https://murray.cds.caltech.edu/api.php?action=feedcontributions&feedformat=atom&user=MerfeldMurray Wiki - User contributions [en]2026-04-24T18:27:51ZUser contributionsMediaWiki 1.41.5https://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Robust_Performance&diff=8586CDS 101/110 - Robust Performance2008-12-07T23:14:47Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be able to represent the uncertainty in a model using additive, multiplicative or feedback uncertainty representations<br />
* Students should be able to analyze robust stability and performance for a system with uncertainty<br />
<br />
'''Monday:''' Robust Performance ({{cds101 handouts|L10-1_robperf.pdf|Slides}}, {{cds101 mp3|cds101-2008-12-01.mp3|MP3}})<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:''' ({{cds101 handouts|L10-2_dfan.pdf|Notes}}, {{cds101 mp3|cds101-2008-12-03.mp3|MP3}})<br />
<br />
In this lecture, we will work through a design exercise, summarizing the main topics of the course, including modeling, analysis and design of feedback systems in the frequency domain and in state space.<br />
<br />
* {{cds101 handouts|L10-2_dfan.pdf|Lecture notes}}<br />
* MATLAB: {{cds101 matlab|L10_2_dfan.m}}<br />
<br />
'''Friday:''' Final exam review review ({{cds101 handouts|L10-3_review.pdf|Notes}}, {{cds101 mp3|cds101-2008-12-05.mp3|MP3}})<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 12 - Robust Performance}}<br />
** CDS 101: Read sections 12.1-12.3, skipping advanced sections [30 min]<br />
** CDS 110: Read sections 12.1-12.3, skim section 12.4-12.5 [60 min]<br />
** CDS 210: Read sections 12.1-12.5 [90 min]<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, 12 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 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2008</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Robust_Performance&diff=8533CDS 101/110 - Robust Performance2008-12-04T07:30:08Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be able to represent the uncertainty in a model using additive, multiplicative or feedback uncertainty representations<br />
* Students should be able to analyze robust stability and performance for a system with uncertainty<br />
<br />
'''Monday:''' Robust Performance ({{cds101 handouts|L10-1_robperf.pdf|Slides}}, {{cds101 mp3|cds101-2008-12-01.mp3|MP3}})<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:''' ({{cds101 handouts|L10-2_dfan.pdf|Notes}}, {{cds101 mp3|cds101-2008-12-03.mp3|MP3}})<br />
<br />
In this lecture, we will work through a design exercise, summarizing the main topics of the course, including modeling, analysis and design of feedback systems in the frequency domain and in state space.<br />
<br />
* {{cds101 handouts|L10-2_dfan.pdf|Lecture notes}}<br />
* MATLAB: {{cds101 matlab|L10_2_dfan.m}}<br />
<br />
'''Friday:''' Final exam review review ({{cds101 handouts placeholder|L10-3_review.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-12-07.mp3|MP3}})<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 12 - Robust Performance}}<br />
** CDS 101: Read sections 12.1-12.3, skipping advanced sections [30 min]<br />
** CDS 110: Read sections 12.1-12.3, skim section 12.4-12.5 [60 min]<br />
** CDS 210: Read sections 12.1-12.5 [90 min]<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, 12 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 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2008</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Robust_Performance&diff=8532CDS 101/110 - Robust Performance2008-12-04T07:29:45Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be able to represent the uncertainty in a model using additive, multiplicative or feedback uncertainty representations<br />
* Students should be able to analyze robust stability and performance for a system with uncertainty<br />
<br />
'''Monday:''' Robust Performance ({{cds101 handouts|L10-1_robperf.pdf|Slides}}, {{cds101 mp3|cds101-2008-12-01.mp3|MP3}})<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:''' ({{cds101 handouts|L10-2_dfan.pdf|Notes}}, {{cds101 mp3|cds101-2008-12-08.mp3|MP3}})<br />
<br />
In this lecture, we will work through a design exercise, summarizing the main topics of the course, including modeling, analysis and design of feedback systems in the frequency domain and in state space.<br />
<br />
* {{cds101 handouts|L10-2_dfan.pdf|Lecture notes}}<br />
* MATLAB: {{cds101 matlab|L10_2_dfan.m}}<br />
<br />
'''Friday:''' Final exam review review ({{cds101 handouts placeholder|L10-3_review.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-12-07.mp3|MP3}})<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 12 - Robust Performance}}<br />
** CDS 101: Read sections 12.1-12.3, skipping advanced sections [30 min]<br />
** CDS 110: Read sections 12.1-12.3, skim section 12.4-12.5 [60 min]<br />
** CDS 210: Read sections 12.1-12.5 [90 min]<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, 12 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 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2008</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Robust_Performance&diff=8527CDS 101/110 - Robust Performance2008-12-02T23:56:20Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be able to represent the uncertainty in a model using additive, multiplicative or feedback uncertainty representations<br />
* Students should be able to analyze robust stability and performance for a system with uncertainty<br />
<br />
'''Monday:''' Robust Performance ({{cds101 handouts|L10-1_robperf.pdf|Slides}}, {{cds101 mp3|cds101-2008-12-01.mp3|MP3}})<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:''' ({{cds101 handouts|L10-2_dfan.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-12-05.mp3|MP3}})<br />
<br />
In this lecture, we will work through a design exercise, summarizing the main topics of the course, including modeling, analysis and design of feedback systems in the frequency domain and in state space.<br />
<br />
* {{cds101 handouts|L10-2_dfan.pdf|Lecture notes}}<br />
* MATLAB: {{cds101 matlab|L10_2_dfan.m}}<br />
<br />
'''Friday:''' Final exam review review ({{cds101 handouts placeholder|L10-3_review.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-12-07.mp3|MP3}})<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 12 - Robust Performance}}<br />
** CDS 101: Read sections 12.1-12.3, skipping advanced sections [30 min]<br />
** CDS 110: Read sections 12.1-12.3, skim section 12.4-12.5 [60 min]<br />
** CDS 210: Read sections 12.1-12.5 [90 min]<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, 12 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 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 10-3, Fall 2008</ncl><br />
'''Final'''<br />
<ncl>CDS 101/110 FAQ - Final, Fall 2007</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_PID_Control&diff=8498CDS 101/110 - PID Control2008-11-30T22:38:55Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be to design a PID controller that satisfies a frequency domain performance specification<br />
