bode_approx - Bode Plot Straight Line Approximation ME365...

ME365 Dynamic System Response
1
Bode Plot – Straight Line
Approximation

ME365 Dynamic System Response
2
Frequency Response
Ex: Find the frequency response
function of the following 1st order
system and sketch its Bode plot.
10
0
10
2
10
4
-150
-100
-50
0
Frequency (rad/sec)
Phase (deg)
10
0
10
2
10
4
dB Magnitude

ME365 Dynamic System Response
3
MATLAB
• omega =0:0.01:10000;
• MagG =
10./sqrt(0.05*omega.^2+1);
% magnitude
• MagGdb = 20*log10(MagG); %
magnitude in dB
• ArgG = -atan(0.05*omega); %
phase in radian
• ArgG = ArgG*180/pi; %
phase in degree
• semilogx(omega, MagGdb);
• semilogx(omega, ArgG);
• g = tf([10],[0.05 1]);
% transfer function
• Bode(g); % Bode plot
1 05 . 0
10


 j
G
1 05 . 0
10


s
G

ME365 Dynamic System Response
4
Bode Plot – Straight Line
Approximation
• 2
nd
Order Systems
– Magnitude
• Identify K, 
res
, 
n
, |G|
max
• K from low frequency to 
n
• Draw roll off down from 
n
at -40 dB/dec
• Draw |G|
max
at 
res
– Phase
• 0° from low frequency to 10 - z 
n
• -180° from 10 + z 
n
to high frequency