Geometrically non-linear von Karman plate vibrations are suppressed using optimal dynamic inversion technique. Two types of controller are considered, a continuous and finite discrete controllers in spatial domain to control the vibrations of the plate. Non-linear Finite Element (FE) method is used to transform the non-linear partial differential equations (PDE) into a set of non-linear algebraic equations and are solved. The non-linear PDE is directly used for controller design i.e. design-then-approximate (DTA) method is followed which ensures the stability and controllability of the system. The simuation study shows the effectiveness of controlling plate vibrations using continuous and discrete controllers. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Shaikh Faruque Ali

Department of Applied Mechanics

L. Vishnu Pradeesh

Algebra

finite element method

Linear algebra

Linear control systems

Linear equations

Mathematical transformations

Plates (structural components)

Vibration control

Vibrations (mechanical)

Active vibration controls

Controller designs

DISCRETE CONTROLLERS

Non linear

Non linear control

NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

OPTIMAL DYNAMICS

Von Karman

Controllers

Fulltext

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IFAC-PapersOnLine

This paper presents active vibration control and morphing of thin plates using an array of piezoelectric actuator-sensor system whose locations are determined by optimization. The sudden application of control input for morphing leads to unwanted vibrations which are suppressed using the piezoelectric actuator-sensor couples, which form a feedback control loop. Dynamic Inversion technique is used to determine the control inputs to morph the plate and to suppress the vibrations in the process. The Dynamic Inversion controlled system is compared to uncontrolled system and as a reference, the results are compared with that of Linear Quadratic Controller. The partial differential equations governing the behaviour of plate and piezoelectric actuation are solved using lower dimensional projection method, following Design-then-Approximate (DTA) method, which will reduce spillover effects. Two reference configurations are considered to perform simulations. The actuators are designed for both vibration control and morphing since thin plates have poor damping characteristics and need external damping. The displacement, velocity and error norm time histories are analysed and the configuration achieved by the system by both controllers are compared. © 2018

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ISSN	24058963
Open Access	Yes