MODELLING AND STRUCTURAL ANALYSIS OF THE BALL-ON-SPHERE SYSTEM
Need help with a related project topic or New topic? Send Us Your Topic
DOWNLOAD THE COMPLETE PROJECT MATERIAL
MODELLING AND STRUCTURAL ANALYSIS OF THE BALL-ON-SPHERE SYSTEM
Chapter One: Introduction 1.1 Background
The ball-on-sphere system consists of three components: a sphere, two motors, and two friction wheels (Moezi et al., 2014). The system’s control purpose is to balance a ball on top of a sphere by rolling it along two horizontal axes using motorised friction wheels.
Controlling the system is problematic due to its non-linear, unstable, and underactuated character (Ho et al., 2009).
Ball-on-sphere balancing systems are widely used in industries such as robotics, transportation, and aerospace (Graf & Röfer, 2010).
1) missile guiding.
2) modelling the posture of a human or humanoid robot
3) Self-transportation machine
4) modelling and simulation of an unstable system in a human or robotic upper limb.
5) Spacecraft and rocket modelling and stabilisation
Figure 1.1 depicts the ball-on-sphere system. It includes a sphere ball, friction wheel, and a DC motor.
Figure 1.1: The Ball on a Sphere System (Moezi et al., 2014).
2
The dynamics of the ball-on-sphere system are nonlinear and complicated, with parameters that are interdependent in multiple directions; they have been regarded as two independent ball and wheel systems orbiting the equilibrium point (Ho et al., 2009).
Parameter identification is one of the most difficult processes in the model design phase and the leading cause of model mistakes (Dauphin-Tanguy et al., 1999). The dynamics of a ball-on-sphere system were modelled using Euler-Lagrange modelling methods.
However, the existing method is limited since it lacks extensive understanding of the system’s properties (Moezi et al., 2014). The dynamic equations of the ball-on-sphere system are nonlinear and linked, making it challenging to extract substantial system dynamics using typical numerical analytical tools.
The bond graph modelling technique captures the majority of physical variables and dynamics in multidomain systems. The bond graph model of multi-domain systems aids in overcoming the mathematical difficulties of traditional modelling methodologies, which are prone to errors (Borutzky, 2011).
The benefits of the bond graph technique were investigated in this work for simulating the ball-on-sphere system, as well as when conducting structural investigations of the system.
Several computer-based simulation tools exist for building and simulating bond graphs. 20-Sim is a graphical modelling and simulation programme designed for creating and processing dynamic systems (Alabakhshizadeh et al., 2011). The 20-Sim software is used to simulate and analyse bond graph structures.
1.2 Motivation.
The modelling of multi-domain systems for control analysis and diagnosis is an important stage in the design and simulation of multi-domain systems (Payner, 1970). Multi-domain systems challenges involve engineering systems from various domains, such as electrical, mechanical, and chemical.
Modelling techniques such as variational and network graphic techniques lack well-defined uniform notations suitable for modelling and analysing all types of physical domain systems (Yu & van Paassen, 2004).
The bond graph technique, which is based on energy and information flow in systems, provides uniform notation for physical systems (Borutzky et al., 2006).
Furthermore, the technique may perform structural analysis to derive information about a number of structural aspects of the system under consideration (Sueur and Dauphin-Tanguy, 1991).
The Euler-Lagrange technique used to describe the ball-on-sphere system is time-consuming and prone to modelling errors due to its computational difficulties, and it lacks the ability to analyse the system’s dynamic behaviour.
As a result, the ball-on-sphere system necessitates a modelling technique that represents the system’s many physical components while also providing a simple and fast method for structural analysis and the production of dynamic equations.
These factors drove the usage of the bond graph approach in this study. The bond graph technique is used to represent and structurally analyse the ball-on-sphere system in order to investigate its dynamics.
This is because the method is based on the energy properties of each individual physical component that contributes to the overall system (Karnopp et al., 2012).
Need help with a related project topic or New topic? Send Us Your Topic