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I can find zeta from the PO given in the graph but I don't know any rule relate wn with tp and I don't have value of the of ts and tr

For part b and c I don't know where to start

please help me to solve this,Thanks to all of you

  • \$\begingroup\$ I wish for a world where we all have discarded two-phase AC servomotors on a shelf in our parts rooms. \$\endgroup\$ – CharlieHanson Dec 9 '15 at 0:42

Commonly used ROT for a standard 2nd order TF (no finite zeroes) are:

Time to 1st peak: \$t_p =\large\frac{\pi}{\omega _n\sqrt{1-\zeta^2}}\$

\$\small \pm 2\%\$ settling time: \$\small T_{S2} \approx \large\frac{4}{\zeta \omega _n}\$

\$\small 10\%-90\%\$ rise time: \$t_r \approx\large \frac {1\:+\:1.1\zeta\:+1.4\zeta^2 }{\omega_n}\$

Peak overshoot to a unit step input: \$\small M_{pt}=1\:+\:\large e^{\small{-\zeta \pi}\large/\small{\sqrt{1-\zeta^2}}}\$

For parts (b) and (c), you might work out the CLTF of the block diagram and compare coefficients with the standard 2nd order TF and ROT


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