Murray Wiki - User contributions [en]

HW 7 Problem 2

2007-11-25T22:40:22Z

Hines:

What you're supposed to take away from this problem is a better intuition for how to come up with your ''first cut'' controller, and then a better understanding of how to tune that controller to meet specifications. By looking at the process transfer function, you can't easily deduce the correct values of the controller gains, but what you should do is look at either the process step response or the process transfer function and reason about

* how the process needs to be modified to meet the specs
* what type of controller (P, PI, PD, PID, etc.) is necessary
* what that controller transfer function should look like

As a side note, if you're convinced that you want a full PID controller, Ziegler-Nichols parameters are a good starting point, but remember that complicated is not always good.

Do NOT simply guess and check gain values. If it is clear that you guessed numbers and they happened to work, you will not get full credit. Explain your thought process in arriving at the controller you choose.

--[[User:Hines|George Hines]] 14:38, 25 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 7]]
[[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]

HW 7 Problem 2

2007-11-25T22:39:26Z

Hines:

What you're supposed to take away from this problem is a better intuition for how to come up with your ''first cut'' controller. By looking at the process transfer function, you can't easily deduce the correct values of the controller gains, but what you should do is look at either the process step response or the process transfer function and reason about

* how the process needs to be modified to meet the specs
* what type of controller (P, PI, PD, PID, etc.) is necessary
* what that controller transfer function should look like

As a side note, if you're convinced that you want a full PID controller, Ziegler-Nichols parameters are a good starting point, but remember that complicated is not always good.

Do NOT simply guess and check gain values. If it is clear that you guessed numbers and they happened to work, you will not get full credit. Explain your thought process in arriving at the controller you choose.

--[[User:Hines|George Hines]] 14:38, 25 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 7]]
[[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]

HW 7 Problem 2

2007-11-25T22:39:15Z

Hines:

What you're supposed to take away from this problem is a better intuition for how to come up with your 'first cut' controller. By looking at the process transfer function, you can't easily deduce the correct values of the controller gains, but what you should do is look at either the process step response or the process transfer function and reason about

* how the process needs to be modified to meet the specs
* what type of controller (P, PI, PD, PID, etc.) is necessary
* what that controller transfer function should look like

As a side note, if you're convinced that you want a full PID controller, Ziegler-Nichols parameters are a good starting point, but remember that complicated is not always good.

Do NOT simply guess and check gain values. If it is clear that you guessed numbers and they happened to work, you will not get full credit. Explain your thought process in arriving at the controller you choose.

--[[User:Hines|George Hines]] 14:38, 25 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 7]]
[[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]

HW 7 Problem 2

2007-11-25T22:38:16Z

Hines:

What you're supposed to take away from this problem is a better intuition for how to make your first cut controller. By looking at the process transfer function, you can't easily deduce the correct values of the controller gains, but what you should do is look at either the process step response or the process transfer function and reason about

* how the process needs to be modified to meet the specs
* what type of controller (P, PI, PD, PID, etc.) is necessary
* what that controller transfer function should look like

As a side note, if you're convinced that you want a full PID controller, Ziegler-Nichols parameters are a good starting point, but remember that complicated is not always good.

Do NOT simply guess and check gain values. If it is clear that you guessed numbers and they happened to work, you will not get full credit. Explain your thought process in arriving at the controller you choose.

--[[User:Hines|George Hines]] 14:38, 25 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 7]]
[[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]

HW 7 Problem 2

2007-11-25T22:38:05Z

Hines:

What you're supposed to take away from this problem is a better intuition for how to make your first cut controller. By looking at the process transfer function, you can't easily deduce the correct values of the controller gains, but what you should do is look at either the process step response or the process transfer function and reason about

* how the process needs to be modified to meet the specs
* what type of controller (P, PI, PD, PID, etc.) is necessary
* what that controller transfer function should look like

As a side note, if you're convinced that you want a full PID controller, Ziegler-Nichols parameters are a good starting point, but remember that complicated is not always good.

Do NOT simply guess and check gain values. If it is clear that you guessed numbers and they happened to work, you will not get full credit. Explain your thought process in arriving at the controller you choose.

--[[User:Hines|Hines]] 14:38, 25 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 7]]
[[Category: CDS 101/110 FAQ - Homework 7, Fall 2007]]

HW 6 Question 4

2007-11-17T00:45:23Z

Hines:

First, this problem has a small bug: in part (a), the problem asks for a gain crossover frequency of 1 rad/sec. It should ask for a bandwidth of 1 rad/sec. There are various definitions of the bandwidth, and the gain crossover frequency is one of them, but satisfying that definition is impossible in this particular problem. You'll need to use a different definition of the bandwidth to find a feasible result.

This problem is meant to help you start thinking about how to "place" poles and zeros intelligently so that you don't have to resort to ridiculously high gains (>1000). Intelligence in this case manifests itself as observing that if you place the controller zero at the right distance between the controller pole and one of the process poles, you can add large amounts of phase, which gives you room to play with the proportional gain to adjust your bandwidth.

So I recommend taking a step back from Matlab, and starting this problem with pencil and paper, so you get an idea of the relative sizes of <math>k_p</math> and <math>k_d</math> before stumbling blindly into a guess/check cycle.

--[[User:Hines|George Hines]] 16:43, 16 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 6]]
[[Category: CDS 101/110 FAQ - Homework 6, Fall 2007]]

HW 6 Question 4

2007-11-17T00:44:20Z

Hines:

HW 6 Question 4

2007-11-17T00:43:23Z

Hines:

First, this problem has a small bug: in part (a), the problem asks for a gain crossover frequency of 1 rad/sec. It should ask for a bandwidth of 1 rad/sec. There are various definitions of the bandwidth, and the gain crossover frequency is one of them, but satisfying that definition is impossible in this particular problem. You'll need to use a different definition of the bandwidth to find a feasible result.

This problem is meant to help you start thinking about how to "place" poles and zeros intelligently so that you don't have to resort to ridiculously high gains (>1000). Intelligence in this case manifests itself as observing that if you place the controller zero at the right distance between the controller pole and one of the process poles, you can add large amounts of phase, which gives you room to play with the proportional gain to adjust your bandwidth.

So I recommend taking a step back from Matlab, and starting this problem with pencil and paper, so you get an idea of the relative sizes of <math>k_p</math> and <math>k_d</math> before stumbling blindly into a guess/check cycle.

--[[User:Hines|Hines]] 16:43, 16 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 6]]
[[Category: CDS 101/110 FAQ - Homework, Fall 2007]]

Why counterclockwise encirclements of -1?

2007-11-13T01:57:33Z

Hines:

There are really two questions here: why counterclockwise? and why -1? First things first: there's nothing innately special about traversing the contour counterclockwise...that's basically a sign convention. The fact that counterclockwise traversal is the tradition is only because the contour integration that is necessary to justify the Nyquist Criterion rigorously is defined to be positive for traversal in the direction that places the interior of the domain on the left, and for this contour, that direction is counterclockwise.

Secondly, why -1? That's because we want the number of RHP zeros of <math>1+L(s)</math>. If we wanted to find the number of RHP zeros of the plain loop transfer function <math>L(s)</math> (for instance), we would count the number of encirclements of the origin, or if we wanted the number of RHP zeros of <math>2+L(s)</math>, we would count the number of encirclements of -2, but these aren't what we're interested in.

For more information on the Nyquist contour, see [http://en.wikipedia.org/wiki/Nyquist_stability_criterion this article], and for more information on the Argument principle of complex analysis, see [http://en.wikipedia.org/wiki/Argument_principle this article].

