http://www.cds.caltech.edu/~murray/wiki/api.php?action=feedcontributions&user=Fuller&feedformat=atomMurrayWiki - User contributions [en]2020-10-30T03:03:14ZUser contributionsMediaWiki 1.23.12http://www.cds.caltech.edu/~murray/wiki/index.php?title=Fall_2008_Meeting_ScheduleFall 2008 Meeting Schedule2008-09-24T13:30:34Z<p>Fuller: /* Thu */</p>
<hr />
<div>__NOTOC__<br />
Sign up for a time to meet. Note that different slots are for different amounts of time. Here are some guides:<br />
* 30 minute slot - weekly meeting; good if you are busy with mainly classes<br />
* 60 minute slot - standard weekly meeting<br />
* 90 minute slot - ''biweekly'' meeting. Pick even or odd weeks (week of 29 Sep = odd)<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=20% |<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|4:30p|Open}}<br />
{{agenda item|5:30p|Open}}<br />
{{agenda item|6:30p|Andrea}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item|1:30p|Julia}}<br />
{{agenda item|2:30p|Open (short)}}<br />
{{agenda item|3:00p|Odd: Open}}<br />
{{agenda item||Even: Open}}<br />
{{agenda item|6:00p|Odd: Open}}<br />
{{agenda item||Even: Open}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|4:30p|Shuo}}<br />
{{agenda item|5:30p|Open}}<br />
{{agenda item|6:30p|Open}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|3:30p|Open (short)}}<br />
{{agenda item|4:00p|Odd: Sawyer}}<br />
{{agenda item||Even: Open}}<br />
{{agenda item|5:30p|Open}}<br />
{{agenda item|6:30p|Open}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Fri ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|3:00p|Open}}<br />
{{agenda item|4:00p|Open}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item||}}<br />
{{agenda end}}<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Summer_2008_Meeting_ScheduleSummer 2008 Meeting Schedule2008-06-10T06:50:50Z<p>Fuller: /* Thu */</p>
<hr />
<div>__NOTOC__<br />
Pick a time that works..<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=20% |<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|2:00p|Mary (June), Julia (July and August)}}<br />
{{agenda item|3:00p|Shuo}}<br />
{{agenda item|4:00p|Ling}}<br />
{{agenda item|5:00p|Yizhar}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item|12:00p|Group meeting}}<br />
{{agenda item|2:00p|Andrea}}<br />
{{agenda item|3:00p|Open}}<br />
{{agenda item|4:00p|Synbio SURF}}<br />
{{agenda item|5:00p|Dionysios}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|2:00p|Open}}<br />
{{agenda item|3:30p|Alice SURF}}<br />
{{agenda item|4:30p|Open}}<br />
{{agenda item|5:30p|Open}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|2:00p|Pete}}<br />
{{agenda item|3:00p|Ophelia}}<br />
{{agenda item|4:00p|Sawyer}}<br />
{{agenda item|5:00p|Nok}}<br />
{{agenda item|6:00p|iGEM SURF?}}<br />
{{agenda end}}<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Vinutha_Kallem,_April_2008Vinutha Kallem, April 20082008-04-28T17:28:58Z<p>Fuller: /* Monday */</p>
<hr />
<div>Vinutha Kallem is a PhD student at Johns Hopkins who is visiting on 28-29 April 2008. __NOTOC__<br />
<br />
=== Schedule ===<br />
{| width=100%<br />
|- valign=top<br />
| width=50% |<br />
==== Monday ====<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Richard}}<br />
{{agenda item|10:00a|Julia}}<br />
{{agenda item|10:45a|Seminar prep}}<br />
{{agenda item|11:00a|Seminar}}<br />
{{agenda item|12:15p|Lunch: Nok et al}}<br />
{{agenda item|1:30p|Mani Chandy}}<br />
{{agenda item|2:00p|Nok}}<br />
{{agenda item|3:15p|Ling}}<br />
{{agenda item|4:00p|Elisa}}<br />
{{agenda item|4:45p|Sawyer}}<br />
{{agenda end}}<br />
| width=50% |<br />
<br />
==== Tuesday ====<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Dionysios}}<br />
{{agenda item|10:15a|Open}}<br />
{{agenda item|11:00a|Erik Winfree}}<br />
{{agenda item|11:30p|Richard}}<br />
{{agenda item|12:00p|Lunch: Mary et al}}<br />
{{agenda item|1:30p|Depart for airport}}<br />
{{agenda end}}<br />
|}<br />
<br />
=== Abstract ===<br />
<br />
TASK-INDUCED REDUCTION WITH APPLICATIONS TO NEEDLE STEERING<br />
<br />
Vinutha Kallem<br><br />
Mechanical Engineering Department<br><br />
Johns Hopkins University<br><br />
<br />
Monday, April 28, 2008<br><br />
11:00 AM to 12:00 PM<br><br />
Steele Bldg. Room 114 (CDS Library)<br><br />
<br />
What if sensitive organs prevents a physician from accessing a percutaneous target using a straight, rigid needle? One promising solution involves steering flexible bevel-tip needles. These needles introduce exciting robotics and control systems challenges because the needle tip evolves on a Lie group, and the system exhibits a high degree of nonholonomy.<br />
<br />
In this work, we present image-guided controllers for steerable needles to improve the accuracy of needle insertions. We build upon a previously proposed needle steering model to develop nonlinear observer-based controllers to drive the needle tip to a desired subspace. These controllers are designed to work in conjunction with subspace planners for the needle tip to reach a desired location in human tissue. We show that the tasks of these controllers induces symmetry, thus resulting in a reduced system which greatly simplifies controller and observer design. We propose a method to perform such reductions for generic nonholonomic kinematic systems on Lie groups with left-invariant vector fields. This technique is used to develop controllers for curve-following of a unicycle and subspace-following in needle steering. We show that this "task-induced" reduction lifts to mechanical systems.</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Spring_2008_Meeting_ScheduleSpring 2008 Meeting Schedule2008-03-25T15:09:43Z<p>Fuller: /* Wed */</p>
<hr />
<div>__NOTOC__<br />
Pick a time that works..<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=20% |<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a| Shuo}}<br />
{{agenda item|11:00a| Julia}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p| Yizhar/Sayan}}<br />
{{agenda item|6:00p| Dionysios}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|3:00p| Dom}}<br />
{{agenda item|5:00p| Mary}}<br />
{{agenda item|6:00p|[[Group Schedule|Group Meeting]]}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p| Johan}}<br />
{{agenda item|6:00p| Open}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Elisa}}<br />
{{agenda item||}}<br />
{{agenda item|3:00p|Sawyer}}<br />
{{agenda item|5:00p| Nok}}<br />
{{agenda item|6:00p| Pete}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Fri ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item|6:00p|Ling}}<br />
{{agenda end}}<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Spring_2008_Meeting_ScheduleSpring 2008 Meeting Schedule2008-03-25T15:09:23Z<p>Fuller: /* Thu */</p>
<hr />
<div>__NOTOC__<br />
Pick a time that works..<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=20% |<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a| Shuo}}<br />
{{agenda item|11:00a| Julia}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p| Yizhar/Sayan}}<br />
{{agenda item|6:00p| Dionysios}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|3:00p| Dom}}<br />
{{agenda item|5:00p| Mary}}<br />
{{agenda item|6:00p|[[Group Schedule|Group Meeting]]}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p| Johan}}<br />
{{agenda item|6:00p| Sawyer}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Elisa}}<br />
{{agenda item||}}<br />
{{agenda item|3:00p|Sawyer}}<br />
{{agenda item|5:00p| Nok}}<br />
{{agenda item|6:00p| Pete}}<br />
{{agenda end}}<br />
| width=20% |<br />
<br />
==== Fri ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item|6:00p|Ling}}<br />
{{agenda end}}<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Group_Schedule,_Winter_2008Group Schedule, Winter 20082008-01-07T18:34:39Z<p>Fuller: /* Group Meetings */</p>
<hr />
<div>This page contains information about various upcoming events that are of interest to the group. __NOTOC__<br />
{| width=100%<br />
|- valign=top<br />
| width=50% |<br />
* [[Winter 2008 Meeting Schedule]]<br />
| width=50% |<br />
* [[Group Schedule, Fall 2007]]<br />
|}<br />
<br />
== Group Meetings ==<br />
Group meetings are on Tuesdays at 6 pm in 114 Steele. Visitors are welcome (but be prepared to get signed up to give a talk!).<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=30% |<br />
{{agenda begin}}<br />
{{agenda item|Date|Speaker}}<br />
{{agenda item|8 Jan|Open}}<br />
{{agenda item|15 Jan|}}<br />
{{agenda item|22 Jan|Yizhar}}<br />
{{agenda item|29 Jan|Sawyer}}<br />
{{agenda end}}<br />
| width=30% |<br />
{{agenda begin}}<br />
{{agenda item|Date|Speaker}}<br />
{{agenda item|5 Feb|Open}}<br />
{{agenda item|12 Feb|No group meeting (ICB)}}<br />
{{agenda item|19 Feb|Ling}}<br />
{{agenda item|26 Feb|Mary}}<br />
{{agenda end}}<br />
| width=30% |<br />
{{agenda begin}}<br />
{{agenda item|Date|Speaker}}<br />
{{agenda item|4 Mar|Shuo}}<br />
{{agenda item|11 Mar|Julia}}<br />
{{agenda item|18 Mar|No group meeting (HYCON)}}<br />
{{agenda item|25 Mar|Pete}}<br />
{{agenda end}}<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=December_2007_MeetingsDecember 2007 Meetings2007-12-17T22:06:49Z<p>Fuller: /* Tue, 18 Dec */</p>
<hr />
<div>The list below has times that I am available to meet between 4 June and 15 June. Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and see if you can switch). __NOTOC__<br />
<br />
{| width=60%<br />
|- valign=top<br />
| width=50% |<br />
==== Mon, 17 Dec ====<br />
{{agenda begin}}<br />
{{agenda item|9:15a|Dionysios}}<br />
{{agenda item|10:00a|Shuo}}<br />
{{agenda item|11:00a|Yizhar}}<br />
{{agenda item|1:00p|Julia}}<br />
{{agenda item|6:30p|Open (if needed)}}<br />
{{agenda end}}<br />
| width=50% |<br />
<br />
==== Tue, 18 Dec ====<br />
{{agenda begin}}<br />
{{agenda item|8:00a|Open (if needed)}}<br />
{{agenda item|12:30p|Dom}}<br />
{{agenda item|3:00p|Mary}}<br />
{{agenda item|4:00p|Nok}}<br />
{{agenda item|5:00p|Michael}}<br />
{{agenda item|6:00p|Sawyer (and Michael D.)}}<br />
{{agenda item|7:00p|Sayan}}<br />
{{agenda end}}<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Robust_PerformanceCDS 101/110 - Robust Performance2007-12-08T00:04:38Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Design Example ({{cds101 handouts|L10-1_robperf.pdf|Slides}}, {{cds101 mp3|cds101-2007-12-03.mp3|MP3}} -- the recording goes blank after minute 5, i think the mic connector got dirty or something, sorry.)<br />
<br />
In this lecture we will discuss how to model uncertainty in control systems. We will focus on the inclusion of unmodeled dynamics in our system descriptions, allow us to reason about the performance of a system even when the dynamics are not exactly known.<br />
<br />
* {{cds101 handouts|L10-1_robperf_h.pdf|Lecture handout}}<br />
<br />
'''Wednesday:''' Robust Performance ({{cds101 handouts|L10-2_robust.pdf|Slides}}, {{cds101 mp3|cds101-2007-12-05.mp3|MP3}})<br />
<br />
'''Friday:''' Final exam review review ({{cds101 mp3|cds101-2007-12-07.mp3|MP3}})<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 12 - Robust Performance}}<br />
<br />
== Final ==<br />
<br />
The exam will consist of 3-5 problems, covering all of the the material in the course. The exam will be open book. You may use the course notes, any of the optional texts, course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out numerical computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam except for accessing local computing resources, such as MATLAB/SIMULINK or accessing copies of presentations, notes, FAQs, or other material posted on the course web site. You are not allowed to access or print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. on riday, 14 December, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2007</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Robust_PerformanceCDS 101/110 - Robust Performance2007-12-08T00:03:44Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Design Example ({{cds101 handouts|L10-1_robperf.pdf|Slides}}, {{cds101 mp3|cds101-2007-12-03.mp3|MP3}} -- the recording goes blank after minute 5, not sure what happened.)<br />
<br />
In this lecture we will discuss how to model uncertainty in control systems. We will focus on the inclusion of unmodeled dynamics in our system descriptions, allow us to reason about the performance of a system even when the dynamics are not exactly known.<br />
