Question

6.7 Mixed real and complex poles. Sketch the asymptotes of the Bode plot magnitude and phase for each of the following open-loop transfer functions. Aftercompleting the hand sketches, verify your results using Matlab. Turn in your hand

sketches and the Matlab results on the same scales.
(2s+4)
(b)L(s)= s2s+8s+5s+27

Answer 1

The Bode plot for the given transfer function L(s) = 2s+4/s²+8s+5s+27 features two real poles and one complex pole.

Step-by-step explanation:

For the Bode plot magnitude, the asymptotic behavior depends on the number of poles and zeros. For the given transfer function, there are two real poles at s = −5 and s = − 27 and one complex pole pair with a real part - 4 (from s²+8s). The slope of the asymptotes for real poles is -20 dB/decade, and for complex poles, it is -40 dB/decade. The phase plot asymptotes for real poles contribute -90 degrees each, and for complex poles, they contribute -180 degrees.

The hand sketches should show asymptotic slopes of -20 dB/decade for real poles, -40 dB/decade for complex poles, and phase slopes of -90 degrees for real poles and -180 degrees for complex poles. Verifying these results using MATLAB should show close agreement between the hand sketches and the computational results, confirming the accuracy of the manual approach in predicting the Bode plot characteristics.