Bode plot and Step Response for 3 Real Poles and 2 Complex Conjugate Zeros

Cuthbert Nyack
This applet shows the Bode plot of a 3 real poles, 2 complex conjugate zeros system.
The phase(green) starts at zero and ends at -0.5p. The magnitude starts with a slope of zero and ends with a slope of -20dB/decade. The gain margin, phase margin and closed loop poles are also shown.

One characteristic of this system is that it may be unstable at small K and stable at large K or stable for small and large K and unstable in between. This happens when the phase is less than -180° for a range of frequencies.
The eg parameters (K, 0.2, 0.2, 0.5, 3.0, 2.0) is stable for K < 0.03, unstable for K > 0.03 and < 1.2 and stable for larger K > 1.2.
eg parameters (K, 0.6, 0.2, 0.5, 0.6, 2.0) is stable for K < ~0.33 and K > ~1.58 but unstable in between.
eg parameters (8.0, 1.0, 1.0, 1.0, 2.4, 0.5), the system with only 3 poles is oscillatory. Adding the zeros at -2.4 ± j0.5 increases the phase margin to 78.4° at 8.45rad/s. The resulting system has little overshoot and oscillation.

Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.