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EE547 Homework 8

Klavins — Tue, 24 Nov 2009 07:00:59 GMT

New page

* 6.15
* 6.20
* 6.23
* Find a state feedback gain <math>k</math> for the system
::<math>\dot x = \left ( \begin{array}{ccc}
-1 & 1 & 0 \\
0 & -1 & 2 \\
1 & 1 & 1
\end{array} \right )x + \left ( \begin{array}{c}
1 \\
0 \\
0
\end{array} \right ) u . </math>
so that the feedback system has eigenvalues <math>-1, \;, -2, \; \mathrm{and} \; -3</math>. Compute <math>k</math> directly without using
equivalence transformations.
* more to come

EE547 Autumn 2009

Klavins — Tue, 24 Nov 2009 06:54:29 GMT

Schedule:

←Older revision		Revision as of 06:54, 24 November 2009
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	<td> -</td>		<td> -</td>
	</tr>		</tr>
		+
		+	<tr>
		+	<td>11/24</td>
		+	<td>LTV Controllability and Observability</td>
		+	<td>Pages 176-180</td>
		+	</tr>
		+
		+	<tr>
		+	<td>11/25</td>
		+	<td>State Feedback</td>
		+	<td>Pages 231-236</td>
		+	</tr>
		+
		+	<tr>
		+	<td>11/27</td>
		+	<td>Thanksgiving Break</td>
		+	<td>-</td>
		+	</tr>
		+
		+
		+	<tr bgcolor="#abcdef">
		+	<td>11/30</td>
		+	<td>[[EE547_Homework_8\|Homework Assignment 8]] due</td>
		+	<td>-</td>
		+	</tr>
		+

	</table>		</table>

Main Page

Klavins — Fri, 20 Nov 2009 15:15:01 GMT

←Older revision		Revision as of 15:15, 20 November 2009
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	<!------------------------ NEW NEWS --------------------------->		<!------------------------ NEW NEWS --------------------------->
	* This year's [http://www.keckfutures.org/conferences/synthetic-biology.html Keck Futures Conference] is about synthetic biology. The organizers have put together a nice introduction to the field in a [http://www.keckfutures.org/conferences/synthetic-biology/Podcast_Tutorials.html series of podcasts].		* This year's [http://www.keckfutures.org/conferences/synthetic-biology.html Keck Futures Conference] is about synthetic biology. The organizers have put together a nice introduction to the field in a [http://www.keckfutures.org/conferences/synthetic-biology/Podcast_Tutorials.html series of podcasts].
-	* UW's [http://2009.igem.org/Team:Washington iGEM] team goes to Cambridge and brings back a '''gold medal'''. Congratulations! [http://dailyuw.com/2009/11/17/uw-students-bring-home-gold-medal-international-sc/ Daily Article]. (11/2009)	+	* UW's [http://2009.igem.org/Team:Washington iGEM] team goes to Cambridge and brings back a '''gold medal'''. Congratulations! [http://uwnews.org/uweek/article.aspx?id=53790 University Week Article], [http://dailyuw.com/2009/11/17/uw-students-bring-home-gold-medal-international-sc/ Daily Article]. (11/2009)
	* The [[Retreat_2009\|SOSLab 2009 Retreat]] was October 3, 2009. Kevin Oishi wins ''best presentation''!		* The [[Retreat_2009\|SOSLab 2009 Retreat]] was October 3, 2009. Kevin Oishi wins ''best presentation''!
	* The 2nd [http://faculty.washington.edu/thorsley/banff09/ Workshop on Stochasticity in Biochemical Reaction Networks] will be held in Banff, Sept. 25-27, 2009.		* The 2nd [http://faculty.washington.edu/thorsley/banff09/ Workshop on Stochasticity in Biochemical Reaction Networks] will be held in Banff, Sept. 25-27, 2009.

People

Klavins — Thu, 19 Nov 2009 07:00:17 GMT

Undergraduate Students:

←Older revision		Revision as of 07:00, 19 November 2009
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	: Synthetic Biology		: Synthetic Biology
	: [[User:Oishi\|more info]]		: [[User:Oishi\|more info]]
-	\|-
-
-	~~\|[[Image:Ssafarik.jpg\|100px]]~~
-	\|
-	~~: '''Steve Safarik'''~~
-	~~: Research Assistant~~
-	~~: Distributed Robotics, Scalable Optimization~~
-	~~: [[User:Safarik\|more info]]~~
	\|-		\|-

