Exam Solutions 1-10

Exam Solutions 1-10 - Written Exam Modern Control...

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Written Exam Modern Control Systems (Et 3-015) On Wednesday the 3rd of November 1999 from 14:00 PM to 17:00 PM Read the following VERY carefully. The exam is composed of 2 Parts: theory and exercises. The £rst part is WITHOUT any books or notes and it will last 40 minutes . At the end of the 40 minutes, the exam will be collected and after 10 minutes the second part of 130 minutes will start. You are allowed to use anything you want for the second part: Part I, 40 minutes (end at 14:40) , no books, hand in at the end. Break, 10 minutes, (end at 14:50) collect books, sheets and the material you are allowed to use for Part II. Part II, 130 minutes (end at 17:00), with books, sheets. .... If you are ready with Part I earlier than the time given, you can start working on Part II, but WITHOUT BOOK and on a NEW SHEET OF PAPER . NEVER talk with your neighbor. If the answers are not easily readable, the corresponding answer will be given 0 points. Therefore WRITE CLEARLY. Read every question well before answering. Write ALL your reasoning steps on paper. Write your name and student number clearly readable on EACH piece of paper. Good luck ! Technische Universiteit Delft Faculteit der Informatie Technologie en Systemen Vakgroep Regeltechniek Mekelweg 4 2628 CD Delft
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Part I: theory (Closed Book) Question 1 (weight:3) Given: For a transfer function F ( s ) , due to the Cauchy’s theorem of complex analysis, we have that: 1 2 πj c F ( s ) F ( s ) ds = Z - P where the integral is along a closed curve encircling Z zeros and P poles of F ( s ) . Asked: Prove the Nyquist criterium formula N enc = Z - P where N enc is the number of clockwise encirclements around the origin of F ( s ) for values of s along a closed curve enclosing Z zeros of F ( s ) and P poles of F ( s ) .
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  • Spring '10
  • Taufik
  • Modern Control Systems, Systemen Vakgroep Regeltechniek Mekelweg, [rad s-1], Systemen Vakgroep Regeltechniek, Vakgroep Regeltechniek Mekelweg

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Exam Solutions 1-10 - Written Exam Modern Control...

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