System characteristics

In designing each compensator, the following system characteristics hold true:

•                                                                                                                LM = Log magnitude, base 10

•                                                                                                                Cross-over frequency of open-loop Bode LM plot

•                                                                                                                  Phase margin of open-loop Bode phase plot

•                                                                                                                 Time constant, s

•                                                                                                                  Damping ratio

The open-loop Bode frequency response can be used to approximate closed-loop system behavior, provided the open-loop frequency response satisfies three conditions:

•      The gain at low frequencies is relatively high for low steady-state errors

•      The gain at high frequencies is relatively low for disturbance attenuation

•      The slope of the Bode plot is approximately

When the above conditions are approximately satisfied, the following correlations are valid: