# Difference between revisions of "CDS 101/110 - Transfer Functions"

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{{cds101-fa08}} | {{cds101-fa08 lecture|prev=Output Feedback|next=Loop Analysis}} | ||

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* Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system | * Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system | ||

'''Monday:''' Transfer Functions ({{cds101 handouts|L6-1_xferfcns.pdf|Slides}}, {{cds101 mp3 | '''Monday:''' Transfer Functions ({{cds101 handouts|L6-1_xferfcns.pdf|Slides}}, {{cds101 mp3 |cds101-2008-11-03.mp3|MP3}}) | ||

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. | 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. | ||

* {{cds101 handouts | * {{cds101 handouts|L6-1_xferfcns_h.pdf|Lecture handout}} | ||

* {{cds101 matlab|ambode.m}} - special version of bode command using powers of 10 for gain (instead of dB) | |||

'''Wednesday:''' | '''Wednesday:''' Bode Plots ({{cds101 handouts|L6-2_bode.pdf|Notes}}, {{cds101 mp3|cds101-2008-11-05.mp3|MP3}}) | ||

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. | 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. | ||

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** CDS 101: Read sections 8.1-8.4 [45 min] | ** CDS 101: Read sections 8.1-8.4 [45 min] | ||

** CDS 110: Read sections 8.1-8.5 [60 min] | ** CDS 110: Read sections 8.1-8.5 [60 min] | ||

** CDS 210: Review | ** CDS 210: Review AM08 Ch 8, DFT Ch 2 [60 min] | ||

== Homework == | == Homework == | ||

* {{cds101 handouts|hw5.pdf|Homework #5}} - due 10 Nov 07 | * {{cds101 handouts|hw5-fa08.pdf|Homework #5}} - due 10 Nov 07 | ||

** {{cds101 handouts|hw5-101-fa08.pdf|CDS 101}} | |||

** {{cds101 handouts|hw5-110-fa08.pdf|CDS 110}} | |||

** {{cds101 handouts|hw5-210-fa08.pdf|CDS 210}} | |||

== FAQ == | == FAQ == | ||

'''Monday''' | '''Monday''' | ||

<ncl>CDS 101/110 FAQ - Lecture 6-1, Fall | <ncl>CDS 101/110 FAQ - Lecture 6-1, Fall 2008</ncl> | ||

'''Wednesday''' | '''Wednesday''' | ||

<ncl>CDS 101/110 FAQ - Lecture 6-2, Fall | <ncl>CDS 101/110 FAQ - Lecture 6-2, Fall 2008</ncl> | ||

'''Homework''' | '''Homework''' | ||

<ncl>CDS 101/110 FAQ - Homework 5, Fall | <ncl>CDS 101/110 FAQ - Homework 5, Fall 2008</ncl> |

## Latest revision as of 05:58, 9 December 2008

CDS 101/110a | ← Schedule → | Recitations | FAQ | AM08 (errata) |

## Overview

The learning objectives for this week are:

- Students should be able to construct a transfer function from a state space system
- Students should be able to sketch the frequency response corresponding to a transfer function and label its key features
- Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system

**Monday:** Transfer Functions (Slides, MP3)

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.

- Lecture handout
- ambode.m - special version of bode command using powers of 10 for gain (instead of dB)

**Wednesday:** Bode Plots (Notes, MP3)

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.

**Friday:** recitation sections

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Chapter 8 -Transfer Functions.
- CDS 101: Read sections 8.1-8.4 [45 min]
- CDS 110: Read sections 8.1-8.5 [60 min]
- CDS 210: Review AM08 Ch 8, DFT Ch 2 [60 min]

## Homework

- Homework #5 - due 10 Nov 07

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 6-1, Fall 2008</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 6-2, Fall 2008</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 5, Fall 2008</ncl>