# Course Title: Mathematical Control Theory

## Part A: Course Overview

Course Title: Mathematical Control Theory

Credit Points: 12.00

### Teaching Period(s)

MATH2141

City Campus

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 2 2006,
Sem 2 2007,
Sem 2 2008,
Sem 2 2009

Course Coordinator: Robin Hill

Course Coordinator Phone: +61 3 99253161

Course Coordinator Email: r.hill@rmit.edu.au

Pre-requisite Courses and Assumed Knowledge and Capabilities

You will need to be familiar with calculus, linear algebra and complex numbers and series at least to first year undergraduate level. Some familiarity with the Laplace transform and its use in solving differential equations would be helpful. Exposure to a software package which uses programming constructs such as looping is also desirable.

Course Description

In this course you will become familiar with the modern state-space description of dynamic systems, and how feedback can be used to modify dynamic response. You will gain an understanding of the basic concepts of stability, observability and controllability of systems and learn how to verify performance using the simulation software package MATLAB. The transfer function description of systems will also be developed using both the Laplace transform, for continuous-time systems, and the Z-transform, for discrete-time systems. There will also be a selection of topics from non-linear systems theory, including Lyapunov theory and the calculus of variations approach to optimal control. Further understanding of these ideas will be developed through examples taken from engineering, and biological and economic systems. Building on these fundamental tools there will be an introduction to predictive control, which is an advanced control methodology that has made a significant impact on industrial control engineering. The course should be of interest to students who wish to acquire a basic understanding of the modern approach to the theory of systems and control.

Objectives/Learning Outcomes/Capability Development

At the conclusion of the course you will be able to select appropriate methodologies for the analysis or design of feedback and open-loop control systems. It is expected that you will be able to set up mathematical models of both linear and non-linear dynamic systems in either state-space format or transfer function form.  You will know how to design a feedback loop around a system to improve that system’s performance, and be able to analyse the input-output behaviour of the closed-loop system using the MATLAB software package.

At the conclusion of this course you will be able to

• set up mathematical models of linear dynamic systems in state-space format,
• convert a system model to transfer function form,
• take a the Laplace transform or Z—transform of a wide class of functions and be able to invert these transforms,
• solve linear constant coefficient differential and difference equations using Laplace and Z-transforms,
• establish whether a dynamical system is stable, marginally stable or unstable,
• analyse the input-output behaviour of a system using the MATLAB software package,
• design a feedback loop around a system to improve system performance,
• formulate calculus of variations problems and apply Pontryagin’s maximum principle to control problems,
• use Matlab to simulate the performance of various controllers including model predictive controllers,
• use the theory of Lyapunov Functions to investigate the stability of non-linear systems.

Overview of Learning Activities

There will be a series of structured written assignments and laboratory exercises that will develop the ability to apply the mathematical theory to a range of applications. There will also be supervised computer laboratory classes where you will learn Matlab syntax and run Matlab programs. The underlying theory will be presented in lectures.

Overview of Learning Resources

You will have access to course material on the online RMIT Learning Hub, including lecture notes and a detailed study program.

Overview of Assessment

Your capability to analyse dynamic system behaviour and improve performance by intelligent controller design will be developed and assessed through written and computer assignments. Assignments will be marked and feedback given.