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

ch6 system characteristics 1

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: