1. Control System Toolbox (Part-III)

2. Outline Frequency Domain Analysis of Control Systems Bode Plot
Nyquist Plot
Nichol’s Chart
Gain & Phase Margins

3. Bode Plots To obtain the bode plot use following MATLAB code
num =10*[ ];
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3);
bode(num,den)
grid on
K =10;
zero=-10;
pole=[ ];
sys=zpk(k, zero, pole);
bode(sys)
grid on
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4. Bode Plots

5. Bode Plots (for specific Frequency range)
To obtain the bode plot for specific frequency range
w=0.1:0.1:100;
num =10*[ ];
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3);
bode(num,den,w)
grid on
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6. Bode Plots (for specific Frequency range)

7. [mag, pha, w] = bode(num, den, w)
Bode Plots (with left hand arguments)
When invoked with left-hand arguments, such as
[mag, pha, w] = bode(num, den, w)
bode returns the magnitude (mag), phase (pha) and frequency (w) of the system in matrices.

8. Bode Plots
Exercise-1: - Obtain the bode plot of the second order system
ωn = 0.1 rad / sec
ζ = 0.1, 0.5, 1, 1.5
G(S) =
(S S+0.01)
0.01
G(S) =
(S S+0.01)
0.01
G(S) =
(S S+0.01)
0.01
G(S) =
(S S+0.01)
0.01
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9. Bode Plots
Exercise-2: - Calculate the magnitude and phase of the following system at w (rad/sec)=0.1, 0.5, 1, 10, 100.

10. Polar plots or Nyquist plot
To obtain the Nyquist plot use the following MATLAB code
num =2500;
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3);
nyquist(num,den)
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11. Polar plots or Nyquist plot-w w
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12. Polar plots or Nyquist plot
To adjust the default axes of Nyquist plot use axis command
num =2500;
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3);
nyquist(num,den)
axis([ ])
grid on
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13. Polar plots or Nyquist plot
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14. Nyquist plot (Open-loop & Closed Loop Frequency Response )

15. Polar plots or Nyquist plot
Exercise-3: - consider following transfer function
Obtain the Nyquist plot of the following system (when w>0).
Determine the open-loop & closed-loop magnitude responses when w=2.5 rad/sec
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16. Magnitude-Phase plot or Nichols Chart
To obtain the Nichols plot use following MATLAB code
num =2500;
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3);
nichols(num,den)
ngrid
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17. Magnitude-Phase plot or Nichols Chart

18. Magnitude-Phase plot or Nichols Chart
To obtain the Nichols plot use following MATLAB code
num =2500;
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3);
nichols(num,den)
ngrid; axis([ ])
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19. Magnitude-Phase plot or Nichols Chart

20. Magnitude-Phase plot or Nichols Chart

21. Exercise-4: - For the following Transfer Function
(i) Obtain the Nichols Chart
(ii) Determine the open-loop as well as closed-loop magnitude and phase when w=1.39 rad/sec.
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22. Phase & Gain Margins
To obtain the gain margin and phase use the following mat lab code.
num =2500;
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3)
[GM, PM, wp, wg]=margin(num,den)

23. Phase & Gain Margins GM = 5.5000 PM = 31.7124 num =2500; den1= [1 0];
To obtain the gain margin and phase use the following mat lab code.
GM =
5.5000
PM =
wp =
wg =
6.2184
num =2500;
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3)
[GM, PM, wp, wg]=margin(num,den)

24. Phase & Gain Margins
To obtain the gain margin and phase use the following mat lab code.
num =2500;
den1= [ ];
den2=[ ];
den3=[ ];
den12=conv(den1,den2);
den=conv(den12,den3)
margin(num,den)

25. Phase & Gain Margins

26. System Characteristics (Bode Plot)

27. System Characteristics (Nyquist Plot)

28. System Characteristics (Nichol’s Chart)

29. Exercise#5
Obtain the phase and gain margins of the system shown in following figure for the two cases where K=10 and K=100.
Also obtain the Bode, Nyquist and Nichol's plots for either cases.

30. Exercise#5

31. Exercise#6
Consider the system shown in following figure. Obtain Bode diagram for the closed-loop transfer function. Obtain also the resonant peak, resonant frequency, and bandwidth.

32. End of Tutorial You can Download this tutorial from
End of Tutorial
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