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Dynamical Modeling and Flatness Based Control of a Belt Drive System
Author(s) -
Jörgl Matthias,
Gattringer Hubert
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410424
Subject(s) - flatness (cosmology) , control theory (sociology) , nonlinear system , kinematics , stiffness , control engineering , torque , controller (irrigation) , computer science , system dynamics , engineering , control (management) , physics , classical mechanics , structural engineering , artificial intelligence , agronomy , cosmology , quantum mechanics , biology , thermodynamics
Belt driven systems are part of many industrial applications, like computerized numerical control (CNC) machines in particular cutting machines and 3D‐printers. In this paper the dynamical modeling and a flatness based controller design for belt driven systems are proposed. Due to the special kinematics, the stiffness of the belt is nonlinear, leading to nonlinear equations of motion. By neglecting some minor dynamical effects, the resulting system simplifies to a differentially flat one. This allows to calculate nominal feed‐forward control torques by using the flat output of the system. To stabilize the error dynamics, an additional PD control law is introduced. The proposed method is compared with a controller, where elastic deflections for the feed forward part are neglected and elastic deformations are compensated by modifying the desired trajectories in a model‐based manner. The tracking performance of both methods is evaluated in certain simulations and experiments. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)