Topic: Control Systems
For a Phase Locked Loop system, the open loop transfer function is $G(s)=\frac{1000}{s(\frac{s}{1192}+1)}$. The phase margin is $50^{\circ}$ and the crossover frequency is approximately $1000~rad/s$. A time delay is introduced in the phase detector reducing the phase margin to $40^{\circ}$. The maximum permissible time delay (in seconds) is
- A. $10^{-4}$
- B. 0.174
- C. $1.192\times10^{-3}$
- D. $0.174\times10^{-3}$
Answer: C. $1.192\times10^{-3}$
Explanation: Detailed step-by-step mathematical derivation for this specific option is obfuscated in the source text, but the maximum permissible phase delay formula applies the change in phase margin over the crossover frequency $\omega_c$.