MSc Advanced Control and Systems Engineering / Course details

Year of entry: 2025

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Course unit details:
State-Space and Multivariable Control

Course unit fact file
Unit code	EEEN60109
Credit rating	15
Unit level	FHEQ level 7 – master's degree or fourth year of an integrated master's degree
Teaching period(s)	Semester 1
Available as a free choice unit?	No

Overview

Brief Description of the Unit:

Introduction to state variables, order and state equations
State space modelling of dynamical systems - applications and examples
Controllable canonical form and observer canonical form
State space realisation of transfer functions
State transition matrix, matrix exponential and time response of state space models
Laplace transform of state equations and matrix transfer functions for MIMO systems
Use of eigenvalues and eigenvectors to diagonalise a state space model
Modal form, modal behaviour and system dynamics
Jacobi linearisation on nonlinear systems
Controllability and observability and links to modal analysis
Minimal representations
State feedback control design
Observer design
Output feedback design and separation principle
Discrete-time state-space counterparts to continuous-time
State space and transfer function matrix representations of multivariable linear systems
Realisation of a MIMO transfer function matrix: minimal representation
Multivariable poles and zeros; directionality
Closed-loop sensitivities; design tradeoffs
Diagonal controllers and decoupling
Internal model control structure design for both single variable and multivariable control
Inner-outer factorisations
Design example

Aims

This course unit detail provides the framework for delivery in the current academic year and may be subject to change due to any additional Covid-19 impact. Please see Blackboard / course unit related emails for any further updates

The course unit aims to:·

Give students a sound understanding of control systems analysis and synthesis using state space techniques
Introduce multivariable control systems
Give students an introduction to internal model control design.

Learning outcomes

On the successful completion of the course, students will be able to:		Developed	Assessed
ILO 1	Describe dynamical systems in mathematical terms using state-space representations.	x	X
ILO 2	Analyse dynamical system properties of state-space models.	x	X
ILO 3	Develop feedback controllers for state-space models using state-feedback and observer techniques.	x	X
ILO 4	Design PID type decoupling controllers for the MIMO systems with transfer function representation	x	X
ILO 5	Design IMC type controllers for both minimum phase and non-minimum phase MIMO systems	x	X
ILO 6	Evaluate the MIMO control system performance in terms of reference tracking, noise suppression and disturbance rejection.	x	X

Assessment methods

Method	Weight
Other	20%
Written exam	80%

Coursework assessment: quiz and report based on laboratory work. Feedback is provided two weeks after report submission

Study hours

Scheduled activity hours
Lectures	30
Practical classes & workshops	6
Tutorials	3

Independent study hours
Independent study	111

Teaching staff

Staff member	Role
Alexander Lanzon	Unit coordinator
Long Zhang	Unit coordinator

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