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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
SSY310 - Automatic control
Syllabus adopted 2020-02-10 by Head of Programme (or corresponding)
Owner: TKKEF
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Major subject: Automation and Mechatronics Engineering, Engineering Physics

Teaching language: Swedish
Application code: 54113
Open for exchange students: No
Maximum participants: 80
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0113 Project 3,0c Grading: UG   3,0c    
0213 Examination 4,5c Grading: TH   4,5c   04 Jun 2021 pm J,  09 Oct 2020 pm J,  27 Aug 2021 am J

In programs

TKTEM ENGINEERING MATHEMATICS, Year 3 (compulsory elective)


Balazs Kulcsar

  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 analysis in one and several variables. Basic theory of matrices, in particular eigenvalues. Komplex numbers. Linear ordinary differential equations and transforms. Basic knowledge in mechanics, electricity as well as electronics for applications. Basic course in programming as a background for use of computer aids.


The purpose of this course is to introduce the concept of a dynamic system, and to demonstrate its application to different areas of technology. Yet another key concept is feedback and in particular the assessment of the stability of such a system. The course will teach theory and techniques for the design of both PID-controllers and state feedback controllers. Feedforward control will be adressed as well.

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

  • Understand and explain the purpose of linear control systems and basic control terminology.
  • Describe and explain the most important properties of linear dynamical systems.
  • Formulate models as dynamic systems, frequently encountered in a technical context. Formulate models as transfer/frequency functions, as state equations.
  • Transform in both directions between linear state equations and transfer/frequency functions, especially for single-input single-output systems. Linearize nonlinear state equations.
  • Analyse feedback systems, emphasizing stability assessment based on the Nyquist criterion. Formulating solutions to state equations, using state transition matrices.
  • Define and explain the principle of P-, I-, PI-, PD- and PID-controllers in a control loop, as well as being able to carry out design for such controllers, in particular by use of Bode plot techniques.
  • Analyse feedback systems, using sensitivity functions, particularly to estimate how large modelling errors a control system can handle without risking instability.
  • Describe and explain the feedforward, cascade control, and dead time compensation.
  • Explain and apply the concept of controllability and observability for the design of state feedback controllers and observers using the pole placement method.
  • Discretize analog systems, explain the function of a computer control system, and explain the sampling technique.


  • The course is a fundamental course in system dynamics and control (linear systems). State-space models for linear and nonlinear systems is introduced. Linearization of state equations and obtaining transfer functions.
  • Analysis of linear dynamical systems. Analysis of feedback systems. The Nyquist stability criterion. Root locus.
  • P-, I-, PI-, PD- and PID-controllers and their most important properties. Bode diagrams. Nichols charts. Non-minimum phase systems. Design of control systems, particularly using compensation in frequency domain. Sensitivity functions and robustness. Feedforward control, cascade control and dead time compensation.
  • Linear state space methodology. Stability. State transition matrices. Controllability and observability. State feedback controllers and observers. Output feedback control.
  • Computer controlled systems by sampling, and time discretization. Sampled transfer functions. A short introduction to linear quadratic control and Kalman filtering.


The course is divided into a series of lectures (in English), problem solving, and a
mandatory project including assignments and laboratory sessions.


Textbook and lecture notes. (Suggestions for literature will be given at the first lecture)

Examination including compulsory elements

Written exam with TH grading, project with assignments and laboratory sessions (pass/fail).

Page manager Published: Thu 04 Feb 2021.