ACS214 Discrete Systems

Module Description

This unit covers methods to represent, analyse and design linear dynamic systems of first or higher order in the discrete domain. This particular module will allow students to discover why digitisation may be needed and how it would be implemented on modern systems, industrial or life-science based. Sampling via Shannon-Nyquist, aliasing, sample holding (data extrapolation), the manipulation of the algebra relating to discrete blocks in open and closed loops, absolute/relative stability and finally the digital control designs will allow students to draw parallels with similar topics already covered in the continuous domain. In addition to this theme, the unit will also include lectures on the principles of sensors and instrumentation, actuation, digital data acquisition, signal pre-processing and hardware interfaces with an emphasis on AD/DA conversions.

Credits: 20 (Academic Year)

Module Leader

Mahdi MafoufProfessor Mahdi Mahfouf
Room D07, Amy Johnson Building

If you have any questions about the module please talk to us 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 one of us via email, or drop in to see one of us.

Other teaching staff

Dr Osman TokhiDr Osman Tokhi, Room C02, Amy Johnson Building,

Learning Outcomes

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

  1. Appreciate the importance and integral role of digitisation in modern technologies from the viewpoint of systematic manipulation of information, including industrial & life sciences applications as well as research, and get to grips with the general idea behind digital systems, their pros and cons, as well as the constraints relating to their implementations across sectors. [EA4p]
  2. Understand the theory of information by highlighting how the optimal selection of the sampling interval helps avoid ‘aliasing’, and explain how this methodology, combined with the appropriate use of digital hardware and interfacing, can help avoid loss of information in modelling (including system identification), digital signal processing, and digital control. [EA1m]
  3. Assess the hardware and software requirements to realise digital as well as hybrid (analogue and digital) loops in off-line and real-time modes for acquiring open/closed loop data, analyse the data in the digital domain using the appropriate mathematical tools and design and implement digital control solutions to achieve performance criteria that include stability as well as economic factors (e.g. energy savings). [EA2m, EA3m, EA4m, ET2p, D1m]
  4. Propose design methodologies in analogue and digital domains and form a ‘critic’ as to the merits of both, and assess particularly whether the move between such domains generated any changes with respect to the original information, its quality and also the overall system’s performance using specific design quantitative as well as qualitative design and analysis criteria including statistical metrics. [D3m]
  5. Be able to describe the basic principles of sensors, signal conditioning, interfaces, and actuation hardware used in the design of modern control system/mechatronic systems applications. [EA1p, EA2p, EA4p]
  6. Be able to implement simple motor control algorithms for use in modern control system /mechatronic systems applications. [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 this webpage.


  • Introduction to mechatronic systems.
  • Sensors/transducers: principles of position, motion and process variable measurement.
  • Actuation: DC motors, servo motors, and stepper motors.
  • Interfacing: Operational amplifiers, differential amplifiers, A/D and D/A conversion, signal conditioning.
  • PID control: Terminology, effects of P, I and D actions, classical form of PID controller and discrete implementation.
  • Introduction to sampled-data systems. The Shannon-Nyquist Theorem.
  • Relationship of sampling to z-transform. The inverse z-transform. Algebra associated with system diagrams.
  • Mapping between the s-plane and the z-plane.
  • Data extrapolators using Zero-Order Hold, the first-order extrapolators. Bilinear (Tustin) transformation.
  • Impulse transfer function.
  • Analysis of absolute stability of sampled-data systems using the Hurwitz and Jury tests.
  • Analysis of relative stability using digital root-locus and frequency domain methods.
  • Compensator design using root-locus and frequency domain methods.

Learning and Teaching Methods

Lectures: 24 hours
Problem Solving Classes: 6 hours
Laboratory Cases: 6 hours
Independent Study: 162 hours

Learning and Teaching Materials

All teaching materials will be available via MOLE.


One two-hour written examination: 60%
Continuous assessment: 40%
(a) Computer Aided Control System Analysis and Design using MATLAB (20%)
(b) Computer Control of a Stepper Motor Unit (10%)
(c) Real-time PID Control Mechatronic System (10%)


Comments on Assignment (Turn-it-in)

Students will have the opportunity to obtain feedback on their progress via the interactive laboratory sessions, two 40-minute exams as well as tutorial sessions.

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

Core Texts:

  • Ogata K. Modern Control Engineering (5th Edition), Prentice Hall, 2009 [Available in Information Commons, 629.8 (O)]
  • DeSilva CW. Mechatronics: A Foundation Course, CRC Press, 2010 [Available in Information Commons, 629.89 (S)]

Secondary Texts:

  • Stefani RT; Shahian B; Savant CJ and Hostetter GH. Design of Feedback Control Systems, (4th Edition), Oxford University Press, 2001 [Available in Information Commons, 629.83 (D)]
  • Golnaraghi F, Kuo BC. Automatic Control Systems (9th Edition), John Wiley, 2009 [Available in Information Commons, 629.831 (G)]
  • Leigh JR. Applied digital control: theory, design and implementation, (2nd Edition), Dover Publications, 2006
  • Dorf RC and Bishop RH. Modern Control Systems (11th Edition), Prentice-Hill, 2007
  • Paraskevopoulos PN. Digital control systems, Prentice Hall, 1996
  • Acarnley P. Stepping Motors: guide to modern theory and practice, (4th Edition), Institution of Electrical Engineers, 2002
  • Gayakwad R. Op-Amps and linear integrated circuits, (4th Edition), Prentice Hall, 1999
  • Hill W and Horowitz P. The Art of Electronics, Cambridge University Press, 1998
  • Basak A. Analogue Electronic Circuits and Systems, Cambridge University Press, 1991
  • Kenjo J. Stepping Motors and their Microprocessor Controls, (2nd Edition), Oxford University Press, 1994
  • Stanley WD. Operational Amplifiers with Linear Integrated Circuits, (4th Edition), Prentice Hall, 2001
  • Bennett S. Real-time Computer Control, Prentice Hall, (2nd Ed), 1994
  • Tanenbaum AS. Structured Computer Organisation, (5th Ed), Prentice Hall, 2005

Peripheral Texts:

  • Omondi AR. Computer Arithmetic Systems, Prentice Hall, 1994