Module 6: Introduction to Signals and Systems

Lectures & Content

Folder description

Please click the folder link above to access the Module 6 instructional content. Module 6 contains 11 video lectures that present the following topics:

Introducing the Laplace Transform (6A)
Some Examples of Simple Laplace Transforms (6B)
First Order Linear ODE Initial Value Problem (Example 1)
Radioactive Decay Solved by Laplace Transform (6C)
Superposition Solutions for Linear First Order ODEs (Example 2)
Damped Harmonic Oscillator (6D)
Control of Blood Sugar as seen by Minimal Compartment Models (6E)
First Order ODEs with Physical Inputs (Example 3)
First Order ODEs Superposition with Delay (Example 4)
Glucose and Insulin Control in Maximal Models (6F)
First Order ODEs Response to Step Input (Example 5)

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:

Explain how convolution and Laplace Transforms are related.
Apply the Laplace Transforms to solve differential equations.
Define the basics of glucose control.
Describe how Laplace Transform solutions apply for radioactive decay and harmonic oscillators.
Apply general aspects of control theory to blood sugar control.
Describe first order differential equations and their solutions.
Apply the concepts of first order differential equations to Laplace Transforms.

How to Complete This Module:

View lectures 6A-6F and Examples 1-5.
Complete the assigned reading to supplement the material presented in the lectures.
Participate in the module discussion.
Complete and submit the module assignment.
Complete the required entry in your personal learning journal.

Technical

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Readings

Cell description

This week's reading assignment includes the following:

Text Books

Astrom, J. K. & Murray, R.M. (2008).Feedback systems: An introduction for scientists and engineers. Princeton, NJ: Princeton University Press.Available at: http://www.cds.caltech.edu/~murray/amwiki/index.php/Main_Page
- Review: Chapters 1-4
Chaparro, L. (2014). Signals and systems using MATLAB (2nd ed.). Academic Press.
- Chapter 3

EReserves

Cobelli, C. Dalla Man, C. Sparacino, G. et. al. (2009). Diabetes: Models, signals, and control. IEEE Reviews in Biomedical Engineering (2) 54-96.

Technical

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Module 6 Discussion Participation GuidelinesQuestion:

Cell description

Discussion forum rubric: 625.260 Discusssion Rubric

Participation Guidelines

Participation in class discussions are important in this course and to your final grade. Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.

Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.

There is one discussion thread in this module. Submit your posts by clicking on the "Module 6 Discussion" link above and creating a new thread. Please contribute to the class discussion with your discussion about:

Question:

Thread 6.1

Have you worked with the Laplace transform before in any context?
Have you solved first order ODEs in the past?
Can you give us some examples of dynamical systems that you care about that have a natural solution in terms of a Laplace Transform?
Do you think that the software defined patients of Cobelli make sense or not?

For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.

Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.

You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.

Required Activity: 1 Original Post / 2 Responses Due by: Original Post 11:59PM Day 4, Responses 11:59PM Day 7

