# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

2 Pages

### nyquist

Course: ECE 486, Spring 2008
School: University of Illinois,...
Rating:

Word Count: 581

#### Document Preview

486 NYQUIST ECE PLOTS Fall 08 Reading: FPE, Section 6.3.2 We will now use the Principle of the Argument and the concept of contours and encirclements to study the stability of a closed loop system. Specifically, suppose we have a system L(s) which we are placing in the following feedback loop: The transfer function from r to y is given by Try (s) = L(s) , 1 + L(s) and the closed loop poles of this system are...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Illinois >> University of Illinois, Urbana Champaign >> ECE 486

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
486 NYQUIST ECE PLOTS Fall 08 Reading: FPE, Section 6.3.2 We will now use the Principle of the Argument and the concept of contours and encirclements to study the stability of a closed loop system. Specifically, suppose we have a system L(s) which we are placing in the following feedback loop: The transfer function from r to y is given by Try (s) = L(s) , 1 + L(s) and the closed loop poles of this system are the set of all values s such that 1 + L(s) = 0. Define H(s) = 1 + L(s) (note that H(s) is a transfer function). Specifically, if we denote L(s) = a(s) , we obtain b(s) H(s) = 1 + a(s) b(s) + a(s) = . b(s) b(s) Note that the poles of H(s) are actually the poles of L(s) (which are the open-loop poles). The zeros of H(s) are the poles of the transfer function Try (s), and thus they are the closed loop poles of the system. To determine how many closed loop poles lie in the CRHP, we use the Principle of the Argument. First, define the contour C as follows: This contour encloses the entire right half plane. Part C1 contains points of the form s = j as ranges from 0 to , and part C2 contains points of the form s = -j, as ranges from to 0. Parts C1 and C2 form the left boundary of the right half plane. Part C3 is a semicircle of infinite radius, and can be described by the points s = ej , where , and starts at 90 degrees and ends at -90 degrees. Suppose we evaluate H(s) on C to produce the contour H(C); for this choice of C, H(C) is called the Plot Nyquist of H. If we let N denote the number of times H(C) encircles the origin, the Principle of the Argument tells us that N =Z -P , where Z is number of zeros of H(s) enclosed by the contour C (which corresponds to the number of closed loop poles in the right half plane), P is the number of poles of H(s) enclosed by the contour C (corresponding to the number of open loop poles in the right half plane). Since P is known (for example, by knowing L(s), or by assuming that L(s) is stable), and since N can be determined by looking at the contour H(C), we can figure out Z, and thus determine the stability of the closed loop system. 10 Example. Suppose L(s) = (s+1)3 . Determine the stability of the closed loop system by examining the Nyquist plot of H, where H(s) = 1 + L(s), and C is the contour containing the right half plane. Solution. In order to apply the above te...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

University of Illinois, Urbana Champaign - PHYS - 569
Vortex Glass Transition in High Tc SuperconductorZhenhua Ning Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA(Dated: December 13, 2006)AbstractThis paper tries to give a clear description of the motion of
University of Illinois, Urbana Champaign - PHYS - 505
