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Control System Engg. OEP
140110111061 Denish Thummar
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.
Transfer Function
4
)
100
1)(
10
1(100
)()( 2
++
++
=
ss
ss
sHsG
401010
)100)(10(
)()( 2
++
++
=
ss
ss
sHsG
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
• 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)
• For Root locusrlocus(c)
• For Bode plotbode(c)
• For Nyquist plotnyquist(c)
• For Nichols chartnichols(c)
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
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
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
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)
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
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)
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
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
response of system for given transfer function
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response of system for given transfer function

  • 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.
  • 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
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