Course: Algebraic Methods Design

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Course title Algebraic Methods Design
Course code MTI/ASR
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
  • Mrázek Petr, Ing. Ph.D.
Course content
The Z-transform as the basic tool useful for description and analysis of dynamic systems is studied. Discrete performance models of continuous system, linear difference equations and their solutions. Polynomial methods of SISO control loop design. The basic operations with polynomials, solution of diophantine equations. Response valuation by means of quadratic criterion is studied as well and the way of its optimisation is discussed. This mathematical technique is consequently used as an algebraic tool in various applications.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Class attendance - 40 hours per semester
Learning outcomes
Discretization of LTI systems. Polynomial description, analysis and synthesis of control systems, polynomial operations, solution of diophantic polynomial equations. Formulation of quadratic functional and its optimization. Algebraic algorithm design of control and minimisation of quadratic functional.
This subject grants orientation and practical experience of special area of theory of control. It introduces into the methodology of algebraic synthesis of control circuit.
Condition of registration: Exam from the courses Automatic control and Digital control.

Assessment methods and criteria
Combined examination, Oral exam, Written exam

Recommended literature
  • -. Polynomial Toolbox Manual. PolyX,Ltd., Prague 1999.
  • Barnett, S. Polynomial and Linear Control Systems. Pure and Applied Mathematics, Marcel Dekker, New York 1983.
  • Gantmacher, F.R. The Theory of Matrices. Vols.I and II, Chelsea Publishing Company, New York 1960.
  • Chen, C.T. Linear Systems Theory and Design. Holt, Rinehart and Winston, New York 1984.
  • Kučera, V. Algebraická teorie diskrétního lineárního řízení. Academia, Praha 1978.
  • Kučera, V. Analysis and Design of Discrete Linear Control Systems. Pretice-Hall, London 1991.
  • Mordell, L.J. Diophantine Equations. Academic Press, London 1969.

Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Automatic Control and Applied Computer Science (2016) Category: Special and interdisciplinary fields 2 Recommended year of study:2, Recommended semester: Summer