Feedback Control for Computer Systems

Chapter 25. Frequency Response and the Bode Plot

In this chapter we study the response of a system subject to an oscillatory input. In particular, we will ask how the output changes when the frequency of the input signal is varied. We will also introduce the Bode plot, which is a versatile method of representing a system’s frequency response graphically.

The topics treated in this chapter are the starting point for many forms of more advanced analysis. For the most part, they rely on having detailed knowledge of a system’s transfer function. The Bode plot, however, is a pretty straightforward technique that is quite generally useful.

Frequency Response

When trying to understand the dynamic response of a system, it is often useful to study how the system responds to sinusoidal input signals of differing frequency. Such signals are (of course) the natural description for any form of oscillatory behavior. Furthermore, because the inverse of the frequency ω = 2 π/T defines a time scale, the response of a system to a sinusoidal input with frequency ω provides information about the response to a more general disturbance that occurs on a time scale comparable to T.

Frequency Response in the Physical World

There is a very general pattern for the dynamic response of objects in the physical world as a function of the stimulating frequency. At very low frequencies, the object will follow the input faithfully and with only a small delay. (That is, small when compared to the period T of the input ...