Answer:
the range of K can be said to be : -3.59 < K< 0.35
Explanation:
The transfer function of a typical tape-drive system is given by;
calculating the characteristics equation; we have:
1 + KG(s) = 0
We can compute a Simulation Table for the Routh–Hurwitz stability criterion Table as follows:
1 5.1 2+ K
1.9 6.2 4K
1.83
0
4K 0
S 0 0
We need to understand that in a given stable system; all the elements in the first column is usually greater than zero
So;
11.34 - 1.9(X) > 0
7.54 +2.1 K > 0
2.1 K > - 7.54
K > - 7.54/2.1
K > - 3.59
Also
4K >0
K > 0/4
K > 0
Similarly;
XY - 7.32 K > 0
0.54(2.1K+7.54)>7.32 K
11.45 K < 4.07
K < 4.07/11.45
K < 0.35
Thus the range of K can be said to be : -3.59 < K< 0.35