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The University of Southampton

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


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

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

Resources & Reading list

Ogata. Discrete time control systems. 

Computer requirements. 



MethodPercentage contribution
Examination  (2 hours) 100%


MethodPercentage contribution
Examination 100%


MethodPercentage contribution
Examination 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisite: ELEC2220

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