Question

For the transfer function

KG(s)=s+8/s(s+4)
Draw the Bode plots, both magnitude and phase. (Note that the transfer function is
not given in the Bode form.)

What is the code for bode plot KG(s) = s+8/s(s+4) Both magnitude and phase

Answer 1

The transfer function KG(s)=s+8/s(s+4) can be written in Bode form as KG(s)=K(1+(s/ω1))/(s/ω2(1+s/ω3)), where K=1/32, ω1=2, ω2=4, and ω3=0.5. To draw the Bode plots, determine the gain magnitude and phase shift at each break frequency in the transfer function. The break frequencies are ω1 = 2 for the zero in the numerator and ω2 = 4 and ω3 = 0.5 for the poles in the denominator.

Step-by-step explanation:

The transfer function KG(s)=s+8/(s(s+4)) can be written in Bode form as KG(s)=K(1+(s/ω1))/(s/ω2(1+s/ω3)), where K=1/32, ω1=2, ω2=4, and ω3=0.5.

To draw the Bode plots, we first determine the gain magnitude and phase shift at each break frequency in the transfer function. The break frequencies are ω1 = 2 for the zero in the numerator and ω2 = 4 and ω3 = 0.5 for the poles in the denominator.

For the magnitude plot, at ω1 = 2, the gain magnitude is 0 dB. At ω2 = 4 and ω3 = 0.5, the gain magnitude is -6 dB and -12 dB, respectively. For the phase plot, at ω1 = 2, the phase is 0°. At ω2 = 4 and ω3 = 0.5, the phase shifts are -90° and +90°, respectively.