Dynamical Analysis of a Tip Balancing Cube. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Gattringer, Hubert; Reiter, Alexander; Stöger, Christoph; Jörgl, Matthias; Müller, Andreas
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 147
• Page End: 148
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710043
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: This paper discusses some dynamical aspects of a self‐balancing Inertia Wheel Cube (IWC). The acceleration and deceleration of actuated flywheels is used to stabilize the IWC when balancing on one of its corners, which is an unstable equilibrium position. The orientation as well as the rotational velocity of the device are measured by an inertial measurement unit (IMU). The equations of motions are derived with the Projection Equation. Using the rotational velocity of the IWC as part of the generalized velocities leads to well‐structured and interpretable dynamical equations. These equations are the basis for simulation, parameter identification, control synthesis, and stability analysis. The stability of the unstable equilibrium is investigated by means of the linearized motion equations. It can be shown that there are always uncontrollable states by invoking the conservation of momentum. Simulations as well as experimental results are presented. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)