Module 3: z-Plane Analysis of Discrete-Time Systems

Folder description

Please click the folder link above to access the Module 3 instructional content. Module 3 contains four video lectures that present the following topics:

  1. Obtaining the z-Transform using the Convolution Integral (3A)
  2. Reconstructing Signals from Sampled Data (3B)
  3. The Pulse Transfer Function (3C)
  4. Pulse Transfer Function Examples (3D)
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 the convolution integral method to obtain the z-Transform of a signal
  • Understand the effects that sampling and signal reconstruction have on a signal and apply the sampling theorem
  • Understand the concept of and compute the pulse transfer function of various systems.

How to Complete This Module:

  1. Read Chapter 3.3 from Ogata 2nd Edition
  2. View “Obtaining the z-Transform using the Convolution Integral” (module 3A video)
  3. Read Chapter 3.4 from Ogata 2nd Edition
  4. View “Reconstructing Signals from Sampled Data” (module 3B video)
  5. Read Chapter 3.5 (pp. 98-110) from Ogata 2nd Edition
  6. View “The Pulse Transfer Function” (module 3C video)
  7. View “Pulse Transfer Function Examples” (module 3D video)
  8. Participate in the module discussions
  9. Complete the module 3 assignment
Technical
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Readings

Cell description

This weeks readings include the following:

Ogata,K. (1995). Discrete-Time Control Systems (2nd Edition). Upper Saddle River, New Jersey. Prentice Hall.

  • Chapter 3.3 – 3.5 (pp. 98-110)

