TABLE OF CONTENTS Show that the transfer function:
is equivalent to a unity-feedback system with a transfer function of the direct path equal to:
The closed-loop transfer function of the unity-feedback system is given by:
which corresponds to the desired result.
For the system depicted in Figure 2.17, calculate the Laplace transform of the system output y ( t), as a function of the Laplace transforms of the input y r( t) and the disturbance d( t).
There exist two methods for solving this problem. The first method consists of introducing secondary variables and writing equations related to the behavior of the system. The second method is based on the superposition principle, which holds for linear systems. This principle can be stated as follows. Consider a linear system with input u and output y. If an output y i results from an input u i, i.e., u i ? y i, then:
We shall solve this problem by using the second method. On the basis of the superposition principle, we derive:
This decomposition of the output into two terms permits us to consider two block diagrams (Figures 2.18 and 2.19).
Observe that the input of the block constituted...
