(Solved): Numerical Question 11 12 and 13Please refer to the image for the question 11. The time constant of a ...

11. The time constant of a unity gain, first order plus time delay process is $5\min$. If the phase lag at a frequency of $0.2\mathrm{rad}/\min$ is $60^{?}$. Then the dead time (in $\min$ ) is? Ans. $5?/12$ 12. The characteristic equation of a closed loop control system is $0.25{\mathrm{s}}^3+0.8{\mathrm{s}}^2+5.6\mathrm{s}+1+0.35\mathrm{K}=0$ Find the limiting value of $\mathrm{K}$, above which the closed loop system will be unstable. (Write answer up to two decimal place) Ans. 48.34 13. A proportional controller is used for two non-interacting liquid level system. The time constant for tanks are 1 and 0.5. The value of the gain of controller is 5 . Assume unity feedback control system. The set point of the control system is given step change of magnitude of 0.4 . Determine the offset. (Write answer up to two decimal place)