Course objectives:
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The aim of of the course is to become acquainted with the fundamental principles of non-linear dynamic systems and systems with static nonlinearities.
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Requirements on student
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Credit prior to exam: Elaborate one semestral work.
Exam: Oral and written examination on the subject is requested.
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Content
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Linear and nonlinear models of causal processes. Nonlinear causal system representations and causal separability. Basic notions of differential geometry and Lie algebras of vector fields. Lyapunov functions, stability, controllability and observability of NS. Approximative and exact linearization (by state and feedback equivalence), pseudolinearization. Passivity and dissipativeness of NS. Principles of stabilization and control of nonlinear systems.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Practical training (number of hours)
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26
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Contact hours
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39
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Preparation for an examination (30-60)
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47
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Preparation for comprehensive test (10-40)
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34
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Presentation preparation (report) (1-10)
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10
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Total
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156
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
rozpoznat lineární systém |
analyzovat jeho typické druhy chování ve fázovém prostoru |
vyšetřit stabilitu a navrhnout stabilizující regulátor metodou přiřazení pólů |
vyřešit soustavu lineárních diferenciálních rovnic |
využít popisu systému ve frekvenční oblasti |
prokázat znalosti z frekvenčních kritérií stability |
prokázat základní znalosti z lineární algebry |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
analyzovat vlastnosti a chování lineárních systémů |
vyšetřit stabilitu lineárního systému |
pracovat s popisem systému s využitím diferenciálních rovnic nebo ve formě stavového popisu |
aplikovat Laplaceovu transformaci |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
základní práce s nelineárními systémy, zejména s možnostmi chování nelinárního systému, problémy a základní možnosti vyšetření stability |
z oblasti Lyapunovovy teorie stability |
z oblasti teorie Absolutní stability |
z možností analýzy nelineárního systému 2.rádu |
Skills - skills resulting from the course: |
v možnostech analýzy chování nelineárního systému na základě Jakobiho linearizace, linearizace podél trajektorie, zpětnovazební linearizace |
v možnostech využití Lyapunovovy teorie stability |
v možnostech aplikace frekvenčních metod, především Absolutní stability |
možnostech analýzy chování nelinárního systému ve fázovém prostoru |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Competences - competence achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Task-based study method |
Practicum |
Individual study |
Skills - the following training methods are used to achieve the required skills: |
Interactive lecture |
Task-based study method |
Practicum |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Task-based study method |
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