ACS317 State-Space Control Design 

Module Description

The aims of this modules are: to introduce state-space methods for the analysis and design of controllers for multivariable systems; to teach the use of analytical tools and methods for state-space control design; to demonstrate similarities between continuous and sampled data systems; and to extend the analysis to non-linear systems.

Material to be covered includes: Structural properties (modal decomposition, reachability, observability, stability); design (pole assignment, observer design, separation principle, internal model principle, optimal control, LQG, reference tracking, integral control) of continuous systems and equivalents for sampled-data systems.

Credits: 10 (Autumn semester)

Pre-requisites: ACS221 (Control systems design and analysis)
                         ACS217 (Mathematics and data modelling)

Module Leader

Dr Bryn JonesDr Bryn Jones

If you have any questions about the module please talk to me during the lectures or the labs in the first instance. It is likely that other students will learn from any questions you ask as well, so don’t be afraid to ask questions.

Outside of lectures please contact me via email during normal working hours (9am-5pm Monday - Friday).

Learning Outcomes

Learning Outcomes

By the end of the module students will be able to:

  1. Explain the relevance of state space techniques as an underpinning methodology for the modelling, analysis, simulation and control of complex real-world systems spanning a wide range of disciplines including engineering, computer science, finance, biology and the natural world. [SM1m]
  2. Describe, classify and explain the mathematical techniques required to analyse, simulate and control systems modelled in state-space form. [SM2m, EA1m]
  3. Develop (i) linearised models of non-linear systems, and appreciate their limitations in the context of subsequent controller design, (ii) discrete-time models of continuous-time systems, appreciating the importance of such models in the context of modern controller implementation and the effect of sample rate upon closed-loop stability and performance. [SM5m, EA1m]
  4. Employ computational methods to perform the analysis, simulation and control system synthesis of systems modelled in state-space form. [EA3m, EA4p]
  5. For a simulation model of a real-world system, design, analyse and implement a multivariable output feedback controller in a simulation environment, and appraise the trade-offs between design decisions and system performance. [EA6m, D3m, EP3m]

This module satisfies the AHEP3 (Accreditation of Higher Education Programmes, Third Edition) Learning Outcomes that are listed in brackets after each learning outcome above. For further details on AHEP3 Learning Outcomes, see the downloads section of our accreditation webpage.



Introduction to state-space: State-space description of multivariable physical systems; continuous-time and sampled-data systems; Linear state-space description; Canonical state-space transformations; Linearisation and equilibrium points.

Analysis: Solution of state-space equations; State-transition matrix; Discretisation of continuous-time systems; Modal decomposition; Transfer functions of state-space systems. Structural Properties. Controllability; Observability; Stability; Minimal realisation; Stabilizability; Detectability.

Controller Design: State-feedback pole assignment; Linear Quadratic Regulator (Optimal control); Reference tracking, Integral control (state augmentation); Internal model principle.

Observer Design: Pole assignment; Separation principle; Kalman filter (Optimal estimation).

Teaching Methods

Learning and Teaching Methods

Lectures: 18 hours
Tutorials: 2 hours
Labs: 2 hours
Independent Study: 78 hours

Teaching Materials

Learning and Teaching Materials

All teaching materials will be available via MOLE.



2 hour written examination.

No resit examination is available for this module.



This module does not include marked assignments, but does involve interactive sessions between the Module Leader and all students as follows:

  • Tutorial Sessions are organised. These serve two purposes. Firstly, they offer students an opportunity to gain feedback by asking questions. Secondly, they enable the module leader to gauge the level of understanding amongst students, and adapt teaching as necessary.
  • A brief summary of how the class performed in the examination, both on the paper overall and on individual questions will be provided shortly after the examination board. Students may also request to view their scripts, in line with departmental procedures.
  • Coursework sessions are organised. Lab assistants will be on hand to respond to student queries concerning the coursework material.
Student Evaluation

Student Evaluation

Students are encouraged to provide feedback during the module direct to the lecturer. Students will also have the opportunity to provide formal feedback via the Faculty of Engineering Student Evaluation Survey at the end of the module.

Recommended Reading

Recommended Reading

Core texts:

  • K.J. Astrom and R.M. Murray, Feedback Systems – An Introduction for Scientists and Engineers (download:

Recommended texts:

  • Franklin, Powell and Workman, 1998, Digital Control of Dynamic Systems (3rd edition), Addison-Wesley, ISBN 0-201-33153-5. [Available in Information Commons, 629.895(F)]
  • Skogestad, S and Postlethwaite, I, 2005 Multivariable Feedback Control (2nd edition), Wiley, ISBN 978-0-470-01168-3. [Available in Information Commons, 629.8312(S)]

Additional texts:

  • Nise, N.S, 2011, Control systems engineering (6th edition), Wiley, ISBN 9780470646120 [Available in Information Commons, 629.8(N)]
  • Dorf, R.C and Bishop, R.H, 2008, Modern Control systems, 11th edition, Addison-Wesley [Available in Information Commons, 629.8312(D)]
  • Ogata, K, 2010, Modern control engineering, Prentice Hall, ISBN 0-13-261389-1 [Available in Information Commons, 629.8(O)]
  • Kuo, B.C and F Golnaraghi. M, F, 2009, Automatic control systems (9th edition), Prentice Hall, 13 978 0470 04896 2 [Available in Information Commons, 629.831(G)]
  • de Silva, C.W, 2009, Modeling and Control of Engineering Systems, CRC Press, Taylor and Francis, 978-1-4200-7686-8 Assessment [Available in Information Commons, 629.8(S)]