Discretization and Control of Rotating Pendulum under Lebesgue Sampling

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  • Ohsaki Hiroshi
    Graduate School of Advanced Science and Technology, Department of Advanced Multidisciplinary Engineering, Tokyo Denki University
  • Iwase Masami
    School of Science and Technology for Future Life, Department of Robotics and Mechatronics, Tokyo Denki University
  • Hatakeyama Shoshiro
    School of Science and Technology for Future Life, Department of Robotics and Mechatronics, Tokyo Denki University

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Other Title
  • ルベーグサンプリング下で回転運動を行う振子モデルの離散化と制御
  • ルベーグサンプリング カ デ カイテン ウンドウ オ オコナウ フリコ モデル ノ リサンカ ト セイギョ

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Abstract

This study addresses a discretization method with Lebesgue sampling for a type of nonlinear system, and proposes a control method based on the discrete system model. A cart-pendulum system is used as this example. Applying this control method to some real system, how to implement the controller is a crucial problem. To overcome the problem, an impulsive Luenberger observer is introduced with a numerical forward mapping from the current system state to the one-step ahead state by well-known Runge-Kutta method. As the result, a cart-pendulum system with a rotary encoder, whose quantization interval is relatively large, can be controlled effectively. Numerical simulations are performed to verify the effectiveness of the proposed method.

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