Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms

The dynamic characteristics of the mechanical arm with a rigid-flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid-flexible coupling. So, accurately positioning and controlling...

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Autores principales:	Lisha Xu, Hua Deng, Chong Lin, Yi Zhang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi-Wiley 2021
Materias:	Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/9b2e7bc741ef4714a7cfafa6575d5ed2
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spelling	oai:doaj.org-article:9b2e7bc741ef4714a7cfafa6575d5ed22021-11-22T01:11:16ZApproximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms1099-052610.1155/2021/8290978https://doaj.org/article/9b2e7bc741ef4714a7cfafa6575d5ed22021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/8290978https://doaj.org/toc/1099-0526The dynamic characteristics of the mechanical arm with a rigid-flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid-flexible coupling. So, accurately positioning and controlling the rigid-flexible mechanical arms could be difficult. Therefore, a model reduction method of rigid-flexible mechanical arms based on the approximate inertial manifold is put forward. To repress the residual vibration of the end of the mechanical arm, a feedforward control strategy is designed. The high-dimensional solution of the vibration equation of the rigid-flexible mechanical arms is projected into the complete space composed of orthogonal decomposition modes. By using Galerkin’s method, the system is simplified and the approximate solution is obtained through the interaction between high-order and low-order modes. The truncated finite mode is also used to construct a lowest-order dynamic model on the basis of approximate inertia manifold. Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. A limited number of sinusoidal signals approximately combine the input signal, by using the particle swarm optimization algorithm to optimize the input signal, and the amplitude of the sinusoidal signal is corrected. The simulation results depict the superiority of the proposed method, which greatly suppresses the end residual vibration of the mechanical arm and realizes the accurate positioning of the end of the mechanical arm. In addition, the hardware experimental device of the rigid-flexible mechanical arms is constructed, and the experimental verification of the above method is put into effect. The simulation results of angular displacement and end vibration of the reduced model are accordant which is shown by the experimental results of the hardware platform.Lisha XuHua DengChong LinYi ZhangHindawi-WileyarticleElectronic computers. Computer scienceQA75.5-76.95ENComplexity, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Electronic computers. Computer science QA75.5-76.95
spellingShingle	Electronic computers. Computer science QA75.5-76.95 Lisha Xu Hua Deng Chong Lin Yi Zhang Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms
description	The dynamic characteristics of the mechanical arm with a rigid-flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid-flexible coupling. So, accurately positioning and controlling the rigid-flexible mechanical arms could be difficult. Therefore, a model reduction method of rigid-flexible mechanical arms based on the approximate inertial manifold is put forward. To repress the residual vibration of the end of the mechanical arm, a feedforward control strategy is designed. The high-dimensional solution of the vibration equation of the rigid-flexible mechanical arms is projected into the complete space composed of orthogonal decomposition modes. By using Galerkin’s method, the system is simplified and the approximate solution is obtained through the interaction between high-order and low-order modes. The truncated finite mode is also used to construct a lowest-order dynamic model on the basis of approximate inertia manifold. Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. A limited number of sinusoidal signals approximately combine the input signal, by using the particle swarm optimization algorithm to optimize the input signal, and the amplitude of the sinusoidal signal is corrected. The simulation results depict the superiority of the proposed method, which greatly suppresses the end residual vibration of the mechanical arm and realizes the accurate positioning of the end of the mechanical arm. In addition, the hardware experimental device of the rigid-flexible mechanical arms is constructed, and the experimental verification of the above method is put into effect. The simulation results of angular displacement and end vibration of the reduced model are accordant which is shown by the experimental results of the hardware platform.
format	article
author	Lisha Xu Hua Deng Chong Lin Yi Zhang
author_facet	Lisha Xu Hua Deng Chong Lin Yi Zhang
author_sort	Lisha Xu
title	Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms
title_short	Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms
title_full	Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms
title_fullStr	Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms
title_full_unstemmed	Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms
title_sort	approximate inertial manifold-based model reduction and vibration suppression for rigid-flexible mechanical arms
publisher	Hindawi-Wiley
publishDate	2021
url	https://doaj.org/article/9b2e7bc741ef4714a7cfafa6575d5ed2
work_keys_str_mv	AT lishaxu approximateinertialmanifoldbasedmodelreductionandvibrationsuppressionforrigidflexiblemechanicalarms AT huadeng approximateinertialmanifoldbasedmodelreductionandvibrationsuppressionforrigidflexiblemechanicalarms AT chonglin approximateinertialmanifoldbasedmodelreductionandvibrationsuppressionforrigidflexiblemechanicalarms AT yizhang approximateinertialmanifoldbasedmodelreductionandvibrationsuppressionforrigidflexiblemechanicalarms
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Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms

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