Question

The system shown in the figure is

• A. Stable
• B. Unstable
• C. conditionally stable
• D. stable for input $u_1$, but unstable for input $u_2$

Answer 1

The correct option is D stable for input $u_1$, but unstable for input $u_2$


$(T/F{)}_1=\frac{\frac{(s-1)}{s+2}}{1+\frac{(s-1)}{(s+2)}\times \frac{1}{(s-1)}}=\frac{(s-1)}{(s+3)}$

pole is in LHS of s-plane, hence stable.


$(T/F{)}_2=\frac{\frac{1}{(s-1)}}{1+\frac{1}{(s-1)}\times \frac{(s-1)}{(s+2)}}=\frac{s+2}{(s-1)(s+3)}$

Hence unstable as it has pole at right hand side of s-plane.