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Adaptive Approximation-Based Feedback Linearization Control for a Nonlinear Smart Thin Plate

Ahmed Hameed Kaleel1, Hayder F. N. Al-Shuka 1, and Omar Ahmed Hussein 2
1. Department of Aeronautical Engineering, University of Baghdad, Baghdad, Iraq
2. Department of Construction and Projects, University of Baghdad, Baghdad, Iraq

Abstract— This paper proposes feedback linearization control (FBLC) based on function approximation technique (FAT) to regulate the vibrational motion of a smart thin plate considering the effect of axial stretching. The FBLC includes designing a nonlinear control law for the stabilization of the target dynamic system while the closed-loop dynamics are linear with ensured stability. The objective of the FAT is to estimate the cubic nonlinear restoring force vector using the linear parameterization of weighting and orthogonal basis function matrices. Orthogonal Chebyshev polynomials are used as strong approximators for adaptive schemes. The proposed control architecture is applied to a thin plate with a large deflection that stimulates the axial loading thus, the plate behaving nonlinearly. The governing partial differential equation for the piezo-plate system is transformed into definite ordinary differential equations (ODEs) using the Galerkin approach; hence, multi-input multi-output ODEs are obtained. Simulation experiments are performed to verify the validity of the proposed control structure.

Index Terms—nonlinear vibrations, feedback linearization, smart plates, piezo-patches

Cite: Ahmed Hameed Kaleel, Hayder F. N. Al-Shuka, and Omar Ahmed Hussein, "Adaptive Approximation-Based Feedback Linearization Control for a Nonlinear Smart Thin Plate," International Journal of Mechanical Engineering and Robotics Research, Vol. 10, No. 8, pp.458-463, August 2021. DOI: 10.18178/ijmerr.10.8.458-463

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.