505Set 2 Due: 2/8/05Problem 1. Consider the following situation in two dimensional electrostatics. The region x 0, and 0 y a is bounded by conductors at x = 0, y = 0 and y = a. You may imagine these as plane conductors (of innite extent in the
University of Illinois, Urbana Champaign - PHYS - 435
MagnetostaticsMagnetic forces cycloidal motion Magnetic momentB z mzUI^ zzxNydyvdxCurrent densities^ zBr - r 'RThe vector potential^ rZRxGriffiths Ex 5.11Id^ xMagnetic multipole expansionsKBio
Sanford-Brown Institute - CSCI - 1950
The Dog Genome: Survey Sequencing and Comparative Analysis Ewen F. Kirkness, et al. Science 301, 1898 (2003); DOI: 10.1126/science.1086432 The following resources related to this article are available online at www.sciencemag.org (this information is
Sanford-Brown Institute - ECON - 156
EC 156Feb. 9, 2005Population and Economic Growth People are born and people die whats the big deal? It determines the amount of resources that can be produced and must be produced (people working, feeding people) Think: for two countries with t
Sanford-Brown Institute - ECON - 156
Econ 156March 9, 2005Outline Technology Creation History Present Day What influences creation? Technology TransferSome Inventions8500 BC: 3400 BC: 3000 BC: 250 BC: 1275 AD: 1453 AD: 1768 AD: 18th cent: 19th cent: 1908 AD: 1947 AD: 1969 AD
East Los Angeles College - UKHR - 0506
Table 76 Welsh housing capital plans and investment million1986/87 1987/88 1988/89 1989/90 1990/91 1991/92 1992/93 1993/94 1994/95 1995/96 1996/97 1997/98 1998/99 1999/00 2000/01 2001/02 2002/03 2003/04 2004/05 2005/06 2006/07 2007/08Local autho
UPenn - SAS - 8510
Judgment and Decision Making, Vol. 3, No. 7, October 2008, pp. 547569Evolution of the interpersonal conict paradigmMandeep K. Dhami University of Cambridge Henrik Olsson Max Planck Institute for Human DevelopmentAbstract Using Brunswiks (1952) l
Georgia Tech - ETD - 08202004
SYNTHESIS AND PROCESSING OF NANOCRYSTALLINE ZIRCONIUM CARBIDE FORMED BY CARBOTHERMAL REDUCTIONA Thesis Presented to The Academic Faculty ByANUBHAV JAINIn Partial Fulfillment Of the Requirements for the Degree Master of Science in Materials Scie
Sanford-Brown Institute - CS - 295
An evaluation of multi-resolution search and storage in resource-constrained sensor networksDeepak Ganesan, Ben Greenstein, Denis Perelyubskiy, Deborah Estrin, John HeidemannAbstract Wireless sensor networks enable dense sensing of the environment,
UPenn - ECON - 054
Department of EconomicsUniversity of PennsylvaniaEconomics 054 International Monetary Economics Instructor: Sanjay Chugh Spring 2004 (CGS) Supplement 2The accompanying two chapters are from a separate set of notes for a course in macroeconomics
Virgin Islands - CSC - 480
Student # 28743 120074 120768 121177 121875 122871 9004207 9011406 9106981 9205719 9307102 9401796 9404907 9501237 9501807 9603162 9605004 9606296 9606823 9607065 9610168 9700886 9705154 9705265 9706619 9706650 9706837 9707577 9707845 9708114 9711098
Sanford-Brown Institute - CSCI - 2560
CS256 Applied Theory of ComputationParallel Computation I John E SavageOverviewMachine and network models Performance metrics Flynn's taxonomy Networked computers Amdahl's law Multidimensional mesh models Sorting on 1-D arrays Matrix multiplicati
Virgin Islands - CSC - 480
SENG480A/CSC576ATopics in Software Engineering Software Development, Architecture &amp; Evolution Lectures, Nov 15, 19, 22, 2001Hausi A. Mller University of VictoriaFall 2001Schedule Teaching Evaluation today12:30-12:45 Assignment 4Due Dec 3
Sanford-Brown Institute - EN - 162
