Question

In order to stabilize the system shown in figure $T_i$ should satisfy,

• A. $T_i=-T$
• B. $T_i=T$
• C. $T_i<T$
• D. $T_i>T$

Answer 1

The correct option is D $T_i>T$

Characteristic equation
$1+GH=0$
$1+\frac{(1+s{T}_i)}{s}\times \frac{1}{s(1+sT)}\times 1=0$
$s^2(1+sT)+(1+s{T}_i)=0$
$s^{3}T+s^2+s{T}_i+1=0$
Using R-H method
$\begin{array}{ccc}{s}^3& T& T_i\\ s^2& 1& 1\\ s^1& T_i-T& \\ s^0& 1& \end{array}$
For stability, 1st column should be positive
So, $T_i-T>0$
$T_i>T$