Module overview
The topics considered are: z transforms, sampling and reconstruction, discretisation, elements of realisation theory, controller design via pole placement, observers, optimal control design.
Linked modules
Pre-requisite: ELEC2220
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Optimal control design method
- Stability theorems and root locus techniques
- Z transform analysis of sampled data feedback loops
- A suite of techniques for digital controller design
Syllabus
Introduction
Basics of z transform theory
- Inverse z transform
- Convolution
- Recursion relation
- Realisability
Sampling and reconstruction of signals
- Zero order hold/D->A conversion
- Shannon's sampling theorem, aliasing and folding
- Choice of the sampling period in sampled-data control systems
- Pulse transfer function and analysis of control systems
- Mapping of poles and zeroes
Case study: PID digital control
Continuous-time state-space systems and their discretisation
- Controllability and observability under discretisation
- Intersample behaviour
Realisation theory
- Canonical forms
- Minimality
- Internal- and BIBO-stability, and relation between the two
Controller design via pole placement
- Continuous-time-based design techniques
- Deadbeat control
Case study: root-locus based digital control design
Observers and their use in state-feedback loops
- Observer-based controllers
- The separation principle
Optimal control design
- Introduction to optimal control
- Finite Horizon LQR
- Infinite Horizon LQR
Learning and Teaching
| Type | Hours |
|---|---|
| Follow-up work | 18 |
| Tutorial | 12 |
| Preparation for scheduled sessions | 18 |
| Lecture | 36 |
| Wider reading or practice | 54 |
| Completion of assessment task | 2 |
| Revision | 10 |
| Total study time | 150 |
Resources & Reading list
Textbooks
Ogata. Discrete time control systems. Prentice Hall.
Computer requirements.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Examination | 100% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Examination | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Examination | 100% |
Repeat Information
Repeat type: Internal & External