Question

7.12 Fig. E7.12 presents the response of a system to a unit step in the input. (a) Use these data to derive an FOPTD model of this system. (b) Plot the response of the model and compare with the data. (c) The FOPTD model does not capture all the features of the original response. What is the feature that the FOPTD model fails to capture? What causes this dynamic behavior? rature fm are d from t units

Answer 1

Hello,
       Please find the answer attached below. If the answer has helped you please give a thumbs up rating. Thank you and have a nice day!

Hello, Please find the answer attached below. If the answer has helped you please give a thumbs up rating. Thank you and have a nice day! From the output response we note the following the steady state value = 2. Therefore dc gain of the system equal 2. The time taken by the system to reach 63% of final value (TildeEqual 1.2) is ofter 7 seconds In the output nested initial with a delay a of approximately 2.55 therefore Actual time constant = 7 - 2.5 = 4.55 therefore C = 4.5, C_d = 2.5 G (s) = 2e^-2.55/1 + 4.55 what the model fails the calculate is the capture is the under sheet during the initial time delay restore (from t = 0 till 2.5s), where the output goes negative this is usually caused by a zero in the transfer function very close to the Jw axis G = tf (2,[4.5 1],'InputDelay',2.5): step (G) grid title ('FOPTD Response') Output:

**** Matlab Code for part b *****

G = tf(2,[4.5 1],'InputDelay',2.5);
step(G)
grid
title('FOPTD Response')

Output: