V.2.2 : Stability of a Cascade Controller

The stability part can also be explained in general derivation, but it will become too cumbersome. So let us take a simple example.

Let us take, . Thus overall system is third order.

In absence of the secondary loop the characteristic equation of the overall process is:

	V.28
In presence of the secondary loop the characteristic equation of the overall process is:
	V.29

Now apply Routh-Hurwitz criteria to find the limits of both these cases:

V.2.2.1 : First case: (In absence of secondary loop)      V.26

 

Routh table: .                                                                                          

For a stable closed loop process, . Thus the upper limit of is 8.

V.2.2.2 : Second case: (In presence of secondary loop)

V.30

Routh table: .                            

For a stable closed loop process, . With further simplification, we get: