# Flexible Multibody System Analysis for Control Purposes - General information

This course is part of the DISC course program 2009/2010. On this page you can read some general information.

## Lecturers

Prof.dr.ir. J.B. Jonker, dr.ir. R.G.K.M. Aarts and dr.ir. J. van Dijk. All from the Laboratory of Mechanical Automation and Mechatronics, University of Twente.

## Objectives

For control design of mechatronic systems it is essential to make use of simple prototype models with a few degrees of freedom that capture only the relevant system dynamics. For this purpose, the multibody system approach is a well-suited method to model the dynamical behaviour of the mechanical part of such systems. In this approach the mechanical components are considered as rigid or flexible bodies that interact with each other through a variety of connections such as hinges and flexible coupling elements like trusses and beams. The method is applicable for flexible multibody systems as well as for flexible structures in which the system members experience only small displacement motions and elastic deformations with respect to an equilibrium position. A mathematical description of these models is represented by the equations of motion derived from the multibody systems approach.

For control synthesis a linearized state-space formulation is required in which an arbitrary combination of positions, velocities, accelerations and forces can be taken both as input variables and as output variables, according to the control problem being solved.

In this course basic concepts of flexible multibody system dynamics are presented using a non-linear finite element method. This formulation accounts for geometric nonlinear effects of flexible elements due to axial and transverse displacements. The approach offers many possibilities for analysis, simulation and prototype modelling of mechatronic systems. This will be illustrated through a variety of design cases.

## Contents

 1 Scope of flexible multibody kinematics and dynamics. Multibody versus finite element formulations. Description of angular orientation: Euler angles, Quarternions.
 2 Finite element representation of flexible multibody systems. Kinematical analysis: the concept of constraints, degrees of freedom and geometric transfer functions. Dynamic analysis: lumped mass formulation, consistent mass formulation, stiffness matrices, equations of motion, equations of reaction.
 3 Linearized equations for control system analysis. Stationary and equilibrium solutions. Linearized state-space equations.
 4 Illustrative design examples e.g. a programmable focus system, a multi axes vibration isolation mount and a multi axes micro stage.

See the roster for a more detailed overview.

## Lecture Notes

See the course material.

## Prerequisites

Basic background in systems modelling and control theory.