— Function File: [mag, phase, w] = bode (sys, w, out_idx, in_idx)

If no output arguments are given: produce Bode plots of a system; otherwise, compute the frequency response of a system data structure

Inputs

sys

a system data structure (must be either purely continuous or discrete; see is_digital)

w

frequency values for evaluation.

if sys is continuous, then bode evaluates G(jw) where G(s) is the system transfer function.

if sys is discrete, then bode evaluates G(exp(jwT)), where

• T is the system sampling time
• G(z) is the system transfer function.

Default the default frequency range is selected as follows: (These steps are not performed if w is specified)

1. via routine __bodquist__, isolate all poles and zeros away from w=0 (jw=0 or exp(jwT)=1) and select the frequency range based on the breakpoint locations of the frequencies.
2. if sys is discrete time, the frequency range is limited to jwT in [0,2 pi /T]
3. A "smoothing" routine is used to ensure that the plot phase does not change excessively from point to point and that singular points (e.g., crossovers from +/- 180) are accurately shown.

out_idx

in_idx

The names or indices of outputs and inputs to be used in the frequency response. See sysprune.

Example

               bode(sys,[],"y_3", {"u_1","u_4"});

Outputs

mag

phase

the magnitude and phase of the frequency response G(jw) or G(exp(jwT)) at the selected frequency values.

w

the vector of frequency values used

1. If no output arguments are given, e.g.,

                  bode(sys);
   

   bode plots the results to the screen. Descriptive labels are automatically placed.

   Failure to include a concluding semicolon will yield some garbage being printed to the screen (ans = []).

2. If the requested plot is for an MIMO system, mag is set to ||G(jw)|| or ||G(exp(jwT))|| and phase information is not computed.