There are two common ways to represent a cascade-control system in transfer function form: series cascade and parallel cascade. The series cascade representation shown in Figure 10-8 is the most common, so it will be used in the analysis performed in this section. Students interested in analysis using the parallel structure can work Exercise 11.
We use the following algebraic manipulations to understand the effect of the secondary (inner-loop) on the primary (or outer) loop. Notice that the secondary output can be written
The secondary closed-loop transfer function ...