step response ,impulse response,ramp response,parabolic response,root locus,bode plot ,nyquist plot , nichols chart

1. Control System Engg. OEP
140110111061 Denish Thummar

2. Objectives…
• To find step ,ramp ,parabolic ,impulse
response of the given Transfer Function.
• To find R-H criteria.
• To plot Root locus, Bode plot, Nyquist,
Nichol’s chart.

3. Transfer Function
4
)
100
1)(
10
1(100
)()( 2
++
++
=
ss
ss
sHsG
401010
)100)(10(
)()( 2
++
++
=
ss
ss
sHsG

4. How to find TF in MATLAB
• num=[1 110 1000]
• num =
• 1 110 1000
• >> den=[10 10 40]
• den =
• 10 10 40
• >> c=tf(num,den)
• c =
•
• s^2 + 110 s + 1000
• ---------------------------
• 10 s^2 + 10 s + 40

5. • c = s^2 + 110 s + 1000
• --------------------------
• 10 s^2 + 10 s + 40
• To find the step, impulse, ramp, parabolic response of transfer function
command used in MATLAB is..
• STEP(C)
• IMPULSE(C)
• For RAMP t=1:10
u=t
lsim(c,u,t)
For Parabolic t=1:10
u=t.^2/2
lsim(c,u,t)

6. • For Root locusrlocus(c)
• For Bode plotbode(c)
• For Nyquist plotnyquist(c)
• For Nichols chartnichols(c)

7. Step Response
Step Response
Time (seconds)
Amplitude
0 2 4 6 8 10 12
0
5
10
15
20
25
30
35
40
System: c
Peak amplitude: 36.3
Overshoot (%): 45.3
At time (seconds): 1.47
System: c
Rise time (seconds): 0.609
System: c
Settling time (seconds): 6.95
System: c
Final value: 25

8. Impulse Response
Impulse Response
Time (seconds)
Amplitude
0 2 4 6 8 10 12
-20
-10
0
10
20
30
40
System: c
Peak amplitude: 36.3
At time (seconds): 0.553
System: c
Settling time (seconds): 7.62

9. Ramp ResponseLinear Simulation Results
Time (seconds)
1 2 3 4 5 6 7 8 9 10
0
50
00
50
00
50
System: c
Peak amplitude: 247
At time (seconds): 10

10. Parabolic Response
1 2 3 4 5 6 7 8 9 10
0
200
400
600
800
1000
1200
1400
Linear Simulation Results
Time (seconds)

11. Root Locus
Root Locus
Real Axis (seconds-1)
-120 -100 -80 -60 -40 -20 0 20
10
-8
-6
-4
-2
0
2
4
6
8
10
0.750.930.970.9850.9930.997
0.999
1
0.750.930.970.9850.9930.997
0.999
1
20406080100120
System: c
Gain: 1.15e+05
Pole: -100
Damping: 1
Overshoot (%): 0
Frequency (rad/s): 100
System: c
Gain: 221
Pole: -10
Damping: 1
Overshoot (%): 0
Frequency (rad/s): 10
System: c
Gain: 0.00129
Pole: -0.507 + 1.97i
Damping: 0.25
Overshoot (%): 44.5
Frequency (rad/s): 2.03

12. Bode Plot
Bode Diagram
Frequency (rad/s)
-20
-10
0
10
20
30
40
System: c
Peak gain (dB): 34.4
At frequency (rad/s): 1.87
Magnitude(dB)
10
-1
10
0
10
1
10
2
10
3
10
4
-180
-135
-90
-45
0
System: c
Phase Margin (deg): 64.3
Delay Margin (sec): 0.0864
At frequency (rad/s): 13
Closed loop stable? Yes
Phase(deg)

13. Nyquist Plot
Nyquist Diagram
Real Axis
-20 -10 0 10 20 30 40
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 dB
-2 dB2 dB
System: c
Phase Margin (deg): 64.3
Delay Margin (sec): 0.0864
At frequency (rad/s): 13
Closed loop stable? Yes
System: c
Peak gain (dB): 34.4
Frequency (rad/s): 1.87
System: c
Real: 21.3
Imag: 48
Frequency (rad/s): -1.9
System: c
Real: 25
Imag: 0.316
Frequency (rad/s): -0.0899

14. Nichols chart
Nichols Chart
Open-Loop Phase (deg)
-180 -135 -90 -45 0 45 90 135 180
-20
-10
0
10
20
30
40
6 dB
3 dB
1 dB
0.5 dB
0.25 dB
0 dB
-1 dB
-3 dB
-6 dB
-12 dB
-20 dB
System: c
Peak gain (dB): 34.4
Frequency (rad/s): 1.87
System: c
Phase Margin (deg): 64.3
Delay Margin (sec): 0.0864
At frequency (rad/s): 13
Closed loop stable? Yes