Nonlinear Control for Pendulums with Limited Pivot Travel and Pendulum Length
| Project/Area Number |
13650253
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Dynamics/Control
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| Research Institution | Shimane University |
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Principal Investigator |
YOSHIDA Kazunobu Shimane University, Faculty of Science and Engineering, Associate Professor, 総合理工学部, 助教授 (50182754)
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| Project Period (FY) |
2001 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2001: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | Pendulum System / Nonlinear Control / Vibration Control / Inverted Pendulum / Swing / Swing-Up Control / Crane System / 制振制御 / 可変長振り子 / 状態制限 / 制御系設計 / 安定化制御 / 準最適制御 |
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| Research Abstract |
(1) A stabilizing control law is obtained for a pendulum whose weight can be moved based on a condition for suppressing vibrations of the swing derived by an energy-based method, and experiments are performed to examine the usefulness of the controller. The controller is realized by a servo system for the position of the weight that simply consists of a second-order lag and a bang-bang reference input obtained from the pendulum trajectory. The control system approaches the optimal one that minimizes the damping ratio of the pendulum when the time constant of the servo system approaches zero. The results of experiments show the effectiveness of the proposed method.
(2) We propose a control law that can swing up and balance a translational inverted pendulum through limited pivot travel. Bearing in mind that the energy of the pendulum can be controlled according to the sign condition of pivot acceleration, we develop a method for swinging up the pendulum which involves controlling acceleration of the pivot as well as limiting its travel. The proposed balancing control law is a linear one designed by applying block control methods to the linearized model about an unstable equilibrium point, which can stabilize the whole system as keeping the amplitude of the pivot small. The results of our simulations and experiments demonstrate the effectiveness of the proposed control law.
(3) For a pendulum system in which the pivot and the weight are constrained to move in specified ranges, a control law that damps the pendulum oscillations quickly is developed based on energy-based methods. In deriving the condition for suppressing vibrations, the nonlinearities of the system are totally considered. Experimental results are shown to demonstrate the effectiveness of the proposed control law.
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Report
(3 results)
Research Products
(11 results)