Constructing the Nyquist plot by hand directly from the transfer function is a huge pain, and I wouldn't recommend ever actually trying it. If you want to do this, just use Matlab's builtin nyquist() command. However, it is sometimes convenient to sketch a Nyquist plot by hand from a Bode plot. To do this, you read off the gain and the phase at a given frequency on the Bode plot, and use those as the polar coordinates of the corresponding point on the Nyquist plot. Going in the opposite direction (Bode plot from Nyquist plot) isn't terribly useful, because both plots are found from the same transfer function, and it's generally easier to plot the Bode plot from the transfer function directly.

--[[User:Hines|George Hines]] 17:43, 12 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Lecture 7-1]]
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]

Why counterclockwise encirclements of -1?

2007-11-13T01:56:20Z

Hines:

There are really two questions here: why counterclockwise? and why -1? First things first: there's nothing innately special about traversing the contour counterclockwise...that's basically a sign convention. The fact that counterclockwise traversal is the tradition is only because the contour integration that is necessary to justify the Nyquist Criterion rigorously is defined to be positive for traversal in the direction that places the interior of the domain on the left, and for this contour, that direction is counterclockwise.

Secondly, why -1? That's because we want the number of RHP zeros of <math>1+L(s)</math>. If we wanted to find the number of RHP zeros of the plain loop transfer function <math>L(s)</math> (for instance), we would count the number of encirclements of the origin, or if we wanted the number of RHP zeros of <math>2+L(s)</math>, we would count the number of encirclements of -2, but these aren't what we're interested in.

For more information on the Nyquist contour and the Argument principle of complex analysis, see [http://en.wikipedia.org/wiki/Nyquist_stability_criterion] or [http://en.wikipedia.org/wiki/Argument_principle]

Constructing the Nyquist plot by hand directly from the transfer function is a huge pain, and I wouldn't recommend ever actually trying it. If you want to do this, just use Matlab's builtin nyquist() command. However, it is sometimes convenient to sketch a Nyquist plot by hand from a Bode plot. To do this, you read off the gain and the phase at a given frequency on the Bode plot, and use those as the polar coordinates of the corresponding point on the Nyquist plot. Going in the opposite direction (Bode plot from Nyquist plot) isn't terribly useful, because both plots are found from the same transfer function, and it's generally easier to plot the Bode plot from the transfer function directly.

--[[User:Hines|George Hines]] 17:43, 12 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Lecture 7-1]]
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]

Why counterclockwise encirclements of -1?

2007-11-13T01:53:12Z

Hines:

There are really two questions here: why counterclockwise? and why -1? First things first: there's nothing innately special about traversing the contour counterclockwise...that's basically a sign convention. The fact that counterclockwise traversal is the tradition is only because the contour integration that is necessary to justify the Nyquist Criterion rigorously is defined to be positive for traversal in the direction that places the interior of the domain on the left, and for this contour, that direction is counterclockwise.

Secondly, why -1? That's because we want the number of RHP zeros of <math>1+L(s)</math>. If we wanted to find the number of RHP zeros of the plain loop transfer function <math>L(s)</math>, we would count the number of encirclements of the ''origin'', but this isn't what we're interested in, so we have to shift the winding center over to -1 to make the answer more relevant.

Constructing the Nyquist plot by hand directly from the transfer function is a huge pain, and I wouldn't recommend ever actually trying it. If you want to do this, just use Matlab's builtin nyquist() command. However, it is sometimes convenient to sketch a Nyquist plot by hand from a Bode plot. To do this, you read off the gain and the phase at a given frequency on the Bode plot, and use those as the polar coordinates of the corresponding point on the Nyquist plot. Going in the opposite direction (Bode plot from Nyquist plot) isn't terribly useful, because both plots are found from the same transfer function, and it's generally easier to plot the Bode plot from the transfer function directly.

--[[User:Hines|George Hines]] 17:43, 12 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Lecture 7-1]]
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]

Why counterclockwise encirclements of -1?

2007-11-13T01:43:30Z

Hines:

There are really two questions here: why counterclockwise? and why -1? First things first: there's nothing innately special about traversing the contour counterclockwise...that's basically a sign convention. The fact that counterclockwise traversal is the tradition is only because the contour integration that is necessary to justify the Nyquist Criterion rigorously is defined to be positive for traversal in the direction that places the interior of the domain on the left, and for this contour, that direction is counterclockwise.

Secondly, why -1? That's because we want the number of RHP zeros of <math>1+L(s)</math>. If we wanted to find the number of RHP zeros of the plain loop transfer function <math>L(s)</math>, we would count the number of encirclements of the ''origin'', but this isn't what we're interested, so we have to shift the winding center over to -1 to make the answer more relevant.

Constructing the Nyquist plot by hand directly from the transfer function is a huge pain, and I wouldn't recommend ever actually trying it. If you want to do this, just use Matlab's builtin nyquist() command. However, it is sometimes convenient to sketch a Nyquist plot by hand from a Bode plot. To do this, you read off the gain and the phase at a given frequency on the Bode plot, and use those as the polar coordinates of the corresponding point on the Nyquist plot. Going in the opposite direction (Bode plot from Nyquist plot) isn't terribly useful, because both plots are found from the same transfer function, and it's generally easier to plot the Bode plot from the transfer function directly.

--[[User:Hines|George Hines]] 17:43, 12 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Lecture 7-1]]
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]

Why counterclockwise encirclements of -1?

2007-11-13T01:43:19Z

Hines:

There are really two questions here: why counterclockwise? and why -1? First things first: there's nothing innately special about traversing the contour counterclockwise...that's basically a sign convention. The fact that counterclockwise traversal is the tradition is only because the contour integration that is necessary to justify the Nyquist Criterion rigorously is defined to be positive for traversal in the direction that places the interior of the domain on the left, and for this contour, that direction is counterclockwise.

Secondly, why -1? That's because we want the number of RHP zeros of <math>1+L(s)</math>. If we wanted to find the number of RHP zeros of the plain loop transfer function <math>L(s)</math>, we would count the number of encirclements of the ''origin'', but this isn't what we're interested, so we have to shift the winding center over to -1 to make the answer more relevant.

Constructing the Nyquist plot by hand directly from the transfer function is a huge pain, and I wouldn't recommend ever actually trying it. If you want to do this, just use Matlab's builtin nyquist() command. However, it is sometimes convenient to sketch a Nyquist plot by hand from a Bode plot. To do this, you read off the gain and the phase at a given frequency on the Bode plot, and use those as the polar coordinates of the corresponding point on the Nyquist plot. Going in the opposite direction (Bode plot from Nyquist plot) isn't terribly useful, because both plots are found from the same transfer function, and it's generally easier to plot the Bode plot from the transfer function directly.

--[[User:Hines|Hines]] 17:43, 12 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Lecture 7-1]]
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]

Why does Z≠0 correspond to instability?

2007-11-13T01:12:59Z

Hines:

First recall some definitions:

* the "loop transfer function" is <math>L(s)=P(s)C(s)</math>
* the closed loop system is described by <math>\frac{L(s)}{1+L(s)}</math>
* Z = #RHP zeros of <math>1+L(s)</math>

So we see that if a point is a zero of <math>1+L(s)</math>, then it is a pole of the closed-loop system. Now, if that pole lies in the right half-plane, then the closed-loop system will be unstable. Thus if the function <math>1+L(s)</math> has any RHP zeros, the closed loop system around the loop transfer function is unstable.

[[User:Hines|George Hines]] 17:12, 12 November 2007 (PST)

[[Category: CDS 101/110 FAQ - Lecture 7-1]]
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]

Why does Z≠0 correspond to instability?

2007-11-13T01:12:17Z

Hines:

Why does Z≠0 correspond to instability?