* Students should understand the limitations imposed by actuator saturation and implement a simple anti-windup compensator<br />
<br />
'''Monday:''' PID Overview ({{cds101 handouts|L9-1_pid.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-24.mp3|MP3}})<br />
<br />
This lecture covers the basic tools in frequency domain control design using proportional + integral + derivative (PID) control. We compare the PID controller to loop shaping designs (such as lead compensation) and show how to obtain initial PID gains using Ziegler-Nichols tuning rules. The issues of windup and anti-windup compensation are briefly discussed.<br />
<br />
* {{cds101 handouts|L9-1_pid_h.pdf|Lecture handout}}<br />
* MATLAB: {{cds101 matlab|L9_1_pid.m}}<br />
<br />
'''Wednesday:''' PID Implementation ({{cds101 handouts|L9-2_implement.pdf|Notes}}, {{cds101 mp3|cds101-2008-11-26.mp3|MP3}})<br />
<br />
This lecture provides more details on the implementation 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|L9-2_implement.pdf|Lecture notes}}<br />
<br />
'''Friday:''' no class (Thanksgiving break)<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 10 - PID Control}}<br />
** CDS 101: Read sections 10.1, 10.3 [30 min]<br />
** CDS 110: Read sections 10.1, 10.3-10.5 [45 min]<br />
** CDS 210: AM08 10.1, 10.3, DFT Ch 6 [90 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts placeholder|hw8.pdf|Homework #8}}<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 9-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_PID_Control&diff=8461CDS 101/110 - PID Control2008-11-25T00:39:38Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be to design a PID controller that satisfies a frequency domain performance specification<br />
* Students should understand the limitations imposed by actuator saturation and implement a simple anti-windup compensator<br />
<br />
'''Monday:''' PID Overview ({{cds101 handouts|L9-1_pid.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-24.mp3|MP3}})<br />
<br />
This lecture covers the basic tools in frequency domain control design using proportional + integral + derivative (PID) control. We compare the PID controller to loop shaping designs (such as lead compensation) and show how to obtain initial PID gains using Ziegler-Nichols tuning rules. The issues of windup and anti-windup compensation are briefly discussed.<br />
<br />
* {{cds101 handouts|L9-1_pid_h.pdf|Lecture handout}}<br />
* MATLAB: {{cds101 matlab|L9_1_pid.m}}<br />
<br />
'''Wednesday:''' PID Implementation ({{cds101 handouts|L8-2_implement.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-11-21.mp3|MP3}})<br />
<br />
This lecture provides more details on the implementation 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_implement.pdf|Lecture notes}}<br />
<br />
'''Friday:''' no class (Thanksgiving break)<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 10 - PID Control}}<br />
** CDS 101: Read sections 10.1, 10.3 [30 min]<br />
** CDS 110: Read sections 10.1, 10.3-10.5 [45 min]<br />
** CDS 210: AM08 10.1, 10.3, DFT Ch 6 [90 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts placeholder|hw8.pdf|Homework #8}}<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 9-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Loop_Shaping&diff=8427CDS 101/110 - Loop Shaping2008-11-20T21:21:31Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be to design a simple compensator with given performance and robustness (phase margin) specifications<br />
* Students should be analyze and understand the overall performance of the system using the Gang of Four<br />
* Students should compute the limits on the performance that arise from right half plane poles and zeros<br />
<br />
'''Monday:''' Loop Shaping ({{cds101 handouts|L8-1_loopsyn.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-17.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|L8-1_loopsyn_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L8_1_dfan.m}}<br />
<br />
'''Wednesday:''' Performance Limits ({{cds101 handouts|L8-2_limits.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-19.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|L8-2_limits_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L8_2_maglev.m}}<br />
<br />
'''Friday:''' Recitation sections<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 11 - Loop Shaping}}<br />
** CDS 101: Read sections 11.1, 11.3-11.4 [45 min]<br />
** CDS 110: Read sections 11.1, 11.2-11.5 [60 min]<br />
** CDS 210: Skim AM08 Ch 11.1-11.4, read AM08 11.5, DFT Ch 4 and 6 [90 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw7-fa08.pdf|Homework #7}} (due 24 Nov 08): {{cds101 handouts|hw7-101-fa08.pdf|CDS 101}}, {{cds101 handouts|hw7-110-fa08.pdf|CDS 110}}, {{cds101 handouts|hw7-210-fa08.pdf|CDS 210}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Loop_Shaping&diff=8423CDS 101/110 - Loop Shaping2008-11-19T15:00:13Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be to design a simple compensator with given performance and robustness (phase margin) specifications<br />
* Students should be analyze and understand the overall performance of the system using the Gang of Four<br />
* Students should compute the limits on the performance that arise from right half plane poles and zeros<br />
<br />
'''Monday:''' Loop Shaping ({{cds101 handouts|L8-1_loopsyn.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-17.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|L8-1_loopsyn_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L8_1_dfan.m}}<br />
<br />
'''Wednesday:''' Performance Limits ({{cds101 handouts|L8-2_limits.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|L8-2_limits_h.pdf|Lecture handout}}<br />
* MATLAB handouts: {{cds101 matlab|L8_2_maglev.m}}<br />
<br />
'''Friday:''' Recitation sections<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 11 - Loop Shaping}}<br />
** CDS 101: Read sections 11.1, 11.3-11.4 [45 min]<br />
** CDS 110: Read sections 11.1, 11.2-11.5 [60 min]<br />
** CDS 210: Skim AM08 Ch 11.1-11.4, read AM08 11.5, DFT Ch 4 and 6 [90 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw7-fa08.pdf|Homework #7}} (due 24 Nov 08): {{cds101 handouts|hw7-101-fa08.pdf|CDS 101}}, {{cds101 handouts|hw7-110-fa08.pdf|CDS 110}}, {{cds101 handouts|hw7-210-fa08.pdf|CDS 210}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 9-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 8, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Loop_Analysis&diff=8391CDS 101/110 - Loop Analysis2008-11-12T23:33:05Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
The learning objectives for this week are:<br />
* Students should be able to draw a Nyquist curve and use the Nyquist criterion to determine stability<br />
* Students should be able to compute the gain a phase margin for a system using Nyquist and Bode plots<br />
<br />
