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Lecturer(s)
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Dušek František, doc. Ing. CSc.
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Course content
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1. Introduction: system (structure, behavior, description), automatic control (regulation and control, forward and feedback, stability and quality), auxiliary tools (MATLAB / SIMULINK) 2. Mathematical models (static and dynamic systems, systems with distributed parameters, time invariant system, steady state, static characteristic, transport delay), mathematical modeling, linear model and linearization 3. Laplace transform, definition, properties, vocabulary 4. Linear differential equations, solution using LT, transfer function, block algebra 5. Linear single and multidimensional models, autonomy and invariance, input / output and state description, characteristics of the system in time and frequency domain. 6. State description, transformation between input / output and state description, state observer 7. Stability of linear dynamic systems (differential equations, transfer function, state description) 8. Closed loop control, stability and quality, critical gain and period, amplitude and phase safety. 9. Fixed Structure Controllers (PID), Types, Properties, Modifications (2DOF, Filtration of Derivatives, Anti Windups) 10. PID controller setting methods (from transition characteristics, from critical values, from approximation transmissions) 11. Principle of controller design by algebraic approach (diophantine equation, asymptotic tracking) 12. Principle of state controller design (basic problem, Riccati equation, finite and infinite interval) 13. LQ controller, monitoring of the desired, principle of LQG controller (state estimation in the presence of noise - Kalman filter) Timetable and content of the exercises: 1.-3. Exercise - Mathematical modeling - linear system (thermal and electrical) and nonlinear system (hydraulic and mechatronic), identification (of differential equation parameters) and simulation - Using the MATLAB/SIMULINK environment for solving and simulating system behavior, numerical solution of differential equations 4. Exercise - Linear differential equations and LP transformation, transfer of linear dynamic system, block algebra 5. Exercise - Characteristics in time and frequency domain, support in MATLAB, measurement of transient and frequency characteristics of RC4 system 6. Exercise - State observer, support in MATLAB, implementation in SIMULINK 7. Exercise - Autonomy and invariance MIMO - static compensator, stability and safety 8. Exercise - PID - modification, behavior simulation 9. Exercise - PID - adjustment methods, determination of critical values 10. Exercise - PA controller - design, modification and simulation of URO, solution of Diophantine equation 11. Exercise - LQ controller - basic design, task of monitoring desired and URO simulation 12th exercise - LQG controller - estimator design as a dual problem, Kalman filter
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Demonstration, Laboratory work
- Term paper
- 35 hours per semester
- Participation in classes
- 65 hours per semester
- Preparation for an exam
- 30 hours per semester
- Home preparation for classes
- 50 hours per semester
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Learning outcomes
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The aim of the course is to acquaint students with mathematical models of linear dynamic systems in continuous area (description, properties, identification), closed loop control (properties, stability and safety, quality). Furthermore, fixed-structure controllers (PID properties, modifications and settings) and selected more complex controllers (PA, LQ) based on linear dynamic model (design principle, properties, parameter selection).
The student demonstrates basic knowledge of mathematical modeling and design of controllers. He can create and work with a mathematical description of continuous linear dynamic systems. He is able to design and set up control loops with both PID and more complex controllers.
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Prerequisites
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The knowledge of mathematics and physics at the basic level of university mathematics is assumed.
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Assessment methods and criteria
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Oral examination, Home assignment evaluation, Discussion
Based on the assignment, the student will prepare three written seminar papers, which will be submitted during the exam - seminar paper A mathematical modeling - seminar paper B experimental identification - seminar paper C regulation The exam is oral. The first part is a discussion of the seminar paper, where the student shows the results and explains the solution procedure. In the second part of the exam, the student will be given one question related to one of the topics of lectures 2 to 12.
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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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Dorf, Richard C. Modern control systems. Menlo Park: Addison-Wesley, 1998. ISBN 0-201-30864-9.
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Mikléš, J., Fikar, M. Modelovanie, identifikácia a riadenie procesov I.. Bratislava, 1999. ISBN 80-227-1289-2.
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VÍTEČKOVÁ, M., VÍTEČEK, A. Základy automatické regulace. Ostrava: VŠB TU, 2008. ISBN 978-80-248-1924-2.
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