Premium
Dynamical Analysis of a Tip Balancing Cube
Author(s) -
Gattringer Hubert,
Reiter Alexander,
Stöger Christoph,
Jörgl Matthias,
Müller Andreas
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710043
Subject(s) - inertia , flywheel , acceleration , cube (algebra) , moment of inertia , orientation (vector space) , angular velocity , position (finance) , classical mechanics , control theory (sociology) , stability (learning theory) , equations of motion , inertial frame of reference , projection (relational algebra) , physics , mathematics , computer science , geometry , engineering , control (management) , aerospace engineering , algorithm , finance , artificial intelligence , machine learning , economics
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)