Module 11: Frequency Domain Techniques; Relative Stability and System Sensitivity

Lectures and Content

Folder description

Please click the folder link above to access the Module 11 instructional content. Module 11 contains three video lectures that present the following topics:

  1. Relative Stability (11A)
  2. Relative Stability via the Bode Plot (11B)
  3. System Sensitivity (11C)
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Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

By the end of this module, you will be able to:

  • Calculate gain and phase margins for a linear, time-invariant system.
  • Determine the relative stability of a linear, time-invariant system in terms of its gain and phase margins.
  • Determine the gain and phase margins by direct observation of the Bode Plot.
  • Calculate the system gain needed to provide a specific gain or phase margin.
  • Calculate the system sensitivity and complimentary sensitivity functions of a linear, time-invariant system.

How to Complete This Module:

  1. View Module 11 Lectures.
  2. Complete the assigned reading: Read Chapter and Sections 8.10-8.12, and 8.16 in the textbook.
  3. Complete the Module 11Practice Assignment.
  4. Complete graded Quiz #2.
  5. Take part in the Module 11 Discussion.
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Module 11 Reading

Cell description

This week's reading assignment includes the following:

  • Golnaraghi, Farid, and Benjamin C. Kuo. Automatic Control Systems (10th Edition).
    • Chapter 10, Sections 10.9-10.11
    • (Or, Chapter 8 Sections 8.10 -8.12, and 8.16 in the 9th Edition.)
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Module 11 Practice Assignment

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Instructions: Download and print the Module 11 Practice Assignment PDF, complete by hand, and then scan and upload your final document to the Blackboard course site.   Please ensure that your scan is of readable quality and oriented in the proper direction for reading.  All final submittals are to be in PDF format.

Submit your file using the following naming structure: Lastname_Firstname_M11Assignment (example: Palumbo_Neil_M11Assignment).

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Module 11 Discussion

Cell description

Students should respond to the following prompt and respond to at least two classmate’s post as well.

Consider the Nyquist plot, below, of the system with transfer function, G(s), also shown below. Apply the Nyquist Criterion to determine if the system is stable or not. Discuss your analysis approach and subsequent conclusions with your classmates, and also comment on the conclusions put forward by your classmates.

If you are still having difficulty with a topic/concept, please elaborate so that I and/or your classmates can assist you.

Technical 
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    "html": "\n\n<img alt=\"Discussion Board\" src=\"/images/ci/sets/set01/discussion_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7500306_1\">\n\n <h3 id=\"anonymous_element_14\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_197015_1&amp;content_id=_7500306_1&amp;mode=view\"><span style=\"color:#0067ac;\">Module 11 Discussion</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7500306_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Module 11 Discussion\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p style=\"margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-style: initial; text-decoration-color: initial;\">Students should respond to the following prompt and respond to at least two classmate’s post as well.</p> \n <p style=\"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-family: inherit; font-size: 13px; display: list-item; list-style-position: outside; list-style-type: inherit;\">Consider the Nyquist plot, below, of the system with transfer function, G(s), also shown below. Apply the Nyquist Criterion to determine if the system is stable or not. Discuss your analysis approach and subsequent conclusions with your classmates, and also comment on the conclusions put forward by your classmates.</p> \n <p style=\"margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-style: initial; text-decoration-color: initial;\"><span class=\"axScoreIndicator axVtbeEmbedded image\"><span data-ally-scoreindicator=\"_86813283_2\"></span></span>\n<img src=\"https://blackboard.jhu.edu/bbcswebdav/pid-7500306-dt-content-rid-86813283_2/xid-86813283_2\" style=\"border: 0px; cursor: default; margin: 0px; padding: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-family: inherit; 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        "body": "\n    <div> \n <p>Students should respond to the following prompt and respond to at least two classmate’s post as well.</p> \n <p>Consider the Nyquist plot, below, of the system with transfer function, G(s), also shown below. Apply the Nyquist Criterion to determine if the system is stable or not. Discuss your analysis approach and subsequent conclusions with your classmates, and also comment on the conclusions put forward by your classmates.</p> \n <p>\n \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.525.609.81.SP20/Module%2011/m11%20discussion.png?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00on&amp;course_id=_197015_1&amp;ctxMenuXythosId=86813283_2&amp;course_id=_197015_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_7d5407dc248a45318272dedc8fc84b61\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_7d5407dc248a45318272dedc8fc84b61',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_7d5407dc248a45318272dedc8fc84b61',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <p>If you are still having difficulty with a topic/concept, please elaborate so that I and/or your classmates can assist you.</p> \n  \n</div>\n  "
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Module 11 Practice Assignment Solutions

Cell description

Please click on the above link to review the solutions to the Module 11 Practice Assignment problems.

To be released on first day of Module 12.

Technical 
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Module 11 Discussion Solution

Cell description

Please click on the above link to review the solutions to the Module 11 Discussion solution.

To be released on first day of Module 12.

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