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Lecturer(s)
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Vašek Vladimír, prof. Ing. CSc.
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Matušů Radek, doc. Ing. Ph.D.
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Course content
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- Discrete control loop, main component properties, sampling unit, shaping unit, Z - transformation. - Modified Z - transformation, analogue part of disrete control loop, its Z ? transfer function, linear differential equation and its solution, Z ? transfer function of the discrete part of the discrete control loop, its programming, impulse characteristics, weighted matrix. - Z-transfer function algebra, transfer functions and signals in the closed discrete control loop, characteristic polynomial, characteristic equation, physical feasibility, steady-state valuwe. - Discrete control loop stability, stability conditions, standard stability criteria, bilinear transformation, stability criteria based on the characteristic equation of the control loop, modified Routh-Schur criterion, Schur algebraic criterion. - Discrete control loop synthesis, conditions, premises, discrete PID controllers, two and three-position controllers, manipulated value penalisation, methods of the integration and derivation compensation. - P, PD, PS, PSD controllers, compatibility with the analogue versions, modifications of PSD controllers, Takahashi PSD controller, wind-up effect, limitation of the manipulated value solving. - Sampling period definition, PSD controllers setting on the basis of the transfer characteristic, Ziegler-Nichols synthesis method for the first order proportional system. - Ziegler-Nichols synthesis method for the second order proportional system, required model synthesis method, pole placement method, value conformation method. - General linear controller, feedback control process, synthesis method based on the physical feasibility and stability condition. - Dead beat general linear controller, limitation of the manipulated value solving, discrete control loop with the disturbance measuring. - Algebraic theory discrete linear control, basic algebraic terms, polynomials, basic and special polynomial operation. - Diofantine equation, its solution, special solution methods. - BIBO stability, stability condition through the algebraic methods, stable-time optimal control synthesis. - Finite-stable-time optimal control synthesis, time optimal control with the limitation of the manipulated value synthesis.
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Learning activities and teaching methods
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Lecturing, Simple experiments, Exercises on PC, Practice exercises
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| prerequisite |
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| Knowledge |
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| It is assumed that the student has basic knowledge of college mathematic, physics and basics of automatic control, which is covered in the preceding semesters of studies. |
| It is assumed that the student has basic knowledge of college mathematic, physics and basics of automatic control, which is covered in the preceding semesters of studies. |
| learning outcomes |
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| - Explain the use of new elements necessary to create a discrete control circuit from a continuous control circuit |
| - Explain the use of new elements necessary to create a discrete control circuit from a continuous control circuit |
| - Explain the function of a discrete control circuit |
| - Explain the function of a discrete control circuit |
| - Explain the realization of the discrete model of the regulated system and the controller |
| - Explain the realization of the discrete model of the regulated system and the controller |
| - Popsat pravidla blokové algebry diskrétních regulačních obvodů |
| - Popsat pravidla blokové algebry diskrétních regulačních obvodů |
| - Explain the application of the discrete circuit analysis methods - the course of discrete circuit quantities, stability, |
| - Explain the application of the discrete circuit analysis methods - the course of discrete circuit quantities, stability, |
| - Define the conditions, assumptions and starting points for the synthesis methods of the discrete control circuit |
| - Define the conditions, assumptions and starting points for the synthesis methods of the discrete control circuit |
| - Describe the design of discrete controllers with a fixed structure - PSD controllers |
| - Describe the design of discrete controllers with a fixed structure - PSD controllers |
| - Define the nature of general linear regulators |
| - Define the nature of general linear regulators |
| - Describe the design methods of general linear controllers using classical methods of complex functions of complex variables |
| - Describe the design methods of general linear controllers using classical methods of complex functions of complex variables |
| - Describe the methods of designing general linear controllers using methods of algebraic discrete control theory |
| - Describe the methods of designing general linear controllers using methods of algebraic discrete control theory |
| Skills |
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| - Realize the identification of a real regulated system |
| - Realize the identification of a real regulated system |
| - Create a mathematical model of the identified system in both continuous and discrete areas |
| - Create a mathematical model of the identified system in both continuous and discrete areas |
| - Verify the created mathematical model with real measurements |
| - Verify the created mathematical model with real measurements |
| - Assess the stability of the designed discrete control circuit |
| - Assess the stability of the designed discrete control circuit |
| - Assess the physical feasibility of the designed discrete control circuit |
| - Assess the physical feasibility of the designed discrete control circuit |
| - Calculate the steady-state control deviation for any input signal shape |
| - Calculate the steady-state control deviation for any input signal shape |
| - Design a PSD controller for the given system |
| - Design a PSD controller for the given system |
| - Design a general linear controller using classical methods of a complex function of a complex variable |
| - Design a general linear controller using classical methods of a complex function of a complex variable |
| - Design a general linear controller using methods of algebraic discrete control theory |
| - Design a general linear controller using methods of algebraic discrete control theory |
| teaching methods |
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| Knowledge |
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| Simple experiments |
| Practice exercises |
| Exercises on PC |
| Exercises on PC |
| Simple experiments |
| Practice exercises |
| Lecturing |
| Lecturing |
| assessment methods |
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| Composite examination (Written part + oral part) |
| Composite examination (Written part + oral part) |
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Recommended literature
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Advanced Control with MATLAB & Simulink. 3rd ed. London : Ellis Horwood Limited, 1996. ISBN 013309667X.
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Balátě, J. Automatické řízení.
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Franclin, G.F. Feedback Kontrol of Dynamics Systéme. London, 2006.
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Kozák, Š. Lineárne číslicové systémy I. Bratislava : STU, 1991. ISBN 80-227-0767-8.
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Kučera, V. The Algebraic Approach to Control Systém Design. In: Polynomial Methods in Optimal Control and Filtering (K. J. Hunt, Ed.). . London, 1993.
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Kučera, Vladimír. Algebraická teorie diskrétního lineárního řízení. 1. vyd. Praha : Academia, 1978.
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Šulc, B., Vítečková, M. Teorie a praxe návrhu regulačních obvodů. Praha, 2004.
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Vašek, Vladimír. Teorie automatického řízení. Vyd. 1. Brno : Vysoké učení technické v Brně, 1990. ISBN 802140115X.
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