Bases: LTI
Input/output model defined by frequency response data (FRD).
The FrequencyResponseData (FRD) class is used to represent systems in frequency response data form. It can be created manually using the class constructor, using the frd factory function, or via the frequency_response function.
The frequency response at each frequency point. If 1D, the system is assumed to be SISO. If 3D, the system is MIMO, with the first dimension corresponding to the output index of the FRD, the second dimension corresponding to the input index, and the 3rd dimension corresponding to the frequency points in omega. When accessed as an attribute, frdata is always stored as a 3D array.
List of monotonically increasing frequency points for the response.
If True, create an interpolation function that allows the frequency response to be computed at any frequency within the range of frequencies give in omega. If False (default), frequency response can only be obtained at the frequencies specified in omega.
System timebase. 0 (default) indicates continuous time, True indicates discrete time with unspecified sampling time, positive number is discrete time with specified sampling time, None indicates unspecified timebase (either continuous or discrete time).
By default, if a system is single-input, single-output (SISO) then the outputs (and inputs) are returned as a 1D array (indexed by frequency) and if a system is multi-input or multi-output, then the outputs are returned as a 2D array (indexed by output and frequency) or a 3D array (indexed by output, trace, and frequency). If squeeze = True, access to the output response will remove single-dimensional entries from the shape of the inputs and outputs even if the system is not SISO. If squeeze = False, the output is returned as a 3D array (indexed by the output, input, and frequency) even if the system is SISO. The default value can be set using config.defaults['control.squeeze_frequency_response'].
Name of the system that generated the data.
complexarray
Complex value of the frequency response.
magnitudearray
Magnitude of the frequency response.
phasearray
Phase of the frequency response.
frequency1D array
Frequencies at which the response is evaluated.
Number of input and output signals.
shapetuple
2-tuple of I/O system dimension, (noutputs, ninputs).
Names for the input and output signals.
System name. For data generated using frequency_response, stores the name of the system that created the data.
Set the type of plot to generate with plot (‘bode’, ‘nichols’).
Set the title to use when plotting.
If set to False, don’t plot the magnitude or phase, respectively.
If True, then a frequency response data object will enumerate as a tuple of the form (mag, phase, omega) where where mag is the magnitude (absolute value, not dB or log10) of the system frequency response, phase is the wrapped phase in radians of the system frequency response, and omega is the (sorted) frequencies at which the response was evaluated.
Notes
The main data members are omega and frdata, where omega is a 1D array of frequency points and and frdata is a 3D array of frequency responses, with the first dimension corresponding to the output index of the FRD, the second dimension corresponding to the input index, and the 3rd dimension corresponding to the frequency points in omega. For example,
>>> frdata[2,5,:] = numpy.array([1., 0.8-0.2j, 0.2-0.8j])
means that the frequency response from the 6th input to the 3rd output at the frequencies defined in omega is set to the array above, i.e. the rows represent the outputs and the columns represent the inputs.
A frequency response data object is callable and returns the value of the transfer function evaluated at a point in the complex plane (must be on the imaginary axis). See FrequencyResponseData.__call__ for a more detailed description.
Subsystem response corresponding to selected input/output pairs can be created by indexing the frequency response data object:
subsys = sys[output_spec, input_spec]
The input and output specifications can be single integers, lists of integers, or slices. In addition, the strings representing the names of the signals can be used and will be replaced with the equivalent signal offsets.
Attributes
Complex value of the frequency response.
System timebase.
Frequencies at which the response is evaluated.
fresp
List of labels for the input signals.
Magnitude of the frequency response.
Number of system inputs.
Number of system outputs.
Number of system states.
List of labels for the output signals.
Phase of the frequency response.
String representation format.
response
2-tuple of I/O system dimension, (noutputs, ninputs).
Squeeze processing parameter.
List of labels for the state signals.
Methods
Evaluate system transfer function at point in complex plane.
Append a second model to the present model.
Evaluate bandwidth of an LTI system for a given dB drop.
Generate a Bode plot for the system.
Make a copy of an input/output system.
Natural frequency, damping ratio of system poles.
Return the zero-frequency (DC) gain.
Evaluate a transfer function at a frequency point.
Feedback interconnection between two FRD objects.
Find the index for an input given its name (None if not found).
Return list of indices matching input spec (None if not found).
Find the index for a output given its name (None if not found).
Return list of indices matching output spec (None if not found).
Find the index for a state given its name (None if not found).
Return list of indices matching state spec (None if not found).
Generate the forced response for the system.
(deprecated) Evaluate transfer function at complex frequencies.
Evaluate LTI system response at an array of frequencies.
Generate the impulse response for the system.
Generate the initial response for the system.
Check to see if a system is a continuous-time system.
Check to see if a system is a discrete-time system.
Indicate if a linear time invariant (LTI) system is passive.
Check to see if a system is single input, single output.
Generate a Nichols plot for the system.
Generate a Nyquist plot for the system.
Plot the frequency response using Bode or singular values plot.
Set the number/names of the system inputs.
Set the number/names of the system outputs.
Set the number/names of the system states.
Generate the step response for the system.
Convert response data to pandas data frame.
