Question

100 H(s) 2. For the transfer function: s3+32s2260s+400 a) create a reduced order model by removing the "high frequency" pole (Hints ... Use zpk() to find poles. Make sure the new transfer function has the same Kdc as the original model) b) Use MatLab to verify that the step response for the two models are "equivalent"

Answer 1

Sal? H(s) = 100 3+32 +2605 +400 The so poles of 8+325² +2605+400 are Sa -2,-10, -20 the Reduced oldan g His) is Tis) = K with DC gain k (5+2) DC gain of His) a 100 a 0.25 - The 400 a to Tos) *20.25 a Kaos so HIS) = 100 ²+ 325²+26087400 TIS) = o.s (ST2) (Reduled older)

step response using matlab:

clc;

clear all;

close all;

s=tf('s');% definition of transfer function

H=100/(s^3+32*s^2+260*s+400); % original transfer function

T=0.5/(s+2); % reduced transfer function

step(H,T);grid

legend('original system','reduced system')

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File Edit View Insert Tools Debug Desktop Window Help x = DISA .. ZO E Figure 1 x O BD Step Response 0.250- original system reduced system 0.15 Amplitude 0.05 0.5 2.5 Time (seconds) Property Editor - timeplot