2007-11-13T01:12:03Z

Hines:

First recall some definitions:

* the "loop transfer function" is <math>L(s)=P(s)C(s)</math>
* the closed loop system is described by <math>\frac{L(s)}{1+L(s)}</math>
* Z=#RHP zeros of <math>1+L(s)</math>

So we see that if a point is a zero of <math>1+L(s)</math>, then it is a pole of the closed-loop system. Now, if that pole lies in the right half-plane, then the closed-loop system will be unstable. Thus if the function <math>1+L(s)</math> has any RHP zeros, the closed loop system around the loop transfer function is unstable.

[[User:Hines|Hines]] 17:12, 12 November 2007 (PST)

[[Category:CDS101/110

Why does Z≠0 correspond to instability?

2007-11-13T01:10:53Z

Hines:

First recall some definitions:

* the "loop transfer function" is <math>L(s)=P(s)C(s)</math>
* the closed loop system is described by <math>\frac{L(s)}{1+L(s)}</math>
* <math>Z=#\text{RHP zeros of}1+L(s)</math>

So we see that if a point is a zero of <math>1+L(s)</math>, then it is a pole of the closed-loop system. Now, if that pole lies in the right half-plane, then the closed-loop system will be unstable. Thus if the function <math>1+L(s)</math> has any RHP zeros, the closed loop system around the loop transfer function is unstable.

Why does Z≠0 correspond to instability?

2007-11-13T01:07:59Z

Hines:

First recall some definitions:
* the "loop transfer function" is <math>L(s)=P(s)C(s)</math>
* the closed loop system is described by <math>\frac{L(s)}{1+L(s)}</math>

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-11-11T07:19:23Z

Hines: /* Section 4: Theory */

{{cds101-fa07}}{{righttoc}}
The purpose of the recitation sections is to provide additional insight into the material for the week, including answer questions on specific topics of interests to the students in that section. The TAs leading the recitation will generally work through one problem from the homework set (same problem in each section) so that students can see what is expected on the homeworks and how the tools from the course can be applied. (Note: students must still work through and turn in the problem that the TAs work through and what you turn in must reflect your understanding of the problem.)

Recitations for CDS 101/110a will be on Fridays from 2-3 pm unless otherwise noted. Each recitation session is tuned for a slightly different audience and we have made initial assignments based on the course you are taking, the option you are in, and your class standing (So, Jr, Sr, G1, G2, etc).

=== Section 1: Feedback and Control in Nature ===

This section is designed for students interested in the application of ideas from feedback and control to systems in nature. It is also suitable for students who do not have lots of prior coursework in linear algebra, ordinary differential equations or complex variables. All students in CDS 101 are initially assigned to this section.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Luis Soto
|
* '''Location:''' 110 STL
|- valign=top
|
* Rebecca Barter
* Arkya Dhar
* Stephan Duewel
|
* Alberto Izarraraz
* Lauren LeBon
* Ophelia Venturelli
|}
</blockquote>

=== Section 2: Ae/ME ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Sawyer Fuller
|
* '''Location:''' 214 STL
|- valign=top
|
* Balakrishnam, Karthik
* Bozorg-Grayeli, Elah
* Chan, Derek
* Coralic, Vedran
* Cui, Shifu
* Elzinga, Michael
* Feldman, Matthew S.
* Grossman, Marc
* Gutschick, David
* Haderlein, Peter
* Heltsley, Drew
* Hires, Bryan
|
* Kramer, Nick
* Kwa, Timothy
* Liang, Joe
* Man, Han Bin
* Merfeld, Max
* Miller, Madeline
* Paulos, Jimmy
* Roa, Mario
* Sheng, Jing
* Stroup, Adrianne
* Winiarz, Christine
|}
</blockquote>

=== Section 3: Ae/ME/EE ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Julia Braman
|
* '''Location:''' 206 TOM
|- valign=top
|
* Arroyo, Jennifer
* Bowers, Steven
* Burt, Jason
* Chen, Jay
* Fuentes Hierro, Manuel
* Grogan, Robert
* Jiang, Michelle
* Ko, Huaising Cindy
* Leichty, John
* Littlepage, Kelly
* Liu, Annie
|
* Liu, Qing
* Pallett, Elliott
* Pantel, Erica
* Spink, Torrey
* Thai, Daniel
* Ueno, Makoto
* Wagner, Glenn
* Wang, Yingying
* Wierman, Matthew
* Wu, Min-Hao
* Zhang, Sebastian
|}
</blockquote>

=== Section 4: Theory ===

This section is intended for more advanced students who would like a more theoretical description of some of the tools of the class. This section will not go through a problem from the homework in much detail, but will instead discuss more advanced approaches to the topics being considered for that week.

* [[Media:EF11092007Recitation.pdf | Notes]] for the recitation of Friday, November 9.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Elisa Franco
|
* '''Location:''' 102 Steele
|- valign=top
|

* Best, Melissa
* Bourel, Alexis
* Carson, Vanessa
* Cayco Gajic, Natasha
* Cho, Angela
* Chen, Kevin
* Cruz, Gerardo
|
* Fette, Nicholas
* Li, Na
* Nair, Jayakrishnan
* Nguyen, Nam
* Richards, Andy
* Sharan, Rangoli
* Zhon, Cheng Shan
|}
</blockquote>

=== Section 5: Off Schedule ===

This section will be held at on Fridays at 8PM in 214 Steele. It will focus on engineering applications of feedback and control and provide brief introductions to some application topics that may not be covered in class. TA: George Hines

Notes from week 4's recitation are available [[Media:GHH_Recitation_10_26_07.pdf|here]].<br>
Notes from week 6's recitation are available [[Media:GHH_Recitation_11_9_07.pdf|here]].

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-11-10T06:40:09Z

Hines: /* Section 5: Off Schedule */

{{cds101-fa07}}{{righttoc}}
The purpose of the recitation sections is to provide additional insight into the material for the week, including answer questions on specific topics of interests to the students in that section. The TAs leading the recitation will generally work through one problem from the homework set (same problem in each section) so that students can see what is expected on the homeworks and how the tools from the course can be applied. (Note: students must still work through and turn in the problem that the TAs work through and what you turn in must reflect your understanding of the problem.)

Recitations for CDS 101/110a will be on Fridays from 2-3 pm unless otherwise noted. Each recitation session is tuned for a slightly different audience and we have made initial assignments based on the course you are taking, the option you are in, and your class standing (So, Jr, Sr, G1, G2, etc).

=== Section 1: Feedback and Control in Nature ===

This section is designed for students interested in the application of ideas from feedback and control to systems in nature. It is also suitable for students who do not have lots of prior coursework in linear algebra, ordinary differential equations or complex variables. All students in CDS 101 are initially assigned to this section.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Luis Soto
|
* '''Location:''' 110 STL
|- valign=top
|
* Rebecca Barter
* Arkya Dhar
* Stephan Duewel
|
* Alberto Izarraraz
* Lauren LeBon
* Ophelia Venturelli
|}
</blockquote>

=== Section 2: Ae/ME ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Sawyer Fuller
|
* '''Location:''' 214 STL
|- valign=top
|
* Balakrishnam, Karthik
* Bozorg-Grayeli, Elah
* Chan, Derek
* Coralic, Vedran
* Cui, Shifu
* Elzinga, Michael
* Feldman, Matthew S.
* Grossman, Marc
* Gutschick, David
* Haderlein, Peter
* Heltsley, Drew
* Hires, Bryan
|
* Kramer, Nick
* Kwa, Timothy
* Liang, Joe
* Man, Han Bin
* Merfeld, Max
* Miller, Madeline
* Paulos, Jimmy
* Roa, Mario
* Sheng, Jing
* Stroup, Adrianne
* Winiarz, Christine
|}
</blockquote>

=== Section 3: Ae/ME/EE ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Julia Braman
|
* '''Location:''' 206 TOM
|- valign=top
|
* Arroyo, Jennifer
* Bowers, Steven
* Burt, Jason
* Chen, Jay
* Fuentes Hierro, Manuel
* Grogan, Robert
* Jiang, Michelle
* Ko, Huaising Cindy
* Leichty, John
* Littlepage, Kelly
* Liu, Annie
|
* Liu, Qing
* Pallett, Elliott
* Pantel, Erica
* Spink, Torrey
* Thai, Daniel
* Ueno, Makoto
* Wagner, Glenn
* Wang, Yingying
* Wierman, Matthew
* Wu, Min-Hao
* Zhang, Sebastian
|}
</blockquote>

=== Section 4: Theory ===

This section is intended for more advanced students who would like a more theoretical description of some of the tools of the class. This section will not go through a problem from the homework in much detail, but will instead discuss more advanced approaches to the topics being considered for that week.

