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Octave Control Toolbox demo: Frequency Response demo.
If no output arguments are given: produce Bode plots of a system; otherwise, compute the frequency response of a system data structure
Inputs
a system data structure (must be either purely continuous or discrete; see is_digital)
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
Default the default frequency range is selected as follows: (These steps are not performed if w is specified)
exp
(jwT)=1) and select the frequency
range based on the breakpoint locations of the frequencies.
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
the magnitude and phase of the frequency response G(jw) or
G(exp
(jwT)) at the selected frequency values.
the vector of frequency values used
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 = []
).
exp
(jwT))||
and phase information is not computed.
Get default range of frequencies based on cutoff frequencies of system poles and zeros. Frequency range is the interval
Used internally in __freqresp__
(bode
, nyquist
)
Used by __freqresp__
to check that input frequency vector w
is valid.
Returns boolean value.
Linear time invariant frequency response of single-input systems.
Inputs
coefficient matrices of dx/dt = A x + B u
system data structure
vector of frequencies
Output
frequency response, that is:
for complex frequencies s = jw.
Produce Nyquist plots of a system; if no output arguments are given, Nyquist plot is printed to the screen.
Compute the frequency response of a system.
Inputs (pass as empty to get default values)
system data structure (must be either purely continuous or discrete;
see is_digital
)
frequency values for evaluation. If sys is continuous, then bode evaluates G(jw); if sys is discrete, then bode evaluates G(exp(jwT)), where T is the system sampling time.
the default frequency range is selected as follows: (These steps are not performed if w is specified)
__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.
for interactive nyquist plots: atol is a change-in-slope tolerance for the of asymptotes (default = 0; 1e-2 is a good choice). This allows the user to "zoom in" on portions of the Nyquist plot too small to be seen with large asymptotes.
Outputs
the real and imaginary parts of the frequency response G(jw) or G(exp(jwT)) at the selected frequency values.
the vector of frequency values used
If no output arguments are given, nyquist plots the results to the screen. If atol != 0 and asymptotes are detected then the user is asked interactively if they wish to zoom in (remove asymptotes) Descriptive labels are automatically placed.
Note: if the requested plot is for an MIMO system, a warning message is presented; the returned information is of the magnitude only; phase information is not computed.
Compute transmission zeros of a continuous system: or of a discrete one:
Outputs
transmission zeros of the system
leading coefficient (pole-zero form) of SISO transfer function returns gain=0 if system is multivariable
References
Compute the transmission zeros of a, b, c, d.
bal = balancing option (see balance); default is "B"
.
Needs to incorporate mvzero
algorithm to isolate finite zeros;
use tzero
instead.
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