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Syllabus for

Academic year
SSY051 - Automatic control  
Syllabus adopted 2021-02-26 by Head of Programme (or corresponding)
Owner: TKAUT
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Main field of study: Automation and Mechatronics Engineering, Electrical Engineering, Biomedical engineering

Course round 1

Teaching language: Swedish
Application code: 47126
Open for exchange students: No
Block schedule: D+
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 5,5 c Grading: TH   5,5 c   26 Oct 2021 pm J,  05 Jan 2022 pm J,  26 Aug 2022 am J  
0207 Laboratory 2,0 c Grading: UG   2,0 c    

In programs

TKTEM ENGINEERING MATHEMATICS, Year 3 (compulsory elective)


Bengt Lennartson

  Go to Course Homepage


General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Mathematical concepts that the student must master before starting the course are:

- Complex numbers
- Linear algebra
- Taylor expansions
- Ordinary differential equations

It is also assumed that the student has basic knowledge about the fundamental physical relations that are necessary to formulate energy, force and material balances.


The aim of the course is to help students to understand how control might be used to analyze, design and implement control functions for technical systems. Furthermore, the aim of the course is to widen the student s perspective on technical systems by understanding how mechanics, electronics, computers, and control interact. This insight gives a system perspective, which might be used to improve and develop new products and systems that offer new functionality, increased performance, and is more environmentally friendly.

Learning outcomes (after completion of the course the student should be able to)

apply control engineering analysis and design methods. This knowledge could be used to systematically solve basic control problems. More specifically, the student should be able to:

  • Define the control problem.

  • Define feedback and feedforward.

  • Describe and explain the most important properties of linear systems.

  • Understand how the frequency content of a signal could be analyzed.

  • Formulate a dynamic model for basic mechanical and electrical systems.

  • Understand how the Laplace transform could be used to analyze dynamical systems.

  • Explain the possibilities and limitations of state-space models and transfer functions.

  • Transform between state-space models and transfers functions, when possible.

  • Compute linear approximations of non-linear models and understand the limitations of the non-linear model.

  • Analyze the stability properties of linear dynamic systems and analyze the closed-loop systems stability properties based upon the Nyquist-criterion.

  • Understand how feedback and feedforward can be used to decrease the influence from process disturbances and measurement noise and parameter variations in the controlled process, and also understand the limitations of feedback and feedforward.

  • Design controllers that fulfills given specifications given as performance, robustness- and stability margin requirements.

  • Analyze and evaluate different controller structures, mainly P, PI, PD, PID and state-feedback controllers.

  • Implement the designed controller in a computer and understand sampling and its consequences.

  • Use modern computer tools to facilitate analysis, design, and evaluation of dynamical systems.


  • Content

    Introduction: Examples of control problems, dynamic systems, open and closed loop control, compensation of disturbances, servo functions. Dynamic models: Transfer functions, block diagrams, transient and frequency analysis, Bode plots. Principles of construction of dynamic models for technical systems. Special attention is paid to similarities between systems from completely different technical areas. State-space models, relation to transfer functions, linearization and simulation. Analysis of feedback systems: Stability, the Nyquist criterion, stability margins, sensitivity and robustness with respect to parameter uncertainties and unmodeled dynamics. Performance and accuracy, transient and stationary performances, specification in the time and frequency domains. Design of control systems: Fundamental principles of controller design, possibilities and limitations depending on interference between different frequency regions. Design of PI and PID controllers, cascade and feedforward control. Design of controllers based on state-space models, controllability and observability, state feedback control. Implementation: Brief theory of discrete-time systems, digital implementation based on analogue design, bump-less transfer when starting and handling control signal limitations. Laboratory session: Tuning of a PID controller for a tank process. Assignments: Assignments that are solved by mainly using Matlab.


    Lectures, group exercises, laboratory session in the department lab, and mandatory home assignments solved in groups of two.


    B Lennartson: Reglerteknikens grunder, Studentlitteratur, 2002. (In Swedish) Reglerteknikens grunder - övningstal + lösningar, compendium (In Swedish) Reglerteknikens grunder - formelsamling, compendium (In Swedish). Other material, see course home page.

    Examination including compulsory elements

    Written examination, approved laboratory lessons and home assignments.

    The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

    Page manager Published: Mon 28 Nov 2016.