MODELLING AND STRUCTURAL ANALYSIS OF THE BALL-ON-SPHERE SYSTEM USING BOND GRAPH TECHNIQUE
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ABSTRACT
This research is aimed at the modelling and structural analysis of the ball-on-sphere system using bond graph technique. To achieve the bond graph model of the ball-on- sphere system, the various subsystems, storage elements, junction structures, transformer elements with appropriate causality assignments and energy exchange that make up the ball-on-sphere system were identified and modelled. The developed bond graph model of the ball-on-sphere system overcame the computational complexities involved using Euler-Lagrange modelling technique which is prone to modelling errors. 20-Sim software was used to validate the developed bond graph model. In the developed bond graph model considering the effect of friction, the time of angular position response of the ball ( b ) achieved was 0.5253s while in the system model without frictional effect, time of 0.5408s was achieved for the angular position response of the ball ( b ). This shows 2.9% improvement of the angular position response of the ball considering frictional effect in the developed bond graph model. It was established from the structural analysis that the developed model of the ball-on-sphere system was controllable and observable. It was also determined from the structural analysis that the system was invertible and input-output decouplable.
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