Question

Homework 04 Due: Final Exam System: G1 Time (seconds): 2 25 Ampltude: 2.4 Problem 1) Considering the four different responses recorded at different occasions to a step input of (t)-2u(t) shown in Figure P1; (a) Propose a transfer function that produced the Step Respons e System: G2 Time (sec.): 323 Amplitude: 1.96 underdamped response System: G4 Time (se conds): 9.11 Amplitude: 1.9 (b) Write a general expression for the response of G1 (c) What would be the order of the system G3? Why? Propose a transfer function (d) Which system would be critically damped? System: G3 Time (seconds): 0.5 Amplitude: 1.26 Why? Write its transfer function using the wn of G1 0.5 (e) Which system would be overdamped? Why? Time (seconds) Figure P1

Answer 1

a)

from the given responses system g1 response is the under damped response.

the proposed response is shown below:

nce ak 24-2-0 10% -52 .5123 E04551

'eakime -s 1-0 20 n53 Yod o.8100 nd lNJ naL cLt)

Is Over damped S^um tte sdHling ime Sinet ed sutei

along wilt LJ

above mentioned transfer function is for critically damped response.

if we write the transfer function using natural frequency of the system G1,the is like this

3.116
-----------------------------
s^2 + 3.53 s + 3.116

nce ak 24-2-0 10% -52 .5123 E04551

'eakime -s 1-0 20 n53 Yod o.8100 nd lNJ naL cLt)

Is Over damped S^um tte sdHling ime Sinet ed sutei

along wilt LJ

ncaches Seu JI 3.33 IN 3.2 3 5836