  Urbant, T. (2016) Digital Control and System Applications

  • Module 3A – Handouts
  • Module 3B – Handouts
  • Module 3C – Handouts
  • Module 3D – Handouts
Technical
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(2016) Digital Control and System Applications</p> \n <ul> \n  <li>Module 3A – Handouts</li> \n  <li>Module 3B – Handouts</li> \n  <li>Module 3C – Handouts</li> \n  <li>Module 3D – Handouts</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_9946486_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Prentice Hall.</p> \n <table summary=\"Discrete-Time Control Text graphic\" border=\"0\"> \n  <tbody> \n   <tr> \n    <td class=\"nowrapCell\"><span class=\"axScoreIndicator axVtbeEmbedded image\"><span data-ally-scoreindicator=\"_103909318_2\"></span></span>\n<img src=\"https://blackboard.jhu.edu/bbcswebdav/pid-9946486-dt-content-rid-103909318_2/xid-103909318_2\" alt=\"Discrete-Time Control Systems Textbook\" title=\"Discrete-Time Control Systems Textbook\" width=\"92\" height=\"119\"> \n<span class=\"contextMenuContainer image\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.535.645.81.SU21/Screen%20Shot%202016-09-29%20at%208.36.15%20AM.png?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00c4&amp;course_id=_233190_1&amp;ctxMenuXythosId=103909318_2&amp;course_id=_233190_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_012c8228b041494eb324c9b76c428802,open_with_browser_012c8228b041494eb324c9b76c428802,open_with_bbdrive_012c8228b041494eb324c9b76c428802,openWebId_012c8228b041494eb324c9b76c428802,view360Id_012c8228b041494eb324c9b76c428802,*separator*,*separator*,ax-ally-placeholder_012c8228b041494eb324c9b76c428802,ax-ally-markForAxAnalysis_012c8228b041494eb324c9b76c428802,*separator*,*separator*,content_settings_012c8228b041494eb324c9b76c428802,content_editSettings_012c8228b041494eb324c9b76c428802,content_edit_012c8228b041494eb324c9b76c428802,properties_folder_012c8228b041494eb324c9b76c428802,itemcarot_managerecord_012c8228b041494eb324c9b76c428802,comments_tool_012c8228b041494eb324c9b76c428802,subscriptions_list_012c8228b041494eb324c9b76c428802,content_readfile_012c8228b041494eb324c9b76c428802,content_overwrite_012c8228b041494eb324c9b76c428802,passes_tool_012c8228b041494eb324c9b76c428802,permissions_tool_012c8228b041494eb324c9b76c428802,content_add_alignment_012c8228b041494eb324c9b76c428802,content_tracking_012c8228b041494eb324c9b76c428802,content_versions_012c8228b041494eb324c9b76c428802,*separator*,*separator*,bookmarkId_012c8228b041494eb324c9b76c428802,itemsId_012c8228b041494eb324c9b76c428802,packagesId_012c8228b041494eb324c9b76c428802,emailId_012c8228b041494eb324c9b76c428802,removeContentFolderId_012c8228b041494eb324c9b76c428802,*separator*,copyContentId_012c8228b041494eb324c9b76c428802,moveContentId_012c8228b041494eb324c9b76c428802,*separator*,removeContentId_012c8228b041494eb324c9b76c428802,*separator*,Metadata_General_012c8228b041494eb324c9b76c428802,Metadata_Dublin_Core_012c8228b041494eb324c9b76c428802,Metadata_IMS_012c8228b041494eb324c9b76c428802,Metadata_Full_IMS_012c8228b041494eb324c9b76c428802,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_012c8228b041494eb324c9b76c428802\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_012c8228b041494eb324c9b76c428802',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_012c8228b041494eb324c9b76c428802',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_012c8228b041494eb324c9b76c428802',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"103909318_2_fileReadWritePermAvl\" id=\"103909318_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('012c8228b041494eb324c9b76c428802');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script></td> \n    <td> \n     <ul> \n      <li>Chapter 3.3 – 3.5 (pp. 98-110)</li> \n     </ul> </td> \n   </tr> \n  </tbody> \n </table> \n <br> \n <p>&nbsp; Urbant, T. (2016) Digital Control and System Applications</p> \n <ul> \n  <li>Module 3A – Handouts</li> \n  <li>Module 3B – Handouts</li> \n  <li>Module 3C – Handouts</li> \n  <li>Module 3D – Handouts</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_9946486_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Readings",
        "body": "\n    <div> \n <p>This weeks readings include the following:</p> \n <p>Ogata,K. (1995). Discrete-Time Control Systems (2nd Edition). Upper Saddle River, New Jersey. Prentice Hall.</p> \n <table summary=\"Discrete-Time Control Text graphic\" border=\"0\"> \n  <tbody> \n   <tr> \n    <td>\n \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.535.645.81.SU21/Screen%20Shot%202016-09-29%20at%208.36.15%20AM.png?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00c4&amp;course_id=_233190_1&amp;ctxMenuXythosId=103909318_2&amp;course_id=_233190_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_012c8228b041494eb324c9b76c428802,open_with_browser_012c8228b041494eb324c9b76c428802,open_with_bbdrive_012c8228b041494eb324c9b76c428802,openWebId_012c8228b041494eb324c9b76c428802,view360Id_012c8228b041494eb324c9b76c428802,*separator*,*separator*,ax-ally-placeholder_012c8228b041494eb324c9b76c428802,ax-ally-markForAxAnalysis_012c8228b041494eb324c9b76c428802,*separator*,*separator*,content_settings_012c8228b041494eb324c9b76c428802,content_editSettings_012c8228b041494eb324c9b76c428802,content_edit_012c8228b041494eb324c9b76c428802,properties_folder_012c8228b041494eb324c9b76c428802,itemcarot_managerecord_012c8228b041494eb324c9b76c428802,comments_tool_012c8228b041494eb324c9b76c428802,subscriptions_list_012c8228b041494eb324c9b76c428802,content_readfile_012c8228b041494eb324c9b76c428802,content_overwrite_012c8228b041494eb324c9b76c428802,passes_tool_012c8228b041494eb324c9b76c428802,permissions_tool_012c8228b041494eb324c9b76c428802,content_add_alignment_012c8228b041494eb324c9b76c428802,content_tracking_012c8228b041494eb324c9b76c428802,content_versions_012c8228b041494eb324c9b76c428802,*separator*,*separator*,bookmarkId_012c8228b041494eb324c9b76c428802,itemsId_012c8228b041494eb324c9b76c428802,packagesId_012c8228b041494eb324c9b76c428802,emailId_012c8228b041494eb324c9b76c428802,removeContentFolderId_012c8228b041494eb324c9b76c428802,*separator*,copyContentId_012c8228b041494eb324c9b76c428802,moveContentId_012c8228b041494eb324c9b76c428802,*separator*,removeContentId_012c8228b041494eb324c9b76c428802,*separator*,Metadata_General_012c8228b041494eb324c9b76c428802,Metadata_Dublin_Core_012c8228b041494eb324c9b76c428802,Metadata_IMS_012c8228b041494eb324c9b76c428802,Metadata_Full_IMS_012c8228b041494eb324c9b76c428802,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_012c8228b041494eb324c9b76c428802\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_012c8228b041494eb324c9b76c428802',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_012c8228b041494eb324c9b76c428802',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n  </span> \n \n \n \n \n \n</td> \n    <td> \n     <ul> \n      <li>Chapter 3.3 – 3.5 (pp. 98-110)</li> \n     </ul> </td> \n   </tr> \n  </tbody> \n </table> \n  \n <p>&nbsp; Urbant, T. (2016) Digital Control and System Applications</p> \n <ul> \n  <li>Module 3A – Handouts</li> \n  <li>Module 3B – Handouts</li> \n  <li>Module 3C – Handouts</li> \n  <li>Module 3D – Handouts</li> \n </ul> \n</div>\n  "
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Module 3 Discussion Question 1 - Ideal Low Pass Filters

Cell description
  • Figure 3-12 is referred to as an “Ideal Low Pass Filter.” What makes it ideal? Can it be realized using some sort of Chebyshev or Butterworth filter, or some kind of fancy signal processing?
  • You will be graded on your participation in this activity, not on the accuracy of your answer. Please share your response by Day 3 of Module 3, then provide feedback to your classmates by Day 5 of Module 3.
Technical
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Module 3 Assignment

Cell description

Please open the attachments above and complete the Problem Set:

  • Module 3 Assignment

As you complete this Problem Set please show all your work. When you are finished, scan the document containing your final work or take a clear and readable picture with a camera or phone. Submit your response by day 7 of Module 3.

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When you are finished, scan the document containing your final work or take a clear and readable picture with a camera or phone. <span style=\"text-decoration: underline;\">Submit your response by day 7 of Module 3</span>.</p> \n</div>\n  </div>\n\n <div id=\"_9826868_1previewModule\" class=\"moduleSample\">\n </div>\n",
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