control.flatsys.LinearFlatSystem¶

class
control.flatsys.
LinearFlatSystem
(linsys, inputs=None, outputs=None, states=None, name=None)¶ 
__init__
(linsys, inputs=None, outputs=None, states=None, name=None)¶ Define a flat system from a SISO LTI system.
Given a reachable, singleinput/singleoutput, linear timeinvariant system, create a differentially flat system representation.
Parameters:  linsys (StateSpace) – LTI StateSpace system to be converted
 inputs (int, list of str or None, optional) – 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 s[i] (where s is one of u, y, or x). If this parameter is not given or given as None, the relevant quantity will be determined when possible based on other information provided to functions using the system.
 outputs (int, list of str or None, optional) – Description of the system outputs. Same format as inputs.
 states (int, list of str, or None, optional) – Description of the system states. Same format as inputs.
 dt (None, True or float, optional) – System timebase. None (default) indicates continuous time, True indicates discrete time with undefined sampling time, positive number is discrete time with specified sampling time.
 params (dict, optional) – Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.
 name (string, optional) – System name (used for specifying signals)
Returns: iosys – Linear system represented as an flat input/output system
Return type:
Methods
__init__
(linsys[, inputs, outputs, states, name])Define a flat system from a SISO LTI system. append
(other)Append a second model to the present model. copy
()Make a copy of an input/output system. damp
()Natural frequency, damping ratio of system poles dcgain
()Return the zerofrequency gain evalfr
(omega)Evaluate a SS system’s transfer function at a single frequency. feedback
([other, sign, params])Feedback interconnection between two input/output systems find_input
(name)Find the index for an input given its name (None if not found) find_output
(name)Find the index for an output given its name (None if not found) find_state
(name)Find the index for a state given its name (None if not found) forward
(x, u)Compute the flat flag given the states and input. freqresp
(omega)Evaluate the system’s transfer function at a list of frequencies horner
(s)Evaluate the systems’s transfer function for a complex variable isctime
([strict])Check to see if a system is a continuoustime system isdtime
([strict])Check to see if a system is a discretetime system issiso
()Check to see if a system is single input, single output lft
(other[, nu, ny])Return the Linear Fractional Transformation. linearize
(x0, u0[, t, params, eps])Linearize an input/output system at a given state and input. minreal
([tol])Calculate a minimal realization, removes unobservable and uncontrollable states pole
()Compute the poles of a state space system. returnScipySignalLTI
()Return a list of a list of scipy.signal.lti objects. reverse
(zflag)Compute the states and input given the flat flag. sample
(Ts[, method, alpha, prewarp_frequency])Convert a continuous time system to discrete time set_inputs
(inputs[, prefix])Set the number/names of the system inputs. set_outputs
(outputs[, prefix])Set the number/names of the system outputs. set_states
(states[, prefix])Set the number/names of the system states. zero
()Compute the zeros of a state space system. 
append
(other)¶ Append a second model to the present model. The second model is converted to statespace if necessary, inputs and outputs are appended and their order is preserved

copy
()¶ Make a copy of an input/output system.

damp
()¶ Natural frequency, damping ratio of system poles
Returns:  wn (array) – Natural frequencies for each system pole
 zeta (array) – Damping ratio for each system pole
 poles (array) – Array of system poles

dcgain
()¶ Return the zerofrequency gain
The zerofrequency gain of a continuoustime statespace system is given by:
and of a discretetime statespace system by:
Returns: gain – An array of shape (outputs,inputs); the array will either be the zerofrequency (or DC) gain, or, if the frequency response is singular, the array will be filled with np.nan. Return type: ndarray

evalfr
(omega)¶ Evaluate a SS system’s transfer function at a single frequency.
self._evalfr(omega) returns the value of the transfer function matrix with input value s = i * omega.

feedback
(other=1, sign=1, params={})¶ Feedback interconnection between two input/output systems
Parameters:  sys1 (InputOutputSystem) – The primary process.
 sys2 (InputOutputSystem) – The feedback process (often a feedback controller).
 sign (scalar, optional) – The sign of feedback. sign = 1 indicates negative feedback, and sign = 1 indicates positive feedback. sign is an optional argument; it assumes a value of 1 if not specified.
Returns: out
Return type: Raises: ValueError
– if the inputs, outputs, or timebases of the systems are incompatible.

find_input
(name)¶ Find the index for an input given its name (None if not found)

find_output
(name)¶ Find the index for an output given its name (None if not found)

find_state
(name)¶ Find the index for a state given its name (None if not found)

forward
(x, u)¶ Compute the flat flag given the states and input.
See
control.flatsys.FlatSystem.forward()
for more info.

