Generalized Quadratic Linearization of Machine Models
In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singul...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2011/926712 |
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| author | Parvathy Ayalur Krishnamoorthy Kamaraj Vijayarajan Devanathan Rajagopalan |
| author_facet | Parvathy Ayalur Krishnamoorthy Kamaraj Vijayarajan Devanathan Rajagopalan |
| author_sort | Parvathy Ayalur Krishnamoorthy |
| collection | DOAJ |
| description | In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed
in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome this problem, in the case of quadratic linearization, a new concept called
“generalized quadratic linearization” is introduced in this paper, which seeks to remove quadratic terms without introducing third- and higher-order terms into the system. Also, solution of generalized quadratic linearization of a class of control affine systems is derived. Two machine models are shown to belong to this class and are reduced to only linear terms through coordinate and state feedback. The result is applicable to other machine models as
well. |
| format | Article |
| id | doaj-art-a30faecdb671489fb8d9272b41c518a3 |
| institution | Kabale University |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-a30faecdb671489fb8d9272b41c518a32025-02-03T01:08:06ZengWileyJournal of Control Science and Engineering1687-52491687-52572011-01-01201110.1155/2011/926712926712Generalized Quadratic Linearization of Machine ModelsParvathy Ayalur Krishnamoorthy0Kamaraj Vijayarajan1Devanathan Rajagopalan2Department of Electrical and Electronics Engineering Department, Hindustan of Science & Technology, Chennai 603103, IndiaDepartment of Electrical and Electronics Engineering, SSN College of Engineering Kalavakkam 603110, IndiaDepartment of Electrical and Electronics Engineering Department, Hindustan of Science & Technology, Chennai 603103, IndiaIn the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome this problem, in the case of quadratic linearization, a new concept called “generalized quadratic linearization” is introduced in this paper, which seeks to remove quadratic terms without introducing third- and higher-order terms into the system. Also, solution of generalized quadratic linearization of a class of control affine systems is derived. Two machine models are shown to belong to this class and are reduced to only linear terms through coordinate and state feedback. The result is applicable to other machine models as well.http://dx.doi.org/10.1155/2011/926712 |
| spellingShingle | Parvathy Ayalur Krishnamoorthy Kamaraj Vijayarajan Devanathan Rajagopalan Generalized Quadratic Linearization of Machine Models Journal of Control Science and Engineering |
| title | Generalized Quadratic Linearization of Machine Models |
| title_full | Generalized Quadratic Linearization of Machine Models |
| title_fullStr | Generalized Quadratic Linearization of Machine Models |
| title_full_unstemmed | Generalized Quadratic Linearization of Machine Models |
| title_short | Generalized Quadratic Linearization of Machine Models |
| title_sort | generalized quadratic linearization of machine models |
| url | http://dx.doi.org/10.1155/2011/926712 |
| work_keys_str_mv | AT parvathyayalurkrishnamoorthy generalizedquadraticlinearizationofmachinemodels AT kamarajvijayarajan generalizedquadraticlinearizationofmachinemodels AT devanathanrajagopalan generalizedquadraticlinearizationofmachinemodels |