'''Monday:''' Stability of Feedback Systems ({{cds101 handouts|L7-1_loopanal.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-10.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|ambode.m}}, {{cds101 matlab|amnyquist.m}}, {{cds101 matlab|arrow.m}}<br />
<br />
'''Wednesday:''' Nyquist Analysis ({{cds101 handouts|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3|cds101-2008-11-12.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 />
'''Friday:''' recitations<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 9 - Frequency Domain Analysis}}<br />
** CDS 101: Read sections 9.1-9.3, skipping advanced subsetions [45 min]<br />
** CDS 110: Read sections 9.1-9.3 [60 min]<br />
** CDS 210: Review AM08 Ch 9.1-9.3, read AM08 9.4-.5, DFT Ch 3 [90 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw6-fa08.pdf|Homework #6}} (due 17 Nov 08): {{cds101 handouts|hw6-101-fa08.pdf|CDS 101}}, {{cds101 handouts|hw6-110-fa08.pdf|CDS 110}}, {{cds101 handouts|hw6-210-fa08.pdf|CDS 210}}<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 />
** amnyquist - same as Nyquist, but sometimes does a better job with arrows<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 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 6, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Loop_Analysis&diff=8382CDS 101/110 - Loop Analysis2008-11-10T23:30:18Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
The learning objectives for this week are:<br />
* Students should be able to draw a Nyquist curve and use the Nyquist criterion to determine stability<br />
* Students should be able to compute the gain a phase margin for a system using Nyquist and Bode plots<br />
<br />
'''Monday:''' Stability of Feedback Systems ({{cds101 handouts|L7-1_loopanal.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-10.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|ambode.m}}, {{cds101 matlab|amnyquist.m}}, {{cds101 matlab|arrow.m}}<br />
<br />
'''Wednesday:''' Nyquist Analysis ({{cds101 handouts|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3 placeholder|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 />
'''Friday:''' recitations<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 9 - Frequency Domain Analysis}}<br />
** CDS 101: Read sections 9.1-9.3, skipping advanced subsetions [45 min]<br />
** CDS 110: Read sections 9.1-9.3 [60 min]<br />
** CDS 210: Review AM08 Ch 9.1-9.3, read AM08 9.4-.5, DFT Ch 3 [90 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts placeholder|hw6-fa08.pdf|Homework #6}} (due 17 Nov 08)<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 />
** amnyquist - same as Nyquist, but sometimes does a better job with arrows<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 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 6, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Transfer_Functions&diff=8381CDS 101/110 - Transfer Functions2008-11-10T21:15:07Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
The learning objectives for this week are:<br />
* Students should be able to construct a transfer function from a state space system<br />
* Students should be able to sketch the frequency response corresponding to a transfer function and label its key features<br />
* Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system<br />
<br />
'''Monday:''' Transfer Functions ({{cds101 handouts|L6-1_xferfcns.pdf|Slides}}, {{cds101 mp3 |cds101-2008-11-03.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 />
* {{cds101 matlab|ambode.m}} - special version of bode command using powers of 10 for gain (instead of dB)<br />
<br />
'''Wednesday:''' Bode Plots ({{cds101 handouts|L6-2_bode.pdf|Notes}}, {{cds101 mp3|cds101-2008-11-05.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 />
* {{AM08|Chapter 8 -Transfer Functions}}<br />
** CDS 101: Read sections 8.1-8.4 [45 min]<br />
** CDS 110: Read sections 8.1-8.5 [60 min]<br />
** CDS 210: Review AM08 Ch 8, DFT Ch 2 [60 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw5-fa08.pdf|Homework #5}} - due 10 Nov 07<br />
** {{cds101 handouts|hw5-101-fa08.pdf|CDS 101}}<br />
** {{cds101 handouts|hw5-110-fa08.pdf|CDS 110}}<br />
** {{cds101 handouts|hw5-210-fa08.pdf|CDS 210}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 5, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Transfer_Functions&diff=8367CDS 101/110 - Transfer Functions2008-11-04T20:49:55Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
The learning objectives for this week are:<br />
* Students should be able to construct a transfer function from a state space system<br />
* Students should be able to sketch the frequency response corresponding to a transfer function and label its key features<br />
* Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system<br />
<br />
'''Monday:''' Transfer Functions ({{cds101 handouts|L6-1_xferfcns.pdf|Slides}}, {{cds101 mp3 |cds101-2008-11-03.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:''' Bode Plots ({{cds101 handouts|L6-2_bode.pdf|Notes}}, {{cds101 mp3 placeholder|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 />
* {{AM08|Chapter 8 -Transfer Functions}}<br />
** CDS 101: Read sections 8.1-8.4 [45 min]<br />
** CDS 110: Read sections 8.1-8.5 [60 min]<br />
** CDS 210: Review AM08 Ch 8, DFT Ch 2 [60 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw5-fa08.pdf|Homework #5}} - due 10 Nov 07<br />
** {{cds101 handouts|hw5-101-fa08.pdf|CDS 101}}<br />
** {{cds101 handouts|hw5-110-fa08.pdf|CDS 110}}<br />
** {{cds101 handouts|hw5-210-fa08.pdf|CDS 210}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 6-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 5, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Output_Feedback&diff=8345CDS 101/110 - Output Feedback2008-10-31T22:07:00Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
<br />
== Overview ==<br />
<br />
'''Monday:''' Observability and Observers ({{cds101 handouts placeholder|L5-1_observability.pdf|Slides}}, {{cds101 mp3 |cds101-2008-10-27.mp3|MP3}})<br />
<br />
This lecture introduces the concept of observability and the use of estimators for linear systems. Observability is defined as the ability to determine the system state from the (past) time history of measurements. The observability matrix test is given to check if a linear system is observable, and the test is applied to an example. The concept of (linear) observer design is introduced and the ability to arbitrarily place eigenvalues of the closed loop observer error dynamics is related to observability. A cart and pendulum system is used as an example.<br />
<br />
<!--{{cds101 handouts placeholder|L5-1_reachability_h.pdf|Lecture handout}} --><br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L5-1_estimators.pdf Lecture handout] <br />
* MATLAB code: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/ObservExamp.m L5 ObservExamp.m],<br />
<br />
'''Wednesday:''' Control Design Example/Demo: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L5-2_demo.pdf Lecture notes] ({{cds101 mp3|cds101-2008-10-29.mp3|MP3}})<br />
<br />