<br />
* {{cds101 handouts|L10-1_robperf_h.pdf|Lecture handout}}<br />
<br />
'''Wednesday:''' Robust Performance ({{cds101 handouts|L10-2_robust.pdf|Slides}}, {{cds101 mp3|cds101-2007-12-05.mp3|MP3}})<br />
<br />
'''Friday:''' Final exam review review ({{cds101 mp3|cds101-2007-12-07.mp3|MP3}})<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 12 - Robust Performance}}<br />
<br />
== Final ==<br />
<br />
The exam will consist of 3-5 problems, covering all of the the material in the course. The exam will be open book. You may use the course notes, any of the optional texts, course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out numerical computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam except for accessing local computing resources, such as MATLAB/SIMULINK or accessing copies of presentations, notes, FAQs, or other material posted on the course web site. You are not allowed to access or print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. on riday, 14 December, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2007</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Robust_PerformanceCDS 101/110 - Robust Performance2007-12-05T23:34:01Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Design Example ({{cds101 handouts|L10-1_robperf.pdf|Notes}}, {{cds101 mp3|cds101-2007-12-03.mp3|MP3}} -- the recording goes blank after minute 5, not sure what happened.)<br />
<br />
In this lecture we will discuss how to model uncertainty in control systems. We will focus on the inclusion of unmodeled dynamics in our system descriptions, allow us to reason about the performance of a system even when the dynamics are not exactly known.<br />
<br />
* {{cds101 handouts|L10-1_robperf_h.pdf|Lecture handout}}<br />
<br />
'''Wednesday:''' Robust Performance ({{cds101 mp3|cds101-2007-12-05.mp3|MP3}})<br />
<br />
'''Friday:''' Final exam review review<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 12 - Robust Performance}}<br />
<br />
== Final ==<br />
<br />
The exam will consist of 3-5 problems, covering all of the the material in the course. The exam will be open book. You may use the course notes, any of the optional texts, course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out numerical computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam except for accessing local computing resources, such as MATLAB/SIMULINK or accessing copies of presentations, notes, FAQs, or other material posted on the course web site. You are not allowed to access or print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. on riday, 14 December, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2007</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=HW8_problem_4HW8 problem 42007-12-05T01:38:16Z<p>Fuller: </p>
<hr />
<div>This problem asks you to design a controller for an unstable system (the magnetically levitating ball demonstrated in lecture) and numerically compute Bode's integral formula for the sensitivity function and show that it is equal to <math>\pi \Sigma Re (p_k)</math>, where <math>p_k</math> are the positions of open-loop right half plane poles. <br />
<br />
<br />
The controller can be designed in a manner similar to the procedure given in the lecture notes. <br />
<br />
<br />
However, the problem deson't specify that your controller have good tracking error or phase margin. All you need is for it to stabilize. I like my controllers to work well, but when I made a "good" controller, my integral never seemed to converge to the right answer. Perhaps because of numerical instability.<br />
<br />
--[[User:Fuller|Fuller]] 17:38, 4 December 2007 (PST)<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 8]]<br />
[[Category: CDS 101/110 FAQ - Homework 8, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=How_is_the_slope_of_the_gain_curve_related_to_robustness%3FHow is the slope of the gain curve related to robustness?2007-12-05T01:21:20Z<p>Fuller: </p>
<hr />
<div>To first approximation, there is a direct relation between the slope of the gain magnitude curve and the amount of phase in a Bode plot:<br />
<br />
<br />
-2 slope --> -180 deg phase<br />
<br />
-1 slope --> -90 deg phse<br />
<br />
0 slope --> 0 deg phase<br />
<br />
1 slope --> 90 deg phase<br />
<br />
2 slope --> 180 deg phase<br />
<br />
etc.<br />
<br />
<br />
An exact relation using a weighting kernel is given in section 9.4 (p. 280) in [http://www.cds.caltech.edu/~murray/books/AM05/pdf/cds101-complete_20Sep07.pdf AM08].<br />
<br />
<br />
For robustness, you want relatively high phase margin, and that is achieved by minimizing the phase (making it greater than -180 deg). This can be achieved by minimizing the slope of the magnitude plot when it crosses unity.<br />
<br />
--[[User:Fuller|Fuller]] 17:17, 4 December 2007 (PST)<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 8]]<br />
[[Category: CDS 101/110 FAQ - Homework 8, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=How_is_the_slope_of_the_gain_curve_related_to_robustness%3FHow is the slope of the gain curve related to robustness?2007-12-05T01:17:12Z<p>Fuller: </p>
<hr />
<div>To first approximation, there is a direct relation between the slope of the gain magnitude curve and the amount of phase in a Bode plot:<br />
<br />
<br />
-2 slope --> -180 deg phase<br />
<br />
-1 slope --> -90 deg phse<br />
<br />
0 slope --> 0 deg phase<br />
<br />
1 slope --> 90 deg phase<br />
<br />
2 slope --> 180 deg phase<br />
<br />
etc.<br />
<br />
<br />
An exact relation using a weighting kernel is given in section 9.4 (p. 280) in the book.<br />
<br />
<br />
For robustness, you want relatively high phase margin, and that is achieved by minimizing the phase (making it greater than -180 deg). This can be achieved by minimizing the slope of the magnitude plot when it crosses unity.<br />
<br />
--[[User:Fuller|Fuller]] 17:17, 4 December 2007 (PST)<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 8]]<br />
[[Category: CDS 101/110 FAQ - Homeowkr 8, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Loop_ShapingCDS 101/110 - Loop Shaping2007-12-05T01:12:03Z<p>Fuller: /* Homework */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Loop Shaping ({{cds101 handouts|L9-1_loopshape_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-26.mp3|MP3}})<br />
<br />
This lecture describes how to design a control system by converting the performance specifications to constraints on the loop transfer function, and then shaping the loop transfer function to satisfy the constraints. Sensitivity functinos are defined and tradeoffs between different input/output transfer functions are discussed.<br />
<br />
* {{cds101 handouts|L9-1_loopshape_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L9_1_dfan.m}}<br />
<br />
'''Wednesday:''' Performance Limits ({{cds101 handouts|L9-2_limits_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-28.mp3|MP3}})<br />
<br />
This lecture investigates some of the limits of performance for feedback systems, including the effects of right half plane poles and zeros on the closed loop system performance. A magnetic levitation system and lateral control of the Caltech ducted fan are used to illustrate the basic concepts.<br />
<br />
* {{cds101 handouts|L9-2_limits_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L9_2_maglev.m}}<br />
<br />
'''Friday:''' Recitation sections<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 11 - Loop Shaping}}<br />
<br />
== Homework ==<br />
<br />
This homework set provides practice in specification, design and limits of control systems using loop shaping. The first problem explores the relationship between the loop transfer function and the closed loop response. The second problem explores some of the effects of right half plane zeros on control performance. The third and fourth problems (CDS 110) are simple design problems for an insect flight control system and a magnetic levitation system.<br />
<br />
<!-- Links to homework materials --><br />
* {{cds101 handouts|hw8.pdf|Homework #8}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Robust_PerformanceCDS 101/110 - Robust Performance2007-12-04T23:49:57Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Design Example ({{cds101 handouts|L10-1_robperf.pdf|Notes}}, {{cds101 mp3|cds101-2007-12-03.mp3|MP3}} -- the recording goes blank after minute 5, not sure what happened.)<br />
<br />
In this lecture we will discuss how to model uncertainty in control systems. We will focus on the inclusion of unmodeled dynamics in our system descriptions, allow us to reason about the performance of a system even when the dynamics are not exactly known.<br />
<br />
* {{cds101 handouts|L10-1_robperf_h.pdf|Lecture handout}}<br />
<br />
'''Wednesday:''' Robust Performance<br />
<br />
'''Friday:''' Final exam review review<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 12 - Robust Performance}}<br />
<br />
== Final ==<br />
<br />
The exam will consist of 3-5 problems, covering all of the the material in the course. The exam will be open book. You may use the course notes, any of the optional texts, course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out numerical computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam except for accessing local computing resources, such as MATLAB/SIMULINK or accessing copies of presentations, notes, FAQs, or other material posted on the course web site. You are not allowed to access or print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. on riday, 14 December, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2007</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Loop_ShapingCDS 101/110 - Loop Shaping2007-11-28T23:54:17Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Loop Shaping ({{cds101 handouts|L9-1_loopshape_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-26.mp3|MP3}})<br />
<br />
This lecture describes how to design a control system by converting the performance specifications to constraints on the loop transfer function, and then shaping the loop transfer function to satisfy the constraints. Sensitivity functinos are defined and tradeoffs between different input/output transfer functions are discussed.<br />
<br />
* {{cds101 handouts|L9-1_loopshape_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L9_1_dfan.m}}<br />
<br />
'''Wednesday:''' Performance Limits ({{cds101 handouts|L9-2_limits_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-28.mp3|MP3}})<br />
<br />
This lecture investigates some of the limits of performance for feedback systems, including the effects of right half plane poles and zeros on the closed loop system performance. A magnetic levitation system and lateral control of the Caltech ducted fan are used to illustrate the basic concepts.<br />
<br />
* {{cds101 handouts|L9-2_limits_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L9_2_maglev.m}}<br />
<br />
'''Friday:''' Recitation sections<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 11 - Loop Shaping}}<br />
<br />
== Homework ==<br />
<br />
This homework set provides practice in specification, design and limits of control systems using loop shaping. The first problem explores the relationship between the loop transfer function and the closed loop response. The second problem explores some of the effects of right half plane zeros on control performance. The third and fourth problems (CDS 110) are simple design problems for an insect flight control system and a magnetic levitation system.<br />
<br />
<!-- Links to homework materials --><br />
* {{cds101 handouts placeholder|hw8.pdf|Homework #8}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Loop_ShapingCDS 101/110 - Loop Shaping2007-11-26T23:30:38Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Loop Shaping ({{cds101 handouts|L9-1_loopshape_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-26.mp3|MP3}})<br />
<br />
This lecture describes how to design a control system by converting the performance specifications to constraints on the loop transfer function, and then shaping the loop transfer function to satisfy the constraints. Sensitivity functinos are defined and tradeoffs between different input/output transfer functions are discussed.<br />
<br />
* {{cds101 handouts|L9-1_loopshape_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L9_1_dfan.m}}<br />
<br />
'''Wednesday:''' Performance Limits ({{cds101 handouts placeholder|L9-2_limits_h.pdf|Slides}}, {{cds101 mp3 placeholder|cds101-2007-11-28.mp3|MP3}})<br />
<br />
This lecture investigates some of the limits of performance for feedback systems, including the effects of right half plane poles and zeros on the closed loop system performance. A magnetic levitation system and lateral control of the Caltech ducted fan are used to illustrate the basic concepts.<br />
<br />
* {{cds101 handouts|L9-2_limits_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L9_2_maglev.m}}<br />
<br />
'''Friday:''' Recitation sections<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 11 - Loop Shaping}}<br />
<br />
== Homework ==<br />
<br />
This homework set provides practice in specification, design and limits of control systems using loop shaping. The first problem explores the relationship between the loop transfer function and the closed loop response. The second problem explores some of the effects of right half plane zeros on control performance. The third and fourth problems (CDS 110) are simple design problems for an insect flight control system and a magnetic levitation system.<br />
<br />
<!-- Links to homework materials --><br />
* {{cds101 handouts placeholder|hw8.pdf|Homework #8}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_PID_ControlCDS 101/110 - PID Control2007-11-26T17:28:02Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' PID Overview ({{cds101 handouts|L8-1_pid.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-19.mp3|MP3}})<br />
<br />
This lecture covers the basic tools in frequency domain control design using proportional + integral + derivative (PID) control. After reviewing the role of the controller on the loop shape and the relationship between the gain and the phase, we introduce PID control and illustrate its use to design a speed controller that satisfies a given set of performance specifications.<br />
<br />
* {{cds101 handouts|L8-1_pid_h.pdf|Lecture handout}}<br />
* MATLAB: {{cds101 matlab|L8_1_pid.m}}<br />
<br />
'''Wednesday:''' PID Analysis ({{cds101 handouts|L8-2_pid2ss.pdf|Notes}}, {{cds101 mp3|cds101-2007-11-21.mp3|MP3}})<br />
<br />
This lecture provides more details on the use of PID control, including the representation of PID controllers in state space. The problems of windup and saturation are also discussed.<br />
<br />
* {{cds101 handouts|L8-2_pid2ss.pdf|Lecture notes}}<br />
<br />
'''Friday:''' no class (Thanksgiving break)<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 10 - PID Control}}<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw7.pdf|Homework #7}}<br />
<br />
This homework set provides practice in specification and design of control systems in the frequency domain using PID control. The first two problems work through examples similar to the ones used in lecture. The third problem, for CDS 110 students, explores the use of PID control to give a desired level of performance for a simplified balance system.<br />
<br />
<!-- Links to homework materials --><br />
* Useful MATLAB commands<br />
** sisotool - display standard linear system plots on a single screen<br />
** feedback - generate a closed loop system from a loop transfer function<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 8-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 8-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 7, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_PID_ControlCDS 101/110 - PID Control2007-11-19T23:43:13Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' PID Overview ({{cds101 handouts|L8-1_pid.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-19.mp3|MP3}})<br />
<br />
This lecture covers the basic tools in frequency domain control design using proportional + integral + derivative (PID) control. After reviewing the role of the controller on the loop shape and the relationship between the gain and the phase, we introduce PID control and illustrate its use to design a speed controller that satisfies a given set of performance specifications.<br />
<br />
* {{cds101 handouts|L8-1_pid_h.pdf|Lecture handout}}<br />
* MATLAB: {{cds101 matlab|L8_1_pid.m}}<br />
<br />
'''Wednesday:''' PID Analysis ({{cds101 handouts|L8-2_pid2ss.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-11-21.mp3|MP3}})<br />
<br />
This lecture provides more details on the use of PID control, including the representation of PID controllers in state space. The problems of windup and saturation are also discussed.<br />
<br />
* {{cds101 handouts|L8-2_pid2ss.pdf|Lecture notes}}<br />
<br />
'''Friday:''' no class (Thanksgiving break)<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 10 - PID Control}}<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw7.pdf|Homework #7}}<br />
<br />
This homework set provides practice in specification and design of control systems in the frequency domain using PID control. The first two problems work through examples similar to the ones used in lecture. The third problem, for CDS 110 students, explores the use of PID control to give a desired level of performance for a simplified balance system.<br />
<br />
<!-- Links to homework materials --><br />
* Useful MATLAB commands<br />
** sisotool - display standard linear system plots on a single screen<br />
** feedback - generate a closed loop system from a loop transfer function<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 8-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 8-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 7, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=%22HW6_Question_3%22"HW6 Question 3"2007-11-16T01:27:37Z<p>Fuller: </p>
<hr />
<div>This questions asks you to examine the effects of a time delay in the loop of a control system. The time delay is modeled by the pade approximation which converts it into a rational polynomial in <math>s</math>. The time delay transfer function <math>G(s) = e^{s\tau}</math> (well, its pade approximation) should be entered in the feedback portion of the control system. <br />
<br />
<br />
Recall that if <math>P(s)C(s)</math> is the forward transfer function and <math>F(s)</math> is the feedback transfer function that feeds from the output back into the summation block, then the closed loop transfer function is <math>\frac{PC}{1+PCF}</math>. <br />
<br />
<br />
And perhaps as importantly, the open loop transfer function is <math>F(s)P(s)C(s)</math> (you can work out the math if you want to see why it is in this order, which is different from the order in the equation in the previous paragraph). The reason for this is that the open loop transfer function is what is used in the Nyquist criterion, and the Nyquist criterion decides whether the input into the summation block is going to cause the system to be unstable. <br />
<br />
<br />
--[[User:Fuller|Fuller]] 17:26, 15 November 2007 (PST)<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 6]]<br />
[[Category: CDS 101/110 FAQ - Homework 6, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=%22HW6_Question_3%22"HW6 Question 3"2007-11-16T01:26:37Z<p>Fuller: </p>
<hr />
<div>This questions asks you to examine the effects of a time delay in the loop of a control system. The time delay is modeled by the pade approximation which converts it into a rational polynomial in <math>s</math>. The time delay transfer function <math>G(s) = e^{s\tau}</math> (well, its pade approximation) should be entered in the feedback portion of the control system. <br />
<br />
<br />
Recall that if <math>P(s)C(s)</math> is the forward transfer function and <math>F(s)</math> is the feedback transfer function that feeds from the output back into the summation block, then the closed loop transfer function is <math>\frac{PC}{1+PCF}</math>. <br />
<br />
<br />
And perhaps as importantly, the open loop transfer function is <math>F(s)P(s)C(s)</math> (you can work out the math if you want to see why it is in this order). The reason for this is that the open loop transfer function is what is used in the Nyquist criterion, and the Nyquist criterion decides whether the input into the summation block is going to cause the system to be unstable. <br />
<br />
<br />
--[[User:Fuller|Fuller]] 17:26, 15 November 2007 (PST)<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 6]]<br />
[[Category: CDS 101/110 FAQ - Homework 6, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Loop_AnalysisCDS 101/110 - Loop Analysis2007-11-15T00:36:07Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Stability of Feedback Systems ({{cds101 handouts|L7-1_loopanal_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-12.mp3|MP3}})<br />
<br />
This lecture describes how to analyze the stability and performance of a feedback system by looking at the open loop transfer function. We introduce the Nyquist criteria for stability and talk about the gain and phase margin as measures of robustness. The cruise control system is used as an example throughout the lecture.<br />
<br />
* {{cds101 handouts|L7-1_loopanal_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L7_1_loopanal.m}}, {{cds101 matlab|amnyquist.m}}<br />
<br />
'''Wednesday:''' Nyquist Analysis ({{cds101 handouts|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3|cds101-2007-11-14.mp3|MP3}})<br />
<br />
In this lecture we will derive the Nyquist criterion using the principle of the argument and show how to apply it to determine stability of a closed loop system. We will also see how to account for right half plane poles in the open loop transfer function. Finally, we will give a brief introduction to time delay and its effects on stability.<br />
<br />
* {{cds101 handouts|L7-2_nyquist.pdf|Lecture notes}}<br />
<br />
'''Friday:''' recitations<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 9 - Loop Analysis}}<br />
<br />
== Homework ==<br />
<br />
This homework set covers stability and robustness using the Nyquist criterion. The first problem consists of two sample systems for which gain and phase margin should be computed using both Nyquist and Bode plots. The second problem investigates the stability and performance of the cruise control system under different PI controllers. The CDS 110 questions explore stability in the presence of delay and the stability and control of a simple disk drive positioning system.<br />
<br />
<!-- Links to homework materials --><br />
* {{cds101 handouts|hw6.pdf|Homework #6}}<br />
* Useful MATLAB commands<br />
** tf - generate a transfer function from numerator/denominator coefficients<br />
** nyquist - generate a Nyquist plot for an open loop system L(s)<br />
** margin - generate a bode plot with gain and phase margin<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 6, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Loop_AnalysisCDS 101/110 - Loop Analysis2007-11-13T18:43:32Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Stability of Feedback Systems ({{cds101 handouts|L7-1_loopanal_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-12.mp3|MP3}})<br />
<br />
This lecture describes how to analyze the stability and performance of a feedback system by looking at the open loop transfer function. We introduce the Nyquist criteria for stability and talk about the gain and phase margin as measures of robustness. The cruise control system is used as an example throughout the lecture.<br />
<br />
* {{cds101 handouts|L7-1_loopanal_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L7_1_loopanal.m}}, {{cds101 matlab|amnyquist.m}}<br />
<br />
'''Wednesday:''' Nyquist Analysis ({{cds101 handouts placeholder|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-11-14.mp3|MP3}})<br />
<br />
In this lecture we will use the concepts of stability and robustness margins to perform simple control systems design in the frequency domain. We will give a brief introduction to time delay and its effects on stability.<br />
<br />
* {{cds101 handouts placeholder|L7-2_nyquist.pdf|Lecture notes}}<br />
<br />
'''Friday:''' recitations<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 9 - Loop Analysis}}<br />
<br />
== Homework ==<br />
<br />
