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Lecturer(s)
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Vašek Vladimír, prof. Ing. CSc.
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Pekař Libor, doc. Ing. Ph.D.
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Navrátil Pavel, Ing. Ph.D.
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Course content
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1. Automatic control - logic control, continuous control of continuous physical quantities, discrete control of continuous physical quantities - basic concepts and principles. 2. Simple continuous control loop (CL), its components, description of quantities, general properties of controlled systems. Mathematical model of part of the CL and the whole CL. Linearity, linearization methods. 3. The concept of differential equations. Solution of a differential equation. Cauchy's problem. Ordinary differential equation of the 1st order. Separable ordinary differential equation of the 1st order. Linear non-homogeneous ordinary differential equation of the 1st order. Examples of systems described by these equations. 4. Ordinary differential equation of nth order. Basic concepts and properties. Homogeneous linear ordinary differential equation of nth order with constant coefficients. Characteristic equation. Non-homogeneous linear ordinary differential equation of nth order with constant coefficients. Solution methods. Examples of systems described by these equations. 5. Set of ordinary differential equations of the 1st order with constant coefficients. Eigenvalues. Eigenvectors. Stability of solving a system of ordinary differential equations of the 1st order. 6. Laplace transform. Definition and basic properties of Laplace transform. Inverse Laplace transform. Laplace transform table. Solution of ordinary differential equations using Laplace transform. Concept of discrete function, application, definition and basic properties of Z-transformation, Z-transformation table. 7. Transfer function. Description of the basic open and closed CL. Transfer functions and signals in a CL. Block algebra of continuous systems. 8. Description of properties of proportional, integral and derivative members of the CL (ideal, with 1st order inertia, with 2nd order inertia), differential equations, transfer functions, step responses. 9. Description of properties of ideal P, I, D controllers, their combinations, basic properties, differential equations, transfer functions, step responses. 10. Methods of analysis of a continuous CL - feasibility, stability, steady-state control error. 11. Methods of synthesis of continuous CL with PID controllers. 12. Detailed scheme of the discrete CL; principle of operation, continuous quantities, sequences of discrete values, numerical quantities, sampling and shaping term. 13. Discrete PID controllers, interpretation of its individual components, design of a digital controller by the desired model method. 14. Principles of other CLs - multi-parameter, extremal, branched circuits, Smith predictor, with internal model, adaptive controllers, robust control.
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Learning activities and teaching methods
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Lecturing, Methods for working with texts (Textbook, book), Simple experiments, Exercises on PC, Teamwork, Individual work of students, Educational trip
- Educational trip
- 6 hours per semester
- Home preparation for classes
- 28 hours per semester
- Preparation for course credit
- 16 hours per semester
- Participation in classes
- 70 hours per semester
- Preparation for examination
- 32 hours per semester
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| prerequisite |
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| Knowledge |
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| Basic knowledge of mathematics and physics at the level of the 1st semester of university. |
| It is assumed that the student has basic knowledge of college mathematics and physics which is covered in the first three semesters of studies. |
| It is assumed that the student has basic knowledge of college mathematics and physics which is covered in the first three semesters of studies. |
| Basic knowledge of mathematics and physics at the level of the 1st semester of university. |
| learning outcomes |
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| - Explain the function of the control circuit |
| - Explain the function of the control circuit |
| - Explain the realization of the model of the regulated system and the controller |
| - Explain the realization of the model of the regulated system and the controller |
| - Describe the rules of the block algebra of control circuits |
| - Describe the rules of the block algebra of control circuits |
| - Explain the application of methods of circuit analysis - the course of circuit quantities, stability, causality |
| - Explain the application of methods of circuit analysis - the course of circuit quantities, stability, causality |
| - Define the conditions, assumptions and starting points for the synthesis methods of the control circuit |
| - Define the conditions, assumptions and starting points for the synthesis methods of the control circuit |
| - Describe the design of controllers with a fixed structure - PID controllers |
| - Describe the design of controllers with a fixed structure - PID controllers |
| - Define the nature of general linear regulators |
| - Define the nature of general linear regulators |
| 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 a continuous area |
| - Create a mathematical model of the identified system in a continuous area |
| - Verify the created mathematical model with real measurements |
| - Verify the created mathematical model with real measurements |
| - Assess the stability of the designed control circuit |
| - Assess the stability of the designed control circuit |
| - Assess the physical feasibility of the designed control circuit |
| - Assess the physical feasibility of the designed control circuit |
| - Design a PID controller for a given system using different methods |
| - Design a PID controller for a given system using different methods |
| teaching methods |
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| Knowledge |
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| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Individual work of students |
| Individual work of students |
| Simple experiments |
| Simple experiments |
| Exercises on PC |
| Exercises on PC |
| Teamwork |
| Teamwork |
| Educational trip |
| Educational trip |
| Lecturing |
| Lecturing |
| assessment methods |
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| Analysis of seminar paper |
| Composite examination (Written part + oral part) |
| Composite examination (Written part + oral part) |
| Preparation of a presentation, giving a presentation |
| Preparation of a presentation, giving a presentation |
| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Analysis of seminar paper |
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Recommended literature
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BALÁTĚ, J. Automatické řízení. BEN Technická literatura, Praha, 2004.
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CORRIOU, J.-P. Process Control: Theory and Applications. London, 2010. ISBN 978-1-84996-911-6.
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FRANKLIN, G.F., POWEL, J.D., EMAMI-NAEINI, A. Feedback Control of Dynamics Systems.
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NAVRÁTIL, P. Automatizace, vybrané statě. FAI,UTB ve Zlíně, 2011.
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OSTRAVSKÝ, J. Diferenciální počet funkce více proměnných. Nekonečné číselné řady. UTB Zlín, 2007.
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REKTORYS, K. a spol. Přehled užité matematiky I, II. Praha: Prometheus, 1995.
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ŘEZNÍČKOVÁ, J. Diferenciální rovnice. FAI UTB Zlín, 2008.
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ŠVARC, I. Automatizace/Automatické řízení. VUT v Brně, 2005.
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VAŠEK, V. Teorie automatického řízení II. Skripta FT VUT.
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VÍTEČKOVÁ, M., VÍTEČEK, A. Základy automatické regulace. VŠB TU Ostrava, 2008.
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