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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

LMI-based State Feedback Control of the Underactuated Inertia Wheel Inverted Pendulum to the Unstable Upright Position

Journal of Vibration Testing and System Dynamics 8(2) (2024) 207--234 | DOI:10.5890/JVTSD.2024.06.005

Hassène Gritli$^{1,2}$, Sahar Jenhani$^{1}$

$^{1}$ Laboratory of Robotics, Informatics and Complex Systems (RISC Lab, LR16ES07), National Engineering School of Tunis, University of Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, Tunisia

$^{2}$ Higher Institute of Information and Communication Technologies, University of Carthage, 1164 Borj Cedria, Tunis, Tunisia

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Abstract

One of the frequent tasks in the robotic research field is to control the position of the robot and then change its current position to the intended state. This study focuses on the position feedback control through a state-feedback control law of an underactuated Lagrangian-type robotic system, called the inertia wheel inverted pendulum (IWIP), to its unstable upright state. Furthermore, using a rescaled dynamic model that describes the difference between the nonlinear dynamics and its approximate linear model, and based on the S-procedure, the Young inequality and the Schur complement lemma, we develop conditions on the feedback gain for the stabilization using two different methodologies. These designed methodologies are realized based on the Linear Matrix Inequality (LMI) techniques. We show that an initially obtained bilinear matrix inequality is converted into an LMI via some mathematical tools. Moreover, we introduce some further LMIs in order to minimize the feedback gain's size. Finally, we show some numerical results to illustrate the effectiveness of the proposed state-feedback control law for stabilizing the underactuated IWIP.

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