Engineering 162 Spring 2005 Answers to Assignment 2: Diode Applications and Bipolar Transistors 1) This problem is entirely about tuning a parallel resonant RLC circuit with back-biased diodes. The RLC part is just what is shown here. Notice that al
Sanford-Brown Institute - CS - 296
SLAM with SIFT(aka Mobile Robot Localization and Mapping with Uncertainty using Scale-Invariant Visual Landmarks )Se, Lowe, and Little+Presented by Matt LoperCS296-3: Robot Learning and Autonomy Brown University April 4th, 2007ObjectiveSL
UC Davis - STATS - 235
University of Illinois, Urbana Champaign - CS - 522
15Cartesian Closed Categories as Models for Simply-Typed -CalculusWe next focus on showing that CCCs can be organized as models of simply-typed -calculus. The idea is to interpret types as objects and -expressions as morphisms. As expected, e
UPenn - UPM - 7200
College for Women, 1919 yearbook (rebound)More yearbooks from the classes of Penn's College for WomenUniversityof Pennsylvania,191 9ColegHalPage OneWomen's Undergraduate RecordPage TwoUniversity of Pen sylvaniaWomen's Undergradua
University of Illinois, Urbana Champaign - M - 478
UPenn - LING - 106
LING 106: MidtermBegins: February 25, 2009, 8:30pm Ends: March 4, 2009, 8:30pmThis is the midterm exam. Please read through all of the instructions on this page before proceeding. Failure to follow any instruction on this page will cost you five po
Sanford-Brown Institute - CS - 1980
University of Illinois, Urbana Champaign - M - 117
Math 117 Unit 1 Review Guide The test next Tuesday covers chapters 1, 9, 10, 11 in the Billstein text, plus the material covered in lecture and labs. The following list should not be considered all-inclusive, but rather a guide for review. To be prep
Sanford-Brown Institute - CS - 1981
University of Illinois, Urbana Champaign - CS - 373
CS 373Lecture 11: Shortest PathsFall 20021111.1Shortest Paths (October 22)IntroductionGiven a weighted directed graph G = (V, E, w) with two special vertices, a source s and a target t, we want to nd the shortest directed path from s to t
East Los Angeles College - DOCS - 20090303
H&amp;S 4USE OF COLLEGE VEHICLESRegulations and guidelines on use of minibus and other vehiclesThe College's Regulations and Guidelines on the use of minibuses and other College vehicles apply to all College vehicles, and are also the minimum standar
East Los Angeles College - CMP - 501
main = InitNodeTwoTags!; TestNode!; if TestTwoNodesNoEdge then (UndoTag; No) else (UndoTag; Yes). TestNode = PickNode; TagNeighbour!; UndoTest!; MarkDone. TagNeighbour = {TagNeighbour1, TagNeighbour2, TagNeighbour3}. UndoTag = UndoTag1!; UndoTag2!.
University of Illinois, Urbana Champaign - CS - 473
AlgorithmsLecture 17: Linear Programming AlgorithmsUt ait ille tragicus, `veritatis simplex oratio est', ideoque illam implicari non oportet. [As the tragic poet says, `The language of truth is simple'; therefore it is improper to be entangled by
UNLV - CEE - 301
Georgia Tech - ETD - 05132004
CSMA with Implicit Scheduling through State-keeping: A Distributed MAC Framework for QoS in Broadcast LANsA Dissertation Presented to The Academic FacultyBy Shantanu KangudeIn Partial Fulfillment Of the Requirements for the Degree Doctor of Phil
Georgia Tech - ETD - 03292006
Bandwidth Efficiency and Power Efficiency Issues for Wireless TransmissionsA Dissertation Presented to The Academic Faculty byNing ChenIn Partial Fulfillment of the Requirements for the Degree Doctor of PhilosophySchool of Electrical and Comp
Georgia Tech - AE - 2020
Georgia Tech - CS - 8803
