Module 2: Block Diagrams, Signal Flow Graphs and Mason’s Gain Formula

Folder description

Please click the folder link above to access the Module 2 instructional content. Module 12 contains five video lectures that present the following topics:

  1. Transfer Function (2A)
  2. Block Diagrams (2B)
  3. Signal Flow Graphs (2C)
  4. Mason’s Gain Formula (2D)
  5. State Diagrams (2E)
Technical
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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:

  • Apply block diagram principles to describe the composition and interconnects between elements in a dynamic system.
  • Derive a multivariable transfer function given a basic multivariable block diagram description.
  • Convert a dynamic system block diagram representation to signal flow graph representation and back.
  • Identify the key elements of a signal flow graph in preparation for the application of Mason’s gain formula.
  • Apply Mason’s Gain Formula, given a signal flow graph, to derive a transfer function.
  • Draw a state diagram given a set of ordinary differential equations or system transfer function.
  • Given a state diagram, derive a transfer function using Mason’s Gain Formula. 

How to Complete This Module:

  1. View Lecture 2A (“Transfer Functions”).
  2. View Lecture 2B (“Block Diagrams”).
  3. View Lecture 2C (“Signal Flow Graphs”).
  4. View Lecture 2D (“Mason’s Gain Formula”).
  5. View Lecture 2E (“State Diagrams”).
  6. Complete the assigned reading: Chapter 4 in the 10th Edition text (Chapter 3 in 9th Edition).
  7. Complete the Module 2 Practice Assignment.
  8. Take part in the Module 2 Discussion.
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Readings

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To access EReserves readings, click the Readings title above or EReserves on the course menu.

This week's reading assignment includes the following:

  • Golnaraghi, Farid, and Benjamin C. Kuo.  Automatic Control Systems (10th Edition).
    • Chapter 4, All sections
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Module 2 Practice Assignment

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Instructions: Download and print the Module 2 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_M2Assignment (example: Palumbo_Neil_M2Assignment).

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All final submittals are to be in PDF format.</p> \n <p><strong>Submit your file using the following naming structure: Lastname_Firstname_M2Assignment (example: Palumbo_Neil_M2Assignment).</strong></p> \n</div>\n  </div>\n\n <div id=\"_7500199_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Module 2 Discussion

Cell description

Explain / discuss how any non-input node can be converted to an output node. Given the transfer functions shown below, use MATLAB to calculate

. Discuss / explain each of your steps and share the result with one another:

  • Note that there is more than one potential approach!
  • 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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an output node.<br> <br> Given the transfer functions shown below, use MATLAB to calculate <span class=\"axScoreIndicator axVtbeEmbedded image\"><span data-ally-scoreindicator=\"_86813286_2\"></span></span>\n<img src=\"https://blackboard.jhu.edu/bbcswebdav/pid-7500200-dt-content-rid-86813286_2/xid-86813286_2\" data-mathml=\"«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»G«/mi»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«/mrow»«/msub»«mo»(«/mo»«mi»s«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«msub»«mi»G«/mi»«mn»2«/mn»«/msub»«mo»(«/mo»«mi»s«/mi»«mo»)«/mo»«/math»\" class=\"Wirisformula\" alt=\"G subscript 1 space end subscript left parenthesis s right parenthesis space plus space G subscript 2 left parenthesis s right parenthesis\" align=\"\" style=\"vertical-align: -12px;\"> \n<span class=\"contextMenuContainer image\" style=\" display: inline;\" 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        "body": "\n    <div> \n <p>Explain / discuss how any non-input node can be converted to an output node.  Given the transfer functions shown below, use MATLAB to calculate \n \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.525.609.81.SP20/Math%20Images/95b859b4560b1f85baf077187cc3aa52.png?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00mq&amp;course_id=_197015_1&amp;ctxMenuXythosId=86813286_2&amp;course_id=_197015_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_96944004ad9b41b7ab9b62673ed5a420,open_with_browser_96944004ad9b41b7ab9b62673ed5a420,open_with_bbdrive_96944004ad9b41b7ab9b62673ed5a420,openWebId_96944004ad9b41b7ab9b62673ed5a420,view360Id_96944004ad9b41b7ab9b62673ed5a420,*separator*,*separator*,ax-ally-placeholder_96944004ad9b41b7ab9b62673ed5a420,ax-ally-markForAxAnalysis_96944004ad9b41b7ab9b62673ed5a420,*separator*,*separator*,content_settings_96944004ad9b41b7ab9b62673ed5a420,content_editSettings_96944004ad9b41b7ab9b62673ed5a420,content_edit_96944004ad9b41b7ab9b62673ed5a420,properties_folder_96944004ad9b41b7ab9b62673ed5a420,itemcarot_managerecord_96944004ad9b41b7ab9b62673ed5a420,comments_tool_96944004ad9b41b7ab9b62673ed5a420,subscriptions_list_96944004ad9b41b7ab9b62673ed5a420,content_readfile_96944004ad9b41b7ab9b62673ed5a420,content_overwrite_96944004ad9b41b7ab9b62673ed5a420,passes_tool_96944004ad9b41b7ab9b62673ed5a420,permissions_tool_96944004ad9b41b7ab9b62673ed5a420,content_add_alignment_96944004ad9b41b7ab9b62673ed5a420,content_tracking_96944004ad9b41b7ab9b62673ed5a420,content_versions_96944004ad9b41b7ab9b62673ed5a420,*separator*,*separator*,bookmarkId_96944004ad9b41b7ab9b62673ed5a420,itemsId_96944004ad9b41b7ab9b62673ed5a420,packagesId_96944004ad9b41b7ab9b62673ed5a420,emailId_96944004ad9b41b7ab9b62673ed5a420,removeContentFolderId_96944004ad9b41b7ab9b62673ed5a420,*separator*,copyContentId_96944004ad9b41b7ab9b62673ed5a420,moveContentId_96944004ad9b41b7ab9b62673ed5a420,*separator*,removeContentId_96944004ad9b41b7ab9b62673ed5a420,*separator*,Metadata_General_96944004ad9b41b7ab9b62673ed5a420,Metadata_Dublin_Core_96944004ad9b41b7ab9b62673ed5a420,Metadata_IMS_96944004ad9b41b7ab9b62673ed5a420,Metadata_Full_IMS_96944004ad9b41b7ab9b62673ed5a420,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_96944004ad9b41b7ab9b62673ed5a420\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_96944004ad9b41b7ab9b62673ed5a420',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_96944004ad9b41b7ab9b62673ed5a420',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n . Discuss / explain each of your steps and share the result with one another: \n <p> \n \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.525.609.81.SP20/Math%20Images/6d3951f43094ecef67378407fda87554.png?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00ms&amp;course_id=_197015_1&amp;ctxMenuXythosId=86813287_2&amp;course_id=_197015_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_9eda542f40404ba6a551f7de8bee23f9,open_with_browser_9eda542f40404ba6a551f7de8bee23f9,open_with_bbdrive_9eda542f40404ba6a551f7de8bee23f9,openWebId_9eda542f40404ba6a551f7de8bee23f9,view360Id_9eda542f40404ba6a551f7de8bee23f9,*separator*,*separator*,ax-ally-placeholder_9eda542f40404ba6a551f7de8bee23f9,ax-ally-markForAxAnalysis_9eda542f40404ba6a551f7de8bee23f9,*separator*,*separator*,content_settings_9eda542f40404ba6a551f7de8bee23f9,content_editSettings_9eda542f40404ba6a551f7de8bee23f9,content_edit_9eda542f40404ba6a551f7de8bee23f9,properties_folder_9eda542f40404ba6a551f7de8bee23f9,itemcarot_managerecord_9eda542f40404ba6a551f7de8bee23f9,comments_tool_9eda542f40404ba6a551f7de8bee23f9,subscriptions_list_9eda542f40404ba6a551f7de8bee23f9,content_readfile_9eda542f40404ba6a551f7de8bee23f9,content_overwrite_9eda542f40404ba6a551f7de8bee23f9,passes_tool_9eda542f40404ba6a551f7de8bee23f9,permissions_tool_9eda542f40404ba6a551f7de8bee23f9,content_add_alignment_9eda542f40404ba6a551f7de8bee23f9,content_tracking_9eda542f40404ba6a551f7de8bee23f9,content_versions_9eda542f40404ba6a551f7de8bee23f9,*separator*,*separator*,bookmarkId_9eda542f40404ba6a551f7de8bee23f9,itemsId_9eda542f40404ba6a551f7de8bee23f9,packagesId_9eda542f40404ba6a551f7de8bee23f9,emailId_9eda542f40404ba6a551f7de8bee23f9,removeContentFolderId_9eda542f40404ba6a551f7de8bee23f9,*separator*,copyContentId_9eda542f40404ba6a551f7de8bee23f9,moveContentId_9eda542f40404ba6a551f7de8bee23f9,*separator*,removeContentId_9eda542f40404ba6a551f7de8bee23f9,*separator*,Metadata_General_9eda542f40404ba6a551f7de8bee23f9,Metadata_Dublin_Core_9eda542f40404ba6a551f7de8bee23f9,Metadata_IMS_9eda542f40404ba6a551f7de8bee23f9,Metadata_Full_IMS_9eda542f40404ba6a551f7de8bee23f9,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_9eda542f40404ba6a551f7de8bee23f9\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_9eda542f40404ba6a551f7de8bee23f9',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_9eda542f40404ba6a551f7de8bee23f9',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <ul> \n  <li>Note that there is more than one potential approach!</li> \n  <li>If you are still having difficulty with a topic/concept, please elaborate so that I and/or your classmates can assist you.</li> \n </ul> \n</div>\n  "
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Module 2 Discussion Assignment Solutions

Cell description

Click on the link below to review the Discussion Topic Solutions.

(To be released on the first day of Module 3.)

Technical
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Module 2 Practice Assignment Solutions

Cell description

Click on the link below to review the Practice Assignment Solutions.

(To be released on the first day of Module 3.)

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