Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function
The stabilization of a Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing control laws by Lyapunov control method is the construction of Lyapunov function. A logarithmic function is constructed as the Lyapunov function and is compared wit...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2017/4091302 |
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| _version_ | 1832564282042089472 |
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| author | Jie Wen Yuanhao Shi Xiaonong Lu |
| author_facet | Jie Wen Yuanhao Shi Xiaonong Lu |
| author_sort | Jie Wen |
| collection | DOAJ |
| description | The stabilization of a Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing control laws by Lyapunov control method is the construction of Lyapunov function. A logarithmic function is constructed as the Lyapunov function and is compared with the usual quadratic function theoretically. The comparative results show that the constructed logarithmic function has higher numerical accuracy and faster convergence speed than the usual quadratic function. On this basis, the control law of stabilizing Rotary Inverted Pendulum is designed based on the constructed logarithmic function by Lyapunov control method. The effectiveness of the designed control law is verified by experiments and is compared with LQR controller and the control law designed based on the quadratic function. Moreover, the system robustness is analyzed when the system parameters contain uncertainties under the designed control law. |
| format | Article |
| id | doaj-art-9bf80db7636a48cc9fd911f34597158f |
| institution | Kabale University |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-9bf80db7636a48cc9fd911f34597158f2025-02-03T01:11:27ZengWileyJournal of Control Science and Engineering1687-52491687-52572017-01-01201710.1155/2017/40913024091302Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov FunctionJie Wen0Yuanhao Shi1Xiaonong Lu2School of Computer Science and Control Engineering, North University of China, Taiyuan 030051, ChinaSchool of Computer Science and Control Engineering, North University of China, Taiyuan 030051, ChinaSchool of Management, Hefei University of Technology, Hefei 230009, ChinaThe stabilization of a Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing control laws by Lyapunov control method is the construction of Lyapunov function. A logarithmic function is constructed as the Lyapunov function and is compared with the usual quadratic function theoretically. The comparative results show that the constructed logarithmic function has higher numerical accuracy and faster convergence speed than the usual quadratic function. On this basis, the control law of stabilizing Rotary Inverted Pendulum is designed based on the constructed logarithmic function by Lyapunov control method. The effectiveness of the designed control law is verified by experiments and is compared with LQR controller and the control law designed based on the quadratic function. Moreover, the system robustness is analyzed when the system parameters contain uncertainties under the designed control law.http://dx.doi.org/10.1155/2017/4091302 |
| spellingShingle | Jie Wen Yuanhao Shi Xiaonong Lu Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function Journal of Control Science and Engineering |
| title | Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function |
| title_full | Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function |
| title_fullStr | Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function |
| title_full_unstemmed | Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function |
| title_short | Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function |
| title_sort | stabilizing a rotary inverted pendulum based on logarithmic lyapunov function |
| url | http://dx.doi.org/10.1155/2017/4091302 |
| work_keys_str_mv | AT jiewen stabilizingarotaryinvertedpendulumbasedonlogarithmiclyapunovfunction AT yuanhaoshi stabilizingarotaryinvertedpendulumbasedonlogarithmiclyapunovfunction AT xiaononglu stabilizingarotaryinvertedpendulumbasedonlogarithmiclyapunovfunction |