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MSc Advanced Control and Systems Engineering with Extended Research / Course details

Year of entry: 2020

Course unit details:
Optimal & Robust Control

Unit code EEEN60114
Credit rating 15
Unit level FHEQ level 7 – master's degree or fourth year of an integrated master's degree
Teaching period(s) Semester 2
Offered by Department of Electrical & Electronic Engineering
Available as a free choice unit? No



Optimal Control

  • Quadratic Lyapunov functions for linear systems
  • LQR (optimal state feedback) control
  • Robustness of LQR control
  • Kalman filter (optimal observers)
  • LQG control (combining LQR state feedback and optimal observer)
  • Loop transfer recovery
  • Adding integral action
  • H2 norms and H2 optimal control

Robust Control

Underpinning concepts:

  • Singular value decomposition, the H-infinity norm and the H-infinity function space
  • Well-posedness and internal stability of feedback interconnections
  • Small-gain theorem

Uncertainty representations and robust stability analysis:

  • Additive, multiplicative and inverse multiplicative uncertainty representations
  • Linear Fractional Transformations (LFT) and LFT uncertainty representation
  • Robust stability tests

Robust controller synthesis and robust control design methodology:

  • Riccati based H-infinity control synthesis
  • H-infinity loopshaping control design methodology


Unit title Unit code Requirement type Description
Control Fundamentals EEEN60108 Pre-Requisite Compulsory
State-Space and Multivariable Control EEEN60109 Pre-Requisite Compulsory


The course unit aims to:

  • Introduce students to the fundamentals of LQG control
  • Introduce students to the fundamentals of robustness analysis, robust control law synthesis and robust control design

Learning outcomes

Students will be able to:

Knowledge and understanding

  • Demonstrate knowledge of optimal control theory
  • Analyse robustness of systems
  • Understand how robust controllers are synthesised
  • Design robust controllers

Intellectual skills

  • Design controllers using optimal control theory
  • Develop skills useful in controlling systems when accurate mathematical models are unavailable

Practical skills

  • Apply optimal control methods to systems from a variety of technological areas
  • Learn design methods that can be used in developing controllers for practical systems

Transferable skills and personal qualities

  • Use the Kalman filter in fields outside control engineering
  • Understand how to use the methods in application

Assessment methods

Method Weight
Other 20%
Written exam 80%

Written Examination:

Four questions, answer all questions

Length of examination: 3 hours

Calculators are permitted

The written examination forms 80% of the total unit assessment


Number of laboratories: One laboratory (Optimal Control)

Length of Laboratory: 8 hours

This laboratory is assessed by a lab report

The coursework forms 20% of the total unit assessment

Study hours

Scheduled activity hours
Lectures 30
Practical classes & workshops 8
Tutorials 3
Independent study hours
Independent study 109

Teaching staff

Staff member Role
William Heath Unit coordinator
Joaquin Carrasco Gomez Unit coordinator

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