Background

Our primary objective in studying control systems is to understand how they behave. Then through understanding their behavior, hopefully we can exert some influence to cause them to perform in a manner that will be beneficial.

Just observing behavior is not quite enough, however. It is necessary to have definite criteria of behavior, and the criteria must be measurable so that comparisons can be made. Frequency response analysis is one method of meeting these needs.

A frequency response test of a control system component (or even of a whole control system) is conducted by forcing a test signal which varies in sine wave fashion into the input of the component. At the same time, the output of the component is tracked so that the input and the output can be compared. The unique property of the sine wave input is that it is the only type of input that produces an output of the identical form. The output will also have the sine wave shape, and its frequency of oscillation will be the same as that of the input. Hence the name, frequency response. This is where the similarity ends, however.

Figure 8-1 is a graph of the frequency response input and output of a component under test. Comparing the output wave with the input, two factors are significant. First, the inherent gain of the component has modified the magnitude of the output wave. In this case it emerges smaller in magnitude than that of the input wave.