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MSc Advanced Control and Systems Engineering / Course details

Year of entry: 2023

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
Offered by Department of Electrical & Electronic Engineering
Available as a free choice unit? No


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



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:




Describe dynamical systems in mathematical terms using state-space representations.




Analyse dynamical system properties of state-space models.




Develop feedback controllers for state-space models using state-feedback and observer techniques.




Design PID type decoupling controllers for the MIMO systems with transfer function representation




Design IMC type controllers for both minimum phase and non-minimum phase MIMO systems




Evaluate the MIMO control system performance in terms of reference tracking, noise suppression and disturbance rejection.




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

Recommended reading

Multivariable part:

1 J. M. Maciejowski: Multivariable Feedback Desgin. Addison Wesley 1989

2 K. Zhou, J. C. Doyle and K. Glover: Robust and Optimal Control. Prentice Hall 1996

3 S. Skogestad and I. Postlethwaite: Multivariable Feedback Control (2nd ed). Wiley 2005.

4 M. Morari and E. Za
riou: Robust Process Control. Prentice Hall 1989.

5 T. Glad and L. Ljung: Control Theory. Taylor and Francis 2000.

6 G. C. Goodwin, S. F. Graebe and M. Salgado: Control System Design. Prentice Hall 2001.

7 K. H. Johansson: The quadruple-tank process: a multivariable laboratory process with an adjustable zero, IEEE Trans. Control Systems Technology, 8, 456465, 2000.


State-space part:

1 “Modern control engineering” by Ogata, Prentice-Hall

2 “Feedback control of dynamic systems” by Franklin and Powell, Prentice-Hall

3 “Modern control systems” by Dorf and Bishop, Prentice-Hall

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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