Question

The first order transfer function G(s) has output of Y(s) = G(s)U(s). The step response Y(s) is plotted below, where: U(t) = \begin{cases} 0 & \text{for } t < 4 \\ 2 & \text{for } t \ge 4 \end{cases} (A) Sketch u(t) on the graph below (B) Identify the time delay ($\theta$), time constant ($\tau$), and stead state value ($y\infty$) on the graph below (C) Write down $\theta$, $\tau$, k and G(s) Amplitude 0.5 Amplitude 1.5 1 30 20 10 Step Response 0 0 5 10 15 20 25 30 35 40 Time (seconds) Unit Step Input 0 5 10 15 20 25 30 35 40 Time (seconds)

          The first order transfer function G(s) has output of Y(s) = G(s)U(s). The step response Y(s) is
plotted below, where:
U(t) = \begin{cases} 0 & \text{for } t < 4 \\ 2 & \text{for } t \ge 4 \end{cases}
(A) Sketch u(t) on the graph below
(B) Identify the time delay ($\theta$), time constant ($\tau$), and stead state value ($y\infty$) on the graph below
(C) Write down $\theta$, $\tau$, k and G(s)
Amplitude
0.5
Amplitude
1.5
1
30
20
10
Step Response
0
0
5
10
15
20
25
30
35
40
Time (seconds)
Unit Step Input
0
5
10
15
20
25
30
35
40
Time (seconds)

Show more…

The first order transfer function G(s) has output of Y(s) = G(s)U(s). The step response Y(s) is
plotted below, where:
U(t) = 0 for t < 4
2 for t ≥4
(A) Sketch u(t) on the graph below
(B) Identify the time delay (θ), time constant (τ), and stead state value (y∞) on the graph below
(C) Write down θ, τ, k and G(s)
Amplitude
0.5
Amplitude
1.5
1
30
20
10
Step Response
0
0
5
10
15
20
25
30
35
40
Time (seconds)
Unit Step Input
0
5
10
15
20
25
30
35
40
Time (seconds)

Added by Jessica K.

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition

Instant Answer

Solved by Expert Kartik Indoliya

Step 1

So, the graph of u(t) will be a horizontal line at 2 for t < 4 and then drop to 0 at t = 4. (B) To identify the time delay (θ), time constant (τ), and steady-state value (y_ss) on the graph, we need to analyze the step response. - The time delay (θ) is the time Show more…

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The first-order transfer function G(s) has an output of Y(s) = G(s)U(s). The step response Y(s) is plotted below, where: (0 â‰¤ t < 4) U(t) = {2 for t < 4 (A) Sketch u(t) on the graph below (B) Identify the time delay (Î¸), time constant (Ï„), and steady-state value (y_ss) on the graph below (C) Write down Î¸, Ï„, k, and G(s) Step Response 30 20 Amplitude 10 0 5 10 15 20 25 Time (seconds) Unit Step Input 30 35 40 1.5 Amplitude 0.5 0 0 5 10 15 20 25 Time (seconds) 30 35 40

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