freqresp
(omega)¶ Evaluate the system’s transfer function at a list of frequencies
Reports the frequency response of the system,
G(j*omega) = mag*exp(j*phase)for continuous time. For discrete time systems, the response is evaluated around the unit circle such that
G(exp(j*omega*dt)) = mag*exp(j*phase).Parameters: omega (array_like) – A list of frequencies in radians/sec at which the system should be evaluated. The list can be either a python list or a numpy array and will be sorted before evaluation. Returns:  mag ((self.outputs, self.inputs, len(omega)) ndarray) – The magnitude (absolute value, not dB or log10) of the system frequency response.
 phase ((self.outputs, self.inputs, len(omega)) ndarray) – The wrapped phase in radians of the system frequency response.
 omega (ndarray) – The list of sorted frequencies at which the response was evaluated.

horner
(s)¶ Evaluate the systems’s transfer function for a complex variable
Returns a matrix of values evaluated at complex variable s.

isctime
(strict=False)¶ Check to see if a system is a continuoustime system
Parameters:  sys (LTI system) – System to be checked
 strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

isdtime
(strict=False)¶ Check to see if a system is a discretetime system
Parameters: strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

issiso
()¶ Check to see if a system is single input, single output

lft
(other, nu=1, ny=1)¶ Return the Linear Fractional Transformation.
A definition of the LFT operator can be found in Appendix A.7, page 512 in the 2nd Edition, Multivariable Feedback Control by Sigurd Skogestad.
An alternative definition can be found here: https://www.mathworks.com/help/control/ref/lft.html
Parameters:

linearize
(x0, u0, t=0, params={}, eps=1e06)¶ Linearize an input/output system at a given state and input.
Return the linearization of an input/output system at a given state and input value as a StateSpace system. See
linearize()
for complete documentation.

minreal
(tol=0.0)¶ Calculate a minimal realization, removes unobservable and uncontrollable states

pole
()¶ Compute the poles of a state space system.

returnScipySignalLTI
()¶ Return a list of a list of scipy.signal.lti objects.
For instance,
>>> out = ssobject.returnScipySignalLTI() >>> out[3][5]
is a signal.scipy.lti object corresponding to the transfer function from the 6th input to the 4th output.

reverse
(zflag)¶ Compute the states and input given the flat flag.
See
control.flatsys.FlatSystem.reverse()
for more info.

sample
(Ts, method='zoh', alpha=None, prewarp_frequency=None)¶ Convert a continuous time system to discrete time
Creates a discretetime system from a continuoustime system by sampling. Multiple methods of conversion are supported.
Parameters:  Ts (float) – Sampling period
 method ({"gbt", "bilinear", "euler", "backward_diff", "zoh"}) –
Which method to use:
 gbt: generalized bilinear transformation
 bilinear: Tustin’s approximation (“gbt” with alpha=0.5)
 euler: Euler (or forward differencing) method (“gbt” with alpha=0)
 backward_diff: Backwards differencing (“gbt” with alpha=1.0)
 zoh: zeroorder hold (default)
 alpha (float within [0, 1]) – The generalized bilinear transformation weighting parameter, which should only be specified with method=”gbt”, and is ignored otherwise
 prewarp_frequency (float within [0, infinity)) – The frequency [rad/s] at which to match with the input continuous time system’s magnitude and phase (the gain=1 crossover frequency, for example). Should only be specified with method=’bilinear’ or ‘gbt’ with alpha=0.5 and ignored otherwise.
Returns: sysd – Discrete time system, with sampling rate Ts
Return type: Notes
Uses the command ‘cont2discrete’ from scipy.signal
Examples
>>> sys = StateSpace(0, 1, 1, 0) >>> sysd = sys.sample(0.5, method='bilinear')

set_inputs
(inputs, prefix='u')¶ Set the number/names of the system inputs.
Parameters:  inputs (int, list of str, or None) – 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).
 prefix (string, optional) – 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_outputs
(outputs, prefix='y')¶ Set the number/names of the system outputs.
Parameters:  outputs (int, list of str, or None) – 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 u[i] (where the prefix u can be changed using the optional prefix parameter).
 prefix (string, optional) – 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_states
(states, prefix='x')¶ Set the number/names of the system states.
Parameters:  states (int, list of str, or None) – 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 u[i] (where the prefix u can be changed using the optional prefix parameter).
 prefix (string, optional) – 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].

zero
()¶ Compute the zeros of a state space system.