CS8803:CompilersforEmbeddedSystem SantoshPande Summer2007 S t hP d S 2007Chapter3 AnOverviewofISADesign An Overview of ISA Design1Outline AOverviewofISADesignO Overview:WhattoHide i Wh Hid BasicVLIWDesignPrinciple DesigningaVLIWISAforEmbedde
East Los Angeles College - DOCS - 20090303
PROBATIONARY PERIOD PROCEDURE Introduction New Eastleigh College employees are recruited in the belief that they are capable of carrying out the tasks and responsibilities required within their particular role to an acceptable standard. This belief i
W. Alabama - CP - 317
Department of Physics &amp; Computing CP 317 Software Engineering (Fall 2002) Course Project Outline: Reverse Engineering Application DomainProject Outline: For your course project, you are to collect relevant domain information from an approved, by th
Sanford-Brown Institute - CS - 250
Algorithms for Planar Graphs Lecture 4: More vector spaces for graphsPhilip N. Klein February 3, 20091Subspaces of the arc spaceFor a graph G = V, E , we will consider vector spaces over the reals consisting of vectors having one component per
East Los Angeles College - DOCS - 20090303
EASTLEIGH COLLEGE RECORD RETENTION PROCEDURE Statement of Principles In accordance with the core values of the governing body, the record retention procedure will comply with the basic principles of ethics, legality, prudence, equality, safety, time
Sanford-Brown Institute - EN - 0291
Physical Design of Digital Integrated Circuits (EN0291 S40)Sherief Reda Division of Engineering, Brown University Fall 20061Lecture 06: Power Analysis and Reduction Power Analysis Power Optimizations: Dynamic Power Optimizations: Leakage Im
Sanford-Brown Institute - EN - 2912
ENGN 2912C - Future Directions in Computing:From Bio and Quantum to Nano and 3D Topics discussed in the class include the following: Fundamental limits to technology scaling Nano-based technologies 3D technology Reversible computing Quantum co
Georgia Tech - ISYE - 4231
Homework #3Engineering Optimization (ISyE 4231) - Spring 2001 Due January 29, 2001Show all your steps to get full credit. Reading assignment: Read Chapters 1 and 2. 1. A small manufacturer is producing two types of steel products on two machines. P
Georgia Tech - MATH - 1501
MATH 1501 Homework Assignments for Chapter 5, Fall 2007, WTTMain Topics. Definition of a definite integral of a continuous function as a limit of a Reimann sum;bf (x)dx = lim n f (ti )(xi - xi-1 ) i=1a (P )0 In the preceding definition, it i
UPenn - V - 981215
JanuaryAT P E N NWhenever there is more than meets the eye, see our website, www.upenn.edu/almanacACADEMIC CALENDAR7Registration for undergraduate transfer students. Through January 8. 11 Spring semester classes begin. 22 Add period ends.CHIL
UPenn - V - 981124
DecemberAT P E N NWhenever there is more than meets the eye, see our website, www.upenn.edu/almanacInfo: www.upenn.edu/museum/. 5 Mesoamerica 12 China 13 Canaan and Ancient Israel 19 Egypt 20 Africa6FILMSSamurai Film Festival Japanese w/ Eng
UPenn - V - 990126
ACADEMIC CALENDAR 12 Drop period ends. CHILDRENS ACTIVITIES6Rock Art; children create their own rock art and learn more about the ancient art forms of pictograph and petroglyph; 10 a.m.-noon; University Museum; \$5 materials fee, preregistration req
Georgia Tech - ECE - 2025
GEORGIA INSTITUTE OF TECHNOLOGYSCHOOL of ELECTRICAL and COMPUTER ENGINEERINGEE 2200 Spring 1999 Lab #2: Introduction to Complex ExponentialsDate: week of 15 April 1999 Next Week: A short Lab Quiz will be held during the first 1520 minutes of lab.