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Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.</p> \n <p style=\"margin-left: 30px;\">Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.&nbsp;</p> \n <p style=\"margin-left: 30px;\">There is one discussion thread in this module. Submit your posts by clicking on the \"Module 6 Discussion\" link above and creating a new thread. Please contribute to the class discussion with your discussion about:</p> \n <h3 style=\"color: #0067ac;\" id=\"anonymous_element_15\">Question:</h3> \n <p style=\"margin-left: 30px;\"><strong style=\"font-size: 13px;\">Thread 6.1</strong></p> \n <ul style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"> \n  <li style=\"font-size: 13px;\">Have you worked with the Laplace transform before in any context?</li> \n  <li style=\"font-size: 13px;\">Have you solved first order ODEs in the past?</li> \n  <li style=\"font-size: 13px;\">Can you give us some examples of dynamical systems that you care about that have a natural solution in terms of a Laplace Transform?</li> \n  <li style=\"font-size: 13px;\">Do you think that the software defined patients of Cobelli make sense or not?</li> \n </ul> \n <p style=\"margin-left: 30px;\">For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.</p> \n <p style=\"margin-left: 30px;\">Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.</p> \n <p style=\"margin-left: 30px;\">You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.</p> \n <p style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"><span style=\"text-decoration: underline;\">Required Activity</span>: 1 Original Post / 2 Responses<br> <span style=\"text-decoration: underline;\">Due by</span>: Original Post 11:59PM Day 4, Responses 11:59PM Day 7</p> \n <br> \n</div>\n  </div>\n\n <div id=\"_5740774_1previewModule\" class=\"moduleSample\">\n </div>\n",
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font-size: small;\"><strong style=\"font-size: 13px;\"><strong style=\"font-size: 13px;\"><strong style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px;\">Discussion forum rubric:&nbsp;<span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_51355346_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-5740774-dt-content-rid-51355346_2/xid-51355346_2\" target=\"_blank\" style=\"font-size: 13px;\">625.260 Discusssion Rubric</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.260.81.FA18/Module%201/Discussion_Rubric.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00u9&amp;course_id=_169707_1&amp;ctxMenuXythosId=51355346_2&amp;course_id=_169707_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_129df4d9160e47a28240d9e93e948069,open_with_browser_129df4d9160e47a28240d9e93e948069,open_with_bbdrive_129df4d9160e47a28240d9e93e948069,openWebId_129df4d9160e47a28240d9e93e948069,view360Id_129df4d9160e47a28240d9e93e948069,*separator*,*separator*,ax-ally-placeholder_129df4d9160e47a28240d9e93e948069,ax-ally-markForAxAnalysis_129df4d9160e47a28240d9e93e948069,*separator*,*separator*,content_settings_129df4d9160e47a28240d9e93e948069,content_editSettings_129df4d9160e47a28240d9e93e948069,content_edit_129df4d9160e47a28240d9e93e948069,properties_folder_129df4d9160e47a28240d9e93e948069,itemcarot_managerecord_129df4d9160e47a28240d9e93e948069,comments_tool_129df4d9160e47a28240d9e93e948069,subscriptions_list_129df4d9160e47a28240d9e93e948069,content_readfile_129df4d9160e47a28240d9e93e948069,content_overwrite_129df4d9160e47a28240d9e93e948069,passes_tool_129df4d9160e47a28240d9e93e948069,permissions_tool_129df4d9160e47a28240d9e93e948069,content_add_alignment_129df4d9160e47a28240d9e93e948069,content_tracking_129df4d9160e47a28240d9e93e948069,content_versions_129df4d9160e47a28240d9e93e948069,*separator*,*separator*,bookmarkId_129df4d9160e47a28240d9e93e948069,itemsId_129df4d9160e47a28240d9e93e948069,packagesId_129df4d9160e47a28240d9e93e948069,emailId_129df4d9160e47a28240d9e93e948069,removeContentFolderId_129df4d9160e47a28240d9e93e948069,*separator*,copyContentId_129df4d9160e47a28240d9e93e948069,moveContentId_129df4d9160e47a28240d9e93e948069,*separator*,removeContentId_129df4d9160e47a28240d9e93e948069,*separator*,Metadata_General_129df4d9160e47a28240d9e93e948069,Metadata_Dublin_Core_129df4d9160e47a28240d9e93e948069,Metadata_IMS_129df4d9160e47a28240d9e93e948069,Metadata_Full_IMS_129df4d9160e47a28240d9e93e948069,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_129df4d9160e47a28240d9e93e948069\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_129df4d9160e47a28240d9e93e948069',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_129df4d9160e47a28240d9e93e948069',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_129df4d9160e47a28240d9e93e948069',true);\"></a> \n </span></strong></strong></strong></p><strong style=\"font-size: 13px;\"><strong style=\"font-size: 13px;\"><strong style=\"font-style: normal; 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Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.</p> \n <p style=\"margin-left: 30px;\">Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.&nbsp;</p> \n <p style=\"margin-left: 30px;\">There is one discussion thread in this module. Submit your posts by clicking on the \"Module 6 Discussion\" link above and creating a new thread. Please contribute to the class discussion with your discussion about:</p> \n <h3 style=\"color: #0067ac;\" id=\"anonymous_element_15\">Question:</h3> \n <p style=\"margin-left: 30px;\"><strong style=\"font-size: 13px;\">Thread 6.1</strong></p> \n <ul style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"> \n  <li style=\"font-size: 13px;\">Have you worked with the Laplace transform before in any context?</li> \n  <li style=\"font-size: 13px;\">Have you solved first order ODEs in the past?</li> \n  <li style=\"font-size: 13px;\">Can you give us some examples of dynamical systems that you care about that have a natural solution in terms of a Laplace Transform?</li> \n  <li style=\"font-size: 13px;\">Do you think that the software defined patients of Cobelli make sense or not?</li> \n </ul> \n <p style=\"margin-left: 30px;\">For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.</p> \n <p style=\"margin-left: 30px;\">Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.</p> \n <p style=\"margin-left: 30px;\">You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.</p> \n <p style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"><span style=\"text-decoration: underline;\">Required Activity</span>: 1 Original Post / 2 Responses<br> <span style=\"text-decoration: underline;\">Due by</span>: Original Post 11:59PM Day 4, Responses 11:59PM Day 7</p> \n <br> \n</div>\n  </div>\n\n <div id=\"_5740774_1previewModule\" class=\"moduleSample\">\n </div>\n",
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file_1.pdf
./attachments/cell_589/file_1.pdf

Module 6 Assignment

Cell description

In this module, you will complete the problem sets listed below as an assignment:

Chaparro: problems 3.2, 3.3 and 3.4
Astrom and Murray (2nd edition: http://www.cds.caltech.edu/~murray/amwiki/index.php/Second_Edition) 4.10

Follow the general guidelines below to complete and submit the assignment.

Problems should be done neatly on paper and scanned or completed electronically using markup on a tablet device.
At the top of the page, include your name, module number, and page number (page 1 of 2, etc.)
Submit your answers in PDF (.pdf) format by uploading to Blackboard using the "Module 6 Assignment" link above.

Required Activity: Submit answers to the problem sets. Due by: 11:59 PM Day 7

Technical

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Module 6 Personal Learning Journal

Cell description

In your learning journal entries for this week comment about:

Whether you see any first order ODEs that have a connection to your project work?
Do you have any thoughts or additions to the control systems introduced for the artificial pancreas?

Click on the “Module 6 Personal Learning Journal” above to access your journal and create your entry.

Required Activity: Create a reflective personal journal entry post in response to the prompts given. Due by: 11:59 PM Day 7

Technical

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