Open AccessModeling of the dynamics of GBB1005 Ball & Beam Educational Control System as a controlled mechanical system with a redundant coordinate
Author(s) -
A.Ya. Krasinskii,
E. M. Krasinskaya
Publication year - 2014
Publication title -
nauka i obrazovanie
Language(s) - English
Resource type - Journals
ISSN - 1994-0408
DOI - 10.7463/0114.0646446
Subject(s) - ball (mathematics) , mechanical system , coordinate system , beam (structure) , system dynamics , control theory (sociology) , physics , computer science , classical mechanics , structural engineering , mechanical engineering , control (management) , engineering , mathematics , mathematical analysis , geometry , artificial intelligence
The method of research stability and stabilization of equilibrium of systems with geometrical constraints is elaborated and used for equilibrium for real mechatronic arrangement GBB1005 Ball & Beam. For mathematical model construction is used Shul'gin's equations with redundant coordinates. The through differentiation geometrical constraints obtained kinematic (holonomic) constraints is necessary add for stability analysis. Asymptotic stability equilibrium for mechanical systems with redundant coordinates is possible , in spite of formal reduction to Lyapunov's especial case, if the number zero roots is equal the number constraints . More exact nonlinear mathematical model of the mechanical component Ball &Beam is considered in this paper. One nonlinear geometric constrain in this problem is allow find the new equilibrium position. The choice of linear control subsystem is depend from the choice of redundant coordinate