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	: Robotic Self-Assembly, Synthetic Biology: Directed Evolution		: Robotic Self-Assembly, Synthetic Biology: Directed Evolution
	: [http://students.washington.edu/acleone/about.html more info]		: [http://students.washington.edu/acleone/about.html more info]
-
-	\|-
-	~~\|[[Image:KenLo.jpg\|100px]]~~
-	\|
-	~~: '''Ken Lo'''~~
-	~~: Sophomore, Electrical Engineering, University of Washington~~
-	~~: Directed Evolution~~

	\|-		\|-
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	'''Undergraduate Projects''':		'''Undergraduate Projects''':
		+	Ken Lo (Turbidostat);
	Ernest Doeleman, Fedja Karalic, Yevgeniy Maksimenko, Alida Mendes (Turbidostat);		Ernest Doeleman, Fedja Karalic, Yevgeniy Maksimenko, Alida Mendes (Turbidostat);
	Yi-Wei Li (Robotic Chemistry);		Yi-Wei Li (Robotic Chemistry);

Main Page

Klavins — Wed, 18 Nov 2009 22:07:27 GMT

←Older revision		Revision as of 22:07, 18 November 2009
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		+	<font size=5>The Self-Organizing Systems Lab</font>
	{\|style="border-spacing:8px; margin:0px -8px;"		{\|style="border-spacing:8px; margin:0px -8px;"
	\|class="MainPageBG" style="width:350px; border:1px solid #cef2e0; background:#f5fffa; vertical-align:top; color:#000;"\|		\|class="MainPageBG" style="width:350px; border:1px solid #cef2e0; background:#f5fffa; vertical-align:top; color:#000;"\|
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-	\|<font size=4>Welcome ~~to the Self-Organizing Systems Lab~~</font>	+	\|<font size=4>Welcome</font>
	\|}		\|}
	\|-		\|-

EE547 Autumn 2009

Klavins — Wed, 18 Nov 2009 22:03:46 GMT

Schedule:

←Older revision		Revision as of 22:03, 18 November 2009
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	<td>11/16</td>		<td>11/16</td>
	<td>[[EE547_Homework_6\|Homework Assignment 6]] due</td>		<td>[[EE547_Homework_6\|Homework Assignment 6]] due</td>
-	<td> -</td>	+	<td>[http://faculty.washington.edu/klavins/controller-hw6.nb Mathematica Code]</td>
	</tr>		</tr>

Main Page

Klavins — Wed, 18 Nov 2009 21:56:50 GMT

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	\|style="color:#000;"\|		\|style="color:#000;"\|
	<!------------------------ PICTURE ------------------------------->		<!------------------------ PICTURE ------------------------------->
-	<randomimage options="350px">Nutriostat.jpg\|Soslab-parts.jpg\|SingleCellDetectionGFP.jpg\|Chembots.jpg\|Calibration.jpg</randomimage>	+	<randomimage options="350px">Nutriostat.jpg\|Soslab-parts.jpg\|Auxsynbio.png\|SingleCellDetectionGFP.jpg\|Chembots.jpg\|Calibration.jpg</randomimage>
	\|-		\|-
	\|		\|

Image:Auxsynbio.png

Klavins — Wed, 18 Nov 2009 21:56:20 GMT

uploaded "[[Image:Auxsynbio.png]]"

New page

Main Page

Klavins — Wed, 18 Nov 2009 21:53:10 GMT

←Older revision		Revision as of 21:53, 18 November 2009
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	\|style="color:#000;"\|		\|style="color:#000;"\|
	<!------------------------ PICTURE ------------------------------->		<!------------------------ PICTURE ------------------------------->
-	<randomimage options="350px">Soslab-parts.jpg\|SingleCellDetectionGFP.jpg\|Chembots.jpg\|Calibration.jpg</randomimage>	+	<randomimage options="350px">Nutriostat.jpg\|Soslab-parts.jpg\|SingleCellDetectionGFP.jpg\|Chembots.jpg\|Calibration.jpg</randomimage>
	\|-		\|-
	\|		\|

Image:Nutriostat.jpg

Klavins — Wed, 18 Nov 2009 21:52:42 GMT

uploaded "[[Image:Nutriostat.jpg]]"

New page

Prospective

Klavins — Wed, 18 Nov 2009 21:44:04 GMT

←Older revision		Revision as of 21:44, 18 November 2009
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	__NOTOC__		__NOTOC__
-	[[Image:SOSlabRetreat_all.jpg\|right\|450px\|Group ~~pic~~ from ~~Lab~~ Retreat 2009]]	+	[[Image:SOSlabRetreat_all.jpg\|thumb\|right\|450px\|Group photo from the SOSLab Retreat in October of 2009. Pictured are SOSLab graduate students, undergraduates and postdocs as well as a few collaborators from Seelig's and Nemhauser's and Fazel's Labs. The SOSLab collaborates with faculty members in Biology, Chemical Engineering, Biochemistry, Bioengineering, and beyond.]]