This lecture will use an in-class demo to work through a real-world control example.<br />
<br />
'''Friday:''' Midterm Review: ({{cds101 mp3|cds101-2008-10-31.mp3|MP3}})<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 7 - Output Feedback}}<br />
<br />
== Midterm/Homework ==<br />
<br />
* CDS 101/110: [[CDS 101/110 Midterm, Fall 2008|Midterm exam information]]<br />
* CDS 210: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hwM-210-fa08.pdf hwM - 210]<br />
** [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/heat_pde.m heat_pde.m] - A, B, C matrix for discretized 1-D heat equation<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework M, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Output_Feedback&diff=8344CDS 101/110 - Output Feedback2008-10-30T07:26:01Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
<br />
== Overview ==<br />
<br />
'''Monday:''' Observability and Observers ({{cds101 handouts placeholder|L5-1_observability.pdf|Slides}}, {{cds101 mp3 |cds101-2008-10-27.mp3|MP3}})<br />
<br />
This lecture introduces the concept of observability and the use of estimators for linear systems. Observability is defined as the ability to determine the system state from the (past) time history of measurements. The observability matrix test is given to check if a linear system is observable, and the test is applied to an example. The concept of (linear) observer design is introduced and the ability to arbitrarily place eigenvalues of the closed loop observer error dynamics is related to observability. A cart and pendulum system is used as an example.<br />
<br />
<!--{{cds101 handouts placeholder|L5-1_reachability_h.pdf|Lecture handout}} --><br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L5-1_estimators.pdf Lecture handout] <br />
* MATLAB code: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/ObservExamp.m L5 ObservExamp.m],<br />
<br />
'''Wednesday:''' Control Design Example/Demo: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L5-2_demo.pdf Lecture notes] ({{cds101 mp3|cds101-2008-10-29.mp3|MP3}})<br />
<br />
This lecture will use an in-class demo to work through a real-world control example.<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 7 - Output Feedback}}<br />
<br />
== Midterm/Homework ==<br />
<br />
* CDS 101/110: [[CDS 101/110 Midterm, Fall 2008|Midterm exam information]]<br />
* CDS 210: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hwM-210-fa08.pdf hwM - 210]<br />
** [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/heat_pde.m heat_pde.m] - A, B, C matrix for discretized 1-D heat equation<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework M, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Output_Feedback&diff=8338CDS 101/110 - Output Feedback2008-10-29T17:59:58Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
<br />
== Overview ==<br />
<br />
'''Monday:''' Observability and Observers ({{cds101 handouts placeholder|L5-1_observability.pdf|Slides}}, {{cds101 mp3 |cds101-2008-10-27.mp3|MP3}})<br />
<br />
This lecture introduces the concept of observability and the use of estimators for linear systems. Observability is defined as the ability to determine the system state from the (past) time history of measurements. The observability matrix test is given to check if a linear system is observable, and the test is applied to an example. The concept of (linear) observer design is introduced and the ability to arbitrarily place eigenvalues of the closed loop observer error dynamics is related to observability. A cart and pendulum system is used as an example.<br />
<br />
<!--{{cds101 handouts placeholder|L5-1_reachability_h.pdf|Lecture handout}} --><br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L5-1_estimators.pdf Lecture handout] <br />
* MATLAB code: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/ObservExamp.m L5 ObservExamp.m],<br />
<br />
'''Wednesday:''' Control Design Example/Demo: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L5-2_demo.pdf Lecture notes] ({{cds101 mp3 placeholder|cds101-2008-10-22.mp3|MP3}})<br />
<br />
This lecture will use an in-class demo to work through a real-world control example.<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 7 - Output Feedback}}<br />
<br />
== Midterm/Homework ==<br />
<br />
* CDS 101/110: [[CDS 101/110 Midterm, Fall 2008|Midterm exam information]]<br />
* CDS 210: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hwM-210-fa08.pdf hwM - 210]<br />
** [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/heat_pde.m heat_pde.m] - A, B, C matrix for discretized 1-D heat equation<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework M, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_State_Feedback&diff=8303CDS 101/110 - State Feedback2008-10-23T20:25:40Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
'''Monday:''' Reachability and State Feedback ({{cds101 handouts placeholder|L5-1_reachability.pdf|Slides}}, {{cds101 mp3|cds101-2008-10-20.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 placeholder|L5-1_reachability_h.pdf|Lecture handout}}--><br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L4-1_statefbk.pdf Lecture handout]<br />
* MATLAB code: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/predprey_calcs.m L5 predprey_calcs.m], {{cds101 matlab|predprey.m}}, [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/predprey_rh.m predprey_rh.m],<br />
<br />
'''Wednesday:''' State Feedback Design: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L4-2_statefbk.pdf Lecture notes] ({{cds101 mp3|cds101-2008-10-22.mp3|MP3}})<br />
<br />
This lecture will present more advanced analysis on reachability and on control using state feedback. <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 />
== Reading ==<br />
<br />
* {{AM08|Chapter 6 - State Feedback}}<br />
<br />
== Homework ==<br />
<br />
This homework set covers reachability and state feedback. The Whipple bicycle model is used as an example to illustrate state feedback with pole placement, and the dependence of both the tracking behaviour and the command response on the location chosen for the closed-loop poles.<br />
<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-101-fa08.pdf hw4 - 101]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-110-fa08.pdf hw4 - 110]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-210-fa08.pdf hw4 - 210]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/bike_linmod.m bike_linmod.m] - Mass, damping and stiffness matrices for Whipple bicycle model<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 4-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 4, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Linear_Systems&diff=8267CDS 101/110 - Linear Systems2008-10-16T22:06:14Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}__NOTOC__<br />
== Overview ==<br />
<br />
'''Monday:''' Linear Time-Invariant Systems ({{cds101 handouts placeholder|L4-1_linsys.pdf|Slides}}, {{cds101 mp3|cds101-2008-10-13.mp3|MP3}})<br />
