Module 6: State-Space Analysis for Time-varying and Time-invariant Systems

Lectures and Content

Folder description

Please click the folder link above to access the Module 6 instructional content. Module 6 contains four video lectures that present the following topics:

State-Space Analysis (6A)
Solving Discrete-Time State-Space Equations (6B)
Solving Discrete-Time Linear Time Varying State-Space Equations (6C)
Controllability (6D)

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:

Describe the concepts of a state-space representation of a system and transform a pulse-transfer function into a state-space equation
Compute a discrete-time state transition matrix and use it to derive the state-space solution for linear time-invariant systems
Efficiently compute the state-transition matrix and use it to derive the state-space solution for linear-time varying systems
Describe the concept of controllability and determine if a system is controllable .

How to Complete This Module:

Read Chapter 5.1 – 5.2 from Ogata 2nd Edition
View “State-Space Analysis” (module 6A video)
Read Chapter 5.3 from Ogata 2nd Edition
View “Solving Discrete-Time State-Space Equations” (module 6B video)
View “Solving Discrete-Time Linear Time Varying State-Space Equations” (module 6C video)
Read Chapter 6.1 – 6.2 from Ogata 2nd Edition
View “Controllability”
Participate in the module discussions
Complete the module 6 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 5.1 - 5.3, 6.1 - 6.2

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

Module 6A – Handouts
Module 6B – Handouts
Module 6C – Handouts
Module 6D – Handouts

Technical

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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-9946491-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=vd00cq&amp;course_id=_233190_1&amp;ctxMenuXythosId=103909318_2&amp;course_id=_233190_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_47b0d3c2125c4dd883d5b6154c262a5c,open_with_browser_47b0d3c2125c4dd883d5b6154c262a5c,open_with_bbdrive_47b0d3c2125c4dd883d5b6154c262a5c,openWebId_47b0d3c2125c4dd883d5b6154c262a5c,view360Id_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,*separator*,ax-ally-placeholder_47b0d3c2125c4dd883d5b6154c262a5c,ax-ally-markForAxAnalysis_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,*separator*,content_settings_47b0d3c2125c4dd883d5b6154c262a5c,content_editSettings_47b0d3c2125c4dd883d5b6154c262a5c,content_edit_47b0d3c2125c4dd883d5b6154c262a5c,properties_folder_47b0d3c2125c4dd883d5b6154c262a5c,itemcarot_managerecord_47b0d3c2125c4dd883d5b6154c262a5c,comments_tool_47b0d3c2125c4dd883d5b6154c262a5c,subscriptions_list_47b0d3c2125c4dd883d5b6154c262a5c,content_readfile_47b0d3c2125c4dd883d5b6154c262a5c,content_overwrite_47b0d3c2125c4dd883d5b6154c262a5c,passes_tool_47b0d3c2125c4dd883d5b6154c262a5c,permissions_tool_47b0d3c2125c4dd883d5b6154c262a5c,content_add_alignment_47b0d3c2125c4dd883d5b6154c262a5c,content_tracking_47b0d3c2125c4dd883d5b6154c262a5c,content_versions_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,*separator*,bookmarkId_47b0d3c2125c4dd883d5b6154c262a5c,itemsId_47b0d3c2125c4dd883d5b6154c262a5c,packagesId_47b0d3c2125c4dd883d5b6154c262a5c,emailId_47b0d3c2125c4dd883d5b6154c262a5c,removeContentFolderId_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,copyContentId_47b0d3c2125c4dd883d5b6154c262a5c,moveContentId_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,removeContentId_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,Metadata_General_47b0d3c2125c4dd883d5b6154c262a5c,Metadata_Dublin_Core_47b0d3c2125c4dd883d5b6154c262a5c,Metadata_IMS_47b0d3c2125c4dd883d5b6154c262a5c,Metadata_Full_IMS_47b0d3c2125c4dd883d5b6154c262a5c,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_47b0d3c2125c4dd883d5b6154c262a5c\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_47b0d3c2125c4dd883d5b6154c262a5c',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_47b0d3c2125c4dd883d5b6154c262a5c',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_47b0d3c2125c4dd883d5b6154c262a5c',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('47b0d3c2125c4dd883d5b6154c262a5c');\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 5.1 - 5.3, 6.1 - 6.2</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 6A – Handouts</li> \n  <li>Module 6B – Handouts</li> \n  <li>Module 6C – Handouts</li> \n  <li>Module 6D – Handouts</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_9946491_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-9946491-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=vd00cq&amp;course_id=_233190_1&amp;ctxMenuXythosId=103909318_2&amp;course_id=_233190_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_47b0d3c2125c4dd883d5b6154c262a5c,open_with_browser_47b0d3c2125c4dd883d5b6154c262a5c,open_with_bbdrive_47b0d3c2125c4dd883d5b6154c262a5c,openWebId_47b0d3c2125c4dd883d5b6154c262a5c,view360Id_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,*separator*,ax-ally-placeholder_47b0d3c2125c4dd883d5b6154c262a5c,ax-ally-markForAxAnalysis_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,*separator*,content_settings_47b0d3c2125c4dd883d5b6154c262a5c,content_editSettings_47b0d3c2125c4dd883d5b6154c262a5c,content_edit_47b0d3c2125c4dd883d5b6154c262a5c,properties_folder_47b0d3c2125c4dd883d5b6154c262a5c,itemcarot_managerecord_47b0d3c2125c4dd883d5b6154c262a5c,comments_tool_47b0d3c2125c4dd883d5b6154c262a5c,subscriptions_list_47b0d3c2125c4dd883d5b6154c262a5c,content_readfile_47b0d3c2125c4dd883d5b6154c262a5c,content_overwrite_47b0d3c2125c4dd883d5b6154c262a5c,passes_tool_47b0d3c2125c4dd883d5b6154c262a5c,permissions_tool_47b0d3c2125c4dd883d5b6154c262a5c,content_add_alignment_47b0d3c2125c4dd883d5b6154c262a5c,content_tracking_47b0d3c2125c4dd883d5b6154c262a5c,content_versions_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,*separator*,bookmarkId_47b0d3c2125c4dd883d5b6154c262a5c,itemsId_47b0d3c2125c4dd883d5b6154c262a5c,packagesId_47b0d3c2125c4dd883d5b6154c262a5c,emailId_47b0d3c2125c4dd883d5b6154c262a5c,removeContentFolderId_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,copyContentId_47b0d3c2125c4dd883d5b6154c262a5c,moveContentId_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,removeContentId_47b0d3c2125c4dd883d5b6154c262a5c,*separator*,Metadata_General_47b0d3c2125c4dd883d5b6154c262a5c,Metadata_Dublin_Core_47b0d3c2125c4dd883d5b6154c262a5c,Metadata_IMS_47b0d3c2125c4dd883d5b6154c262a5c,Metadata_Full_IMS_47b0d3c2125c4dd883d5b6154c262a5c,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_47b0d3c2125c4dd883d5b6154c262a5c\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_47b0d3c2125c4dd883d5b6154c262a5c',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_47b0d3c2125c4dd883d5b6154c262a5c',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_47b0d3c2125c4dd883d5b6154c262a5c',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('47b0d3c2125c4dd883d5b6154c262a5c');\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 5.1 - 5.3, 6.1 - 6.2</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 6A – Handouts</li> \n  <li>Module 6B – Handouts</li> \n  <li>Module 6C – Handouts</li> \n  <li>Module 6D – Handouts</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_9946491_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Module 6 Discussion Question 1 - Exam Preparation