	Dear Prospective Student or Postdoc,		Dear Prospective Student or Postdoc,

EE547 Autumn 2009

Klavins — Tue, 17 Nov 2009 23:08:37 GMT

Schedule:

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	<td>Pages 5-8</td>		<td>Pages 5-8</td>
	</tr>		</tr>
-	<tr>	+	<tr bgcolor="#abcdef">
	<td>10/5</td>		<td>10/5</td>
	<td>[[EE547_Homework_1\|Homework Assignment 1]] due </td>		<td>[[EE547_Homework_1\|Homework Assignment 1]] due </td>
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	<td>Pages 44-53</td>		<td>Pages 44-53</td>
	</tr>		</tr>
-	<tr>	+	<tr bgcolor="#abcdef">
	<td>10/12</td>		<td>10/12</td>
	<td>[[EE547_Homework_2\|Homework Assignment 2]] due</td>		<td>[[EE547_Homework_2\|Homework Assignment 2]] due</td>
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	</tr>		</tr>

-	<tr>	+	<tr bgcolor="#abcdef">
	<td>10/19</td>		<td>10/19</td>
	<td>[[EE547_Homework_3\|Homework Assignment 3]] due</td>		<td>[[EE547_Homework_3\|Homework Assignment 3]] due</td>
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	</tr>		</tr>

-	<tr>	+	<tr bgcolor="#abcdef">
	<td>10/26</td>		<td>10/26</td>
	<td>[[EE547_Homework_4\|Homework Assignment 4]] due</td>		<td>[[EE547_Homework_4\|Homework Assignment 4]] due</td>
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	</tr>		</tr>

-	<tr>	+	<tr bgcolor="#abcdef">
	<td>11/2</td>		<td>11/2</td>
	<td>[[EE547_Homework_5\|Homework Assignment 5]] due</td>		<td>[[EE547_Homework_5\|Homework Assignment 5]] due</td>
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	</tr>		</tr>

-	<tr>	+	<tr bgcolor="#abfdef">
	<td>11/6</td>		<td>11/6</td>
	<td>MIDTERM</td>		<td>MIDTERM</td>
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	<tr>		<tr>
	<td>11/9</td>		<td>11/9</td>
-	<td>~~Stability~~ of ~~time Varying Systems~~</td>	+	<td>Discussion of the MIDTERM solutions</td>
-	<td>~~Pages 137~~-~~140~~</td>	+	<td>-</td>
	</tr>		</tr>

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-	<tr>	+	<tr bgcolor="#abcdef">
	<td>11/16</td>		<td>11/16</td>
	<td>[[EE547_Homework_6\|Homework Assignment 6]] due</td>		<td>[[EE547_Homework_6\|Homework Assignment 6]] due</td>
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	<tr>		<tr>
	<td>11/20</td>		<td>11/20</td>
-	<td>No Class: Makeup session to be scehduled</td>	+	<td>No Class Friday: Makeup session to be scehduled</td>
	<td>-</td>		<td>-</td>
	</tr>		</tr>

-	<tr>	+	<tr bgcolor="#abcdef">
	<td>11/23</td>		<td>11/23</td>
	<td>[[EE547_Homework_7\|Homework Assignment 7]] due</td>		<td>[[EE547_Homework_7\|Homework Assignment 7]] due</td>

