Question

 The loop-gain function L(s) of a control system with unity feedback is given to be \(L\left( s \right) = \frac{k}{{\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}\), where k > 0. If the gain cross-over frequency of the loop-gain function is less than its phase cross-over frequency, the closed-loop system is
1. unstable
2. marginally stable
3. conditionally stable
4. stable

Answer 1

Correct Answer - Option 4 : stable

\(L\left( s \right) = \frac{k}{{\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}\)

For any given system

i) System is stable if ω_pc > ω_gc, in this case gain margin and phase margin are positive.

ii) System is unstable if ω_pc > ω_gc in this case both gain margin and phase margin are negative.

iii) System is just stable (or) marginally stable, in this case both gain margin and phase margin are equal to zero.