<br />
This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced.<br />
<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-1_linsys.pdf Lecture handout]<br />
* MATLAB code: {{cds101 matlab|L4_1_linsys.m}}<br />
<br />
'''Wednesday:''' Linear Systems Analysis ([http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-2_linsys.pdf Notes], {{cds101 mp3|cds101-2008-10-15.mp3.mp3|MP3}})<br />
<br />
Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system.<br />
* {{cds101 handouts placeholder|L4-2_linearization.pdf|Lecture notes}}<br />
<br />
'''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|recitations]]<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 5 - Linear Systems}}<br />
<br />
== Homework ==<br />
<br />
This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linearization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions.<br />
<br />
<!-- Links to homework materials --><br />
<!--* {{cds101 handouts placeholder|hw3.pdf|Homework #3}} --><br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-101-fa08.pdf hw3 - 101]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-110-fa08.pdf hw3 - 110]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-210-fa08.pdf hw3 - 210]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/balance_simple.mdl balance_simple.mdl] - SIMULINK model of a balance system<br />
* [[Media:Ambode.m|ambode.m]] - Bode plot with AM unit choices<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 3, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Linear_Systems&diff=8266CDS 101/110 - Linear Systems2008-10-16T22:03:50Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}__NOTOC__<br />
== Overview ==<br />
<br />
'''Monday:''' Linear Time-Invariant Systems ({{cds101 handouts placeholder|L4-1_linsys.pdf|Slides}}, {{cds101 mp3|cds101-2008-10-13.mp3|MP3}})<br />
<br />
This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced.<br />
<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-1_linsys.pdf Lecture handout]<br />
* MATLAB code: {{cds101 matlab|L4_1_linsys.m}}<br />
<br />
'''Wednesday:''' Linear Systems Analysis ([http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-2_linsys.pdf Notes], {{cds101 mp3|cds101-2008-10-15.mp3|MP3}})<br />
<br />
Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system.<br />
* {{cds101 handouts placeholder|L4-2_linearization.pdf|Lecture notes}}<br />
<br />
'''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|recitations]]<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 5 - Linear Systems}}<br />
<br />
== Homework ==<br />
<br />
This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linearization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions.<br />
<br />
<!-- Links to homework materials --><br />
<!--* {{cds101 handouts placeholder|hw3.pdf|Homework #3}} --><br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-101-fa08.pdf hw3 - 101]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-110-fa08.pdf hw3 - 110]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-210-fa08.pdf hw3 - 210]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/balance_simple.mdl balance_simple.mdl] - SIMULINK model of a balance system<br />
* [[Media:Ambode.m|ambode.m]] - Bode plot with AM unit choices<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 3, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Linear_Systems&diff=8234CDS 101/110 - Linear Systems2008-10-14T03:02:21Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}__NOTOC__<br />
== Overview ==<br />
<br />
'''Monday:''' Linear Time-Invariant Systems ({{cds101 handouts placeholder|L4-1_linsys.pdf|Slides}}, {{cds101 mp3|cds101-2008-10-13.mp3|MP3}})<br />
<br />
This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced.<br />
<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-1_linsys.pdf Lecture handout]<br />
* MATLAB code: {{cds101 matlab|L4_1_linsys.m}}<br />
<br />
'''Wednesday:''' Linear Systems Analysis ({{cds101 handouts placeholder|L4-2_linsys.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-10-24.mp3|MP3}})<br />
<br />
Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system.<br />
* {{cds101 handouts placeholder|L4-2_linearization.pdf|Lecture notes}}<br />
<br />
'''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|recitations]]<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 5 - Linear Systems}}<br />
<br />
== Homework ==<br />
<br />
This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linearization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions.<br />
<br />
<!-- Links to homework materials --><br />
<!--* {{cds101 handouts placeholder|hw3.pdf|Homework #3}} --><br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-101-fa08.pdf hw3 - 101]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-110-fa08.pdf hw3 - 110]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-210-fa08.pdf hw3 - 210]<br />
* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/balance_simple.mdl balance_simple.mdl] - SIMULINK model of a balance system<br />
* [[Media:Ambode.m|ambode.m]] - Bode plot with AM unit choices<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 3-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 3, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8225Phaseplot2008-10-13T03:31:28Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, be sure that you are correctly inputting the arguments. Below is a proper example of how to call phaseplot:<br />
<br />
phaseplot('f',X1Range,X2Range, scale, Xinit)<br />
<br />
phaseplot('oscillator', [-1 1 10], [-1 1 10], 0.1,boxgrid([-1 1 10], [-1 1 10]))<br />
<br />
Note that oscillator is the function that defines the derivative (look at week two and download oscillator.m if you don't know how to define the derivative function) and it is called with apostrophes:<br />
<br />
Correct way: 'oscillator'<br />
<br />
Incorrect ways: oscillator or @oscillator<br />
<br />
X1Range and X2Range are of the form [min, max, num]. They define the axes of the plot and num determines how many arrows will be drawn along each corresponding axis. Make sure that the axes ranges include the equilibrium points. Scale is the final argument and it scales the arrows created on the quiver plot; 0.1 seems to be a good choice, but if your arrows are to small or too big try a different scale factor.<br />
<br />
Finally, Xinit determines what points to start the trajectories that get drawn on the phase diagram. For this you can either just make a list of points around the edge of the axes or you can use Professor Murray's boxgrid.m which is located on the Week 2 page of the wiki. If you choose to use boxgrid, call it as follows:<br />
<br />
boxgrid(X1Range, X2Range)<br />
<br />
X1Range and X2Range don't have to be the same as those that were put into the phaseplot command, but they do take the same form: [min max num].<br />
<br />
