EMVCE$4$A $-$ VIBRATION AND CONTROL ENGINEERING $4$

VAAL University of Technology

Department of Industrial Engineering, Operation Management and Mechanical Engineering

Project: Control System Analysis and Design for a Vertically Constrained CartPendulum System

This project helps students build intuition about system vibration while practicing MATLAB programming and visual interpretation of results.

The project encourages them to explore the underlying mathematical concepts, analyze the transformations, and interpret their results using MATLAB.

Project: Affine Transformation of Geometrical Shapes

Introduction

In many fields of engineering, computer graphics, and robotics, understanding how objects are transformed in space is crucial. This project will explore the concept of affine transformations, which consist of a combination of linear transformations $($like scaling, rotating, and shearing$)$ and translations $($shifting$).$ These transformations can be represented mathematically and applied to geometric objects like squares and circles.

The objective of this project is to study how a two$-$dimensional affine transformation affects basic shapes such as a unit square and a unit circle. You will apply a given affine transformation, visualize the results in MATLAB, and interpret the geometrical effects of the transformation.

Problem Statement

You are given the following two$-$dimensional motion that defines how points $,($:$x_2$