Bode plot and Step Response for 1 Real Pole and 2 Complex Conjugate Poles

Cuthbert Nyack

This applet shows the Bode plot of a 1 real pole, 2 cc pole system:-
The phase(green) goes from 0 to -1.5p and at high frequencies the slope of the magnitude curve is -60dB/decade. The magnitude vs phase plot is shown in yellow and the step response is in pink.
Some examples of oscillatory systems are shown by parameter values:-
(40.0, 1.0, 2.0, 1.0, 1.0, 1.0)
(10.0, 1.0, 1.0, 1.0, 1.0, 1.0) with angular frequency ~2rad/s
(1.6-1.7, 1.0, 0.3, 1.0, 3.0, 1.0)
(8.0, 1.0, 1.0, 0.1, 1.0, 1.0) with period ~3.65s
(31.3, 1.0, 0.3, 7.0, 0.4, 4.0) with period ~0.88s
When oscillatory, the magnitude response has a sharp peak and the phase curve shows a rapid drop eg (5.4, 5.0, 0.1, 1.0, 3.0, 4.0). The peak does not have to be the highest point in the response eg when the real pole is close to the imaginary axis (3.6, 0.1, 0.1, 4.0, 3.0, 4.0)
To get a step response without overshoot a small value of K is required eg:
(0.5, 1.0, 1.0, 1.0, 1.0, 1.0)

Gif image below shows how applet should appear.

Return to main page
Return to page index