The University of Southampton
Courses

# ELEC3206 Digital Control System Design

## 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

#### Module Aims

To introduce the student to the fundamentals of control theory as applied to digital controllers or sampled data control systems in general.

#### 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
• Stability theorems and root locus techniques
• A suite of techniques for digital controller design
• Optimal control design method

### 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

TypeHours
Follow-up work18
Lecture36
Completion of assessment task2
Preparation for scheduled sessions18
Revision10
Wider reading or practice54
Tutorial12
Total study time150

#### Resources & Reading list

Ogata. Discrete time control systems.

Computer requirements.

### Assessment

#### Summative

MethodPercentage contribution
Exam  (2 hours) 100%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External