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Lecturer(s)
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Dušek František, doc. Ing. CSc.
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Kupka Libor, Ing. Ph.D.
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Course content
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1. Introduction to discrete control theory, discrete control circuits. Sampling of continuous systems, filtering, discrete models of continuous systems. 2. Z transform and inverse Z transform, difference equations. Transfer function models. Stability analysis of discrete systems. 3. Stochastic process and its statistically characteristics, ARX, ARMAX, OE and BJ model structures. Parameter model estimation ARX and ARMAX minimal squares method and estimation using correlation functions method. 4. Discrete controller, digital approximation of continuous PID. Optimization of discrete PID controller according to the selected criterion. 5. Design and implementation of digital control algorithms, selection of sampling period, aliasing. 6. Algebraic methods of discrete control theory. Selected operations with polynomials, polynomial fractions and matrices. Diophantine equation. 7. Digital controllers with optimized structure. Design of digital controller according to finite steps of regulation (weak, strong version). 8. Discrete state space description of the continuous system. The relationship between internal and external description of a dynamical system. 9. Introduction to observers. Full- and reduced-order Luenberger deterministic observers. 10. State feedback control, discrete state-space controller, pole placement method, Ackermann's formula. Adding an integral part to the controller, remove a permanent deviation. 11. Design of linear-quadratic optimal digital controller, Riccati equation. Control of time-delay systems. 12. Non-linear dynamic systems: its mathematical description, common types of nonlinearity, analysis in phase space, isocline method, analytical and numerical method. 13. Stability criteria for nonlinear systems, linearization methods.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Work with text (with textbook, with book), Methods of individual activities, Laboratory work
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Learning outcomes
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Students will acquire the state space analysis and the design of discrete controllers, including controllers based on the estimated states by using discrete time observer.
This course is designed to provide the students with a good understanding of the basics of discrete control circuits. The course includes basics principles of digital control: digital approximation of continuous PID controllers, design and implementation of digital controllers with optimised structure, state space controllers and state space observers. Students will learn the necessary mathematical foundations. They will learn basic theory of nonlinear systems.
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Prerequisites
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Basic knowledge of the theory of automatic control, identification and modeling of dynamic systems is needed.
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Assessment methods and criteria
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Oral examination, Written examination, Home assignment evaluation
The student will attend lectures and exercises and in addition student will work out an individual exercises.
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Recommended literature
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Balátě, Jaroslav. Automatické řízení. Praha: BEN - technická literatura, 2004. ISBN 80-7300-148-9.
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FRANKLIN, G.F., POWELL, J.D., WOEKMAN, M.L. Digital Control of Dynamic Systems (3. vydání). Stanford (USA): Prentice Hall, 1998. ISBN 0-201-82054-44.
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HANUŠ, B., OLEHLA, M., MODRLÁK, O. Číslicová regulace technologických procesů: algoritny, matematicko-fyzikální analýza, identifikace, adaptace. Brno: VUT, 2000. ISBN 80-214-1460-X.
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HAVLENA, V., ŠTĚCHA, J. Moderní teorie řízení. Praha: ČVUT, 2000. ISBN 80-01-02095-9.
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HLAVA, J. Prostředky automatického řízení II: analogové a číslicové regulátory, elektrické pohony, průmyslové komunikační systémy. Praha: ČVUT, 2000. ISBN 80-01-02221-8.
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KWAKERNAAK, H. Linear Optimal Control Systems. New York: John Wiley & Sons, 1972. ISBN 0-471-51110-2.
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RAZÍM, M., ŠTĚCHA, J. Nelineární systémy. Praha: ČVUT, 1997.
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Štecha, Jan. Teorie dynamických systémů. Praha: Vydavatelství ČVUT, 1999. ISBN 80-01-01971-3.
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