* [[Image:EF11092007Recitation.pdf | Notes]] for the recitation of Friday, November 9.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Elisa Franco
|
* '''Location:''' 102 Steele
|- valign=top
|

* Best, Melissa
* Bourel, Alexis
* Carson, Vanessa
* Cayco Gajic, Natasha
* Cho, Angela
* Chen, Kevin
* Cruz, Gerardo
|
* Fette, Nicholas
* Li, Na
* Nair, Jayakrishnan
* Nguyen, Nam
* Richards, Andy
* Sharan, Rangoli
* Zhon, Cheng Shan
|}
</blockquote>

=== Section 5: Off Schedule ===

This section will be held at on Fridays at 8PM in 214 Steele. It will focus on engineering applications of feedback and control and provide brief introductions to some application topics that may not be covered in class. TA: George Hines

Notes from week 4's recitation are available [[Media:GHH_Recitation_10_26_07.pdf|here]].<br>
Notes from week 6's recitation are available [[Media:GHH_Recitation_11_9_07.pdf|here]].

File:GHH Recitation 11 9 07.pdf

2007-11-10T06:39:42Z

Hines: Week 6 recitation notes.

Week 6 recitation notes.

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-11-10T06:39:06Z

Hines: /* Section 5: Off Schedule */

{{cds101-fa07}}{{righttoc}}
The purpose of the recitation sections is to provide additional insight into the material for the week, including answer questions on specific topics of interests to the students in that section. The TAs leading the recitation will generally work through one problem from the homework set (same problem in each section) so that students can see what is expected on the homeworks and how the tools from the course can be applied. (Note: students must still work through and turn in the problem that the TAs work through and what you turn in must reflect your understanding of the problem.)

Recitations for CDS 101/110a will be on Fridays from 2-3 pm unless otherwise noted. Each recitation session is tuned for a slightly different audience and we have made initial assignments based on the course you are taking, the option you are in, and your class standing (So, Jr, Sr, G1, G2, etc).

=== Section 1: Feedback and Control in Nature ===

This section is designed for students interested in the application of ideas from feedback and control to systems in nature. It is also suitable for students who do not have lots of prior coursework in linear algebra, ordinary differential equations or complex variables. All students in CDS 101 are initially assigned to this section.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Luis Soto
|
* '''Location:''' 110 STL
|- valign=top
|
* Rebecca Barter
* Arkya Dhar
* Stephan Duewel
|
* Alberto Izarraraz
* Lauren LeBon
* Ophelia Venturelli
|}
</blockquote>

=== Section 2: Ae/ME ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Sawyer Fuller
|
* '''Location:''' 214 STL
|- valign=top
|
* Balakrishnam, Karthik
* Bozorg-Grayeli, Elah
* Chan, Derek
* Coralic, Vedran
* Cui, Shifu
* Elzinga, Michael
* Feldman, Matthew S.
* Grossman, Marc
* Gutschick, David
* Haderlein, Peter
* Heltsley, Drew
* Hires, Bryan
|
* Kramer, Nick
* Kwa, Timothy
* Liang, Joe
* Man, Han Bin
* Merfeld, Max
* Miller, Madeline
* Paulos, Jimmy
* Roa, Mario
* Sheng, Jing
* Stroup, Adrianne
* Winiarz, Christine
|}
</blockquote>

=== Section 3: Ae/ME/EE ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Julia Braman
|
* '''Location:''' 206 TOM
|- valign=top
|
* Arroyo, Jennifer
* Bowers, Steven
* Burt, Jason
* Chen, Jay
* Fuentes Hierro, Manuel
* Grogan, Robert
* Jiang, Michelle
* Ko, Huaising Cindy
* Leichty, John
* Littlepage, Kelly
* Liu, Annie
|
* Liu, Qing
* Pallett, Elliott
* Pantel, Erica
* Spink, Torrey
* Thai, Daniel
* Ueno, Makoto
* Wagner, Glenn
* Wang, Yingying
* Wierman, Matthew
* Wu, Min-Hao
* Zhang, Sebastian
|}
</blockquote>

=== Section 4: Theory ===

This section is intended for more advanced students who would like a more theoretical description of some of the tools of the class. This section will not go through a problem from the homework in much detail, but will instead discuss more advanced approaches to the topics being considered for that week.

* [[Image:EF11092007Recitation.pdf | Notes]] for the recitation of Friday, November 9.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Elisa Franco
|
* '''Location:''' 102 Steele
|- valign=top
|

* Best, Melissa
* Bourel, Alexis
* Carson, Vanessa
* Cayco Gajic, Natasha
* Cho, Angela
* Chen, Kevin
* Cruz, Gerardo
|
* Fette, Nicholas
* Li, Na
* Nair, Jayakrishnan
* Nguyen, Nam
* Richards, Andy
* Sharan, Rangoli
* Zhon, Cheng Shan
|}
</blockquote>

=== Section 5: Off Schedule ===

This section will be held at on Fridays at 8PM in 214 Steele. It will focus on engineering applications of feedback and control and provide brief introductions to some application topics that may not be covered in class. TA: George Hines

Notes from week 4's recitation are available [[Media:GHH_Recitation_10_26_07.pdf|here]].<br>
Notes from week 6's recitation are available [[Link title|here]].

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-11-10T06:37:49Z

Hines: /* Section 5: Off Schedule */

{{cds101-fa07}}{{righttoc}}
The purpose of the recitation sections is to provide additional insight into the material for the week, including answer questions on specific topics of interests to the students in that section. The TAs leading the recitation will generally work through one problem from the homework set (same problem in each section) so that students can see what is expected on the homeworks and how the tools from the course can be applied. (Note: students must still work through and turn in the problem that the TAs work through and what you turn in must reflect your understanding of the problem.)

Recitations for CDS 101/110a will be on Fridays from 2-3 pm unless otherwise noted. Each recitation session is tuned for a slightly different audience and we have made initial assignments based on the course you are taking, the option you are in, and your class standing (So, Jr, Sr, G1, G2, etc).

