National Instruments 370753C-01

Chapter 5 Classical Feedback Analysis

Figure 5-4. Bode Plot Showing System Gain and Phase Margins

These plots illustrate how the location of the system poles and zeros shapes

the gain and phase curves. Each pole contributes a factor of –20 dB per

decade (frequency interval from ω to 2ω). The two poles at zero cause the

magnitude response of the system to start with a slope of –40 dB/decade.

The zero at 0.5 radians/sec (about 0.08 Hz) contributes a factor of

approximately 20 dB. These gain magnitude factors add, so the slope of the

gain plot changes from –40 dB/decade to about –20 dB/decade until you

begin to see the influence of the poles at 2 radians/sec. (0.318 Hz) and

10 radians/sec (1.59 Hz), each of which contribute another –20 dB/decade

to the slope of the magnitude plot.

The phase is a function only of the pole and zero locations. Notice that in

creating the phase plot with bode( ), you specified the !wrap keyword.

This created a phase plot where range goes down to the full angle value of

the phase, rather than wrapping the phase between +180°. Each pole at zero

contributes –90° of phase.

The remaining poles are called first-order poles because they are of the

following form:

gain margin

phase margin