The University of Southampton
Courses

# ELEC3205 Control System Design

## Module Overview

### Aims and Objectives

#### Module Aims

- To develop skills for design of linear multivariable control systems by pole placement. - To introduce basic nonlinear system analysis and design methods.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Design controller using frequency domain methods
• Analyse linear dynamical systems by state space methods
• Derive state space representation from a given transfer function representation
• Check controllability/observability by rank test of the controllability/observability matrix
• Design pole placement state-feedback controller in the state space setting, also with observers in the loop
• Model, analyse, and synthesise nonlinear dynamical systems
• Derive state space representations for nonlinear systems from first principles
• Analyse stability of nonlinear autonomous systems by state space methods
• Analyse nonlinear input--output systems by describing functions

### Syllabus

Frequency Domain Methods for Controller Design - Lead-lag compensator - Introduction to loop shaping State-space representations for linear systems - Transfer function canonical realisations - State space representations Structural properties - Controllability and state transfer - Observability and state estimation Multivariable control by pole placement - Pole placement by state feedback - Elements of optimal control State estimation - Observer design by pole placement Joint observer-controller schemes Nonlinear systems and mathematical modelling Introduction to the phase plane analysis method Stability and Lyapunov analysis - Lyapunov indirect method - Lyapunov direct method - Lasalle’s Theorem Describing functions Nonlinear control system design - Design via linearisation - Design via feedback linearisation - Introduction to Lyapunov based design method

### Learning and Teaching

TypeHours
Follow-up work18
Revision10
Lecture36
Preparation for scheduled sessions18
Total study time150

H. Khalil (2002). Nonlinear Systems.

Slotine and Li (1991). Applied Nonlinear Control.

K. Astrom and R. Murray. Feedback Systems: An Introduction for Scientists and Engineers.

K. Astrom and B. Wittenmark (1997). Computer-controlled systems: theory and design.

### Assessment

#### Summative

MethodPercentage contribution
Examination  (2 hours) 80%
Problem Sheets 20%

#### Repeat

MethodPercentage contribution
Examination 100%

#### Referral

MethodPercentage contribution
Examination 100%

#### Repeat Information

Repeat type: Internal & External