=== Section 1: Feedback and Control in Nature ===

This section is designed for students interested in the application of ideas from feedback and control to systems in nature. It is also suitable for students who do not have lots of prior coursework in linear algebra, ordinary differential equations or complex variables. All students in CDS 101 are initially assigned to this section.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Luis Soto
|
* '''Location:''' 110 STL
|- valign=top
|
* Rebecca Barter
* Arkya Dhar
* Stephan Duewel
|
* Alberto Izarraraz
* Lauren LeBon
* Ophelia Venturelli
|}
</blockquote>

=== Section 2: Ae/ME ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Sawyer Fuller
|
* '''Location:''' 214 STL
|- valign=top
|
* Balakrishnam, Karthik
* Bozorg-Grayeli, Elah
* Chan, Derek
* Coralic, Vedran
* Cui, Shifu
* Elzinga, Michael
* Feldman, Matthew S.
* Grossman, Marc
* Gutschick, David
* Haderlein, Peter
* Heltsley, Drew
* Hires, Bryan
|
* Kramer, Nick
* Kwa, Timothy
* Liang, Joe
* Man, Han Bin
* Merfeld, Max
* Miller, Madeline
* Paulos, Jimmy
* Roa, Mario
* Sheng, Jing
* Stroup, Adrianne
* Winiarz, Christine
|}
</blockquote>

=== Section 3: Ae/ME/EE ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Julia Braman
|
* '''Location:''' 206 TOM
|- valign=top
|
* Arroyo, Jennifer
* Bowers, Steven
* Burt, Jason
* Chen, Jay
* Fuentes Hierro, Manuel
* Grogan, Robert
* Jiang, Michelle
* Ko, Huaising Cindy
* Leichty, John
* Littlepage, Kelly
* Liu, Annie
|
* Liu, Qing
* Pallett, Elliott
* Pantel, Erica
* Spink, Torrey
* Thai, Daniel
* Ueno, Makoto
* Wagner, Glenn
* Wang, Yingying
* Wierman, Matthew
* Wu, Min-Hao
* Zhang, Sebastian
|}
</blockquote>

=== Section 4: Theory ===

This section is intended for more advanced students who would like a more theoretical description of some of the tools of the class. This section will not go through a problem from the homework in much detail, but will instead discuss more advanced approaches to the topics being considered for that week.

* [[Image:EF11092007Recitation.pdf | Notes]] for the recitation of Friday, November 9.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Elisa Franco
|
* '''Location:''' 102 Steele
|- valign=top
|

* Best, Melissa
* Bourel, Alexis
* Carson, Vanessa
* Cayco Gajic, Natasha
* Cho, Angela
* Chen, Kevin
* Cruz, Gerardo
|
* Fette, Nicholas
* Li, Na
* Nair, Jayakrishnan
* Nguyen, Nam
* Richards, Andy
* Sharan, Rangoli
* Zhon, Cheng Shan
|}
</blockquote>

=== Section 5: Off Schedule ===

This section will be held at on Fridays at 8PM in 214 Steele. It will focus on engineering applications of feedback and control and provide brief introductions to some application topics that may not be covered in class. TA: George Hines

Notes from week 4's recitation are available [[Image:GHH_Recitation_10_26_07.pdf|here]].<br>
Notes from week 6's recitation are available [[Link title|here]].

File:GHH Recitation 10 26 07.pdf

2007-11-10T06:37:09Z

Hines: Recitation notes from week 4.

Recitation notes from week 4.

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-11-10T06:36:21Z

Hines: /* Section 5: Off Schedule */

{{cds101-fa07}}{{righttoc}}
The purpose of the recitation sections is to provide additional insight into the material for the week, including answer questions on specific topics of interests to the students in that section. The TAs leading the recitation will generally work through one problem from the homework set (same problem in each section) so that students can see what is expected on the homeworks and how the tools from the course can be applied. (Note: students must still work through and turn in the problem that the TAs work through and what you turn in must reflect your understanding of the problem.)

Recitations for CDS 101/110a will be on Fridays from 2-3 pm unless otherwise noted. Each recitation session is tuned for a slightly different audience and we have made initial assignments based on the course you are taking, the option you are in, and your class standing (So, Jr, Sr, G1, G2, etc).

=== Section 1: Feedback and Control in Nature ===

This section is designed for students interested in the application of ideas from feedback and control to systems in nature. It is also suitable for students who do not have lots of prior coursework in linear algebra, ordinary differential equations or complex variables. All students in CDS 101 are initially assigned to this section.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Luis Soto
|
* '''Location:''' 110 STL
|- valign=top
|
* Rebecca Barter
* Arkya Dhar
* Stephan Duewel
|
* Alberto Izarraraz
* Lauren LeBon
* Ophelia Venturelli
|}
</blockquote>

=== Section 2: Ae/ME ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Sawyer Fuller
|
* '''Location:''' 214 STL
|- valign=top
|
* Balakrishnam, Karthik
* Bozorg-Grayeli, Elah
* Chan, Derek
* Coralic, Vedran
* Cui, Shifu
* Elzinga, Michael
* Feldman, Matthew S.
* Grossman, Marc
* Gutschick, David
* Haderlein, Peter
* Heltsley, Drew
* Hires, Bryan
|
* Kramer, Nick
* Kwa, Timothy
* Liang, Joe
* Man, Han Bin
* Merfeld, Max
* Miller, Madeline
* Paulos, Jimmy
* Roa, Mario
* Sheng, Jing
* Stroup, Adrianne
* Winiarz, Christine
|}
</blockquote>

=== Section 3: Ae/ME/EE ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Julia Braman
|
* '''Location:''' 206 TOM
|- valign=top
|
* Arroyo, Jennifer
* Bowers, Steven
* Burt, Jason
* Chen, Jay
* Fuentes Hierro, Manuel
* Grogan, Robert
* Jiang, Michelle
* Ko, Huaising Cindy
* Leichty, John
* Littlepage, Kelly
* Liu, Annie
|
* Liu, Qing
* Pallett, Elliott
* Pantel, Erica
* Spink, Torrey
* Thai, Daniel
* Ueno, Makoto
* Wagner, Glenn
* Wang, Yingying
* Wierman, Matthew
* Wu, Min-Hao
* Zhang, Sebastian
|}
</blockquote>

=== Section 4: Theory ===

This section is intended for more advanced students who would like a more theoretical description of some of the tools of the class. This section will not go through a problem from the homework in much detail, but will instead discuss more advanced approaches to the topics being considered for that week.

* [[Image:EF11092007Recitation.pdf | Notes]] for the recitation of Friday, November 9.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Elisa Franco
|
* '''Location:''' 102 Steele
|- valign=top
|

* Best, Melissa
* Bourel, Alexis
* Carson, Vanessa
* Cayco Gajic, Natasha
* Cho, Angela
* Chen, Kevin
* Cruz, Gerardo
|
* Fette, Nicholas
* Li, Na
* Nair, Jayakrishnan
* Nguyen, Nam
* Richards, Andy
* Sharan, Rangoli
* Zhon, Cheng Shan
|}
</blockquote>

=== Section 5: Off Schedule ===

This section will be held at on Fridays at 8PM in 214 Steele. It will focus on engineering applications of feedback and control and provide brief introductions to some application topics that may not be covered in class. TA: George Hines

Notes from week 4's recitation are available [[Link title|here]].<br>
Notes from week 6's recitation are available [[Link title|here]].

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-11-10T06:36:10Z

Hines: /* Section 5: Off Schedule */

{{cds101-fa07}}{{righttoc}}
The purpose of the recitation sections is to provide additional insight into the material for the week, including answer questions on specific topics of interests to the students in that section. The TAs leading the recitation will generally work through one problem from the homework set (same problem in each section) so that students can see what is expected on the homeworks and how the tools from the course can be applied. (Note: students must still work through and turn in the problem that the TAs work through and what you turn in must reflect your understanding of the problem.)

Recitations for CDS 101/110a will be on Fridays from 2-3 pm unless otherwise noted. Each recitation session is tuned for a slightly different audience and we have made initial assignments based on the course you are taking, the option you are in, and your class standing (So, Jr, Sr, G1, G2, etc).