NOTE: If you are going to use boxgrid on this problem, you need to do a small alteration to the boxgrid.m file. Open the boxgrid.m file and delete the first element,which is a zero, of both the sx1 and sx2 vectors defined on lines 11 and 12.<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8221Phaseplot2008-10-12T18:27:21Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, be sure that you are correctly inputting the arguments. Below is a proper example of how to call phaseplot:<br />
<br />
phaseplot('f',X1Range,X2Range, scale, Xinit)<br />
<br />
phaseplot('oscillator', [-1 1 10], [-1 1 10], 0.1,boxgrid([-1 1 10], [-1 1 10]))<br />
<br />
Note that oscillator is the function that defines the derivative (look at week two and download oscillator.m if you don't know how to define the derivative function) and it is called with apostrophes:<br />
<br />
Correct way: 'oscillator'<br />
<br />
Incorrect ways: oscillator or @oscillator<br />
<br />
X1Range and X2Range are of the form [min, max, num]. They define the axes of the plot and num determines how many arrows will be drawn along each corresponding axis. Make sure that the axes ranges include the equilibrium points. Scale is the final argument and it scales the arrows created on the quiver plot; 0.1 seems to be a good choice, but if your arrows are to small or too big try a different scale factor.<br />
<br />
Finally, Xinit determines what points to start the trajectories that get drawn on the phase diagram. For this you can either just make a list of points around the edge of the axes or you can use Professor Murray's boxgrid.m which is located on the Week 2 page of the wiki. If you choose to use boxgrid, call it as follows:<br />
<br />
boxgrid(X1Range, X2Range)<br />
<br />
X1Range and X2Range don't have to be the same as those that were put into the phaseplot command, but they do take the same form: [min max num].<br />
<br />
NOTE: If you are going to use boxgrid on this problem, you need to do a small alteration to the boxgrid.m file. Open the boxgrid.m file and delete the first element of both the sx1 and sx2 vectors defined on lines 11 and 12. This element should be a zero in each vector.<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8220Phaseplot2008-10-12T18:18:37Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, be sure that you are correctly inputting the arguments. Below is a proper example of how to call phaseplot:<br />
<br />
phaseplot('f',X1Range,X2Range, scale, Xinit)<br />
<br />
phaseplot('oscillator', [-1 1 10], [-1 1 10], 0.1,boxgrid([-1 1 10], [-1 1 10]))<br />
<br />
Note that oscillator is the function that defines the derivative (look at week two and download oscillator.m if you don't know how to define the derivative function) and it is called with apostrophes:<br />
<br />
Correct way: 'oscillator'<br />
<br />
Incorrect ways: oscillator or @oscillator<br />
<br />
X1Range and X2Range are of the form [min, max, num]. They define the axes of the plot and num determines how many arrows will be drawn along each corresponding axis. Make sure that the axes ranges include the equilibrium points. Scale is the final argument and it scales the arrows created on the quiver plot; 0.1 seems to be a good choice, but if your arrows are to small or too big try a different scale factor.<br />
<br />
Finally, Xinit determines what points to start the trajectories that get drawn on the phase diagram. For this you can either just make a list of points around the edge of the axes or you can use Professor Murray's boxgrid.m which is located on the Week 2 page of the wiki. If you choose to use boxgrid, call it as follows:<br />
<br />
boxgrid(X1Range, X2Range)<br />
<br />
X1Range and X2Range don't have to be the same as those that were put into the phaseplot command, but they do take the same form: [min max num].<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8219Phaseplot2008-10-12T02:04:04Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, be sure that you are correctly inputting the arguments. Below is a proper example of how to call phaseplot:<br />
<br />
phaseplot('f',X1Range,X2Range, scale)<br />
<br />
phaseplot('oscillator', [-1 1 10], [-1 1 10], 0.1)<br />
<br />
Note that oscillator is the function that defines the derivative (look at week two and download oscillator.m if you don't know how to define the derivative function) and it is called with apostrophes:<br />
<br />
Correct way: 'oscillator'<br />
<br />
Incorrect ways: oscillator or @oscillator<br />
<br />
X1Range and X2Range are of the form [min, max, num]. They define the axes of the plot and num determines how many arrows will be drawn along each corresponding axis. Make sure that the axes ranges include the equilibrium points. Scale is the final argument and it scales the arrows created on the quiver plot; 0.1 seems to be a good choice, but if your arrows are to small or too big try a different scale factor.<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8218Phaseplot2008-10-12T01:06:30Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, make sure to call the function in the first argument correctly:<br />
<br />
Incorrect Ways: 1. phaseplot( F, .... )<br />
<br />
Correct Way: phaseplot( 'F', ..... )<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8217Phaseplot2008-10-12T01:05:03Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, make sure to call the function in the first argument correctly:<br />
<br />
Incorrect Ways: phaseplot( F, .... )<br />
phasep<nowiki>Insert non-formatted text here</nowiki>lot( @F, ..... )<br />
<br />
Correct Way: phaseplot( 'F', ..... )<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8216Phaseplot2008-10-12T01:02:52Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, make sure to call the function in the first argument correctly:<br />
<br />
Incorrect Ways: phaseplot( F, .... )<br />
phaseplot( @F, ..... )<br />
<br />
Correct Way: phaseplot( 'F', ..... )<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8215Phaseplot2008-10-11T22:41:31Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, make sure to call the function in the first argument correctly:<br />
<br />
Incorrect Way: phaseplot( F, ..... )<br />
<br />
Correct Way: phaseplot( 'F', ..... )<br />
<br />
--[[User:Merfeld| Max Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8214Phaseplot2008-10-11T22:41:18Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, make sure to call the function in the first argument correctly:<br />
<br />
Incorrect Way: phaseplot( F, ..... )<br />
<br />
Correct Way: phaseplot( 'F', ..... )<br />
<br />
--[[user:Merfeld]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 2]]<br />
[[Category:CDS 101/110 FAQ - Homework 2, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phasplot&diff=8213Phasplot2008-10-11T22:40:52Z<p>Merfeld: Phasplot moved to Phaseplot</p>
<hr />
<div>#redirect [[Phaseplot]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8212Phaseplot2008-10-11T22:40:52Z<p>Merfeld: Phasplot moved to Phaseplot</p>
<hr />