This homework set covers stability and robustness using the Nyquist criterion. The first problem consists of two sample systems for which gain and phase margin should be computed using both Nyquist and Bode plots. The second problem investigates the stability and performance of the cruise control system under different PI controllers. The CDS 110 questions explore stability in the presence of delay and the stability and control of a simple disk drive positioning system.<br />
<br />
<!-- Links to homework materials --><br />
* {{cds101 handouts|hw6.pdf|Homework #6}}<br />
* Useful MATLAB commands<br />
** tf - generate a transfer function from numerator/denominator coefficients<br />
** nyquist - generate a Nyquist plot for an open loop system L(s)<br />
** margin - generate a bode plot with gain and phase margin<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 6, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Lecture_7.1_bugsLecture 7.1 bugs2007-11-13T06:27:06Z<p>Fuller: </p>
<hr />
<div>UPDATE: (12 Nov 2007 10pm) the arrows on the online copies of the handouts have been corrected to align with the convention in the book, of CCW traversal of the "D contour". So bugs 1 and 2 have been addressed in the online version of the lecture notes. <br />
<br />
<br />
The Nyquist D contour is defined as being traversed in the counter-clockwise direction. On Page 5, if there were arrows on the "D" countour, they would show the tracing starting at the origin and moving downard toward <math>-j\infty</math>, traversing around toward <math>+j \infty</math> at <math>|s|=R</math> where <amsmath>R \approx \infty</amsmath>, and then traversing back to the origin. Then the Nyquist mapping (the second figure on P. 5) shows the value of <math>L(s)</math> in the complex plane as <math>s</math> takes on all of the values of the "D" contour. <br />
<br />
Bug 1: With that convention, which is the one used in the book, the Nyquist mapping would have arrows in the opposite direction as shown. They are different because that plot was generated in MATLAB, which uses a convention that the traverse is performed in the opposite direction. So you should mentally reverse the arrows in all Nyquist plots shown in this lecture. <br />
<br />
With this convention established, then the Nyquist theorem works with N=#counter-clockwise encirclements of -1, as stated in the notes. As stated in lecture, amnyquist() from the book's web page will draw the nyquist diagrams with the arrows in the convention used in the course and by mathematicians. <br />
<br />
Bug 2: On page 13, N is #CCW encirclements, not #CW encirclements (as above).<br />
<br />
Bug 3: The Nyquist diagrams on P. 10 and 13 show a unit circle referring to unity gain magnitude. But they are not drawn to scale according to the axes on the figures -- the width is correct, but they should be squished vertically (along the imaginary axis) by a factor of 2. <br />
<br />
--[[User:Fuller|Fuller]] 16:33, 12 November 2007 (PST)<br />
<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Lecture_7.1_bugsLecture 7.1 bugs2007-11-13T06:26:20Z<p>Fuller: </p>
<hr />
<div>Notes and bugs from Lecture 7.1. <br />
<br />
UPDATE: (12 Nov 2007 10pm) the arrows on the online copies of the handouts have been corrected to align with the convention in the book, of CCW traversal of the "D contour". So bugs 1 and 2 have been addressed in the online version of the lecture notes. <br />
<br />
The Nyquist D contour is defined as being traversed in the counter-clockwise direction. On Page 5, if there were arrows on the "D" countour, they would show the tracing starting at the origin and moving downard toward <math>-j\infty</math>, traversing around toward <math>+j \infty</math> at <math>|s|=R</math> where <amsmath>R \approx \infty</amsmath>, and then traversing back to the origin. Then the Nyquist mapping (the second figure on P. 5) shows the value of <math>L(s)</math> in the complex plane as <math>s</math> takes on all of the values of the "D" contour. <br />
<br />
Bug 1: With that convention, which is the one used in the book, the Nyquist mapping would have arrows in the opposite direction as shown. They are different because that plot was generated in MATLAB, which uses a convention that the traverse is performed in the opposite direction. So you should mentally reverse the arrows in all Nyquist plots shown in this lecture. <br />
<br />
With this convention established, then the Nyquist theorem works with N=#counter-clockwise encirclements of -1, as stated in the notes. As stated in lecture, amnyquist() from the book's web page will draw the nyquist diagrams with the arrows in the convention used in the course and by mathematicians. <br />
<br />
Bug 2: On page 13, N is #CCW encirclements, not #CW encirclements (as above).<br />
<br />
Bug 3: The Nyquist diagrams on P. 10 and 13 show a unit circle referring to unity gain magnitude. But they are not drawn to scale according to the axes on the figures -- the width is correct, but they should be squished vertically (along the imaginary axis) by a factor of 2. <br />
<br />
--[[User:Fuller|Fuller]] 16:33, 12 November 2007 (PST)<br />
<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Lecture_7.1_bugsLecture 7.1 bugs2007-11-13T06:25:55Z<p>Fuller: </p>
<hr />
<div>Notes and bugs from Lecture 7.1. <br />
<br />
UPDATE (12 Nov 2007 10pm): the arrows on the online copies of the handouts have been corrected to align with the convention in the book, of CCW traversal of the "D contour". So bugs 1 and 2 have been addressed in the online version of the lecture notes. <br />
<br />
The Nyquist D contour is defined as being traversed in the counter-clockwise direction. On Page 5, if there were arrows on the "D" countour, they would show the tracing starting at the origin and moving downard toward <math>-j\infty</math>, traversing around toward <math>+j \infty</math> at <math>|s|=R</math> where <amsmath>R \approx \infty</amsmath>, and then traversing back to the origin. Then the Nyquist mapping (the second figure on P. 5) shows the value of <math>L(s)</math> in the complex plane as <math>s</math> takes on all of the values of the "D" contour. <br />
<br />
Bug 1: With that convention, which is the one used in the book, the Nyquist mapping would have arrows in the opposite direction as shown. They are different because that plot was generated in MATLAB, which uses a convention that the traverse is performed in the opposite direction. So you should mentally reverse the arrows in all Nyquist plots shown in this lecture. <br />
<br />
With this convention established, then the Nyquist theorem works with N=#counter-clockwise encirclements of -1, as stated in the notes. As stated in lecture, amnyquist() from the book's web page will draw the nyquist diagrams with the arrows in the convention used in the course and by mathematicians. <br />
<br />
Bug 2: On page 13, N is #CCW encirclements, not #CW encirclements (as above).<br />
<br />
Bug 3: The Nyquist diagrams on P. 10 and 13 show a unit circle referring to unity gain magnitude. But they are not drawn to scale according to the axes on the figures -- the width is correct, but they should be squished vertically (along the imaginary axis) by a factor of 2. <br />
<br />
--[[User:Fuller|Fuller]] 16:33, 12 November 2007 (PST)<br />
<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Lecture_7.1_bugsLecture 7.1 bugs2007-11-13T00:33:51Z<p>Fuller: </p>
<hr />
<div>Notes and bugs from Lecture 7.1. <br />
<br />
The Nyquist D contour is defined as being traversed in the counter-clockwise direction. On Page 5, if there were arrows on the "D" countour, they would show the tracing starting at the origin and moving downard toward <math>-j\infty</math>, traversing around toward <math>+j \infty</math> at <math>|s|=R</math> where <math>R \approx \infty</math>, and then traversing back to the origin. Then the Nyquist mapping (the second figure on P. 5) shows the value of <math>L(s)</math> in the complex plane as <math>s</math> takes on all of the values of the "D" contour. <br />
<br />
Bug 1: With that convention, which is the one used in the book, the Nyquist mapping would have arrows in the opposite direction as shown. They are different because that plot was generated in MATLAB, which uses a convention that the traverse is performed in the opposite direction. So you should mentally reverse the arrows in all Nyquist plots shown in this lecture. <br />
<br />
With this convention established, then the Nyquist theorem works with N=#counter-clockwise encirclements of -1, as stated in the notes. As stated in lecture, amnyquist() from the book's web page will draw the nyquist diagrams with the arrows in the convention used in the course and by mathematicians. <br />
<br />
Bug 2: On page 13, N is #CCW encirclements, not #CW encirclements (as above).<br />
<br />
Bug 3: The Nyquist diagrams on P. 10 and 13 show a unit circle referring to unity gain magnitude. But they are not drawn to scale according to the axes on the figures -- the width is correct, but they should be squished vertically (along the imaginary axis) by a factor of 2. <br />
<br />
--[[User:Fuller|Fuller]] 16:33, 12 November 2007 (PST)<br />
<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Can_I_cascade_(multiply)_transfer_functions_in_MATLAB%3FCan I cascade (multiply) transfer functions in MATLAB?2007-11-12T23:45:31Z<p>Fuller: </p>
<hr />
<div>You can multiply transfer functions sys1=tf(num1,den1) and sys2 =<br />
tf(num2, den2) using sys3=sys1*sys2. you can also add them, subtract them,<br />
etc. if you want you can also use feedback(sys1,sys2) which finds the<br />
result of the feedback loop where sys1 is the transfer function going<br />
forward on the top half of the loop, and sys2 is the bottom half<br />
transfer function going backward in the loop. this is equivalent to<br />
sys1/(1+sys1*sys2), the closed-loop transfer function. Note: be careful of signs when <br />
you are using positive feedback instead of negative feedback, the 'feedback' command<br />
assumes negative feedback. <br />
<br />
For instance, in Problem 2 (d), you can use these techniques to calculate <br />
the closed loop transfer function Hyr if you have all of the intermediate transfer functions<br />
entered into MATLAB. <br />
<br />
--[[User:Fuller|Fuller]] 15:45, 12 November 2007 (PST)<br />
<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 5]]<br />
[[Category: CDS 101/110 FAQ - Homework 5, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Loop_AnalysisCDS 101/110 - Loop Analysis2007-11-12T23:25:47Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Stability of Feedback Systems ({{cds101 handouts placeholder|L7-1_loopanal_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-12.mp3|MP3}})<br />
<br />
This lecture describes how to analyze the stability and performance of a feedback system by looking at the open loop transfer function. We introduce the Nyquist criteria for stability and talk about the gain and phase margin as measures of robustness. The cruise control system is used as an example throughout the lecture.<br />
<br />
* {{cds101 handouts placeholder|L7-1_loopanal_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L7_1_loopanal.m}}<br />
<br />
'''Wednesday:''' Nyquist Analysis ({{cds101 handouts placeholder|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-11-14.mp3|MP3}})<br />
<br />
In this lecture we will use the concepts of stability and robustness margins to perform simple control systems design in the frequency domain. We will give a brief introduction to time delay and its effects on stability.<br />
<br />
* {{cds101 handouts placeholder|L7-2_nyquist.pdf|Lecture notes}}<br />
<br />
'''Friday:''' recitations<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 9 - Loop Analysis}}<br />
<br />
== Homework ==<br />
<br />
This homework set covers stability and robustness using the Nyquist criterion. The first problem consists of two sample systems for which gain and phase margin should be computed using both Nyquist and Bode plots. The second problem investigates the stability and performance of the cruise control system under different PI controllers. The CDS 110 questions explore stability in the presence of delay and the stability and control of a simple disk drive positioning system.<br />
<br />
<!-- Links to homework materials --><br />
* {{cds101 handouts|hw6.pdf|Homework #6}}<br />
* Useful MATLAB commands<br />