Convert to state space representation.
Convert to transfer function representation.
Update signal and system names for an I/O system.
Add two LTI objects (parallel connection).
Evaluate system transfer function at point in complex plane.
Returns the value of the system’s transfer function at a point x in the complex plane, where x is s for continuous-time systems and z for discrete-time systems. For a frequency response data object, the argument should be an imaginary number (since only the frequency response is defined) and only the imaginary component of x will be used.
By default, a (complex) scalar will be returned for SISO systems and a p x m array will be return for MIMO systems with m inputs and p outputs. This can be changed using the squeeze keyword.
To evaluate at a frequency omega in radians per second, enter x = omega * 1j for continuous-time systems, x = exp(1j * omega * dt) for discrete-time systems, or use the frequency_response method.
If x is not given, this function creates a copy of a frequency response data object with a different set of output settings.
Imaginary value(s) at which frequency response will be evaluated. The real component of x is ignored. If not specified, return a copy of the frequency response data object with updated settings for output processing (squeeze, return_magphase).
Squeeze output, as described below. Default value can be set using config.defaults['control.squeeze_frequency_response'].
(x = None only) If True, then a frequency response data object will enumerate as a tuple of the form (mag, phase, omega) where where mag is the magnitude (absolute value, not dB or log10) of the system frequency response, phase is the wrapped phase in radians of the system frequency response, and omega is the (sorted) frequencies at which the response was evaluated.
The value of the system transfer function at x. If the system is SISO and squeeze is not True, the shape of the array matches the shape of x. If the system is not SISO or squeeze is False, the first two dimensions of the array are indices for the output and input and the remaining dimensions match x. If squeeze is True then single-dimensional axes are removed.
If s is not purely imaginary, because FrequencyResponseData systems are only defined at imaginary values (corresponding to real frequencies).
Multiply two LTI objects (serial connection).
Negate a transfer function.
Right add two LTI objects (parallel connection).
Right Multiply two LTI objects (serial connection).
Right subtract two LTI objects.
Right divide two LTI objects.
Subtract two LTI objects.
Divide two LTI objects.
Append a second model to the present model.
The second model is converted to FRD if necessary, inputs and outputs are appended and their order is preserved.
LTI
System to be appended.
FrequencyResponseData
System model with other appended to self.
Evaluate bandwidth of an LTI system for a given dB drop.
Evaluate the first frequency that the response magnitude is lower than DC gain by dbdrop dB.
A strictly negative scalar in dB (default = -3) defines the amount of gain drop for deciding bandwidth.
The first frequency (rad/time-unit) where the gain drops below dbdrop of the dc gain of the system, or nan if the system has infinite dc gain, inf if the gain does not drop for all frequency.
If sys is not an SISO LTI instance.
If dbdrop is not a negative scalar.
Generate a Bode plot for the system.
See bode_plot for more information.
Complex value of the frequency response.
Value of the frequency response as a complex number, indexed by either the output and frequency (if only a single input is given) or the output, input, and frequency (for multi-input systems). See FrequencyResponseData.squeeze for a description of how this can be modified using the squeeze keyword.
Input and output signal names can be used to index the data in place of integer offsets.
1D, 2D, or 3D array
Make a copy of an input/output system.
A copy of the system is made, with a new name. The name keyword can be used to specify a specific name for the system. If no name is given and use_prefix_suffix is True, the name is constructed by prepending config.defaults['iosys.duplicate_system_name_prefix'] and appending config.defaults['iosys.duplicate_system_name_suffix']. Otherwise, a generic system name of the form ‘sys[<id>]’ is used, where ‘<id>’ is based on an internal counter.
Name of the newly created system.
If True and name is None, set the name of the new system to the name of the original system with prefix config.defaults['duplicate_system_name_prefix'] and suffix config.defaults['duplicate_system_name_suffix'].
InputOutputSystem
Natural frequency, damping ratio of system poles.
Natural frequency for each system pole.
Damping ratio for each system pole.
System pole locations.
Return the zero-frequency (DC) gain.
System timebase.
Evaluate a transfer function at a frequency point.
Note that a “normal” FRD only returns values for which there is an entry in the omega vector. An interpolating FRD can return intermediate values.
Frequency(s) for evaluation, in radians per second.
If squeeze = True, remove single-dimensional entries from the shape of the output even if the system is not SISO. If squeeze = False, keep all indices (output, input and, if omega is array_like, frequency) even if the system is SISO. The default value can be set using config.defaults['control.squeeze_frequency_response'].
The frequency response of the system. If the system is SISO and squeeze is not True, the shape of the array matches the shape of omega. If the system is not SISO or squeeze is False, the first two dimensions of the array are indices for the output and input and the remaining dimensions match omega. If squeeze is True then single-dimensional axes are removed.
Feedback interconnection between two FRD objects.
LTI
System in the feedback path.
Gain to use in feedback path. Defaults to -1.
Find the index for an input given its name (None if not found).
Signal name for the desired input.
Index of the named input.
Return list of indices matching input spec (None if not found).
List of signal specifications for the desired inputs. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.
List of indices for the specified inputs.