UPenn - CIS - 610
3.3. THE L-GENUS AND THE TODD GENUS2093.3The L-Genus and the Todd GenusThe material in this section and the next two was first published in Hirzebruch [8]. Let B be a commutative ring with 1, and let Z, 1 , . . . , n , . . . be some independe
University of Illinois, Urbana Champaign - MATH - 0182
Version of 12.02.97On dynamical systems and their possible signicance for arithmetic geometryby Christopher Deninger0IntroductionIn the papers [D1], [D5], [D3] a cohomological formalism for algebraic schemes X0 over spec Z or spec Q was conj
East Los Angeles College - DOCS - 20090303
REDUNDANCY PROCEDURE FOR SENIOR POST-HOLDERS 1. Introduction 1.1. 1.2. This procedure applies to all board appointments as defined in the college's Articles of Government. The procedure for dismissal as set out in the Disciplinary Procedure for senio
UCSD - PS - 204
PS204B - Lecture 8Kristian Skrede Gleditsch Department of Political Science University of California, San Diego See http:/weber.ucsd.edu/kgledits/ &amp;http:/weber.ucsd.edu/kgledits/ps204b w2005/ps204b.htmlPS204B - Lecture 8 p. 1/2Model building
Sanford-Brown Institute - EN - 160
Brown University Design of VLSI SystemsMultiple Read/Write Port CellWL2 WL1Brown University Design of VLSI SystemsEN160 Design and Implementation of VLSI Systems Spring 2005 Lecture 28: Semiconductor MemoriesApril 11, 2005 Prof. Iris Bahar Re
Sanford-Brown Institute - EN - 160
Brown University Design of VLSI SystemsSense AmplifiersAmplification resolves data with small bit line swings (in some DRAMs required for proper functionality)SA inputBrown University Design of VLSI SystemsEN160 Design and Implementation of
UPenn - HIST - 363
University of Pennsylvania Department of History CIVIL WAR AND RECONSTRUCTION History 363 Spring, 2006 Professor Robert Engs 309A College Hall 215-898-4956 rengs@sas.upenn.eduCauses, Conduct, and Consequences of the US Civil WarBrothers do not ki
University of Illinois, Urbana Champaign - PHYS - 498
UIUC Physics 498POM Physics of Music/Musical InstrumentsDerivation of the Sabine Equation: Conservation of EnergyConsider a room of volume V = HWL (m3) with perfectly reflecting walls, filled with a uniform, steady-state (i.e. equilibrium) acousti
Sanford-Brown Institute - CS - 295
WEB SEARCH FOR A PLANET: THE GOOGLE CLUSTER ARCHITECTUREAMENABLE TO EXTENSIVE PARALLELIZATION, GOOGLE'S WEB SEARCHAPPLICATION LETS DIFFERENT QUERIES RUN ON DIFFERENT PROCESSORS AND, BY PARTITIONING THE OVERALL INDEX, ALSO LETS A SINGLE QUERY USE MU
Sanford-Brown Institute - CSCI - 2950
Cloud ArchitecturesJinesh Varia Technology Evangelist Amazon Web Services (jvaria@amazon.com)IntroductionThis paper illustrates the style of building applications using services available in the Internet cloud. Cloud Architectures are designs of
W. Alabama - ECE - 327
LEC-24 Preliminaries313LEC-24: ReviewLecture Notes Sections: 7 7.9University of Waterloo Dept of Electrical and Computer Engineering E&amp;CE 427ScheduleDigital Systems Engineering 2002-Winter.. VHDL Design and Optimization Functional Valida
Sanford-Brown Institute - AM - 194
W. Alabama - CS - 489
ConsolidationGROUPS Xingcheng, Davisson, Dacheng Xingcheng,Davisson,Dacheng Personaltrainers Librariansthenpoliceofficersasbackups p p Alexandra,Graham,Kyle Childcare workers CAS focused Childcareworkers CASfocused Ultrasoundtechnologistsas
University of Illinois, Urbana Champaign - CS - 476
Program Verication: Lecture 15Jos Meseguer eComputer Science Department University of Illinois at Urbana-Champaign1The Infrastructure for Java: Continuations Within continuations all the execution context is stored. This can be viewed as the
W. Alabama - CS - 489
DataAnalysis(1) Data Analysis (1)Coding ModelsAdministrivia Project groups Projectgroups Newclassmembers? See me! Seeme! Musthavedone: Assignment1 EmailedtargetgroupQuestions/CommentsDataAnalysis Data Analysis Datafrominterviews: Look