=== Section 1: Feedback and Control in Nature ===

This section is designed for students interested in the application of ideas from feedback and control to systems in nature. It is also suitable for students who do not have lots of prior coursework in linear algebra, ordinary differential equations or complex variables. All students in CDS 101 are initially assigned to this section.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Luis Soto
|
* '''Location:''' 110 STL
|- valign=top
|
* Rebecca Barter
* Arkya Dhar
* Stephan Duewel
|
* Alberto Izarraraz
* Lauren LeBon
* Ophelia Venturelli
|}
</blockquote>

=== Section 2: Ae/ME ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Sawyer Fuller
|
* '''Location:''' 214 STL
|- valign=top
|
* Balakrishnam, Karthik
* Bozorg-Grayeli, Elah
* Chan, Derek
* Coralic, Vedran
* Cui, Shifu
* Elzinga, Michael
* Feldman, Matthew S.
* Grossman, Marc
* Gutschick, David
* Haderlein, Peter
* Heltsley, Drew
* Hires, Bryan
|
* Kramer, Nick
* Kwa, Timothy
* Liang, Joe
* Man, Han Bin
* Merfeld, Max
* Miller, Madeline
* Paulos, Jimmy
* Roa, Mario
* Sheng, Jing
* Stroup, Adrianne
* Winiarz, Christine
|}
</blockquote>

=== Section 3: Ae/ME/EE ===

This section is intended for students who are interested in the application of feedback and control to mechanical and electro-mechanical systems such as airplanes, cars, robots, etc.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Julia Braman
|
* '''Location:''' 206 TOM
|- valign=top
|
* Arroyo, Jennifer
* Bowers, Steven
* Burt, Jason
* Chen, Jay
* Fuentes Hierro, Manuel
* Grogan, Robert
* Jiang, Michelle
* Ko, Huaising Cindy
* Leichty, John
* Littlepage, Kelly
* Liu, Annie
|
* Liu, Qing
* Pallett, Elliott
* Pantel, Erica
* Spink, Torrey
* Thai, Daniel
* Ueno, Makoto
* Wagner, Glenn
* Wang, Yingying
* Wierman, Matthew
* Wu, Min-Hao
* Zhang, Sebastian
|}
</blockquote>

=== Section 4: Theory ===

This section is intended for more advanced students who would like a more theoretical description of some of the tools of the class. This section will not go through a problem from the homework in much detail, but will instead discuss more advanced approaches to the topics being considered for that week.

* [[Image:EF11092007Recitation.pdf | Notes]] for the recitation of Friday, November 9.

<blockquote>
{| width=100% cellspacing=0 cellpadding = 0
|-
| width=50% |
* '''TA:''' Elisa Franco
|
* '''Location:''' 102 Steele
|- valign=top
|

* Best, Melissa
* Bourel, Alexis
* Carson, Vanessa
* Cayco Gajic, Natasha
* Cho, Angela
* Chen, Kevin
* Cruz, Gerardo
|
* Fette, Nicholas
* Li, Na
* Nair, Jayakrishnan
* Nguyen, Nam
* Richards, Andy
* Sharan, Rangoli
* Zhon, Cheng Shan
|}
</blockquote>

=== Section 5: Off Schedule ===

This section will be held at on Fridays at 8PM in 214 Steele. It will focus on engineering applications of feedback and control and provide brief introductions to some application topics that may not be covered in class. TA: George Hines

Notes from week 4's recitation are available [[Link title|here]].
Notes from week 6's recitation are available [[Link title|here]].

CDS 101/110a, Fall 2007

2007-10-22T23:07:36Z

Hines: /* Announcements */

{{cds101-fa07}}
<table align=right border=1 width=20% cellpadding=6>
<tr><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Texts]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 101 (Analysis and Design of Feedback Systems) and CDS 110 (Introduction to Control Theory) for Fall 2007. __NOTOC__

<table width=80%>
<tr valign=top>
<td width=50%>
'''Instructor'''
* [[Main Page|Richard Murray]], murray@cds.caltech.edu
* Lectures: MWF, 2-3 pm, 74 JRG
* Office hours: Fridays, 3-4 pm (by appt)
* 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]]
<td>
'''Teaching Assistants''' ([mailto:cds101-tas@cds.caltech.edu cds110-tas@cds])
* Julia Braman, Elisa Franco, Sawyer Fuller, George Hines, Luis Soto
* Office hours: Sundays, 4-5; Tuesdays, 4-5 in 114 STL
'''Course Ombuds'''
* Vanessa Carson and Matthew Feldman
</table>

== Announcements ==
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table>
* 22 Oct 07: [[CDS 101/110, Week 4 - Linear Systems]]
* 22 Oct 07: {{cds101 handouts|soln2.pdf|Solutions to homework #2}} will soon be posted
** CDS 110: Average score = 22.4 (<math>\sigma</math> = 4.3); average time = 9.7 hours
** CDS 101: Average score = 14.8 (<math>\sigma</math> = 3.6); average time = 8.1 hours
* 15 Oct 07: [[CDS 101/110, Week 3 - Dynamic Behavior]]
** {{cds101 handouts|hw3.pdf|HW #3}} is now posted; due 22 Oct @ 5 pm
* 15 Oct 07: {{cds101 handouts|soln1.pdf|Solutions to homework #1}} are now available
** CDS 110: Average score = 35.7 (<math>\sigma</math> = 3.4); average time = 6.2 hours
** CDS 101: Average score = 18.7 (<math>\sigma</math> = 1.6); average time = 3.4 hours
* 8 Oct 07: [[CDS 101/110, Week 2 - System Modeling]]
* 1 Oct 07: [[CDS 101/110, Week 1 - Introduction to Feedback and Control]]
* 20 Aug 07: created wiki page for CDS 101/110a, Fall 2007

== Course Syllabus ==

CDS 101/110 provides an introduction to feedback and control in physical,
biological, engineering, and information sciences. Basic principles of
feedback and its use as a tool for altering the dynamics of systems and
managing uncertainty. Key themes throughout the course will include
input/output response, modeling and model reduction, linear versus nonlinear
models, and local versus global behavior.

CDS 101 is a 6 unit (2-0-4) class intended for advanced students in science
and engineering who are interested in the principles and tools of feedback
control, but not the analytical techniques for design and synthesis of control
systems. CDS 110 is a 9 unit class (3-0-6) that provides a traditional first
course in control for engineers and applied scientists. It assumes a stronger
mathematical background, including working knowledge of linear algebra and
ODEs. Familiarity with complex variables (Laplace transforms, residue theory)
is helpful but not required.

=== Grading ===
The final grade will be based on homework sets, a midterm exam, and a final exam:

*''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).

* ''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).

* ''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).

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult
outside reference materials, other students, the TA, or the
instructor, but you cannot consult homework solutions from
prior years and you must cite any use of material from outside
references. All solutions that are handed in should be written up
individually and should reflect your own understanding of the subject
matter at the time of writing. MATLAB scripts and plots are
considered part of your writeup and should be done individually (you
can share ideas, but not code).

No collaboration is allowed on the midterm or final exams.

=== Course Text and References ===

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:

* A. D. Lewis, ''A Mathematical Approach to Classical Control'', 2003. [http://penelope.mast.queensu.ca/math332/notes.shtml Online access].

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.

* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', McGraw-Hill, 1986.
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.

=== Course Schedule ===
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.

