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GATE ECE 2005 | Question-67

A double integrator plant, $\mathrm{G}(s)=\frac{\mathrm{K}}{s^{2}}, \mathrm{H}(\mathrm{s})=1$ is to be compensated to achieve the damping ratio $\zeta=0.5$, and an undamped natural frequency, $\omega_{n}=5 \; \mathrm{rad/s}$. Which one of the following compensator $G_{e}(s)$ will be suitable?

  1. $\frac{\mathrm{s}+3}{\mathrm{~s}+9.9}$
  2. $\frac{\text{s}+9.9}{\text{s}+3}$
  3. $\frac{\mathrm{s}-6}{\mathrm{~s}+8.33}$
  4. $\frac{\text{s}-6}{\text{s}}$
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