Week 6: Transfer Functions
Overview
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.
Reading Material and Handouts
Handouts from lecture
- Monday lecture handout
- MATLAB files: (none)
- Homework #5
Required reading
-
K. J. Åström and R. M. Murray, Analysis and Design of Feedback Systems, Preprint, 2003. Chapter 6. (Caltech access only).
Supplemental reading
- Packard, Poola and Horowitz, Dynamic Systems and Feedback, Section 5-6
- K. J. Åström, Control Systems Design, Preprint, 2002. Sections 5.1-5.3.
- CDS 110: A. D. Lewis, A Mathematical Introduction to Feedback Control. Sections 3.1 (block diagram algebra), 3.2 (SISO transfer functions) and 4.3 (Bode plots).
- CDS 110: Franklin, Powell and A. Emami-Naeni, Feedback Control of Dynamic Systems, Addison-Wesley, 2002. Sec. 3.1 (Laplace transforms)
Homework Set
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.