1724. doi:10.1109/ICCAS.2013.6704213
[9] Ghareeb N, Schmidt R. Active vibration control of a super element model of a thin-walled structure. 2014 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO). 2014; 01:657-664.
[10] Omidi E, Mahmoodi SN. Sensitivity analysis of the Nonlinear Integral Positive Position Feedback and Integral Resonant controllers on vibration suppression of nonlinear oscillatory systems. Commun Nonlinear Sci Numer Simul. 2015; 22:149-166.
[11] Kaushik AK, Krishna Y and Bangarubabu P. Active vibration control of smart beam under random vibrations. International Journal of Innovations in Engineering and Technology. 2015; 5(1):8 – 16.
[12] El-Sayed AT, Bauomy HS. Nonlinear analysis of vertical conveyor with positive position feedback (PPF) controllers. Nonlinear Dynamics. 2016; 83:919-939.
[13] Amer Y, EL-Sayed A, Salem AM. Vibration Control in MEMS Resonator Using Positive Position Feedback (PPF) Controller. Advances in Mathematics. 2016; 12:6821-6834. doi:10.24297/jam.v12i11.1114
[14] Syed HH. Comparative study between positive position feedback and negative derivative feedback for vibration control of a flexible arm featuring piezoelectric actuator. International Journal of Advanced Robotic Systems. 2017;14.
[15] EL-Ganaini WA. Vibration control of a nonlinear dynamical system excited at simultaneous resonance case. Electronic Journal of Mathematical Analysis and Applications. 2018; 6(2) :86 – 100.
[16] Wu Y, Zhang W, Meng X, Su Y. Compensated positive position feedback for active control of piezoelectric structures. Journal of Intelligent Material Systems and Structures. 2017; 29:397-410.
[17] Enríquez-Zárate J, Trujillo L, Toledo-Ramirez G, Ramos-Cirilo ÁJ, Hernández C. Optimization of PPF Control of a Building-like Structure for Vibration Control. Computación y Sistemas. 2018;22.
[18] Abdollahzadeh Jamalabadi MY. Positive Position Feedback Control of a Galloping Structure. Acoustics. 2019;1(1):47-58. doi:10.3390/acoustics1010005
[19] Kumar P, Kumar A, Racic V, Erlicher S. Modelling vertical human walking forces using self-sustained oscillator. Mechanical Systems and Signal Processing. 2018; 99:345-363.
[20] Amer YA, El-Sayed AT, Abdel-Wahab AM, Salman HF. The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances. Journal of Vibroengineering. 2019; 21:133-153.
[21] Bauomy HS, EL-Sayed AT. A new six-degrees of freedom model designed for a composite plate through PPF controllers. Applied Mathematical Modelling. 2020; 88:604-630. doi:https://doi.org/10.1016/j.apm.2020.06.067
[22] Ali KK, Salam MAA el, Mohamed EMH. Chebyshev operational matrix for solving fractional order delay-differential equations using spectral collocation method. Arab Journal of Basic and Applied Sciences. 2019; 26:342-353.
[23] Raslan KR, Salam MAA el, Ali KK, Mohamed EMH. Spectral Tau method for solving general fractional order differential equations with linear functional argument. Journal of the Egyptian Mathematical Society. 2019; 27:1-16. | ||
|
Statistics Article View: 222 PDF Download: 293 |
||
