1. Reduce the block diagram to a single transfer function.
Figure 1 – Block Diagram reduction.
2. For the following second order systems:
a.
b.
c.
i.
ii.
iii.
16
𝑠 2 +3𝑠+16
0.04
𝑠 2 +0.02𝑠+0.04
1.05𝑥107
𝑠 2 +1.6𝑥103 𝑠+1.05𝑥107
Find ζ, 𝜔𝑛 , 𝑡𝑠 , 𝑡𝑝 , 𝑡𝑟 , %𝑂𝑆 by using approximate formulas for the time response of a 2nd order
system.
Repeat (i) by plotting the step response using MATLAB and obtain the parameters by using
the experimental modeling approach.
Use LTI viewer in MATLAB to check your answers.
3. Consider the transfer function of a system given by:
1
𝑠 2 + 2𝜁𝑠 + 1
a. Plot 2-D Plot unit-step response when ζ takes the values (0, 0.2, 0.4, 0.6, 0.8, 1.0)
b. Obtain a 3-D plot with axis (y, t, ζ)