Course: System Theory

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Course title System Theory
Course code AUART/A5TES
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech, English
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Navrátil Pavel, Ing. Ph.D.
  • Prokop Roman, prof. Ing. CSc.
  • Pekař Libor, doc. Ing. Ph.D.
Course content
- History, basic concepts and notions, personalities, systems, signals. - Feedback systems, control objectives and loops, , discrete and continuous-time systems. - Linear continuous-time systems ( LCTS), properties and linear differential equations. - Laplace transforms (LT), properties, solution of differential equations by LT. - Solution of differential equations by LT. Transfer functions (TF). - State space (SS) descriptions. Various choose of state variables. - Transfer of TF description to SS one and vice versa. Realization and singular systems. - Fundamental matrices of SS, solution of state space equation. - Solution of non-homogeneous state equation. - Lyapunov and BIBO stability, stability regions, criteria of stability. - System properties (controllability, observability,...). Multivariable systems. - State space (Luenberger) observer. Reconstruction of state variables. - State feedback. Ackermann formula. - Non-linear, adaptive and robust systems (an overview).

Learning activities and teaching methods
Methods for written tasks (e.g. comprehensive exams, written tests), Demonstration, Exercises on PC, Individual work of students
Learning outcomes
The course is focused on basic properties on dynamical systems. The emphasis is laid on single input-output and multivariable continuous-time linear sytems. The attention covers state space as well as transfer function description, realizations, feedback and stability concepts and other properties of systems. Tools and notions of algebra and differential calculas are used. The knowledge of the course is necessary for understanding ofmodern control and cybernetic engineering.
The student has knowledge about following items: external and internal description, state variable, state space descriptions, transfer function description, realizations of state space models, transformations of various descriptions, stability concepts and criteria, system properties (controllability, observability,...), reconstruction and estimation of state variables, feedback and control, controller design. The graduate is qualified for analysis, design and simulation of control systems at bachelor level.
The course goes on to the course Automation. Also, knowledge of Mahematics I and Mqathematics II is necessary.

Assessment methods and criteria
Analysis of seminar paper, Analysis of a presentation given by the student, Composite examination (Written part + oral part)

Compulsory 80 % attendance at exercises, passing out two tests during semester out of which 60 % is minimum requirement. Examination consists of two parts, a written part with questions and examples (maximum 20 points) and a theoretical part (maximum 20 points). A student must gain at least 20 points from both parts together. The result of a subject examination is expressed on a six-point scale: A "výborně" (i.e. "excellent"), B "velmi dobře" (i.e. "very good"), C "dobře" (i.e. "good"), D "uspokojivě" (i.e. "satisfactory"), E "dostatečně" (i.e. "sufficient"), F "nedostatečně" (i.e. "fail").
Recommended literature
  • Dorf, R.C., Bishop, R. Modern Control Systems. Addison-Wesley, Menlo Park, California, 1998.
  • Kailath, T. Linear Systems. Prentice Hall, Englewood Cliffs, 1980.
  • OGATA, K. Modern Control Engineering. Prentice Hall, 2002.
  • Prokop, R. Základy automatizace pro bakalářské studium. Brno : VUT, 1998.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester