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Problem 6.26PP
Suppose that in Fig.,
2 5 ( s + l )
G{s) = -
s(s + 2 ) ( j2 + 2 r + 1 6 )
Use Matlab’s margin to calculate the PM and GM for G(s) and, on the basis of the Bode plots, 
conclude which margin would provide more useful information to the control designer for this 
system.
Figure Control system
G(s) -O Y
Step-by-step solution
step 1 of 4
The loop transfer function is, 
2S (j- t-l)C(s)=
s(5+2)(s^+2s + 6)
Write the MATLAB code to calculate the gain margin and phase margin.
num=[25 2 5 ];» den=conv{[1 2 0],[1 2 16 ]);» sys=tf{num,den)sys = 25 s + 25 —
------------ sM + 4 s '̂3 + 20 s '̂2 + 32 s Continuous-time transfer function.» margin(sys)
Draw the bode plot.
Step 2 of 4
Bode Diagram
Figure 1
Frequency (rad/s)
Step 3 of 4
From Figure 1,
The gain margin is, A/Is | |q| o|.
Step 4 of 4
The phase margin is more commonly used to specify control system performance it is most 
closely related to the damping ratio of the system.