Digital Control System Design

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
• Stability theorems and root locus techniques
• Optimal control design method

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

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

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.