== Old Announcements ==

[[Category: Courses]] [[Category: 2007-08 Courses]]

CDS 101/110a, Fall 2007

2007-10-22T23:06:45Z

Hines: /* Announcements */

{{cds101-fa07}}
<table align=right border=1 width=20% cellpadding=6>
<tr><td>
<center>'''Contents'''</center>
<ul>
<li> [[#Grading|Grading]] <br>
<li> [[#Collaboration Policy|Collaboration Policy]] <br>
<li> [[#Course Text and References|Course Texts]] <br>
<li> [[#Course_Schedule|Course Schedule]]<br>
<li> [[#Course Project|Course Project]]
</ul>
</table>
This is the homepage for CDS 101 (Analysis and Design of Feedback Systems) and CDS 110 (Introduction to Control Theory) for Fall 2007. __NOTOC__

<table width=80%>
<tr valign=top>
<td width=50%>
'''Instructor'''
* [[Main Page|Richard Murray]], murray@cds.caltech.edu
* Lectures: MWF, 2-3 pm, 74 JRG
* Office hours: Fridays, 3-4 pm (by appt)
* 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]]
<td>
'''Teaching Assistants''' ([mailto:cds101-tas@cds.caltech.edu cds110-tas@cds])
* Julia Braman, Elisa Franco, Sawyer Fuller, George Hines, Luis Soto
* Office hours: Sundays, 4-5; Tuesdays, 4-5 in 114 STL
'''Course Ombuds'''
* Vanessa Carson and Matthew Feldman
</table>

== Announcements ==
<table align=right border=0><tr><td>[[#Old Announcements|Archive]]</table>
* 22 Oct 07: [[CDS 101/110, Week 4 - Linear Systems]]
* 22 Oct 07:
** Solutions to homework #2 will soon be posted
** CDS 110: Average score = 22.4 (<math>\sigma</math> = 4.3); average time = 9.7 hours
** CDS 101: Average score = 14.8 (<math>\sigma</math> = 3.6); average time = 8.1 hours
* 15 Oct 07: [[CDS 101/110, Week 3 - Dynamic Behavior]]
** {{cds101 handouts|hw3.pdf|HW #3}} is now posted; due 22 Oct @ 5 pm
* 15 Oct 07: {{cds101 handouts|soln1.pdf|Solutions to homework #1}} are now available
** CDS 110: Average score = 35.7 (<math>\sigma</math> = 3.4); average time = 6.2 hours
** CDS 101: Average score = 18.7 (<math>\sigma</math> = 1.6); average time = 3.4 hours
* 8 Oct 07: [[CDS 101/110, Week 2 - System Modeling]]
* 1 Oct 07: [[CDS 101/110, Week 1 - Introduction to Feedback and Control]]
* 20 Aug 07: created wiki page for CDS 101/110a, Fall 2007

== Course Syllabus ==

CDS 101/110 provides an introduction to feedback and control in physical,
biological, engineering, and information sciences. Basic principles of
feedback and its use as a tool for altering the dynamics of systems and
managing uncertainty. Key themes throughout the course will include
input/output response, modeling and model reduction, linear versus nonlinear
models, and local versus global behavior.

CDS 101 is a 6 unit (2-0-4) class intended for advanced students in science
and engineering who are interested in the principles and tools of feedback
control, but not the analytical techniques for design and synthesis of control
systems. CDS 110 is a 9 unit class (3-0-6) that provides a traditional first
course in control for engineers and applied scientists. It assumes a stronger
mathematical background, including working knowledge of linear algebra and
ODEs. Familiarity with complex variables (Laplace transforms, residue theory)
is helpful but not required.

=== Grading ===
The final grade will be based on homework sets, a midterm exam, and a final exam:

*''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).

* ''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).

* ''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).

=== Collaboration Policy ===

Collaboration on homework assignments is encouraged. You may consult
outside reference materials, other students, the TA, or the
instructor, but you cannot consult homework solutions from
prior years and you must cite any use of material from outside
references. All solutions that are handed in should be written up
individually and should reflect your own understanding of the subject
matter at the time of writing. MATLAB scripts and plots are
considered part of your writeup and should be done individually (you
can share ideas, but not code).

No collaboration is allowed on the midterm or final exams.

=== Course Text and References ===

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:

* A. D. Lewis, ''A Mathematical Approach to Classical Control'', 2003. [http://penelope.mast.queensu.ca/math332/notes.shtml Online access].

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.

* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', McGraw-Hill, 1986.
* G. F. Franklin, J. D. Powell, and A. Emami-Naeni, ''Feedback Control of Dynamic Systems'', Addison-Wesley, 2002.

=== Course Schedule ===
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.

== Old Announcements ==

[[Category: Courses]] [[Category: 2007-08 Courses]]

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-10-17T23:06:16Z

Hines: /* Section 5: Off Schedule */

CDS 101/110a, Fall 2007 - Recitation Schedule

2007-10-17T23:05:06Z

Hines: /* Section 5: Off Schedule */

On prob. 2, how closely do I have to follow the block diagram in the book?

2007-10-16T01:28:58Z

Hines:

The block diagram in Fig. 3.1 is only meant to demonstrate the flow of information in the abstract sense through the system, not to guide your simulation down to the details.

If you're concerned about exactly where the variables v and u enter the equations, the punch line is equation 3.3 in the book. How you split this up in your implementation is up to you. In order to satisfy any issues with where the saturated signal u connects in, just put it into the Torque and Engine block along with v, and simply use the Gears and Wheels block to scale by the gear ratio. As long as it's clear you have an understanding of how the system fits together, we don't particularly care exactly where specific inputs go. Just be explicit in the description that you turn in for part (a).

Don't lose sight of the high-level purpose of these problem sets, which is to gain an intuition for system modeling and simulation, and not necessarily to follow a cookbook recipe of equation interactions.

-[[User:Hines|George Hines]] 18:28, 15 October 2007 (PDT)

[[Category:CDS 101/110 FAQ - Homework 2, Fall 2007]]

On prob. 2, how closely do I have to follow the block diagram in the book?

2007-10-16T01:28:51Z

Hines:

The block diagram in Fig. 3.1 is only meant to demonstrate the flow of information in the abstract sense through the system, not to guide your simulation down to the details.

If you're concerned about exactly where the variables v and u enter the equations, the punch line is equation 3.3 in the book. How you split this up in your implementation is up to you. In order to satisfy any issues with where the saturated signal u connects in, just put it into the Torque and Engine block along with v, and simply use the Gears and Wheels block to scale by the gear ratio. As long as it's clear you have an understanding of how the system fits together, we don't particularly care exactly where specific inputs go. Just be explicit in the description that you turn in for part (a).

Don't lose sight of the high-level purpose of these problem sets, which is to gain an intuition for system modeling and simulation, and not necessarily to follow a cookbook recipe of equation interactions.

-[[User:Hines|Hines]] 18:28, 15 October 2007 (PDT)

[[Category:CDS 101/110 FAQ - Homework 2, Fall 2007]]

Does my Simulink model need to change gears?

2007-10-14T22:52:45Z

Hines:

The Simulink model created for question 2 of this week's homework does NOT need to shift gears while accelerating. All velocity changes are assumed to take place within a single gear. You will need to change the gear manually, but never while a sim is running.

-[[User:Hines|George Hines]] 15:52, 14 October 2007 (PDT)

[[Category:CDS 101/110 FAQ - Homework 2, Fall 2007]]

Does my Simulink model need to change gears?

2007-10-14T22:52:38Z

Hines:

The Simulink model created for question 2 of this week's homework does NOT need to shift gears while accelerating. All velocity changes are assumed to take place within a single gear. You will need to change the gear manually, but never while a sim is running.

-[[User:Hines|Hines]] 15:52, 14 October 2007 (PDT)

[[Category:CDS 101/110 FAQ - Homework 2, Fall 2007]]

Do I need to turn in a block diagram of my PI controller for problem 2?