EE547 Homework 7

Klavins — Tue, 17 Nov 2009 22:52:43 GMT

New page

* 6.6
* 6.8
* 6.10
* 6.11 and 6.12 (they go together)
* Find the set of all 2D state space systems that have the transfer function <math>T(s)=\frac{1}{s+1}</math>. Which are controllable? Which are observable?
* The system
::<math>\dot x = \left ( \begin{array}{ccc}
-1 & 1 & 0 \\
0 & -1 & -1 \\
1 & 0 & -2
\end{array} \right )x + \left ( \begin{array}{cc}
0 & 1 \\
1 & 0 \\
0 & 0
\end{array} \right ) u . </math>
::<math>y = ( 1 \; 0 \; 1 ) x</math>
was excited by the input <math>u(t)=(0 \; 0)^T</math> for <math>t = 0</math> to <math>5</math> seconds and the following data was obtained by sampling every 0.1 seconds. Approximately what was the initial condition <math>x(0)</math>?
<pre>
t y(t)
0.0 0.0000
0.1 0.556011
0.2 1.02816
0.3 1.42273
0.4 1.74606
0.5 2.00443
0.6 2.20402
0.7 2.35082
0.8 2.45059
0.9 2.50882
1.0 2.5307
1.1 2.52112
1.2 2.48461
1.3 2.4254
1.4 2.34736
1.5 2.25403
1.6 2.14863
1.7 2.03404
1.8 1.91286
1.9 1.78739
2.0 1.65964
2.1 1.53138
2.2 1.40411
2.3 1.27914
2.4 1.15753
2.5 1.04019
2.6 0.927817
2.7 0.82098
2.8 0.720091
2.9 0.625442
3.0 0.53721
3.1 0.455476
3.2 0.380238
3.3 0.311418
3.4 0.248879
3.5 0.192432
3.6 0.141847
3.7 0.0968592
3.8 0.0571798
3.9 0.0225006
4.0 -0.00749888
4.1 -0.0331464
4.2 -0.0547719
4.3 -0.0727038
4.4 -0.0872657
4.5 -0.0987728
4.6 -0.10753
4.7 -0.11383
4.8 -0.11795
4.9 -0.120156
5.0 -0.120694
</pre>

EE547 Autumn 2009

Klavins — Tue, 17 Nov 2009 22:22:15 GMT

Schedule:

←Older revision		Revision as of 22:22, 17 November 2009
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	<tr>		<tr>
	<td>11/13</td>		<td>11/13</td>
-	<td>~~TBA~~</td>	+	<td>Controllability Indices</td>
-	<td>-</td>	+	<td>Pages 150-152</td>
	</tr>		</tr>

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	</tr>		</tr>

		+	<tr>
		+	<td>11/17</td>
		+	<td>Observability</td>
		+	<td>Pages 153-158</td>
		+	</tr>
		+
		+	<tr>
		+	<td>11/18</td>
		+	<td>Canonical Decomposition</td>
		+	<td>Pages 158-164</td>
		+	</tr>
		+
		+
		+	<tr>
		+	<td>11/20</td>
		+	<td>No Class: Makeup session to be scehduled</td>
		+	<td>-</td>
		+	</tr>
		+
		+	<tr>
		+	<td>11/23</td>
		+	<td>[[EE547_Homework_7\|Homework Assignment 7]] due</td>
		+	<td> -</td>
		+	</tr>

	</table>		</table>

Main Page

Klavins — Tue, 17 Nov 2009 21:07:04 GMT

←Older revision		Revision as of 21:07, 17 November 2009
(2 intermediate revisions not shown.)
Line 41:		Line 41:
	<!------------------------ NEW NEWS --------------------------->		<!------------------------ NEW NEWS --------------------------->
	* This year's [http://www.keckfutures.org/conferences/synthetic-biology.html Keck Futures Conference] is about synthetic biology. The organizers have put together a nice introduction to the field in a [http://www.keckfutures.org/conferences/synthetic-biology/Podcast_Tutorials.html series of podcasts].		* This year's [http://www.keckfutures.org/conferences/synthetic-biology.html Keck Futures Conference] is about synthetic biology. The organizers have put together a nice introduction to the field in a [http://www.keckfutures.org/conferences/synthetic-biology/Podcast_Tutorials.html series of podcasts].
-	* UW's [http://2009.igem.org/Team:Washington iGEM] team goes to Cambridge and brings back a '''gold medal'''. Congratulations! (11/2009)	+	* UW's [http://2009.igem.org/Team:Washington iGEM] team goes to Cambridge and brings back a '''gold medal'''. Congratulations! [http://dailyuw.com/2009/11/17/uw-students-bring-home-gold-medal-international-sc/ Daily Article]. (11/2009)
	* The [[Retreat_2009\|SOSLab 2009 Retreat]] was October 3, 2009. Kevin Oishi wins ''best presentation''!		* The [[Retreat_2009\|SOSLab 2009 Retreat]] was October 3, 2009. Kevin Oishi wins ''best presentation''!
	* The 2nd [http://faculty.washington.edu/thorsley/banff09/ Workshop on Stochasticity in Biochemical Reaction Networks] will be held in Banff, Sept. 25-27, 2009.		* The 2nd [http://faculty.washington.edu/thorsley/banff09/ Workshop on Stochasticity in Biochemical Reaction Networks] will be held in Banff, Sept. 25-27, 2009.