Nonlinear Systems of Automation Control (ETF AEO NSU 4760) |
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General information |
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Module title | Nonlinear Systems of Automation Control |
Module code | ETF AEO NSU 4760 |
Study | ETF-B |
Department | Control and Electronics |
Year | 1 |
Semester | 1 |
Module type | Mandatory |
ECTS | 7 |
Hours | 60 |
Lectures | 36 |
Exercises | 10 |
Tutorials | 14 |
Module goal - Knowledge and skill to be achieved by students |
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| Course objective is to give students knowledge that refer to concepts and methods used in analysis and synthesis of nonlinear systems of automation control, and to develop the capability of using these concepts in specific cases. An emphasis is put on understanding mathematical descriptions of physical laws, stability problems, as well as problems of tracking and response to external excitations in nonlinear systems of automation control. <br> |
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Syllabus |
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| 1. Introduction. <br> 2. Definition and description of nonlinear systems. <br> 2.1 Nonlinear transfer elements. <br> 2.2 Description of nonlinear dynamic systems in state-space. <br> 2.3 Correlations between nonlinear transfer elements and nonlinear descriptions in state-space. <br> 3. Stability of nonlinear transfer elements. <br> 4. Stability of equilibrium state in state-space. <br> 4.1 Equilibria of dynamic systems. <br> 4.2 Transformations in equilibria. <br> 4.3 Stability in terms of Lyapunov. <br> 4.4 Stability analysis in phase plane. <br> 5. Stability criteria in equilibria states. <br> 5.1 Direct method of Lyapunov. <br> 5.2 La Salle's theorem. <br> 5.3 Construction of Lyapunov functions. <br> 5.4 First convergence method. <br> 5.5 Stability analysis of standard nonlinear contour equilibrium (Popov criterion and circle criterion). <br> 6. Limit cycles in standard nonlinear contours. <br> 6.1 Linear and nonlinear oscillations. <br> 6.2 Determination of limit cycles existence using Poincare-Bendix theorem. <br> 6.3 Limit cycles stability. <br> 6.4 Analysis of standard nonlinear contours using harmonic balance method. <br> 7. Empirical analysis of stability. <br> 8. Consideration of input signal constraints problem in controller design. <br> |
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Literature |
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| Recommended | 1. Lecture notes and slides (will be available at the Web site) <br> 2. Mujo Hebibovic: "Teorija automatskog upravljanja", Elektrotehnicki fakultet Sarajevo 2003.godine. <br> 3. Adnan Tahirovic, Mujo Hebibovic: "MATLAB u teoriji automatskog upravljanja-praktikum za laboratorijske vježbe", ETF u Sarajevu 2002.godine. <br> 4. Z. Vukic, Lj. Kuljaca: "Automatsko upravljanje-analiza linearnih sustava", Kigen, Zagreb 2005.godine. <br> 5. Milic Stojic: Kontinualni sistemi automatskog upravljanja, Naucna knjiga Beograd. <br> 6. Tugomir Ćurina: Automatska regulacija, Školska knjiga Zagreb. <br> 7. Thaler G.J.: Automatic Control Systems, West publishing company, St. Paul, New York, Los Angeles, San Francisco, 1989. godine. <br> |
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Didactic methods |
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| Course is being held through three kinds of activities: <br> Lectures in an auditory. During the lectures teacher solves tasks, so that students acquire tools and methods introduced during the lectures. <br> Laboratory exercises. Students are introduced to MATLAB/Simulink software environment and under tutor's guidance implement examples from previously learned material. Students do their assignments independently in the computer laboratory by use of MATLAB/Simulink software. <br> Tutorial. Under tutor's guidance students solve other assignments including assignments from previous exams. These activities are structured in such way that level of students knowledge and skills, meant to be achieved in this course, is being continuously examined through homework and partial exams. <br> |
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Exams |
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| Through the course, student gains points according to following system. <br> Attendance to lectures and tutorials: 10 points, student which misses lectures and/or tutorials more than three times cannot get points for these activities. Students are obligated to attend all laboratory hours. <br> Homework and laboratory assignments: maximum 10 points. There are 5 homework exercises, equally allocated through semester; these 5 exercises worth 5 points; 5 successfully finished laboratory assignments are also worth 5 points. <br> Partial exams: two partial exams, each worth 20 points. <br> Partial exam lasts for 90 minutes and is structured in the following way: <br> - answers on simple questions, whose purpose is to verify if student has basic theory knowledge. Student which answers all the questions correctly gets 5 points. <br> - solving the assignments with given multiple answers, of which only one is correct. Student which answers all the assignments correctly gets 5 points. <br> - solving one assignment without given answer; correctly solved assignment is worth 10 points. <br> Student which in the end of the course has less than 20 points has to take the course again. <br> Student which in the end of the course has 40 or more points can take final exam; this exam is consisted of discussion on partial exams tasks, homework and answers to questions referring to course subjects. <br> Final verbal examination is worth maximum 40 points. To pass the course, on this examination student must have minimum 20 points. Student which has less than 20 points on final verbal examination takes verbal corrective examination. <br> Student which has gained more than 20 but less than 40 points during the course takes corrective exam. Corrective exam is structured in the following way: <br> - written examination, structured in the same way as partial exam; on this examination student solves tasks from subjects he/she did not pass (10 or more points) by taking partial written exams. <br> - verbal examination, structured in the same way as final verbal exam. <br> Student can take verbal corrective examination only if after passing written corrective examination has made total score of 40 or more points; this score is made of points gained through: attendance, homework, passing partial exams and passing written corrective examination. <br> Verbal corrective examination is worth maximum 40 points. To pass the course, on this examination student must have minimum 20 points. Student which has less than 20 points on verbal corrective examination has to take the course again. <br> |
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Aditional notes |
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| During written examination students can use sets of formulae prepared by the teacher that can be of use for solving the tasks. Use of other notes, books, mobile phones or any other electronic tools, is not allowed. Tasks and theory questions on the examination are similar to those solved on lectures and auditory exercises. <br> |
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