Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method
The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2015/496085 |
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| author | Radiša Ž. Jovanović Zoran M. Bučevac |
| author_facet | Radiša Ž. Jovanović Zoran M. Bučevac |
| author_sort | Radiša Ž. Jovanović |
| collection | DOAJ |
| description | The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple fuzzy controller. The analytical structure of the proposed controller is derived and used to prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, DC servo motor, and simulation and experimental results are given. |
| format | Article |
| id | doaj-art-da491e1d4eba42539a9a66f6fc88f754 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-da491e1d4eba42539a9a66f6fc88f7542025-02-03T00:59:28ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2015-01-01201510.1155/2015/496085496085Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s MethodRadiša Ž. Jovanović0Zoran M. Bučevac1Faculty of Mechanical Engineering, University of Belgrade, 16 Kraljice Marije, 11120 Belgrade 35, SerbiaFaculty of Mechanical Engineering, University of Belgrade, 16 Kraljice Marije, 11120 Belgrade 35, SerbiaThe exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple fuzzy controller. The analytical structure of the proposed controller is derived and used to prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, DC servo motor, and simulation and experimental results are given.http://dx.doi.org/10.1155/2015/496085 |
| spellingShingle | Radiša Ž. Jovanović Zoran M. Bučevac Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method Advances in Fuzzy Systems |
| title | Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method |
| title_full | Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method |
| title_fullStr | Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method |
| title_full_unstemmed | Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method |
| title_short | Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method |
| title_sort | discrete time exponentially stabilizing fuzzy sliding mode control via lyapunov s method |
| url | http://dx.doi.org/10.1155/2015/496085 |
| work_keys_str_mv | AT radisazjovanovic discretetimeexponentiallystabilizingfuzzyslidingmodecontrolvialyapunovsmethod AT zoranmbucevac discretetimeexponentiallystabilizingfuzzyslidingmodecontrolvialyapunovsmethod |