2007-10-14T17:51:41Z

Hines:

Good question, because the printout is in response to part (a), but you don't actually have to design the controller until part (c).

However, your diagram for part (a) should at least have a block in it representing the controller, so as long as there is a description of the equations in this block as stipulated in part (a), don't worry about turning in a printout of your actual PI implementation.

-[[User:Hines|George Hines]] 10:51, 14 October 2007 (PDT)

[[Category:CDS 101/110 FAQ - Homework 2, Fall 2007]]

Do I need to turn in a block diagram of my PI controller for problem 2?

2007-10-14T17:51:32Z

Hines:

Good question, because the printout is in response to part (a), but you don't actually have to design the controller until part (c).

However, your diagram for part (a) should at least have a block in it representing the controller, so as long as there is a description of the equations in this block as stipulated in part (a), don't worry about turning in a printout of your actual PI implementation.

-[[User:Hines|Hines]] 10:51, 14 October 2007 (PDT)

[[Category:CDS 101/110 FAQ - Homework 2, Fall 2007]]

Do I need to turn in a block diagram of my PI controller for problem 2?

2007-10-14T17:51:06Z

Hines:

Good question, because the printout is in response to part (a), but you don't actually have to design the controller until part (c).

However, your diagram for part (a) should at least have a block in it representing the controller, so as long as there is a description of the equations in this block as stipulated in part (a), don't worry about turning in a printout of your actual PI implementation.

-[User:Hines|George Hines]

[[Category:CDS 101/110 FAQ - Homework 2, Fall 2007]]

CDS 101/110 - System Modeling

2007-10-12T01:10:06Z

Hines: /* Homework */

{{cds101-fa07}}

{{righttoc}}
== Overview ==

'''Monday:''' Introduction to Modeling ({{cds101 handouts|L2-1_modeling.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-08.mp3|MP3}} )

This lecture provides an overview of modeling for control systems. We discuss what a model is and what types of questions it can be used to answer. The concepts of state, dynamics, inputs and outputs are described, including running examples to demonstrate the concepts. Several different modeling techniques are summarized, with emphasis on differential equations. Two examples are included to demonstrate the main concepts.

* {{cds101 handouts|L2-1_modeling_h.pdf|Lecture handout}}
* MATLAB files: {{cds101 matlab|L2_1_modeling.m}}, {{cds101 matlab|springmass.m}}
* [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-demo.mp4 cds101-demo.mp4] spring-mass system frequency response demonstration video from lecture

'''Wednesday:''' Modeling using Ordinary Differential Equation ({{cds101 handouts|L2-2_odes.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-10.mp3|MP3}})

This lecture provides a more detailed introduction to the use of ordinary differential equations (ODEs) for modeling dynamical systems. A brief review of the solutions of second order linear ODEs is provided to make connection with prior coursework. The general form of nonlinear and linear ODEs is provided, along with an overview of some of the techniques for solving linear ODEs in special forms (scalar and diagonal systems). Analysis tools, including stability and frequency response, are illustrated. Finally, the use of block diagrams in control systems is introduced, including the standard symbology used in the text and an extended example (insect flight).
* {{cds101 handouts|L2-2_odes_h.pdf|Lecture handout}}

'''Friday:''' {{cds101 lecture|SIMULINK Tutorial}} - George Hines

This tutorial will provide an overview of the SIMULINK modeling tool.

== Reading ==

* {{AM07|Chapter 2 - System Modeling}}

== Homework ==

* {{cds101 handouts|hw2.pdf|HW #2}}

This homework set demonstrates the construction and use of models for control systems. The first problem asks the student to identify the states, inputs, outputs, and dynamics for a sample systems. The second problem consists of a detailed construction of a vehicle model that can be used for cruise control. The last problem (CDS 110 only) explores discrete time modeling techniques.



== FAQ ==
'''Monday'''
<ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2007</ncl>
'''Wednesday'''
<ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2007</ncl>
'''Friday'''
<ncl>CDS 101/110 FAQ - Lecture 2-3, Fall 2007</ncl>
'''Homework'''
<ncl>CDS 101/110 FAQ - Homework 2, Fall 2007</ncl>

CDS 101 - SIMULINK Tutorial

2007-10-10T02:58:09Z

Hines:

[[Media:SimulinkHandout.pdf|Simulink tutorial handout]]<br>
[[Media:SimTut.mdl|Simulink tutorial example model]]<br>
[[Media:SimTutNotes.pdf|Simulink tutorial notes]]

File:SimTutNotes.pdf

2007-10-10T02:57:24Z

Hines:

Why was there only one damper in the mass/spring model?

2007-10-08T22:35:12Z

Hines:

There were actually two dampers on the physical system that we used as a demostrator today in lecture, but the damper on mass 2 was tuned so that its damping was much less than that of the damper on mass 1; so the state-space model (which only had one damper) and the physical system behaved qualitatively the same.

--[[User:Hines|George Hines]] 15:33, 8 October 2007 (PDT)

[[Category: CDS 101/110 FAQ - Lecture 2-1]]
[[Category: CDS 101/110 FAQ - Lecture 2-1, Fall 2007]]

Why was there only one damper in the mass/spring model?

2007-10-08T22:33:34Z

Hines:

Why was there only one damper in the mass/spring model?

2007-10-08T22:33:25Z

Hines:

It's a bit unclear to me when you talk about "error" in PID control

2007-10-04T00:05:36Z

Hines:

The error is the difference between the reference operating point and the current operating point. In the cruise control example, the reference operating point is the desired speed, and the current operating point is the current speed. So if you want a car to go 60 mph (reference) and it's only going 55 mph (current), then the error is 5 mph (reference - current).

--[[User:Hines|George Hines]] 17:04, 3 October 2007 (PDT)

[[Category: CDS 101/110 FAQ - Lecture 1-1]]
[[Category: CDS 101/110 FAQ - Lecture 1-1, Fall 2007]]

It's a bit unclear to me when you talk about "error" in PID control

2007-10-04T00:04:45Z

Hines:

The error is the difference between the reference operating point and the current operating point. In the cruise control example, the reference operating point is the desired speed, and the current operating point is the current speed. So if you want a car to go 60 mph (reference) and it's only going 55 mph (current), then the error is 5 mph (reference - current).

--[[User:Hines|Hines]] 17:04, 3 October 2007 (PDT) 17:01, 3 October 2007 (PDT)

[[Category: CDS 101/110 FAQ - Lecture 1-1]]
[[Category: CDS 101/110 FAQ - Lecture 1-1, Fall 2007]]

CDS 101 - SIMULINK Tutorial

2007-10-03T06:29:36Z

Hines:

[[Media:SimulinkHandout.pdf|Simulink tutorial handout]]<br>
[[Media:SimTut.mdl|Simulink tutorial example model]]

CDS 101 - SIMULINK Tutorial

2007-10-03T06:29:27Z

Hines:

[[Media:SimulinkHandout.pdf|Simulink tutorial handout]]
[[Media:SimTut.mdl|Simulink tutorial example model]]

File:SimTut.mdl

2007-10-03T06:28:46Z

Hines: Implements a simple controller on a trivial system. Uses many of the blocks described in the accompanying handout.

Implements a simple controller on a trivial system. Uses many of the blocks described in the accompanying handout.

CDS 101 - SIMULINK Tutorial

2007-10-03T06:26:33Z

Hines:

[[Media:SimulinkHandout.pdf|Simulink tutorial handout]]

CDS 101 - SIMULINK Tutorial

2007-10-03T06:26:08Z

Hines:

[[Media:SimulinkTutorial.pdf|Simulink tutorial handout]]