III.1.a.
w=tf(20,[1 0])

Transfer function:
20

s

>> ltiview({'step','impulse','bode','nyquist'},w)
0 0.2 0.4 0.6 0.8 1
0
10
20
30
0 0.2 0.4 0.6 0.8 1
19
19.5
20
20.5
21
0
20
40
Magnitude (dB)
10
0
10
1
-91
-90
-89

50
Magnitude (dB)
10
0
10
2
0
45
90
Phase (deg)
-50 0 50 100 150 200
-100
-50
0
50
100
III.1.c
TH1
w=tf(20,[50 1])

Transfer function:
20

50 s + 1

>> ltiview({'step','impulse','bode','nyquist'},w)
0 100 200 300
0
5
10

TH2
w=tf(20,[100 1])

Transfer function:
20

100 s + 1

>> ltiview({'step','impulse','bode','nyquist'},w)
0 200 400 600
0
5
10
15
20
0 200 400 600
0
0.05
0.1
0.15
0.2
-50
0
50
Magnitude (dB)
10
-4
10
-2
10

1
-
s

>> H1=tf(1,[1 2])

Transfer function:
1

s + 2

>> G13=G1+G3

Transfer function:
2 s^2 + 9 s + 15

s^3 + 8 s^2 + 15 s

>> G21=feedback(G2,H1)

Transfer function:
s^2 + 2 s

s^3 + 4 s^2 + 13 s + 16

>> G=G13*G21

Transfer function:
2 s^4 + 13 s^3 + 33 s^2 + 30 s


-50
0
Magnitude (dB)
10
-1
10
0
10
1
10
2
-180
-90
0
Phase (deg)
-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25
-0.2
0
0.2
III.3.a.
>> G1=tf(8,[1 2])

Transfer function:
8

s + 2

>> G2=tf(1,conv([0.5 1],[1 1]))

Transfer function:

0.8
1
0 10 20 30 40 50 60 70 80 90 100
-1
0
1
2
>> Gh=G*1

Transfer function:
0.04 s + 8

0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 10

>> ltiview({'bode','nyquist'},Gh)
-200
0
200
Magnitude (dB)
10
-1
10
0
10
1
10
2
10
3
-360


>> G=feedback(G1*G2,H)

Transfer function:
0.1 s + 20

0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 22

>> Gk=feedback(G,1)

Transfer function:
0.1 s + 20

0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.11 s + 42

>> ltiview({'step','impulse'},Gk)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-5
0
5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-20
-10
0
10
20
>> Gh=G*1

Transfer function:
0.1 s + 20

>> G1=tf(17.564411,[1 2])

Transfer function:
17.56

s + 2

>> G2=tf(1,conv([0.5 1],[1 1]))

Transfer function:
1

0.5 s^2 + 1.5 s + 1

>> H=tf(1,[0.005 1])

Transfer function:
1

0.005 s + 1

>> G=feedback(G1*G2,H)

Transfer function:
0.08782 s + 17.56

0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 19.56

>> Gk=feedback(G,1)


10
-1
10
0
10
1
10
2
10
3
-450
-360
-270
-180
Phase (deg)
-2 -1 0 1 2 3 4 5 6
x 10
7
-2
-1
0
1
2
x 10
8
III.4.
>> num=[2]
num = 2
>> den=[0.04 0.54 1.5 3]
den = 0.0400 0.5400 1.5000 3.0000

0.8
1
1.2
Impulse Response
Time (sec)
Amplitude
>> nyquist(A,B,C,D)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Nyquist Diagram
Real Axis
Imaginary Axis
>> bode(A,B,C,D)
-150
-100
-50
0
Magnitude (dB)
10
-1

100 s^2 + 5 s + 1

>> step(w)
>> w=tf(20,[100 10 1])

Transfer function:
20

100 s^2 + 10 s + 1

>> step(w)
>> w=tf(20,[100 15 1])

Transfer function:
20

100 s^2 + 15 s + 1

>> step(w)
>> w=tf(20,[100 20 1])

Transfer function:
20

100 s^2 + 20 s + 1

>> step(w)
>> hold off
0 50 100 150 200 250
0

Transfer function:
20

100 s^2 + 10 s + 1

>> impulse(w)
>> w=tf(20,[100 15 1])

Transfer function:
20

100 s^2 + 15 s + 1

>> impulse(w)
>> w=tf(20,[100 20 1])

Transfer function:
20

100 s^2 + 20 s + 1

>> impulse(w)
>> hold off
0 50 100 150 200 250
-2
-1.5
-1
-0.5
0
0.5

>> nyquist(w)
>> w=tf(20,[100 15 1])

Transfer function:
20

100 s^2 + 15 s + 1

>> nyquist(w)
>> w=tf(20,[100 20 1])

Transfer function:
20

100 s^2 + 20 s + 1

>> nyquist(w)
>> hold off
-7 -6 -5 -4 -3 -2 -1 0 1
x 10
8
-50
-40
-30
-20
-10
0
10
20
30

>> w=tf(20,[100 15 1])

Transfer function:
20

100 s^2 + 15 s + 1

>> bode(w)
>> w=tf(20,[100 20 1])

Transfer function:
20

100 s^2 + 20 s + 1

>> bode(w)
>> hold off
-50
0
50
100
150
200
Magnitude (dB)
10
-3
10
-2
10
-1