Iterative Optimal Control for Flexible Rotor–AMB System
In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations.The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control nonaffineequations. The basic model of the system...
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| Format: | Article |
| Language: | English |
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Technical University of Kosice
2010-06-01
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| Series: | Acta Montanistica Slovaca |
| Subjects: | |
| Online Access: | http://actamont.tuke.sk/pdf/2010/n1/2tombul.pdf |
| _version_ | 1811249623334912000 |
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| author | G. Serdar Tombul Stephen P. Banks Nizami Akturk |
| author_facet | G. Serdar Tombul Stephen P. Banks Nizami Akturk |
| author_sort | G. Serdar Tombul |
| collection | DOAJ |
| description | In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations.The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control nonaffineequations. The basic model of the system will be a Timoshenko beam supported at the ends by magnetic frictionless bearings.The effective control of such systems is extremely important for very high angular velocity shafts which are a feature of many modernmachines. The control must be able to cope with unbalanced masses and hence be very robust.In this paper we shall approach the problem by discretising the Timoshenko beam model and using standard difference formulaeto develop a finite-dimensional model of the system. Then we use a recently developed technique for controlling nonlinear systemsby reducing the problem to a sequence of linear time-varying (LTV) systems. An optimal control designed for each approximating linear,time-varying system and recent results show that this method will converge uniformly on compact time intervals to the optimal solution. |
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| format | Article |
| id | doaj.art-8e2b2272a1cb4b14920ffc54d97d5db0 |
| institution | Directory Open Access Journal |
| issn | 1335-1788 |
| language | English |
| last_indexed | 2024-04-12T15:49:52Z |
| publishDate | 2010-06-01 |
| publisher | Technical University of Kosice |
| record_format | Article |
| series | Acta Montanistica Slovaca |
| spelling | doaj.art-8e2b2272a1cb4b14920ffc54d97d5db02022-12-22T03:26:32ZengTechnical University of KosiceActa Montanistica Slovaca1335-17882010-06-01151913Iterative Optimal Control for Flexible Rotor–AMB SystemG. Serdar TombulStephen P. BanksNizami AkturkIn this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations.The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control nonaffineequations. The basic model of the system will be a Timoshenko beam supported at the ends by magnetic frictionless bearings.The effective control of such systems is extremely important for very high angular velocity shafts which are a feature of many modernmachines. The control must be able to cope with unbalanced masses and hence be very robust.In this paper we shall approach the problem by discretising the Timoshenko beam model and using standard difference formulaeto develop a finite-dimensional model of the system. Then we use a recently developed technique for controlling nonlinear systemsby reducing the problem to a sequence of linear time-varying (LTV) systems. An optimal control designed for each approximating linear,time-varying system and recent results show that this method will converge uniformly on compact time intervals to the optimal solution.http://actamont.tuke.sk/pdf/2010/n1/2tombul.pdfApproximation schemeLQR controlTimoshenko beamActive Magnetic Bearings1 Introduction |
| spellingShingle | G. Serdar Tombul Stephen P. Banks Nizami Akturk Iterative Optimal Control for Flexible Rotor–AMB System Acta Montanistica Slovaca Approximation scheme LQR control Timoshenko beam Active Magnetic Bearings 1 Introduction |
| title | Iterative Optimal Control for Flexible Rotor–AMB System |
| title_full | Iterative Optimal Control for Flexible Rotor–AMB System |
| title_fullStr | Iterative Optimal Control for Flexible Rotor–AMB System |
| title_full_unstemmed | Iterative Optimal Control for Flexible Rotor–AMB System |
| title_short | Iterative Optimal Control for Flexible Rotor–AMB System |
| title_sort | iterative optimal control for flexible rotor amb system |
| topic | Approximation scheme LQR control Timoshenko beam Active Magnetic Bearings 1 Introduction |
| url | http://actamont.tuke.sk/pdf/2010/n1/2tombul.pdf |
| work_keys_str_mv | AT gserdartombul iterativeoptimalcontrolforflexiblerotorambsystem AT stephenpbanks iterativeoptimalcontrolforflexiblerotorambsystem AT nizamiakturk iterativeoptimalcontrolforflexiblerotorambsystem |