https://murray.cds.caltech.edu/index.php?action=history&feed=atom&title=HW_7_Prob_3_Hint 2026-07-25T17:55:59Z Revision history for this page on the wiki MediaWiki 1.44.2 https://murray.cds.caltech.edu/index.php?title=HW_7_Prob_3_Hint&diff=6935&oldid=prev 2007-11-25T18:14:43Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:14, 25 November 2007</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</td> <td colspan="2" class="diff-lineno">Line 5:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Part c asks you to manipulate the specific system in part b by making k_p a parameter once again and plotting how the closed loop poles vary as k_p is varied.  The first set of plots asked for should have 4 subplots: Re(pole 1) vs k_p, Im(pole 1) vs k_p, Re(pole 2) vs k_p, and Im(pole 2) vs k_p.  The second plot is a root locus plot, with k_p acting as the loop gain (as discussed in class on Wednesday)- don&#039;t forget to label gains at interesting features!</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Part c asks you to manipulate the specific system in part b by making k_p a parameter once again and plotting how the closed loop poles vary as k_p is varied.  The first set of plots asked for should have 4 subplots: Re(pole 1) vs k_p, Im(pole 1) vs k_p, Re(pole 2) vs k_p, and Im(pole 2) vs k_p.  The second plot is a root locus plot, with k_p acting as the loop gain (as discussed in class on Wednesday)- don&#039;t forget to label gains at interesting features!</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>--[[User:Braman|Braman]] 10:14, 25 November 2007 (PST)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>--[[User:Braman|<ins style="font-weight: bold; text-decoration: none;">Julia </ins>Braman]] 10:14, 25 November 2007 (PST)</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: CDS 101/110 FAQ - Lecture 8-3]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: CDS 101/110 FAQ - Lecture 8-3]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]</div></td></tr> <!-- diff cache key acs_math_mw_144-murraycds_:diff:1.41:old-6934:rev-6935:php=table --> </table>

Braman https://murray.cds.caltech.edu/index.php?title=HW_7_Prob_3_Hint&diff=6934&oldid=prev 2007-11-25T18:14:33Z

<p></p> <p><b>New page</b></p><div>This question&#039;s purpose is to give you some intuition about how controller gains affect the closed loop system, particularly the poles.<br /> <br /> Part a is a simple manipulation. You are given the form of the denominator of the closed loop system (T(s)= L(s)/(1+L(s))), the plant, and the controller. You must then find expressions for k_p and T_i in terms of the other parameters. Part b follows from this part, solving for a specific system.<br /> <br /> Part c asks you to manipulate the specific system in part b by making k_p a parameter once again and plotting how the closed loop poles vary as k_p is varied. The first set of plots asked for should have 4 subplots: Re(pole 1) vs k_p, Im(pole 1) vs k_p, Re(pole 2) vs k_p, and Im(pole 2) vs k_p. The second plot is a root locus plot, with k_p acting as the loop gain (as discussed in class on Wednesday)- don&#039;t forget to label gains at interesting features!<br /> <br /> --[[User:Braman|Braman]] 10:14, 25 November 2007 (PST)<br /> <br /> [[Category: CDS 101/110 FAQ - Lecture 8-3]]<br /> [[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]</div>

Braman