Lecturer(s)


Navrátil Pavel, Ing. Ph.D.

Prokop Roman, prof. Ing. CSc.

Pekař Libor, Ing. Ph.D.

Course content

 History, basic concepts and notions, personalities, systems, signals.  Feedback systems, control objectives and loops, , discrete and continuoustime systems.  Linear continuoustime 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 nonhomogeneous 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.  Nonlinear, 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 inputoutput and multivariable continuoustime 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.

Prerequisites

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 sixpoint 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. AddisonWesley, 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.
