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Lecturer(s)
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Course content
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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.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 40 hours per semester
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Learning outcomes
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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.
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Prerequisites
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Condition of registration: Exam from the courses Automatic control and Digital control.
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Assessment methods and criteria
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Combined examination, Oral exam, Written exam
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Recommended literature
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-. Polynomial Toolbox Manual. PolyX,Ltd., Prague 1999.
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Barnett, S. Polynomial and Linear Control Systems. Pure and Applied Mathematics, Marcel Dekker, New York 1983.
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Gantmacher, F.R. The Theory of Matrices. Vols.I and II, Chelsea Publishing Company, New York 1960.
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Chen, C.T. Linear Systems Theory and Design. Holt, Rinehart and Winston, New York 1984.
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Kučera, V. Algebraická teorie diskrétního lineárního řízení. Academia, Praha 1978.
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Kučera, V. Analysis and Design of Discrete Linear Control Systems. Pretice-Hall, London 1991.
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Mordell, L.J. Diophantine Equations. Academic Press, London 1969.
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