Logarithms, trigonometry, and binomial expansions

Complex numbers

Exponentials and logarithms

Roots of polynomials

Laplace transforms

Inverse Laplace transforms

Matrices and determinants

Differentiation

Simultaneous equations

Modelling principles

Modelling first order systems

Responses of first order systems

Modelling second order systems

Responses of second order systems

Behaviour characterisation for any order system

Case studies on modelling and behaviour

Linearisation of non-linear models

Introduction to feedback

Basic analysis of feedback loops

Block diagrams

Introduction to PID

Dealing with uncertainty

Introduction to feedback with MATLAB

Root-loci

Frequency response and Bode diagrams

Nyquist diagrams

Gain and phase margins

Classical feedback analysis tools with MATLAB

Time series models

Sampling and Z-transforms

Discrete time models

Discrete controller design

MATLAB basics

Introduction to feedback with MATLAB (from chapter three)

Classical feedback analysis tools with MATLAB (from chapter four)

State space model definitions

State space behaviours

State space observability and controllability

State space feedback control and observers

Classical control and weaknesses

Introduction to predictive control and forming system predictions

Predictive functional control

Finite horizon predictive control laws: definitions and tuning

Infinite horizon predictive control laws: dual-mode

Introducing constraints into predictive control

The use of target information within predictive control

Chapter one: Mathematical skills

Chapter two: Modelling and behaviour

Chapter three: Introduction to feedback

Chapter four: Classical control analysis techniques

Foundational mathematics quiz

Chapter two: Modelling and behaviour quizzes

Chapter three: Introduction to feedback quizzes

Chapter four: Classical analysis and design technique quizzes