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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
SSY050 - Automatic control
Owner: TKAUT
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: B

Teaching language: Swedish

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0105 Examination 4,0 c Grading: TH   4,0 c   29 May 2007 am M,  16 Jan 2007 pm V,  23 Aug 2007 pm V
0205 Laboratory 1,0 c Grading: UG   1,0 c    

In programs

TKIEK INDUSTRIAL ENGINEERING AND MANAGEMENT - Systems and mathematics, Year 2 (compulsory)


Professor  Bengt Lennartson


For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

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 widen their perspective on technical systems by understanding how mechanics, electronics, computers, and control interact. Further more, the aim of the course is to help the student get a systems perspective where the student understand the value of integrated control and mechanical/electrical design. These insights could be used to improve and develop new products that offer new functionality, increased performance, and is more environmentally friendly.
The course uses knowledge from fundamental courses in mathematics, mechanics, electric circuits and computer programming, and will prepare the student for further studies in subjects where fundamental knowledge in dynamical systems and control engineering is required.


After finishing the course the student will have basic knowledge in 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:

Formulate a dynamic model for basic mechanical, electrical and chemical systems.
Compute linear approximations of non linear models and understand the limitations of the non-linear model.
Understand how the Laplace transform could be used to analyze dynamical systems.
Understand how feedback and feedforward can be used to decrease the influence from process- and measurements disturbances and parameter variations in the controlled process, and also understand the limitations of feedback and feedforward.
Specify performance, robustness, and stability-margin requirements on the controlled system.
Design basic controllers that satisfy the given requirements.
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.


Introduction: Examples of control problems, dynamic systems, open and closed loop control, compensation of disturbances, servo functions, treatment of parameter variations.

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 models, linearisation and simulation.

Analysis of feedback systems: Stability, the Nyquist criterion, stability margins, sensitivity and robustness with respect to parameter uncertainties and non-modelled 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 areas. Design of PI and PID controllers, different control structures such as one and two degrees of freedom, cascade and feedforward. Design of controllers based on state space models, controllability and observability, state feedback.

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, compendium (In Swedish)
Reglerteknikens grunder - formelsamling, kompendium (In Swedish).
Other material, see course home page.


Written examination, approved laboratory lessons and home assignments.

Page manager Published: Thu 04 Feb 2021.