A Mechanical Feedback Classification of Linear Mechanical Control Systems

We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechani...

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Autores principales:	Marcin Nowicki, Witold Respondek
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	mechanical systems linear feedback classification decomposition stabilizability Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/e304ff4e12b1411ba64388fdef52a55a
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spelling	oai:doaj.org-article:e304ff4e12b1411ba64388fdef52a55a2021-11-25T16:34:47ZA Mechanical Feedback Classification of Linear Mechanical Control Systems10.3390/app1122106692076-3417https://doaj.org/article/e304ff4e12b1411ba64388fdef52a55a2021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/22/10669https://doaj.org/toc/2076-3417We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems (not necessarily controllable) which leads to a mechanical canonical decomposition. The classification of Lagrangian systems is given afterwards. Next, we show an application of the classification results to the stability and stabilization problem and illustrate them with several examples. All presented results in this paper are expressed in terms of objects on the configuration space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup></semantics></math></inline-formula> only, while the state-space of a mechanical control system is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup><mo>×</mo><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup></mrow></semantics></math></inline-formula> consisting of configurations and velocities.Marcin NowickiWitold RespondekMDPI AGarticlemechanical systemslinear feedbackclassificationdecompositionstabilizabilityTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10669, p 10669 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	mechanical systems linear feedback classification decomposition stabilizability Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	mechanical systems linear feedback classification decomposition stabilizability Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Marcin Nowicki Witold Respondek A Mechanical Feedback Classification of Linear Mechanical Control Systems
description	We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems (not necessarily controllable) which leads to a mechanical canonical decomposition. The classification of Lagrangian systems is given afterwards. Next, we show an application of the classification results to the stability and stabilization problem and illustrate them with several examples. All presented results in this paper are expressed in terms of objects on the configuration space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup></semantics></math></inline-formula> only, while the state-space of a mechanical control system is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup><mo>×</mo><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup></mrow></semantics></math></inline-formula> consisting of configurations and velocities.
format	article
author	Marcin Nowicki Witold Respondek
author_facet	Marcin Nowicki Witold Respondek
author_sort	Marcin Nowicki
title	A Mechanical Feedback Classification of Linear Mechanical Control Systems
title_short	A Mechanical Feedback Classification of Linear Mechanical Control Systems
title_full	A Mechanical Feedback Classification of Linear Mechanical Control Systems
title_fullStr	A Mechanical Feedback Classification of Linear Mechanical Control Systems
title_full_unstemmed	A Mechanical Feedback Classification of Linear Mechanical Control Systems
title_sort	mechanical feedback classification of linear mechanical control systems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/e304ff4e12b1411ba64388fdef52a55a
work_keys_str_mv	AT marcinnowicki amechanicalfeedbackclassificationoflinearmechanicalcontrolsystems AT witoldrespondek amechanicalfeedbackclassificationoflinearmechanicalcontrolsystems AT marcinnowicki mechanicalfeedbackclassificationoflinearmechanicalcontrolsystems AT witoldrespondek mechanicalfeedbackclassificationoflinearmechanicalcontrolsystems
_version_	1718413108886634496

A Mechanical Feedback Classification of Linear Mechanical Control Systems

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