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.
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Z transform analysis of sampled data feedback loops
- A suite of techniques for digital controller design
- Optimal control design method
- Stability theorems and root locus techniques
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 |
| Revision | 10 |
| Preparation for scheduled sessions | 18 |
| Wider reading or practice | 54 |
| Lecture | 36 |
| Tutorial | 12 |
| Completion of assessment task | 2 |
| Total study time | 150 |
Resources & Reading list
Textbooks
Computer requirements.
Ogata. Discrete time control systems. Prentice Hall.
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