Question

The system  \(\frac{{1600}}{{s\left( {s + 1} \right)\left( {s + 16} \right)}}\) is to be compensated such that its gain-crossover frequency becomes same as its uncompensated Phase-crossover frequency. Which of the following is the phase crossover frequency of the compensated system?
1. 4 rad/sec
2. 8 rad/sec
3. 16 rad/sec
4. None of the above

Answer 1

Correct Answer - Option 4 : None of the above

Concept:

Gain crossover frequency (ω_gc)

The frequency at which magnitude is 0 dB or 1

Phase crossover frequency (ω_pc)

The frequency at which the angle is – 180°

Calculation:

The phase crossover frequency of the compensated system is defined as;

\({\omega _{pc}} = \sqrt {{\omega _{c1}}{\omega _{c2}}} = \frac{1}{{\sqrt {{\tau _1}{\tau _2}} }}\)

Compensated ω_gc = Uncompensated ω_pc

But phase cross-over frequency of the compensated system cannot be solved with given data.

So option D is correct.