- 0,2018 7. (10 pts) A closed-loop control system with second-order plant GET430

Question

- 0,2018 7. (10 pts) A closed-loop control system with second-order plant GET430 EET 440 Midterm 82A Page 6 ef 6 and P controller is shown here: Ge Gp When parameters are inserted into this model, the unit step response for controller gain (K,) is shown here. for three different values of a) Which response has the larglest value of proportional gain: #1 or #3? #3 "1,02, ,02, , ?1 t 82 b) Which response has the smallest time onstant: #1, #2, or 37 L #1 c) The steady state value of response #2 is '0 - 0.1 - 02- -0.1 .. 0 When the controller is changed to a Pl type, G K,(1 +K,/s), the unit step response for three different sets of controller gains (K, & K.) is shown here. Response #2 is obtained with the following controller settings: Kp- 2 and K,- 50. Response #2 and response #3 are obtained by changing one controller coefficient at a time. identify which response (#2 or #3) corresponds to the alternate controller gains. #3 U2 #1 Response #2: K-2, Ki-50 d) Holding K, constant, which response shows an increase in K: #1 or #37 (Choose one) e) Holding K, constant, which response shows an increase in Kp: #1 or #37 (Choose one)

Explanation / Answer

a)

#3 has largest value of proportional as it has largest amplitude.

b)

#3 has smallest time constant as it reaches it's 63.2 % of its final value faster than others

c)

The steady state response value #2 is 0.5 as its final value is 0.5

d)

#3 shows increase in Ki as it's time constant is less than #1

e)

#1 shows increase in Kp as as it has amplitude than #3.

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