Cell description

We have the mid-term exam next week. What concepts, approaches and problems are confusing to you or that you would like to have clarification on? Engage the class to see if they can help you better understand and try to help clarify things that others are confused about.

You will be graded on your participation in this activity, not on the accuracy of your answer. Please share your response by Day 5 of Module 6, then provide feedback to your classmates by Day 7 of Module 6.

Technical

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Module 6 Discussion 2 - Pratice Assignment

Cell description

For this activity, you will work with a partner to practice solving problems.

Partner’s will be paired up based on the order of initial posts. 1st & 2nd responders will pair up, 3rd & 4th will pair up, etc.
Download the following Practice Assignment and complete the problems. Practice Assignment
After you have completed the problem, scan your work or take a very clear picture with your phone or camera.
Respond to this discussion forum and attach the file with your completed work.
Find your assigned partner’s attached files and download their work.
Review their solution to the problem and provide any corrections or comments on their work. You may want to do this on paper and then scan or take a picture of your corrections.
Reply to their post by attaching a new file with your corrections and comments. You may also choose to respond using the discussion textbox, whatever best allows you to exchange ideas with your partner.

You will be graded on your participation in this activity, not on the accuracy of solving the problem. Please upload your first attempt at solving this problem by Day 4 of Module 6, then provide your feedback by Day 6 of Module 6. Please note that this is a chance to practice solving similar to the Module 6 Assignment where you will be graded on your accuracy, so take full advantage of this exercise..

Technical

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file_1.pdf
./attachments/cell_42/file_1.pdf

Module 6 Assignment

Cell description

Please open the attachments above and complete the Problem Set:

Module 6 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 6.

Technical

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Module 6 Homework Solutions

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