Analyze stability of the system above for k 10 a without fe

Analyze stability of the system above for k = 10 a without feedback (open loop condition) b with the feedback find Range of k that include the system stable.

Solution

solution:

1)here for given system with open feedback we have transfer function as

T.F=K*[10/(s)(s+4)(s+10)]

here for stability finding roots of numerator and denometer we have

poles are

s=0,s=-4 and s=-10 as smallest root is at imaginary axis hence system is unstable for given value of k=10

3)for closed loop system T.F is

T/.F1=T.f./1+T.f*H(s)

T.f1=N(s/D(s)=10K/[s(s+4)(s+10)+10k]

here finding poles by

D(s)=0

s=-10k

s=-9

s=-3

hence system would be stable for value of K is positive

K>0

hence value of K that make the system stable in close loop is K=1

and hence system is stable for K=10 in closed loop

5)hence for k=10 system is unstable in open loop and stable in close loop and value of k to make system stable is k=1