** tf - generate a transfer function from numerator/denominator coefficients<br />
** nyquist - generate a Nyquist plot for an open loop system L(s)<br />
** margin - generate a bode plot with gain and phase margin<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 6, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Transfer_FunctionsCDS 101/110 - Transfer Functions2007-11-08T00:57:06Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Transfer Functions ({{cds101 handouts|L6-1_xferfcns.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-05.mp3|MP3}})<br />
<br />
This lecture introduces transfer functions as a tool for analyzing feedback systems using frequency response and Bode plots. The lecture uses the example of a spring, mass, damper system to show how transfer functions can be used to compute the frequency response of an interconnected system of components. We also define poles and zeros and indicate how they affect the frequency response of a system. Finally, we introduce the general computations of block diagram algebra.<br />
<br />
* {{cds101 handouts|L6-1_xferfcns_h.pdf|Lecture handout}}<br />
<br />
'''Wednesday:''' Laplace Transforms ({{cds101 handouts|L6-2_bode.pdf|Notes}}, {{cds101 mp3|cds101-2007-11-07.mp3|MP3}})<br />
<br />
This lecture gives will discuss how to construct the frequency response corresponding to a transfer function (Bode plots). We'll cover both the properties of the frequency response as a function of gain, poles and zeros, as well as how to sketch a bode plot for a given transfer function.<br />
<br />
'''Friday:''' recitation sections<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 8 -Transfer Functions}}<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw5.pdf|Homework #5}} - due 12 Nov 07<br />
<br />
This homework set covers basic transfer function concepts. The conceptual problems show how to create a frequency response for a complex system of components using MATLAB. The analytical problems cover basic anaytical concepts in transfer functions.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 5, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110a,_Fall_2007_-_Course_ScheduleCDS 101/110a, Fall 2007 - Course Schedule2007-11-06T00:40:00Z<p>Fuller: /* {{cds110 topic|5|State Feedback}} */</p>
<hr />
<div>{{cds101-fa07}} __NOTOC__<br />
This page contains the course schedule for CDS 101/110a. The bold links for each week take you to a page that contains the a summary of the lectures for that week plus links to all course handouts.<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading || Homework<br />
|-<br />
| align=center rowspan=4 | 1 <br />
| colspan=4 |<br />
===== {{cds110 topic|1|Introduction to Feedback and Control}} =====<br />
|-<br />
| 1 Oct (M)<br />
| Introduction to Feedback<br />
| [[AM:Introduction|AM 1.1-1.4]]<br />
| rowspan=3 align=center | {{cds101 homework|1}}<br />
|-<br />
| 3 Oct (W)<br />
| Introduction to Control<br />
| [[AM:Introduction|AM 1.5-1.6]]<br />
|-<br />
| 5 Oct (F)<br />
| {{cds101 lecture|MATLAB Tutorial}}<br />
| <br />
|-<br />
| align=center rowspan=4 | 2<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|2|System Modeling}} =====<br />
|-<br />
| 8 Oct (M)<br />
| Introduction to Modeling<br />
| [[AM:System Modeling|AM 2.1--2.3]]<br />
| rowspan=3 align=center | {{cds101 homework|2}}<br />
|-<br />
| 10 Oct (W)<br />
| Modeling using Ordinary Differential Equations<br />
| [[AM:System Modeling|AM 2.4]], [[AM:Examples|AM 3.1]]<br />
|-<br />
| 12 Oct (F)<br />
| {{cds101 lecture|SIMULINK Tutorial}}<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|3|Dynamic Behavior}} =====<br />
|-<br />
| 15 Oct (M)<br />
| Qualitative Analysis and Stability<br />
| [[AM:Dynamic Behavior|AM 4.1-4.2]]<br />
| rowspan=3 align=center | {{cds101 homework|3}}<br />
|-<br />
| 17 Oct (W)<br />
| Stability Analysis<br />
| [[AM:Dynamic Behavior|AM 4.3]]<br />
|-<br />
| 19 Oct (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|4|Linear Systems}} =====<br />
|-<br />
| 22 Oct (M)<br />
| Linear Time-Invariant Systems<br />
| [[AM:Linear Systems|AM 5.1-5.2]]<br />
| rowspan=3 align=center | {{cds101 homework|4}}<br />
|-<br />
| 24 Oct (W)<br />
| Linear Systems Analysis<br />
| [[AM:Linear Systems|AM 5.5]]<br />
|-<br />
| 26 Oct* (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|5|State Feedback}} =====<br />
|-<br />
| 29 Oct (M)*<br />
| Reachability and State Feedback<br />
| [[AM:State Feedback|AM 6.1-6.3]]<br />
| rowspan=3 align=center | {{cds101 exam|Midterm}}<br />
|-<br />
| 31 Oct (W)*<br />
| Eigenvalue Placement<br />
| [[AM:State Feedback|AM 6.4-6.5]]<br />
|-<br />
| 2 Nov (F)<br />
| [[Media:Sawyer_reviewnotes.pdf|Midterm review]] (Sawyer Fuller)<br />
| <br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|6|Transfer Functions}} =====<br />
|-<br />
| 5 Nov (M)<br />
| Transfer Functions<br />
| [[AM:Transfer Funtions|AM 8.1-8.3]]<br />
| rowspan=3 align=center | {{cds101 homework|5}}<br />
|-<br />
| 7 Nov (W)<br />
| Laplace Transforms<br />
| [[AM:Transfer Functions|AM 8.6]]<br />
|-<br />
| 9 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|7|Loop Analysis}} =====<br />
|-<br />
| 12 Nov Nov (M)<br />
| Stability of Feedback Systems<br />
| [[AM:Loop Analysis|AM 9.1-9.2]]<br />
| rowspan=3 align=center | {{cds101 homework|6}}<br />
|-<br />
| 14 Nov (W)<br />
| Nyquist Criterion<br />
| [[AM:Loop Analysis|AM 9.3-9.4]]<br />
|-<br />
| 16 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|8|PID Control}} =====<br />
|-<br />
| 19 Nov (M)<br />
| The PID Controller<br />
| [[AM:PID Control|AM 10.1-10.2]]<br />
| rowspan=3 align=center | {{cds101 homework|7}}<br />
|-<br />
| 21 Nov (W)<br />
| PID Analysis and Implementation<br />
| [[AM:PID Control|AM 10.3, 10.5]]<br />
|-<br />
| 23 Nov (F)<br />
| No class (Thanksgiving)<br />
| <br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|9|Loop Shaping}} =====<br />
|-<br />
| 26 Nov (M)<br />
| Control Design using Loop Shaping<br />
| [[AM:Loop Shaping|AM 11.1-11.3]]<br />
| rowspan=3 align=center | {{cds101 homework|8}}<br />
|-<br />
| 28 Nov (W)<br />
| Limits of Performance<br />
| [[AM:Loop Shaping|AM 11.4]]<br />
|-<br />
| 30 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 10<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|10|Robust Performance}} =====<br />
|-<br />
| 3 Dec* (M)<br />
| Design Example<br />
| [[AM:Loop Shaping|AM 11.5]]<br />
| rowspan=3 align=center | {{cds101 exam|Final}}<br />
|-<br />
| 5 Dec* (W)<br />
| Robust Performance<br />
| [[AM:Robust Performance|AM 12.1-12.4]]<br />
|- <br />
| 7 Dec* (F)<br />
| Final review<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_Transfer_FunctionsCDS 101/110 - Transfer Functions2007-11-06T00:32:53Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Transfer Functions ({{cds101 handouts placeholder|L6-1_xferfcns.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-05.mp3|MP3}})<br />
<br />
This lecture introduces transfer functions as a tool for analyzing feedback systems using frequency response and Bode plots. The lecture uses the example of a spring, mass, damper system to show how transfer functions can be used to compute the frequency response of an interconnected system of components. We also define poles and zeros and indicate how they affect the frequency response of a system. Finally, we introduce the general computations of block diagram algebra.<br />
<br />
* {{cds101 handouts|L6-1_xferfcns_h.pdf|Lecture handout}}<br />
<br />
'''Wednesday:''' Laplace Transforms ({{cds101 handouts placeholder|L6-2_laplace.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-11-05.mp3|MP3}})<br />
<br />
This lecture gives a brief introduction to the Laplace transfrom and describes how it relates to the transfer function for an input/output system.<br />
<br />
'''Friday:''' recitation sections<br />
<br />
== Reading ==<br />
<br />
* {{AM07|Chapter 8 -Transfer Functions}}<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts placeholder|hw5.pdf|Homework #5}} - due 12 Nov 07<br />
<br />
This homework set covers basic transfer function concepts. The conceptual problems show how to create a frequency response for a complex system of components using MATLAB. The analytical problems cover basic anaytical concepts in transfer functions.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-2, Fall 2007</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 5, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=What_is_matrix_rank_and_how_do_i_calculate_it%3FWhat is matrix rank and how do i calculate it?2007-11-05T19:12:03Z<p>Fuller: </p>
<hr />
<div>The rank of a matrix <math>A</math> is the number of independent columns of <math>A</math>. A square matrix is full rank if all of its columns are independent. That is, a square full rank matrix has no column vector <math>v_i</math> of <math>A</math> that can be expressed as a linear combination of the other column vectors. That is, <math>v_j \neq \Sigma_{i = 1, i\neq j}^{n} a_i v_i</math> for any set of <math>a_i</math>. For example, if one column of <math>A</math> is equal to twice another one, then those two columns are linearly dependent (with a scaling factor 2) and thus the matrix would not be full rank. <br />
<br />
<br />
A simple test for determining if a square matrix is full rank is to calculate its [http://mathworld.wolfram.com/Determinant.html determinant]. If the determinant is zero, there are linearly dependent columns and the matrix is not full rank. Prof. John Doyle also mentioned during lecture that one can perform the [http://mathworld.wolfram.com/SingularValueDecomposition.html singular value decomposition] of a matrix, and if the lowest singular value <br />
is near or equal to zero the matrix is likely to be not full rank ("singular"). <br />
<br />
For Single-input-single-output (SISO) systems, which are the focus of this course, the reachability matrix will always be square; more inputs make it wider (because the width <math>B</math> is equal to the number of inputs). In the case of non-square matrices, full rank means that the number of independent vectors is as large as possible. <br />
<br />
--[[User:Fuller|Sawyer Fuller]] 16:22, 29 October 2007 (PDT)<br />
<br />
modified by [[User:Fuller|Sawyer Fuller]] 18:12, 3 November 2007 (PDT) to be more specific about square and non-square matrices<br />
<br />
fix an error in summation index 11:12 5 November 2007 (PDT)<br />
<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=What_is_matrix_rank_and_how_do_i_calculate_it%3FWhat is matrix rank and how do i calculate it?2007-11-04T01:13:42Z<p>Fuller: </p>
<hr />
<div>The rank of a matrix <math>A</math> is the number of independent columns of <math>A</math>. A square matrix is full rank if all of its columns are independent. That is, a square full rank matrix has no column vector <math>v_i</math> of <math>A</math> that can be expressed as a linear combination of the other column vectors <math>v_j \neq \Sigma_{i = 0, i\neq j}^{n} a_i v_i</math>. For example, if one column of <math>A</math> is equal to twice another one, then those two columns are linearly dependent (with a scaling factor 2) and thus the matrix would not be full rank. <br />
<br />
<br />
A simple test for determining if a square matrix is full rank is to calculate its [http://mathworld.wolfram.com/Determinant.html determinant]. If the determinant is zero, there are linearly dependent columns and the matrix is not full rank. Prof. John Doyle also mentioned during lecture that one can perform the [http://mathworld.wolfram.com/SingularValueDecomposition.html singular value decomposition] of a matrix, and if the lowest singular value <br />
is near or equal to zero the matrix is likely to be not full rank ("singular"). <br />
<br />
For Single-input-single-output (SISO) systems, which are the focus of this course, the reachability matrix will always be square; more inputs make it wider (because the width <math>B</math> is equal to the number of inputs). In the case of non-square matrices, full rank means that the number of independent vectors is as large as possible. <br />
<br />
--[[User:Fuller|Sawyer Fuller]] 16:22, 29 October 2007 (PDT)<br />
<br />
modified by [[User:Fuller|Sawyer Fuller]] 18:12, 3 November 2007 (PDT) to be more specific about square and non-square matrices<br />
<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Will_the_midterm_cover_material_from_Week_5%3FWill the midterm cover material from Week 5?2007-11-04T00:46:31Z<p>Fuller: </p>
<hr />
<div>Yes, but not heavily. Since you haven't had a homework or homework solutions we can't cover it as heavily as the weeks where homework was assigned. <br />
<br />
AM08 sections 6.3 and 6.4 were in the assigned reading, but weren't covered in the lectures, so they aren't fair game for the midterm. <br />
<br />
--[[User:Fuller|Sawyer Fuller]] 17:40, 3 November 2007 (PDT)<br />
<br />
[[Category: CDS 101/110 FAQ - Midterm]]<br />
[[Category: CDS 101/110 FAQ - Midterm, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_State_FeedbackCDS 101/110 - State Feedback2007-11-04T00:45:43Z<p>Fuller: /* FAQ */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Reachability and State Feedback ({{cds101 handouts|L5-1_reachability.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-29.mp3|MP3}})<br />
<br />
This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.<br />
<br />
* {{cds101 handouts|L5-1_reachability_h.pdf|Lecture handout}}<br />
* MATLAB code: {{cds101 matlab|L5_1_reachability.m}}, {{cds101 matlab|predprey.m}}, {{cds101 matlab|predprey_rh.m}}<br />
<br />
'''Wednesday:''' State Feedback Design ({{cds101 mp3|cds101-2007-10-31.mp3|MP3}})<br />
<br />
This lecture will present more advanced analysis on control using state feedback. The material from this lecture will not be covered on the homework.<br />
<!-- This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given. --><br />
<br />
* Midterm: available in class or outside 102 Steele<br />
<br />
'''Friday:''' Midterm review (sorry, forgot to press 'record' on MP3 recorder)<br />
* [[Media:Sawyer_reviewnotes.pdf|Midterm review notes]] Note: the plots at the end show the example problem before (unstable) and after (stable) applying state feedback.<br />
<br />
== Reading ==<br />
<br />
* {{AM06|Chapter 6 - State Feedback}}<br />
<br />
== Midterm ==<br />
<br />
The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback). The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Lewis), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out ''numerical'' computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. Tuesday, 6 November, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl><br />
'''Midterm'''<br />
<ncl>CDS 101/110 FAQ - Midterm, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110a,_Fall_2007_-_FAQCDS 101/110a, Fall 2007 - FAQ2007-11-04T00:44:51Z<p>Fuller: /* Week 5 */</p>
<hr />
<div>{{cds101-fa07}} __NOTOC__<br />
This page contains frequently asked questions for [[CDS 101/110a, Fall 2007|CDS 101/110]]. You can find FAQs for individual lectures and homework sets on the topics page for each week, available via the [[CDS 101/110a, Fall 2007 - Course Schedule|course schedule]].<br />
<br />
Additional FAQs:<br />
* [[CDS 101/110a - FAW|Full list of CDS 101/110a FAQs from previous years]]<br />
* [[AM:Frequently Asked Questions|FAQs for ''Feedback Systems'' (course text)]]<br />
<br />
== Week 1 ==<br />
<ncl>CDS 101/110 FAQ - Lecture 1-1, Fall 2007</ncl><br />
<ncl>CDS 101/110 FAQ - Lecture 1-2, Fall 2007</ncl><br />
Homework:<br />
<ncl>CDS 101/110 FAQ - Homework 1, Fall 2007</ncl><br />
<br />
== Week 2 ==<br />
<ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2007</ncl><br />
<ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2007</ncl><br />
Homework:<br />
<ncl>CDS 101/110 FAQ - Homework 2, Fall 2007</ncl><br />
<br />
== Week 3 ==<br />
<ncl>CDS 101/110 FAQ - Lecture 3-1, Fall 2007</ncl><br />
<ncl>CDS 101/110 FAQ - Lecture 3-2, Fall 2007</ncl><br />
Homework:<br />
<ncl>CDS 101/110 FAQ - Homework 3, Fall 2007</ncl><br />
<br />
== Week 4 ==<br />
<ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2007</ncl><br />
<ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2007</ncl><br />
Homework:<br />
<ncl>CDS 101/110 FAQ - Homework 4, Fall 2007</ncl><br />
<br />
== Week 5 ==<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2007</ncl><br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl><br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl><br />
Midterm:<br />
<ncl>CDS 101/110 FAQ - Midterm, Fall 2007</ncl><br />
<br />
== Week 6 ==<br />
<ncl>CDS 101/110 FAQ - Lecture 6-1, Fall 2007</ncl><br />
<ncl>CDS 101/110 FAQ - Lecture 6-2, Fall 2007</ncl><br />
Homework:<br />
<ncl>CDS 101/110 FAQ - Homework 5, Fall 2007</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Will_the_midterm_cover_material_from_Week_5%3FWill the midterm cover material from Week 5?2007-11-04T00:40:49Z<p>Fuller: </p>
<hr />
<div>Yes, but not heavily. Since you haven't had a homework or homework solutions we can't cover it heavily. <br />
<br />
AM08 sections 6.3 and 6.4 were in the assigned reading, but weren't covered in the lectures, so they aren't fair game for the midterm. <br />
<br />
--[[User:Fuller|Sawyer Fuller]] 17:40, 3 November 2007 (PDT)<br />
<br />
[[Category: CDS 101/110 FAQ - Midterm]]<br />
[[Category: CDS 101/110 FAQ - Midterm, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Will_the_midterm_cover_material_from_Week_5%3FWill the midterm cover material from Week 5?2007-11-04T00:40:34Z<p>Fuller: </p>
<hr />
<div>Yes, but not heavily. Since you haven't had a homework or homework solutions we can't cover it heavily. <br />
<br />
AM08 sections 6.3 and 6.4 were in the assigned reading, but weren't covered in the lectures, so they aren't fair game for the midterm. <br />
<br />
--[[User:Fuller|Fuller]] 17:40, 3 November 2007 (PDT)<br />
<br />
[[Category: CDS 101/110 FAQ - Midterm]]<br />
[[Category: CDS 101/110 FAQ - Midterm, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_State_FeedbackCDS 101/110 - State Feedback2007-11-03T23:57:05Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Reachability and State Feedback ({{cds101 handouts|L5-1_reachability.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-29.mp3|MP3}})<br />
<br />
This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.<br />
<br />
* {{cds101 handouts|L5-1_reachability_h.pdf|Lecture handout}}<br />
* MATLAB code: {{cds101 matlab|L5_1_reachability.m}}, {{cds101 matlab|predprey.m}}, {{cds101 matlab|predprey_rh.m}}<br />
<br />
'''Wednesday:''' State Feedback Design ({{cds101 mp3|cds101-2007-10-31.mp3|MP3}})<br />
<br />
This lecture will present more advanced analysis on control using state feedback. The material from this lecture will not be covered on the homework.<br />
<!-- This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given. --><br />
<br />
* Midterm: available in class or outside 102 Steele<br />
<br />
'''Friday:''' Midterm review (sorry, forgot to press 'record' on MP3 recorder)<br />
* [[Media:Sawyer_reviewnotes.pdf|Midterm review notes]] Note: the plots at the end show the example problem before (unstable) and after (stable) applying state feedback.<br />
<br />
== Reading ==<br />
<br />
* {{AM06|Chapter 6 - State Feedback}}<br />
<br />
== Midterm ==<br />
<br />
The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback). The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Lewis), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out ''numerical'' computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. Tuesday, 6 November, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl><br />
'''Midterm'''<br />
<ncl>CDS 101/110 FAQ - Midterm</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_State_FeedbackCDS 101/110 - State Feedback2007-11-03T23:56:45Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Reachability and State Feedback ({{cds101 handouts|L5-1_reachability.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-29.mp3|MP3}})<br />
<br />
This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.<br />
<br />
* {{cds101 handouts|L5-1_reachability_h.pdf|Lecture handout}}<br />
* MATLAB code: {{cds101 matlab|L5_1_reachability.m}}, {{cds101 matlab|predprey.m}}, {{cds101 matlab|predprey_rh.m}}<br />
<br />
'''Wednesday:''' State Feedback Design ({{cds101 mp3|cds101-2007-10-31.mp3|MP3}})<br />
<br />
This lecture will present more advanced analysis on control using state feedback. The material from this lecture will not be covered on the homework.<br />
<!-- This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given. --><br />
<br />
* Midterm: available in class or outside 102 Steele<br />
<br />
'''Friday:''' Midterm review (sorry, forgot to press 'record' on MP3 recorder)<br />
* [[Media:Sawyer_reviewnotes.pdf|Midterm review]] Note: the plots at the end show the example problem before (unstable) and after (stable) applying state feedback.<br />
<br />
== Reading ==<br />
<br />
* {{AM06|Chapter 6 - State Feedback}}<br />
<br />
== Midterm ==<br />
<br />
The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback). The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Lewis), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out ''numerical'' computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. Tuesday, 6 November, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl><br />
'''Midterm'''<br />
<ncl>CDS 101/110 FAQ - Midterm</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_State_FeedbackCDS 101/110 - State Feedback2007-11-03T23:54:38Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Reachability and State Feedback ({{cds101 handouts|L5-1_reachability.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-29.mp3|MP3}})<br />
<br />
This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.<br />
<br />
* {{cds101 handouts|L5-1_reachability_h.pdf|Lecture handout}}<br />
* MATLAB code: {{cds101 matlab|L5_1_reachability.m}}, {{cds101 matlab|predprey.m}}, {{cds101 matlab|predprey_rh.m}}<br />
<br />
'''Wednesday:''' State Feedback Design ({{cds101 mp3|cds101-2007-10-31.mp3|MP3}})<br />
<br />
This lecture will present more advanced analysis on control using state feedback. The material from this lecture will not be covered on the homework.<br />
<!-- This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given. --><br />
<br />
* Midterm: available in class or outside 102 Steele<br />
<br />
'''Friday:''' Midterm review (sorry, forgot to press 'record' on MP3 recorder)<br />
* [[Image:Sawyer_reviewnotes.pdf|Midterm review]]<br />
<br />
== Reading ==<br />
<br />
* {{AM06|Chapter 6 - State Feedback}}<br />
<br />
== Midterm ==<br />
<br />
The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback). The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Lewis), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out ''numerical'' computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. Tuesday, 6 November, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl><br />
'''Midterm'''<br />
<ncl>CDS 101/110 FAQ - Midterm</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110_-_State_FeedbackCDS 101/110 - State Feedback2007-11-03T23:48:16Z<p>Fuller: /* Overview */</p>
<hr />
<div>{{cds101-fa07}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Reachability and State Feedback ({{cds101 handouts placeholder|L5-1_reachability.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-29.mp3|MP3}})<br />
<br />
This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.<br />
<br />
'''Wednesday:''' State Feedback Design ({{cds101 mp3|cds101-2007-10-31.mp3|MP3}})<br />
<br />
This lecture will present more advanced analysis on control using state feedback. The material from this lecture will not be covered on the homework.<br />
<!-- This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given. --><br />
<br />
'''Friday:''' Midterm review<br />
<br />
== Handouts ==<br />
<br />
{| width=100%<br />
|- valign=top<br />
| width=33% | Monday<br />
* {{cds101 handouts|L5-1_reachability_h.pdf|Lecture handout}}<br />
* MATLAB code: {{cds101 matlab|L5_1_reachability.m}}, {{cds101 matlab|predprey.m}}, {{cds101 matlab|predprey_rh.m}}<br />
| width=33% | Wednesday (CDS 110)<br />
* Midterm: available in class or outside 102 Steele<br />
| width=33% | Friday<br />
* [[Media:Midterm_Review.pdf|Midterm Review Notes]]<br />
|}<br />
<br />
== Reading ==<br />
<br />
* {{AM06|Chapter 6 - State Feedback}}<br />
<br />
== Midterm ==<br />
<br />
The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback). The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Lewis), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.'' <br />
<br />
You may use a computer or calculator for carrying out ''numerical'' computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).<br />
