ACS342 Feedback Systems Design 

Module Description (subject to change)

The module provides an introduction to the modelling, analysis and design of feedback control systems using classical control theory. The focus is linear time-invariant (LTI) systems in the continuous-time domain, although a brief introduction is also provided to digital controllers.

Credits: 10 (Spring semester)

Pre-requisites: EEE224 or equivalent

Module Leader

Paul Trodden

Dr Paul Trodden

Amy Johnson Building

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, or drop in to see me.

Learning Outcomes

Learning Outcomes

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

  1. Model simple electrical and electro-mechanical systems using ordinary differential equations and Laplace transforms. [SM2m, EA1m]
  2. Identify and evaluate transient and steady-state performance criteria. [EA1m, EA2m]
  3. Identify and quantify system stability. [EA1m, EA2m]
  4. Sketch root locus diagrams and Bode diagrams for systems. [EA1m, EA2m]
  5. Design phase lead and phase lag compensators using root locus and frequency domain methods. [EA1m, EA4m, D1fl]
  6. Tune a Proportional-Integral-Derivative (PID) controller. [EA1m, EA2m, D1fl]
  7. Describe the relationship between continuous-time and sampled-data control systems. [SM2m, EA1m]


This module includes the following topics:

  • Feedback control & module introduction
  • * What is "Feedback Systems Design"?
    * What is in this module?
  • System modelling
    * Modelling dynamic systems in the time domain
    * Modelling dynamic systems in the s-domain
  • Transfer functions and block diagrams
    * The transfer function
    * Obtaining the transfer function
    * Block diagrams
  • The system response to inputs and initial conditions
    * The inverse Laplace transform
    * Impulse and step response for systems with distinct real poles
    * More general cases
  • Stability
    * Introduction to stability; relation to pole locations
    * Assessing stability for first-, second- and higher-order systems (Routh Hurwitz)
  • Transient response: first- and second-order systems
    * System performance – the transient response
    * First-order transient response
    * Second-order transient response
  • Steady-state error analysis
    * Tracking error and disturbance rejection error
    * Steady-state error analysis
  • Integral action
    * Eliminating steady-state error with integral action
    * Integral action in the controller versus integral action in the plant: effect on tracking error, disturbance rejection error
  • Root Locus I
    * Effect of open-loop gain on closed-loop poles
    * Root locus construction (up to asymptotes)
  • Root Locus II
    * Root locus construction (break-away/-in points, axis intersections)
    * (Appendix) Departures from complex poles
  • Introduction to compensation
    * Selecting a K to meet a spec.
    * Geometry of the s-plane subject to a spec.
    * Intro. to first-order lead and lag compensators (definitions, idea that they can change poles and steady-state gain, passive networks)
  • Phase-lead compensation
    * Motivation
    * Dominant poles assumption
    * Design procedure using root locus
  • Phase-lag compensation
    * Motivation
    * Design procedure using root locus
  • Introduction to PID control
    * The effect of P, I, D on system response
    * PI/PD/PID controllers as ideal lead‒lag compensators
  • Introduction to frequency response
    * Motivation
    * System response to sinusoidal input
    * The frequency response function
  • Plotting frequency response on the Bode diagram
    * Definition; convention to plot open-loop response
    * Bode plots of canonical factors
    * Constructing Bode plots for more complicated systems
  • Closing the loop I
    * Motivation (inferring closed-loop stability from open-loop frequency response; the peril of phase shift)
    * Assessing absolute stability: Bode stability criterion
    * Assessing relative stability: gain and phase margin (definition, calculation, estimation from Bode plot)
  • Closing the loop II
    * Motivation (inferring closed-loop transient performance from open-loop frequency response)
    * Estimating overshoot, settling time from Bode plot
    * Closed-loop bandwidth; bandwidth–rise time relation
  • Lead compensator design using frequency response methods
    * Recap of lead/lag compensation
    * Frequency response and characteristics of lead compensator
    * Design procedure using Bode plot
    * Comparison with RL-designed compensator
  • Lag compensator design using frequency response methods
    * Frequency response and characteristics of lag compensator
    * Design procedure using Bode plot
    * Comparison with RL-designed compensator
  • Introduction to digital control I
    * Motivation
    * Sampled-data controller with continuous-time plant; the (ideal) A/D and D/A conversion operations
    * The z transform and pulse transfer function; inversion to difference equation
  • Introduction to digital control II
    * Indirect design: discretization of continuous-time controllers
    * Direct design: the Dahlin controller
    * Sampling rate selection
Teaching Methods

Learning and Teaching Methods

NOTE: This summary of teaching methods is representative of a normal Semester. Owing to the ongoing disruption from Covid-19, the exact method of delivery will be different in 2020/21.

  • Lectures: 24 hours
  • Office Hours: 12 hours
  • Independent Study: 64 hours
Teaching Materials

Learning and Teaching Materials

All teaching materials will be available via blackboard (MOLE).



Formal examination 100% (2 hours; answer all 7 questions: 5 short questions, 2 long questions).

No resit examination is available for this module.



  • Formative assessment in this module is via problem sheets, which the students attempt to answer and bring to organized and interactive tutorial classes. In the latter, students have the opportunity to receive support and feedback on their work. Moreover, the module leader has the opportunity to listen to general feedback about the module and the way it is taught, and, if necessary, take action.
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.

You can view the latest Department response to the survey feedback here.

Recommended Reading

Recommended Reading

[1] K. Ogata, Modern control engineering, 5th rev. ed. Upper Saddle River :: Prentice Hall, 2009.

[2] N. S. Nise, Control systems engineering, 6th ed., International student version. Hoboken, N.J. :: Wiley, 2011.

[3] R. C. Dorf, Modern control systems, Twelfth edition, Pearson new international edition. :: Pearson, 2014.

[4] M. F. Golnaraghi and B. C. Kuo, Automatic control systems, 9th ed. Hoboken, NJ  :: Wiley, 2010.

[5] G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback control of dynamic systems, Seventh edition. Upper Saddle River, N.J. :: Pearson/Prentice Hall, 2015.

[6] K. J. Åström and R. M. Murray, Feedback systems : an introduction for scientists and engineers. Princeton :: Princeton University Press, 2008.