Find the index for a output given its name (None if not found).
Signal name for the desired output.
Index of the named output.
Return list of indices matching output spec (None if not found).
List of signal specifications for the desired outputs. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.
List of indices for the specified outputs.
Find the index for a state given its name (None if not found).
Signal name for the desired state.
Index of the named state.
Return list of indices matching state spec (None if not found).
List of signal specifications for the desired states. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.
List of indices for the specified states..
Generate the forced response for the system.
See forced_response for more information.
(deprecated) Evaluate transfer function at complex frequencies.
Frequencies at which the response is evaluated.
1D array
Evaluate LTI system response at an array of frequencies.
See frequency_response for more detailed information.
Generate the impulse response for the system.
See impulse_response for more information.
Generate the initial response for the system.
See initial_response for more information.
List of labels for the input signals.
Check to see if a system is a continuous-time system.
If strict is True, make sure that timebase is not None. Default is False.
Check to see if a system is a discrete-time system.
If strict is True, make sure that timebase is not None. Default is False.
Indicate if a linear time invariant (LTI) system is passive.
See ispassive for details.
Check to see if a system is single input, single output.
Magnitude of the frequency response.
Magnitude of the frequency response, indexed by either the output and frequency (if only a single input is given) or the output, input, and frequency (for multi-input systems). See FrequencyResponseData.squeeze for a description of how this can be modified using the squeeze keyword.
Input and output signal names can be used to index the data in place of integer offsets.
1D, 2D, or 3D array
Generate a Nichols plot for the system.
See nichols_plot for more information.
Number of system inputs.
Number of system outputs.
Number of system states.
Generate a Nyquist plot for the system.
See nyquist_plot for more information.
List of labels for the output signals.
Phase of the frequency response.
Phase of the frequency response in radians/sec, indexed by either the output and frequency (if only a single input is given) or the output, input, and frequency (for multi-input systems). See FrequencyResponseData.squeeze for a description of how this can be modified using the squeeze keyword.
Input and output signal names can be used to index the data in place of integer offsets.
1D, 2D, or 3D array
Plot the frequency response using Bode or singular values plot.
Plot the frequency response using either a standard Bode plot (plot_type=’bode’, default) or a singular values plot (plot_type=’svplot’). See bode_plot and singular_values_plot for more detailed descriptions.
String representation format.
Format used in creating the representation for the system:
‘info’ : <IOSystemType sysname: [inputs] -> [outputs]>
‘eval’ : system specific, loadable representation
‘latex’ : HTML/LaTeX representation of the object
The default representation for an input/output is set to ‘eval’. This value can be changed for an individual system by setting the repr_format parameter when the system is created or by setting the repr_format property after system creation. Set config.defaults['iosys.repr_format'] to change for all I/O systems or use the repr_format parameter/attribute for a single system.
Set the number/names of the system inputs.
Description of the system inputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form ‘u[i]’ (where the prefix ‘u’ can be changed using the optional prefix parameter).
If inputs is an integer, create the names of the states using the given prefix (default = ‘u’). The names of the input will be of the form ‘prefix[i]’.
Set the number/names of the system outputs.
Description of the system outputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form ‘y[i]’ (where the prefix ‘y’ can be changed using the optional prefix parameter).
If outputs is an integer, create the names of the states using the given prefix (default = ‘y’). The names of the input will be of the form ‘prefix[i]’.
Set the number/names of the system states.
Description of the system states. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form ‘x[i]’ (where the prefix ‘x’ can be changed using the optional prefix parameter).
If states is an integer, create the names of the states using the given prefix (default = ‘x’). The names of the input will be of the form ‘prefix[i]’.
2-tuple of I/O system dimension, (noutputs, ninputs).
Squeeze processing parameter.
By default, if a system is single-input, single-output (SISO) then the outputs (and inputs) are returned as a 1D array (indexed by frequency) and if a system is multi-input or multi-output, then the outputs are returned as a 2D array (indexed by output and frequency) or a 3D array (indexed by output, trace, and frequency). If squeeze = True, access to the output response will remove single-dimensional entries from the shape of the inputs and outputs even if the system is not SISO. If squeeze = False, the output is returned as a 3D array (indexed by the output, input, and frequency) even if the system is SISO. The default value can be set using config.defaults[‘control.squeeze_frequency_response’].
List of labels for the state signals.
Generate the step response for the system.
See step_response for more information.
Convert response data to pandas data frame.
Creates a pandas data frame for the value of the frequency response at each omega. The frequency response values are labeled in the form “H_{<out>, <in>}” where “<out>” and “<in>” are replaced with the output and input labels for the system.
Convert to state space representation.
See ss for details.
Convert to transfer function representation.
See tf for details.
Update signal and system names for an I/O system.
New system name.
List of strings that name the individual input signals. If given as an integer or None, signal names default to the form ‘u[i]’. See InputOutputSystem for more information.
Description of output signals; defaults to ‘y[i]’.
Description of system states; defaults to ‘x[i]’.
Set the prefix for input signals. Default = ‘u’.
Set the prefix for output signals. Default = ‘y’.
Set the prefix for state signals. Default = ‘x’.
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