<br />
The exam will be due by 5 p.m. Tuesday, 6 November, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2007</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl><br />
'''Midterm'''<br />
<ncl>CDS 101/110 FAQ - Midterm</ncl></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110a,_Fall_2007CDS 101/110a, Fall 20072007-11-02T12:24:46Z<p>Fuller: /* Announcements */</p>
<hr />
<div>{{cds101-fa07}}<br />
<table align=right border=1 width=20% cellpadding=6><br />
<tr><td><br />
<center>'''Contents'''</center><br />
<ul><br />
<li> [[#Grading|Grading]] <br><br />
<li> [[#Collaboration Policy|Collaboration Policy]] <br><br />
<li> [[#Course Text and References|Course Texts]] <br><br />
<li> [[#Course_Schedule|Course Schedule]]<br><br />
<li> [[#Course Project|Course Project]]<br />
</ul><br />
</table><br />
This is the homepage for CDS 101 (Analysis and Design of Feedback Systems) and CDS 110 (Introduction to Control Theory) for Fall 2007. __NOTOC__<br />
<br />
<table width=80%><br />
<tr valign=top><br />
<td width=50%><br />
'''Instructor'''<br />
* [[Main Page|Richard Murray]], murray@cds.caltech.edu<br />
* Lectures: MWF, 2-3 pm, 74 JRG<br />
* Office hours: Fridays, 3-4 pm (by appt)<br />
* Prior years: [http://www.cds.caltech.edu/~murray/courses/cds101/fa03 FA03], [http://www.cds.caltech.edu/~murray/courses/cds101/fa04 FA04], [[CDS 101/110a, Fall 2006|FA06]]<br />
<td><br />
'''Teaching Assistants''' ([mailto:cds101-tas@cds.caltech.edu cds110-tas@cds])<br />
* Julia Braman, Elisa Franco, Sawyer Fuller, George Hines, Luis Soto<br />
* Office hours: Sundays, 4-5; Tuesdays, 4-5 in 114 STL<br />
'''Course Ombuds'''<br />
* Vanessa Carson and Matthew Feldman<br />
</table><br />
<br />
== Announcements ==<br />
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table><br />
* 1 Nov 07: [[Media:Sawyer_reviewnotes.pdf|Midterm review]] notes are up<br />
* 1 Nov 07: Midterms are outside 102 Steele. Due back by Tuesday 5pm<br />
* 1 Nov 07: No recitations Friday; Midterm review is Friday 2 Nov at the normal recitation hour, 2-3p, in 74 Jorgenson<br />
* 29 Oct 07: HW # 3 is graded and the {{cds101 handouts|soln3.pdf|solutions}} are now posted<br />
** CDS 110: Average score = 30.5/40 (<math>\sigma</math> = 6.49); average time = 11.8 hours<br />
** CDS 101: Average score = 19.3/20 (<math>\sigma</math> = 0.75).<br />
* 22 Oct 07: [[CDS 101/110, Week 4 - Linear Systems]]<br />
** {{cds101 handouts|hw4.pdf|HW #4}} is now posted; due 29 Oct @ 5 pm<br />
<br />
== Course Syllabus ==<br />
<br />
CDS 101/110 provides an introduction to feedback and control in physical,<br />
biological, engineering, and information sciences. Basic principles of<br />
feedback and its use as a tool for altering the dynamics of systems and<br />
managing uncertainty. Key themes throughout the course will include<br />
input/output response, modeling and model reduction, linear versus nonlinear<br />
models, and local versus global behavior. <br />
<br />
CDS 101 is a 6 unit (2-0-4) class intended for advanced students in science<br />
and engineering who are interested in the principles and tools of feedback<br />
control, but not the analytical techniques for design and synthesis of control<br />
systems. CDS 110 is a 9 unit class (3-0-6) that provides a traditional first<br />
course in control for engineers and applied scientists. It assumes a stronger<br />
mathematical background, including working knowledge of linear algebra and<br />
ODEs. Familiarity with complex variables (Laplace transforms, residue theory)<br />
is helpful but not required. <br />
<br />
=== Grading ===<br />
The final grade will be based on homework sets, a midterm exam, and a final exam: <br />
<br />
*''Homework (50%):'' Homework sets will be handed out weekly and due on Mondays by 5 pm to the box outside of 109 Steele. A two day grace period is allowed to turn in your homework. Late homework beyond the grace period will not be accepted without a note from the health center or the Dean. MATLAB code and SIMULINK diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).<br />
<br />
* ''Midterm exam (20%):'' A midterm exam will be handed out at the beginning of midterms period (31 Oct) and due at the end of the midterm examination period (6 Nov). The midterm exam will be open book and computers will be allowed (though not required). <br />
<br />
* ''Final exam (30%):'' The final exam will be handed out on the last day of class (7 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).<br />
<br />
=== Collaboration Policy ===<br />
<br />
Collaboration on homework assignments is encouraged. You may consult<br />
outside reference materials, other students, the TA, or the<br />
instructor, but you cannot consult homework solutions from<br />
prior years and you must cite any use of material from outside<br />
references. All solutions that are handed in should be written up<br />
individually and should reflect your own understanding of the subject<br />
matter at the time of writing. MATLAB scripts and plots are<br />
considered part of your writeup and should be done individually (you<br />
can share ideas, but not code).<br />
<br />
No collaboration is allowed on the midterm or final exams.<br />
<br />
=== Course Text and References ===<br />
<br />
The primary course text is [[AM:Main Page|''Feedback Systems: An Introduction for Scientists and Engineers'']] by {{Astrom}} and Murray (2008). This book is available in the Caltech bookstore and via download from the [[AM:Main Page|companion web site]]. The following additional references may also be useful:<br />
<br />
* A. D. Lewis, ''A Mathematical Approach to Classical Control'', 2003. [http://penelope.mast.queensu.ca/math332/notes.shtml Online access].<br />
<br />
In addition to the books above, the textbooks below may also be useful. They are available in the library (non-reserve), from other students, or you can order them online.<br />
<br />
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', McGraw-Hill, 1986.<br />
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.<br />
<br />
=== Course Schedule ===<br />
The course is scheduled for MWF 2-3 pm in 74 Jorgenson. CDS 101 meets on Monday and Friday only. A detailed course schedule is available on the [[CDS 101/110a, Fall 2007 - Course Schedule|course schedule]] page.<br />
<br />
== Old Announcements ==<br />
* 20 Aug 07: created wiki page for CDS 101/110a, Fall 2007<br />
* 1 Oct 07: [[CDS 101/110, Week 1 - Introduction to Feedback and Control]]<br />
* 8 Oct 07: [[CDS 101/110, Week 2 - System Modeling]]<br />
* 15 Oct 07: {{cds101 handouts|soln1.pdf|Solutions to homework #1}} are now available<br />
** CDS 110: Average score = 35.7/40 (<math>\sigma</math> = 3.4); average time = 6.2 hours<br />
** CDS 101: Average score = 18.7/20 (<math>\sigma</math> = 1.6); average time = 3.4 hours<br />
* 15 Oct 07: [[CDS 101/110, Week 3 - Dynamic Behavior]]<br />
* 22 Oct 07: {{cds101 handouts|soln2.pdf|Solutions to homework #2}} are now available<br />
** CDS 110: Average score = 22.4/30 (<math>\sigma</math> = 4.3); average time = 9.7 hours<br />
** CDS 101: Average score = 14.8/20 (<math>\sigma</math> = 3.6); average time = 8.1 hours<br />
<br />
[[Category: Courses]] [[Category: 2007-08 Courses]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110a,_Fall_2007_-_Course_ScheduleCDS 101/110a, Fall 2007 - Course Schedule2007-11-02T12:23:22Z<p>Fuller: /* {{cds110 topic|5|State Feedback}} */</p>
<hr />
<div>{{cds101-fa07}} __NOTOC__<br />
This page contains the course schedule for CDS 101/110a. The bold links for each week take you to a page that contains the a summary of the lectures for that week plus links to all course handouts.<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading || Homework<br />
|-<br />
| align=center rowspan=4 | 1 <br />
| colspan=4 |<br />
===== {{cds110 topic|1|Introduction to Feedback and Control}} =====<br />
|-<br />
| 1 Oct (M)<br />
| Introduction to Feedback<br />
| [[AM:Introduction|AM 1.1-1.4]]<br />
| rowspan=3 align=center | {{cds101 homework|1}}<br />
|-<br />
| 3 Oct (W)<br />
| Introduction to Control<br />
| [[AM:Introduction|AM 1.5-1.6]]<br />
|-<br />
| 5 Oct (F)<br />
| {{cds101 lecture|MATLAB Tutorial}}<br />
| <br />
|-<br />
| align=center rowspan=4 | 2<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|2|System Modeling}} =====<br />
|-<br />
| 8 Oct (M)<br />
| Introduction to Modeling<br />
| [[AM:System Modeling|AM 2.1--2.3]]<br />
| rowspan=3 align=center | {{cds101 homework|2}}<br />
|-<br />
| 10 Oct (W)<br />
| Modeling using Ordinary Differential Equations<br />
| [[AM:System Modeling|AM 2.4]], [[AM:Examples|AM 3.1]]<br />
|-<br />
| 12 Oct (F)<br />
| {{cds101 lecture|SIMULINK Tutorial}}<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|3|Dynamic Behavior}} =====<br />
|-<br />
| 15 Oct (M)<br />
| Qualitative Analysis and Stability<br />
| [[AM:Dynamic Behavior|AM 4.1-4.2]]<br />
| rowspan=3 align=center | {{cds101 homework|3}}<br />
|-<br />
| 17 Oct (W)<br />
| Stability Analysis<br />
| [[AM:Dynamic Behavior|AM 4.3]]<br />
|-<br />
| 19 Oct (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|4|Linear Systems}} =====<br />
|-<br />
| 22 Oct (M)<br />
| Linear Time-Invariant Systems<br />
| [[AM:Linear Systems|AM 5.1-5.2]]<br />
| rowspan=3 align=center | {{cds101 homework|4}}<br />
|-<br />
| 24 Oct (W)<br />
| Linear Systems Analysis<br />
| [[AM:Linear Systems|AM 5.5]]<br />
|-<br />
| 26 Oct* (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|5|State Feedback}} =====<br />
|-<br />
| 29 Oct (M)*<br />
| Reachability and State Feedback<br />
| [[AM:State Feedback|AM 6.1-6.3]]<br />
| rowspan=3 align=center | {{cds101 exam|Midterm}}<br />
|-<br />
| 31 Oct (W)*<br />
| Eigenvalue Placement<br />
| [[AM:State Feedback|AM 6.4-6.5]]<br />
|-<br />
| 2 Nov (F)<br />
| [[Image:Sawyer_reviewnotes.pdf|Midterm review]] (Sawyer Fuller)<br />
| <br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|6|Transfer Functions}} =====<br />
|-<br />
| 5 Nov (M)<br />
| Transfer Functions<br />
| [[AM:Transfer Funtions|AM 8.1-8.3]]<br />
| rowspan=3 align=center | {{cds101 homework|5}}<br />
|-<br />
| 7 Nov (W)<br />
| Laplace Transforms<br />
| [[AM:Transfer Functions|AM 8.6]]<br />
|-<br />
| 9 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|7|Loop Analysis}} =====<br />
|-<br />
| 12 Nov Nov (M)<br />
| Stability of Feedback Systems<br />
| [[AM:Loop Analysis|AM 9.1-9.2]]<br />
| rowspan=3 align=center | {{cds101 homework|6}}<br />
|-<br />
| 14 Nov (W)<br />
| Nyquist Criterion<br />
| [[AM:Loop Analysis|AM 9.3-9.4]]<br />
|-<br />
| 16 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|8|PID Control}} =====<br />
|-<br />
| 19 Nov (M)<br />
| The PID Controller<br />
| [[AM:PID Control|AM 10.1-10.2]]<br />
| rowspan=3 align=center | {{cds101 homework|7}}<br />
|-<br />
| 21 Nov (W)<br />
| PID Analysis and Implementation<br />
| [[AM:PID Control|AM 10.3, 10.5]]<br />
|-<br />
| 23 Nov (F)<br />
| No class (Thanksgiving)<br />
| <br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|9|Loop Shaping}} =====<br />
|-<br />
| 26 Nov (M)<br />
| Control Design using Loop Shaping<br />
| [[AM:Loop Shaping|AM 11.1-11.3]]<br />
| rowspan=3 align=center | {{cds101 homework|8}}<br />
|-<br />
| 28 Nov (W)<br />
| Limits of Performance<br />
| [[AM:Loop Shaping|AM 11.4]]<br />
|-<br />
| 30 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 10<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|10|Robust Performance}} =====<br />
|-<br />
| 3 Dec* (M)<br />
| Design Example<br />
| [[AM:Loop Shaping|AM 11.5]]<br />
| rowspan=3 align=center | {{cds101 exam|Final}}<br />
|-<br />
| 5 Dec* (W)<br />
| Robust Performance<br />
| [[AM:Robust Performance|AM 12.1-12.4]]<br />
|- <br />
| 7 Dec* (F)<br />
| Final review<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110a,_Fall_2007_-_Course_ScheduleCDS 101/110a, Fall 2007 - Course Schedule2007-11-02T12:17:48Z<p>Fuller: /* {{cds110 topic|5|State Feedback}} */</p>
<hr />
<div>{{cds101-fa07}} __NOTOC__<br />
This page contains the course schedule for CDS 101/110a. The bold links for each week take you to a page that contains the a summary of the lectures for that week plus links to all course handouts.<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading || Homework<br />
|-<br />
