PASSIVITY-BASED NONLINEAR STABILIZING CONTROL FOR A MOBILE INVERTED PENDULUM

Kazuto Yokoyama, Masaki Takahashi

2011

Abstract

Mobile inverted pendulums (MIPs) need to be stabilized at all times using a reliable control method. Previous studies were based on a linearized model or feedback linearization. In this study, interconnection and damping assignment passivity-based control (IDA-PBC) is applied. The IDA-PBC is a nonlinear control method which has been shown to be powerful in stabilizing underactuated mechanical systems. Although partial differential equations (PDEs) must be solved to derive the IDA-PBC controller and this is a difficult task in general, we show that the IDA-PBC controller for the MIP can be derived solving the PDEs. We also formulate conditions which must be satisfied to guarantee asymptotic stability and show a procedure to estimate the domain of attraction. Simulation results indicate that the IDA-PBC controller achieves fast performance theoretically ensuring a large domain of attraction. We also verify its effectiveness in experiments. In particular control performance under an impulsive disturbance to the MIP are verified. The IDA-PBC achieves as fast transient performance as a linear-quadratic regulator (LQR). In addition, we show that even when the pendulum declines quickly and largely because of the disturbance, the IDA-PBC controller is able to stabilize it whereas the LQR can not.

Paper Citation

in Harvard Style

Yokoyama K. and Takahashi M. (2011). PASSIVITY-BASED NONLINEAR STABILIZING CONTROL FOR A MOBILE INVERTED PENDULUM . In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-8425-75-1, pages 128-134. DOI: 10.5220/0003451501280134

in Bibtex Style

@conference{icinco11,
author={Kazuto Yokoyama and Masaki Takahashi},
title={PASSIVITY-BASED NONLINEAR STABILIZING CONTROL FOR A MOBILE INVERTED PENDULUM},
booktitle={Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2011},
pages={128-134},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003451501280134},
isbn={978-989-8425-75-1},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - PASSIVITY-BASED NONLINEAR STABILIZING CONTROL FOR A MOBILE INVERTED PENDULUM
SN - 978-989-8425-75-1
AU - Yokoyama K.
AU - Takahashi M.
PY - 2011
SP - 128
EP - 134
DO - 10.5220/0003451501280134