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Unformatted text preview: Written Exam Modern Control Systems (Et 3015) On Wednesday the 1st of November 2000 from 2:00 PM to 5:00 PM Read the following VERY carefully. • The exam is composed of 2 Parts: theory and exercises. The first 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 2:40 PM) , no books, hand in at the end. – Break, 10 minutes, (end at 2:50 PM) collect books, sheets and the material you are allowed to use for Part II. – Part II, 130 minutes (end at 5:00 PM), 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 Part I: theory (Closed Book) Question 1 (weight:1) Define the vector margin of the loop transfer function L ( s ) , and prove that it is equal to the inverse of the peaking value of the module of the sensitivity function S ( jω ) . Write all your reasoning and be as precise as possible. Question 2 (weight:4) Given: A system in state space form: ˙ x = Fx + Gu y =...
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 Spring '10
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 Nyquist plot, Ju

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