| align=center rowspan=4 | 1 <br />
| colspan=4 |<br />
===== {{cds110 topic|1|Introduction to Feedback and Control}} =====<br />
|-<br />
| 1 Oct (M)<br />
| Introduction to Feedback<br />
| [[AM:Introduction|AM 1.1-1.4]]<br />
| rowspan=3 align=center | {{cds101 homework|1}}<br />
|-<br />
| 3 Oct (W)<br />
| Introduction to Control<br />
| [[AM:Introduction|AM 1.5-1.6]]<br />
|-<br />
| 5 Oct (F)<br />
| {{cds101 lecture|MATLAB Tutorial}}<br />
| <br />
|-<br />
| align=center rowspan=4 | 2<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|2|System Modeling}} =====<br />
|-<br />
| 8 Oct (M)<br />
| Introduction to Modeling<br />
| [[AM:System Modeling|AM 2.1--2.3]]<br />
| rowspan=3 align=center | {{cds101 homework|2}}<br />
|-<br />
| 10 Oct (W)<br />
| Modeling using Ordinary Differential Equations<br />
| [[AM:System Modeling|AM 2.4]], [[AM:Examples|AM 3.1]]<br />
|-<br />
| 12 Oct (F)<br />
| {{cds101 lecture|SIMULINK Tutorial}}<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|3|Dynamic Behavior}} =====<br />
|-<br />
| 15 Oct (M)<br />
| Qualitative Analysis and Stability<br />
| [[AM:Dynamic Behavior|AM 4.1-4.2]]<br />
| rowspan=3 align=center | {{cds101 homework|3}}<br />
|-<br />
| 17 Oct (W)<br />
| Stability Analysis<br />
| [[AM:Dynamic Behavior|AM 4.3]]<br />
|-<br />
| 19 Oct (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|4|Linear Systems}} =====<br />
|-<br />
| 22 Oct (M)<br />
| Linear Time-Invariant Systems<br />
| [[AM:Linear Systems|AM 5.1-5.2]]<br />
| rowspan=3 align=center | {{cds101 homework|4}}<br />
|-<br />
| 24 Oct (W)<br />
| Linear Systems Analysis<br />
| [[AM:Linear Systems|AM 5.5]]<br />
|-<br />
| 26 Oct* (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|5|State Feedback}} =====<br />
|-<br />
| 29 Oct (M)*<br />
| Reachability and State Feedback<br />
| [[AM:State Feedback|AM 6.1-6.3]]<br />
| rowspan=3 align=center | {{cds101 exam|Midterm}}<br />
|-<br />
| 31 Oct (W)*<br />
| Eigenvalue Placement<br />
| [[AM:State Feedback|AM 6.4-6.5]]<br />
|-<br />
| 2 Nov (F)<br />
| Midterm review [[Image:Sawyer_reviewnotes.pdf]]<br />
| <br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|6|Transfer Functions}} =====<br />
|-<br />
| 5 Nov (M)<br />
| Transfer Functions<br />
| [[AM:Transfer Funtions|AM 8.1-8.3]]<br />
| rowspan=3 align=center | {{cds101 homework|5}}<br />
|-<br />
| 7 Nov (W)<br />
| Laplace Transforms<br />
| [[AM:Transfer Functions|AM 8.6]]<br />
|-<br />
| 9 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|7|Loop Analysis}} =====<br />
|-<br />
| 12 Nov Nov (M)<br />
| Stability of Feedback Systems<br />
| [[AM:Loop Analysis|AM 9.1-9.2]]<br />
| rowspan=3 align=center | {{cds101 homework|6}}<br />
|-<br />
| 14 Nov (W)<br />
| Nyquist Criterion<br />
| [[AM:Loop Analysis|AM 9.3-9.4]]<br />
|-<br />
| 16 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|8|PID Control}} =====<br />
|-<br />
| 19 Nov (M)<br />
| The PID Controller<br />
| [[AM:PID Control|AM 10.1-10.2]]<br />
| rowspan=3 align=center | {{cds101 homework|7}}<br />
|-<br />
| 21 Nov (W)<br />
| PID Analysis and Implementation<br />
| [[AM:PID Control|AM 10.3, 10.5]]<br />
|-<br />
| 23 Nov (F)<br />
| No class (Thanksgiving)<br />
| <br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|9|Loop Shaping}} =====<br />
|-<br />
| 26 Nov (M)<br />
| Control Design using Loop Shaping<br />
| [[AM:Loop Shaping|AM 11.1-11.3]]<br />
| rowspan=3 align=center | {{cds101 homework|8}}<br />
|-<br />
| 28 Nov (W)<br />
| Limits of Performance<br />
| [[AM:Loop Shaping|AM 11.4]]<br />
|-<br />
| 30 Nov (F)<br />
| Recitation sections<br />
| <br />
|-<br />
| align=center rowspan=4 | 10<br />
| colspan=4 |<br />
<br />
===== {{cds110 topic|10|Robust Performance}} =====<br />
|-<br />
| 3 Dec* (M)<br />
| Design Example<br />
| [[AM:Loop Shaping|AM 11.5]]<br />
| rowspan=3 align=center | {{cds101 exam|Final}}<br />
|-<br />
| 5 Dec* (W)<br />
| Robust Performance<br />
| [[AM:Robust Performance|AM 12.1-12.4]]<br />
|- <br />
| 7 Dec* (F)<br />
| Final review<br />
|}</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=File:Sawyer_reviewnotes.pdfFile:Sawyer reviewnotes.pdf2007-11-02T12:15:44Z<p>Fuller: </p>
<hr />
<div></div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_101/110a,_Fall_2007CDS 101/110a, Fall 20072007-11-01T21:09:10Z<p>Fuller: /* Announcements */</p>
<hr />
<div>{{cds101-fa07}}<br />
<table align=right border=1 width=20% cellpadding=6><br />
<tr><td><br />
<center>'''Contents'''</center><br />
<ul><br />
<li> [[#Grading|Grading]] <br><br />
<li> [[#Collaboration Policy|Collaboration Policy]] <br><br />
<li> [[#Course Text and References|Course Texts]] <br><br />
<li> [[#Course_Schedule|Course Schedule]]<br><br />
<li> [[#Course Project|Course Project]]<br />
</ul><br />
</table><br />
This is the homepage for CDS 101 (Analysis and Design of Feedback Systems) and CDS 110 (Introduction to Control Theory) for Fall 2007. __NOTOC__<br />
<br />
<table width=80%><br />
<tr valign=top><br />
<td width=50%><br />
'''Instructor'''<br />
* [[Main Page|Richard Murray]], murray@cds.caltech.edu<br />
* Lectures: MWF, 2-3 pm, 74 JRG<br />
* Office hours: Fridays, 3-4 pm (by appt)<br />
* Prior years: [http://www.cds.caltech.edu/~murray/courses/cds101/fa03 FA03], [http://www.cds.caltech.edu/~murray/courses/cds101/fa04 FA04], [[CDS 101/110a, Fall 2006|FA06]]<br />
<td><br />
'''Teaching Assistants''' ([mailto:cds101-tas@cds.caltech.edu cds110-tas@cds])<br />
* Julia Braman, Elisa Franco, Sawyer Fuller, George Hines, Luis Soto<br />
* Office hours: Sundays, 4-5; Tuesdays, 4-5 in 114 STL<br />
'''Course Ombuds'''<br />
* Vanessa Carson and Matthew Feldman<br />
</table><br />
<br />
== Announcements ==<br />
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table><br />
* 1 Nov 07: Midterms are outside 102 Steele. Due back by Tuesday 5pm<br />
* 1 Nov 07: No recitations Friday; Midterm review is Friday 2 Nov at the normal recitation hour, 2-3p, in 74 Jorgenson<br />
* 29 Oct 07: HW # 3 is graded and the {{cds101 handouts|soln3.pdf|solutions}} are now posted<br />
** CDS 110: Average score = 30.5/40 (<math>\sigma</math> = 6.49); average time = 11.8 hours<br />
** CDS 101: Average score = 19.3/20 (<math>\sigma</math> = 0.75).<br />
* 22 Oct 07: [[CDS 101/110, Week 4 - Linear Systems]]<br />
** {{cds101 handouts|hw4.pdf|HW #4}} is now posted; due 29 Oct @ 5 pm<br />
<br />
== Course Syllabus ==<br />
<br />
CDS 101/110 provides an introduction to feedback and control in physical,<br />
biological, engineering, and information sciences. Basic principles of<br />
feedback and its use as a tool for altering the dynamics of systems and<br />
managing uncertainty. Key themes throughout the course will include<br />
input/output response, modeling and model reduction, linear versus nonlinear<br />
models, and local versus global behavior. <br />
<br />
CDS 101 is a 6 unit (2-0-4) class intended for advanced students in science<br />
and engineering who are interested in the principles and tools of feedback<br />
control, but not the analytical techniques for design and synthesis of control<br />
systems. CDS 110 is a 9 unit class (3-0-6) that provides a traditional first<br />
course in control for engineers and applied scientists. It assumes a stronger<br />
mathematical background, including working knowledge of linear algebra and<br />
ODEs. Familiarity with complex variables (Laplace transforms, residue theory)<br />
is helpful but not required. <br />
<br />
=== Grading ===<br />
The final grade will be based on homework sets, a midterm exam, and a final exam: <br />
<br />
*''Homework (50%):'' Homework sets will be handed out weekly and due on Mondays by 5 pm to the box outside of 109 Steele. A two day grace period is allowed to turn in your homework. Late homework beyond the grace period will not be accepted without a note from the health center or the Dean. MATLAB code and SIMULINK diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).<br />
<br />
* ''Midterm exam (20%):'' A midterm exam will be handed out at the beginning of midterms period (31 Oct) and due at the end of the midterm examination period (6 Nov). The midterm exam will be open book and computers will be allowed (though not required). <br />
<br />
* ''Final exam (30%):'' The final exam will be handed out on the last day of class (7 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).<br />
<br />
=== Collaboration Policy ===<br />
<br />
Collaboration on homework assignments is encouraged. You may consult<br />
outside reference materials, other students, the TA, or the<br />
instructor, but you cannot consult homework solutions from<br />
prior years and you must cite any use of material from outside<br />
references. All solutions that are handed in should be written up<br />
individually and should reflect your own understanding of the subject<br />
matter at the time of writing. MATLAB scripts and plots are<br />
considered part of your writeup and should be done individually (you<br />
can share ideas, but not code).<br />
<br />
No collaboration is allowed on the midterm or final exams.<br />
<br />
=== Course Text and References ===<br />
<br />
The primary course text is [[AM:Main Page|''Feedback Systems: An Introduction for Scientists and Engineers'']] by {{Astrom}} and Murray (2008). This book is available in the Caltech bookstore and via download from the [[AM:Main Page|companion web site]]. The following additional references may also be useful:<br />
<br />
* A. D. Lewis, ''A Mathematical Approach to Classical Control'', 2003. [http://penelope.mast.queensu.ca/math332/notes.shtml Online access].<br />
<br />
In addition to the books above, the textbooks below may also be useful. They are available in the library (non-reserve), from other students, or you can order them online.<br />
<br />
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', McGraw-Hill, 1986.<br />
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.<br />
<br />
=== Course Schedule ===<br />
The course is scheduled for MWF 2-3 pm in 74 Jorgenson. CDS 101 meets on Monday and Friday only. A detailed course schedule is available on the [[CDS 101/110a, Fall 2007 - Course Schedule|course schedule]] page.<br />
<br />
== Old Announcements ==<br />
* 20 Aug 07: created wiki page for CDS 101/110a, Fall 2007<br />
* 1 Oct 07: [[CDS 101/110, Week 1 - Introduction to Feedback and Control]]<br />
* 8 Oct 07: [[CDS 101/110, Week 2 - System Modeling]]<br />
* 15 Oct 07: {{cds101 handouts|soln1.pdf|Solutions to homework #1}} are now available<br />
** CDS 110: Average score = 35.7/40 (<math>\sigma</math> = 3.4); average time = 6.2 hours<br />
** CDS 101: Average score = 18.7/20 (<math>\sigma</math> = 1.6); average time = 3.4 hours<br />
* 15 Oct 07: [[CDS 101/110, Week 3 - Dynamic Behavior]]<br />
* 22 Oct 07: {{cds101 handouts|soln2.pdf|Solutions to homework #2}} are now available<br />
** CDS 110: Average score = 22.4/30 (<math>\sigma</math> = 4.3); average time = 9.7 hours<br />
** CDS 101: Average score = 14.8/20 (<math>\sigma</math> = 3.6); average time = 8.1 hours<br />
<br />
[[Category: Courses]] [[Category: 2007-08 Courses]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Can_you_recommend_a_good_linear_algebra_resource%3FCan you recommend a good linear algebra resource?2007-10-30T17:23:41Z<p>Fuller: </p>
<hr />
<div>I recommend Gilbert Strang's ''Linear Algebra and its Applications''.<br />
<br />
Here are two controls-oriented review notes from Hideo Mabuchi from CDS110a '05: [[Media:Wed-9-28v2.pdf|1. Matrices and vectors]], [[Media:Wed-10-5.pdf|2. Systems of linear ODE's]]<br />
<br />
--[[User:Fuller|Sawyer Fuller]] 16:35, 29 October 2007 (PDT)<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1, Fall 2007]]</div>Fullerhttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Can_you_recommend_a_good_linear_algebra_resource%3FCan you recommend a good linear algebra resource?2007-10-30T17:21:54Z<p>Fuller: </p>
<hr />
<div>I recommend Gilbert Strang's ''Linear Algebra and its Applications''.<br />
<br />
Here are two controls-oriented review notes from Hideo Mabuchi from CDS110a '05: [[Media:Wed-9-28v2.pdf|1. Matrices and vectors]], [[Media:Wed-10-5.pdf|2. Linear ODE's]]<br />
<br />
--[[User:Fuller|Sawyer Fuller]] 16:35, 29 October 2007 (PDT)<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 5-1, Fall 2007]]</div>Fuller