<div>When calling the phaseplot command, make sure to call the function in the first argument correctly:<br />
<br />
Incorrect Way: phaseplot( F, ..... )<br />
<br />
Correct Way: phaseplot( 'F', ..... )<br />
<br />
--[[user:Merfeld]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=Phaseplot&diff=8211Phaseplot2008-10-11T22:37:32Z<p>Merfeld: </p>
<hr />
<div>When calling the phaseplot command, make sure to call the function in the first argument correctly:<br />
<br />
Incorrect Way: phaseplot( F, ..... )<br />
<br />
Correct Way: phaseplot( 'F', ..... )<br />
<br />
--[[user:Merfeld]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Dynamic_Behavior&diff=8188CDS 101/110 - Dynamic Behavior2008-10-08T22:09:42Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
The learning objectives for this week are:<br />
* Students should be able to use a phase portraits to describe the behavior of dynamical systems and determine the stability of an equilibrium point<br />
* Students should be able to find equilibrium points for a nonlinear system and determine whether they are stable using linearizations (all) and Lyapunov functions (CDS 110/210)<br />
* Students should be able to explain the difference between stability, asymptotic stability, and global stability<br />
<br />
'''Monday:''' Qualitative Analysis and Stability ({{cds101 handouts|L2-1_stability.pdf|Slides}}, [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-2007-10-15.mp3 MP3]- due to technical difficulties, this is last year's lecture)<br />
<p><br />
:This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples. <br />
<br />
:* {{cds101 handouts|L2-1_stability_h.pdf|Lecture handout}}<br />
:* MATLAB code: {{cds101 matlab|phaseplot.m}}, {{cds101 matlab|boxgrid.m}}, {{cds101 matlab|L2_1_stability.m}}, {{cds101 matlab|oscillator.m}}, {{cds101 matlab|invpend.m}}, {{cds101 matlab|predprey.m}}<br />
</p><br />
'''Wednesday:''' Stability Analysis using Lyapunov Functions ({{cds101 handouts|L2-2_lyapunov.pdf|Notes}}, [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-2007-10-17.mp3 MP3]- due to technical difficulties, this is last year's lecture)<br />
:Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts.<br />
<br />
:* {{cds101 handouts|L2-2_lyapunov.pdf|Lecture notes}}<br />
<br />
'''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|Recitations]]<br />
:* [[CDS 210 - Stability Analysis]]<br />
<br />
== Reading ==<br />
<br />
* {{AM08|Chapter 4 - Dynamic Behavior}} <br />
** CDS 101: Read sections 4.1-4.3 [30 min]<br />
** CDS 110: Read sections 4.1-4.4, up to Krasolvski-Lasalle (p 118) [60 min]<br />
** CDS 210: Review sections 4.1-4.3, read sections 4.4-4.5 [60 min]<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw2-fa08.pdf|Homework #2}}<br />
<br />
== FAQ ==<br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 2, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8159SIMULINK License2008-10-07T20:31:39Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--[[User:Merfeld|Max]]<br />
<br />
[[Category:CDS 101/110 FAQ - Homework 1]]<br />
[[Category:CDS 101/110 FAQ - Homework 1, Fall 2008]]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8158SIMULINK License2008-10-07T20:26:04Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--Max<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 1]]<br />
[[Category: CDS 101/110 FAQ - Homework 1, Fall 2008]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8157SIMULINK License2008-10-07T20:25:49Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--Max<br />
<br />
[[Category: CDS 101/110 FAQ - Homework1]]<br />
[[Category: CDS 101/110 FAQ - Homework1, Fall 2008]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8156SIMULINK License2008-10-07T20:25:37Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--Max<br />
<br />
[[Category: CDS 101/110 FAQ - Homework n]]<br />
[[Category: CDS 101/110 FAQ - Homework n, Fall 2008]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8155SIMULINK License2008-10-07T20:25:17Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--Max<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 1]]<br />
[[Category: CDS 101/110 FAQ - Homework 1, Fall 2008]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8154SIMULINK License2008-10-07T20:24:50Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
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--Max<br />
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[[Category: CDS 101/110 FAQ - Homework 1, Fall 2008]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8153SIMULINK License2008-10-07T20:23:38Z<p>Merfeld: </p>
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<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--Max<br />
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[[Category: CDS 101/110 FAQ - Homework 1]]<br />
[[Category: CDS 101/110 FAQ - Homework 1, Fall 2008]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8152SIMULINK License2008-10-07T20:20:40Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--Max<br />
<br />
[[Category: CDS 101/110 FAQ - Homework 1]]<br />
[[Category: CDS 101/110 FAQ - Homework 1, Fall 2008]</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=SIMULINK_License&diff=8151SIMULINK License2008-10-07T20:19:45Z<p>Merfeld: </p>
<hr />
<div>If you have recently installed MATLAB and have never ran Simulink before, I believe it could be a problem with you license file. Make sure to go back to software.caltech.edu and go back to the page where you downloaded MATLAB (in My Software) and follow the instructions on updating your network.lic file in the Matlab source folder. <br />
<br />
--Max</div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Introduction_and_Review&diff=8077CDS 101/110 - Introduction and Review2008-10-01T22:24:27Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
The learning objectives for this week are:<br />
* Students should know what a feedback system is and how to identify the key components and properties of a control system in the everyday world<br />
* Students should be able to model a simple system (using ODEs) and use their model to make predictions about the behavior of a system<br />
* Students should be able to use MATLAB and SIMULINK to run a simulation of a control system and generate plots showing the performance of the system<br />
<br />
'''Monday:''' Introduction to Feedback and Control ({{cds101 handouts|L1-1_introduction.pdf|Slides}}, {{cds101 mp3|lecture_0929.mp3|MP3}}) <br />
The goal of this lecture is to introduce some of the basic ideas in feedback and control systems and provide examples that will allow students to identify and recognize control systems in their everyday world. Two major principles of control--robustness through feedback and design of dynamics--are emphasized throughout the lecture. CDS 101/110 course administration is also covered.<br />
* {{cds101 handouts|L1-1_introduction_h.pdf|Lecture handout}}<br />
* {{cds101 handouts|bgsurvey.pdf|Course survey}} (turn in by 1 Oct)<br />
<br />
