Again simplifying the above eqn:

 

	V.23
Now see what happens if the secondary loop is absent. In that case:
	V.24
and
	V.25
Simplifying
	V.26

V.2.1: Response time of a cascade Controller

First analyze the secondary loop:

In absence of the secondary loop and the slave controller

; Time constant =

In presence of the secondary loop and the slave controller (say a pure gain controller)

	V.27
Time constant =

Clearly there is a decrease in time constant in presence of slave loop. This will guarantee that the time constant of the overall process decreases when a secondary loop is introduced to the system. Eventually that decreases the overall response time.