Home > Published Issues > 2021 > Volume 10, No. 10, October 2021 >

Proportional-Derivative PD Vibration Control with Adaptive Approximation Compensator for a Nonlinear Smart Thin Beam Interacting with Fluid

Abdnoor Jameel Shaheed Al-hamadani, Kareem Jawad Kadhim, and Hayder F. N. Al-Shuka
Department of Aeronautical Engineering, University of Baghdad, Baghdad, Iraq

Abstract—This work is concerned with the vibration attenuation of a smart beam interacting with fluid using proportional-derivative PD control and adaptive approximation compensator AAC. The role of the AAC is to improve the PD performance by compensating for unmodelled dynamics using the concept of function approximation technique FAT. The key idea is to represent the unknown parameters using the weighting coefficient and basis function matrices/vectors. The weighting coefficient vector is updated using Lyapunov theory. This controller is applied to a flexible beam provided with surface bonded piezo-patches while the vibrating beam system is submerged in a fluid. Two main effects are considered: 1) axial stretching of the vibrating beam that leads to the appearance of cubic stiffness term in beam modelling, and 2) fluid effect. Fluid forces are decomposed into two components: hydrodynamic forces due to the beam oscillations and external (disturbance) hydrodynamic loads independent of beam oscillations. Simulation experiments are implemented using MATLAB/SIMULINK to verify the correctness of the proposed controller. Two piezo-patches are bonded on the beam while an impulse force with multi-pulse is applied to excite the beam vibration. The results show the strength of the proposed control structure.
 
Index Terms—fluid-structure interaction, smart beam, PD control, adaptive approximation control, hydrodynamic forces

Cite: Abdnoor Jameel Shaheed Al-hamadani, Kareem Jawad Kadhim, and Hayder F. N. Al-Shuka, "Proportional-Derivative PD Vibration Control with Adaptive Approximation Compensator for a Nonlinear Smart Thin Beam Interacting with Fluid," International Journal of Mechanical Engineering and Robotics Research, Vol. 10, No.10, pp. 566-571, October 2021. DOI: 10.18178/ijmerr.10.10.566-571

Copyright © 2021 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.