'''Wednesday:''' Review of Modeling using ODEs ({{cds101 handouts|L1-2_modeling.pdf|Slides}}, {{cds101 mp3 placeholder|cds101-2007-10-03.mp3|MP3}})<br />
*NOTE: Due to technical difficulties, this Wednesday's lecture was not recorded. Sorry for the inconvenience.<br />
<br />
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.<br />
<br />
* {{cds101 handouts|L1-2_modeling_h.pdf|Lecture handout}}<br />
* MATLAB: {{cds101 matlab|L1_2_modeling.m}}, {{cds101 matlab|springmass.m}}<br />
<br />
'''Friday:''' {{cds101 lecture|MATLAB/SIMULINK Tutorial}}<br />
<br />
This lecture provides an introduction to MATLAB/SIMULINK, a software package that will be used extensively throughout the course and on the homework assignments. Students who have not used MATLAB and SIMULINK in previous courses are strongly encouraged to attend. '''Note:''' This tutorial will be offered from 2-4 pm and 4-6 pm in 328 SFL. Students may attend either session.<br />
<br />
* {{cds101 handouts placeholder|L1-3_matlab.pdf|Lecture handout}}<br />
<br />
== Reading ==<br />
<br />
The reading for the week is out of the main text. The material in Chapter 2 should be review (Ph1, Ma 2, mainly), but introduces some important concepts in terms of control-oriented modeling (inputs, outputs, state). Section 3.1 gives an overview of the cruise control model, which is part of this week's homework.<br />
* {{AM08 book}}<br />
** {{AM08 chapter|Chapter 1 - Introduction}} - Read sections 1.1-1.2 and 1.4-1.5 (skim 1.3) [30 min]<br />
** {{AM08 chapter|Chapter 2 - System Modeling}} - Read sections 2.1-2.3 [30 min]<br />
** {{AM08 chapter|Chapter 3 - Examples}} - Skim section 3.1 (cruise control model) [10 min]<br />
<br />
Students interested in more advanced material should read Chapter 1 of Lewis:<br />
* {{Lew03|Chapter 1 - An introduction to linear control theory}}<br />
<br />
In addition, for the MATLAB/SIMULINK tutorial, students may want to have a look at [http://www.engin.umich.edu/class/ctms/basic/basic.htm MATLAB basics], part of the [http://www.engin.umich.edu/class/ctms Control Tutorials for MATLAB] web site.<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw1-fa08.pdf|Homework #1}} (due 6 Oct)<br />
* SIMULINK speed control module: {{cds101 matlab|cruise_ctrl.mdl}}, [[AM:Cruise control|documentation]]<br />
<br />
== FAQ ==<br />
<table align=right><tr><td><nowiki>[</nowiki>[[CDS 101/110a - FAQ|Prior years]]<nowiki>]</nowiki></td></tr></table><br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 1-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 1-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 1-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 1, Fall 2008</ncl></div>Merfeldhttps://murray.cds.caltech.edu/index.php?title=CDS_101/110_-_Introduction_and_Review&diff=8076CDS 101/110 - Introduction and Review2008-10-01T22:23:13Z<p>Merfeld: </p>
<hr />
<div>{{cds101-fa08}}<br />
<br />
{{righttoc}}<br />
== Overview ==<br />
<br />
The learning objectives for this week are:<br />
* Students should know what a feedback system is and how to identify the key components and properties of a control system in the everyday world<br />
* Students should be able to model a simple system (using ODEs) and use their model to make predictions about the behavior of a system<br />
* Students should be able to use MATLAB and SIMULINK to run a simulation of a control system and generate plots showing the performance of the system<br />
<br />
'''Monday:''' Introduction to Feedback and Control ({{cds101 handouts|L1-1_introduction.pdf|Slides}}, {{cds101 mp3|lecture_0929.mp3|MP3}}) <br />
The goal of this lecture is to introduce some of the basic ideas in feedback and control systems and provide examples that will allow students to identify and recognize control systems in their everyday world. Two major principles of control--robustness through feedback and design of dynamics--are emphasized throughout the lecture. CDS 101/110 course administration is also covered.<br />
* {{cds101 handouts|L1-1_introduction_h.pdf|Lecture handout}}<br />
* {{cds101 handouts|bgsurvey.pdf|Course survey}} (turn in by 1 Oct)<br />
<br />
'''Wednesday:''' Review of Modeling using ODEs ({{cds101 handouts|L1-2_modeling.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-03.mp3|MP3}})<br />
*NOTE: Due to technical difficulties, this Wednesday's lecture was not recorded. The above mp3 is last year's second lecture and may not accurately represent this year's lecture.<br />
<br />
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.<br />
<br />
* {{cds101 handouts|L1-2_modeling_h.pdf|Lecture handout}}<br />
* MATLAB: {{cds101 matlab|L1_2_modeling.m}}, {{cds101 matlab|springmass.m}}<br />
<br />
'''Friday:''' {{cds101 lecture|MATLAB/SIMULINK Tutorial}}<br />
<br />
This lecture provides an introduction to MATLAB/SIMULINK, a software package that will be used extensively throughout the course and on the homework assignments. Students who have not used MATLAB and SIMULINK in previous courses are strongly encouraged to attend. '''Note:''' This tutorial will be offered from 2-4 pm and 4-6 pm in 328 SFL. Students may attend either session.<br />
<br />
* {{cds101 handouts placeholder|L1-3_matlab.pdf|Lecture handout}}<br />
<br />
== Reading ==<br />
<br />
The reading for the week is out of the main text. The material in Chapter 2 should be review (Ph1, Ma 2, mainly), but introduces some important concepts in terms of control-oriented modeling (inputs, outputs, state). Section 3.1 gives an overview of the cruise control model, which is part of this week's homework.<br />
* {{AM08 book}}<br />
** {{AM08 chapter|Chapter 1 - Introduction}} - Read sections 1.1-1.2 and 1.4-1.5 (skim 1.3) [30 min]<br />
** {{AM08 chapter|Chapter 2 - System Modeling}} - Read sections 2.1-2.3 [30 min]<br />
** {{AM08 chapter|Chapter 3 - Examples}} - Skim section 3.1 (cruise control model) [10 min]<br />
<br />
Students interested in more advanced material should read Chapter 1 of Lewis:<br />
* {{Lew03|Chapter 1 - An introduction to linear control theory}}<br />
<br />
In addition, for the MATLAB/SIMULINK tutorial, students may want to have a look at [http://www.engin.umich.edu/class/ctms/basic/basic.htm MATLAB basics], part of the [http://www.engin.umich.edu/class/ctms Control Tutorials for MATLAB] web site.<br />
<br />
== Homework ==<br />
<br />
* {{cds101 handouts|hw1-fa08.pdf|Homework #1}} (due 6 Oct)<br />
* SIMULINK speed control module: {{cds101 matlab|cruise_ctrl.mdl}}, [[AM:Cruise control|documentation]]<br />
<br />
== FAQ ==<br />
<table align=right><tr><td><nowiki>[</nowiki>[[CDS 101/110a - FAQ|Prior years]]<nowiki>]</nowiki></td></tr></table><br />
'''Monday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 1-1, Fall 2008</ncl><br />
'''Wednesday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 1-2, Fall 2008</ncl><br />
'''Friday'''<br />
<ncl>CDS 101/110 FAQ - Lecture 1-3, Fall 2008</ncl><br />
'''Homework'''<br />
<ncl>CDS 101/110 FAQ - Homework 1, Fall 2008</ncl></div>Merfeld