To introduce the students to the fundamentals of applied digital control.
To familiarise the students with digital control design techniques through realistic control examples and applications.
To introduce digital P,PI,PID and full state feedback controller design.
To introduce how to implement a digital control algorithm in software.
To introduce the basic concept of optimisation.
To introduce the conventional optimisation techniques.
To introduce gradient based optimisation methods and their properties.
To familiarise the student with the application of optimisation methods.

(LO1) 1: The student will be able to use Z transforms and state-space modelling to design and implement digital control algorithms.

(LO2) 2: The student will be able to set-up optimisation problems and utilise conventional and gradient based methods to solve these problems.

(S1) Critical thinking and problem solving - Problem identifcation / synthesis

(S2) Numeracy/computational skills - Reason with numbers/mathematical concepts/problem solving/numerical methods.

(S3) An understanding of linear systems

(S4) An ability to develop system models and to use them to design feedback control laws in order to enhance system performance

(S5) An good understanding of controlling continuous systems via digital controllers

(S6) A knowledge of typical computer controlled system artitectures

(S7) An appreciation of the use of optimisation methods for system analysis and modelling

(S8) An understanding of linear programming, non-linear programming and Dynamic programming can be used to solve system optimisation problems

(S9) An appreciation of how computer-aided design and simulation tools operate

(S10) An understanding of how the optimisation methods are applied to industrial and engineering optimisation problems

(S11) An understanding of optimisation algorithm development

Part 1 - Digital Control;
- Introduction
- Transform Difference equations; the z-transform
- The properties of the z-transform
- Inversion of the z-transform
- The initial value theorem
- The final value theorem
- Block Diagrams using z-transform
- Stability analysis of closed-loop systems in the z domain
- Sampling Theorem
- Selection of the sampling frequency
- Hold Quantization 
- State Space Analysis State space representation in continuous and discrete-time domains
- Nonuniqueness of state space representation
- Solving discrete-time state space equations
- Controllability of linear systems
- Observability of linear systems
- Design of Digital Control Systems
- Introduction P, PI, PID controllers
- Simple tuning of P, PI, PID
- Zeigler-Nichols method
- Optimisation approach to tuning Inverse Dynamic approach to full state-feedback.

PART 2 - OPTIMISATION;
- Int roduction of basic concepts of optimisation
- Classification of optimisation problems
- Optimisation of quadratic function
- Quadratic function
- Properties of quadratic function
- Sylvester criterion for definiteness of a quadratic form
- Classic optimisation techniques
- Unconstrained optimisation
- Constrained optimisation
- Equality constrained optimisation
- Inequality constrained optimisation
- Gradient-based optimisation and steepest descent method (optimum gradient method)
- Gradient vector and gradient direction
- Gradients of common functions
- Search in gradient direction
- Steepest descent
- Determination of optimum step length
- The character of steepest descent method
- Convergence of the steepest descent method
- Newton method (Newton - Raphson method)
- Newton direction and Newton step length
- Discussion on Newton method
- Convergence of Newton method
- Quasi- Newton method

Due to Covid-19, one or more of the following delivery methods will be implemented based on the current local conditions and the situation of registered students.
(a) Hybrid delivery, with social distancing on Campus
Teaching Method 1 - On-line asynchronous lectures
Description: Lectures to explain the material
Attendance Recorded: No
Notes: On average two per week

Teaching Method 2 - Synchronous face to face tutorials
Description: Tutorials on the Assignments and Problem Sheets
Attendance Recorded: Yes
Notes: On average one per week

(b) Fully online delivery and assessment
Teaching Method 1 - On-line asynchronous lectures
Description: Lectures to explain the material
Attendance Recorded: No
Notes: On average two per week

Teaching Method 2 - On-line synchronous tutorials
Description: Tutorials on the Assignments and Problem Sheets
Atten dance Recorded: Yes
Notes: On average one per week

(c) Standard on-campus delivery with minimal social distancing
Teaching Method 1 - Lecture
Description: Lectures to explain the material
Attendance Recorded: Yes
Notes: On average two per week

Teaching Method 2 - Tutorial
Description: Tutorials on the Assignments and Problem Sheets
Attendance Recorded: Yes
Notes: On average one per week