CDS 101: Principles of Feedback and Control Lecture 6.1: Transfer Functions 4 November 2002

Lecture

This lecture is the first lecture of the course to introduce transfer functions in a formal way (we have already seen frequency response and body 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 Presentation

Mud card responses [advanced search]:

• I did not understand the bandwidth and 3dB part of the lecture. What is a crossover point and why is it important?
• Is dB (decibel) equal to 20*log10(x) or -20*log10(x)? Also, why 20?
• ^(updated) Can you explain again how the zeros of a transfer function are represented on a Bode plot?
• On slide 15, can you include the animation that was used in lecture.

Reading Material and Handouts

Handouts from lecture

• Lecture handout
• Homework #5

Required reading

• Packard, Poola and Horowitz, Dynamic Systems and Feedback, Section 5-6
• Astrom, Control Systems Design, Sections 5.1-5.3
  

Supplemental reading

• A. D. Lewis, A Mathematical Introduction to Feedback Control, Chapter 3 [pdf] and Chapter 4 [pdf]

Homework

This homework set covers basic transfer function concepts. The conceptual problems show how to create a frequency response for a complex system of components using MATLAB. The analytical problems cover basic anaytical concepts in transfer functions.

• Homework Assignment [pdf]

Modifications to the homework (link above is always the latest version):

• 4 Nov 02: problem set release

Frequently asked questions on homework and TA hints:

• Is the transfer function for the cruise control system in problem 2 of HW6 the same as it was in problem 2 of HW5?
• In problem 2(c), is e=r-y or e=y-r?
• In problem 2(b), is the Kp=1000 (the same as in #2) or Kp=500 (the same as in (d))?