can anyone elaborate the question lots of short cut...TIA In the system shown ab

Question

can anyone elaborate the question lots of short cut...TIA

In the system shown above. G (s -K, and G, Tr+1) What is the system type? What is the condition for the system to have an underdamped response? ii) For as underdamped response, derive the expressions for the undamped natural frequency and the damping ratio, The forward transfer function The system is a Type I systent. Characteristic equation 4TA, the system will be an underdamped system (ii) Comparing to the standard form s +20u.sta: 0. Undamped natural fiequency +K

Explanation / Answer

This is a series system, so the transfer functions get multiplied .

Mulitply G1 and Gp and you get the answer after reduction.

CHARACTERISTIC eqn for this system: equate the denominator of the T.F to zero . With the feedback, the overall TF is TF /(1+TF) so you get the denom =0 which is what is shown.

Mltply out this fraction and put it equal to zero, so you say the Numerator =0 = Ts^2 +s + --- =0 = Ts^2 +(1+K)s + K

It is straightforward, only you need to know the rules for series transfer function and the characteristic eqn with the feedback.

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