Bona Basilio. Dynamic Modelling of Mechatronic Systems

Celid, 2014. — 321 p.How to describe the structure of a system; various types of analytical representation (linear, non-linear, time invariant, time-varying, etc.) and their representations based on physical principles.Vectors, matrices, reference systems: how to use this concepts to represent motions of solid bodies in space
Rigid displacements in space: translations and rotation matrices , homogeneous representation of the body pose
Kinetic and potential energy: the building block for modeling approaches based on Lagrange equations.
The concept of state variables.
From Lagrange equations to state variable equations.
The concepts of flows and efforts; power and the bond-graph methodology;
The student develops the following abilities
Ability to describe a rigid body in space and its motion using vectors and matrices (rotation and homogeneous)
Ability to compute analytically and numerically the kinetic and potential energy of a system that includes many bodies (multi-body analysis)
Ability to write the Lagrange equation, to transform in state variable equations and use for model simulation
Ability to write the Bond-Graph model, to transform in state variable equations and use for model simulation
Ability to use the above methods for modeling mechanical, electromagnetic and electromechanical systems such that actuators and transducer (electromagnets, capacitive, moving-coil transducers, piezoelectric material, etc.).1. Introduction, examples of mechanical, electrical, hydraulic, electromechanical equipment, definition of power, energy and co-energy. (8 hours)
2. Analytical models: understanding of the system structure, of the analytical representation (linear, nonlinear, time invariant, time varying, etc.) and its representation based on physical principles.
3. Definition of the effort and flux variables in mechanical, electrical and hydraulic systems.
4. State functions: kinetic co-energy and potential energy.
5. Mathematical language needed in the course: vectors and matrices, rigid body kinematics and dynamics, generalized variables, degrees of freedom, constraints, holonomicity. Roto-translations of rigid bodies. general properties of the body dynamics: inertia, dissipation, elasticity.
6. Lagrange Equations.
7. Bond-graph modelling based on power exchange between subsystems. Power variables, reversibility, construction rules, relation between bond-graphs and block diagrams.
8. Configuration space and state equations. The dynamic system as a unifying mathematical representation. Linear and nonlinear models, Fundamental properties: stability and passivity.
9. How to write the equations that describe the interactions inside electromechanical actuators and transducer, as electromagnets, capacitive transducers, moving coil transducers, piezoelectric materials, synchronous motors.
10. Mechanical models of the rigid body, finite elements models. Finite elements models of lumped parameters electrical and electronic systems. Modal reduction techniques and bond-graph representation.
11. Examples and implementation of simulated systems.