control.TransferFunction¶

class
control.
TransferFunction
(num, den[, dt])¶ A class for representing transfer functions
The TransferFunction class is used to represent systems in transfer function form.
The main data members are ‘num’ and ‘den’, which are 2D lists of arrays containing MIMO numerator and denominator coefficients. For example,
>>> num[2][5] = numpy.array([1., 4., 8.])
means that the numerator of the transfer function from the 6th input to the 3rd output is set to s^2 + 4s + 8.
Discretetime transfer functions are implemented by using the ‘dt’ instance variable and setting it to something other than ‘None’. If ‘dt’ has a nonzero value, then it must match whenever two transfer functions are combined. If ‘dt’ is set to True, the system will be treated as a discrete time system with unspecified sampling time. The default value of ‘dt’ is None and can be changed by changing the value of
control.config.defaults['xferfcn.default_dt']
.The TransferFunction class defines two constants
s
andz
that represent the differentiation and delay operators in continuous and discrete time. These can be used to create variables that allow algebraic creation of transfer functions. For example,>>> s = TransferFunction.s >>> G = (s + 1)/(s**2 + 2*s + 1)

__init__
(*args)¶ TransferFunction(num, den[, dt])
Construct a transfer function.
The default constructor is TransferFunction(num, den), where num and den are lists of lists of arrays containing polynomial coefficients. To create a discrete time transfer funtion, use TransferFunction(num, den, dt) where ‘dt’ is the sampling time (or True for unspecified sampling time). To call the copy constructor, call TransferFunction(sys), where sys is a TransferFunction object (continuous or discrete).
Methods
__init__
(*args)TransferFunction(num, den[, dt])
damp
()Natural frequency, damping ratio of system poles
dcgain
()Return the zerofrequency (or DC) gain
evalfr
(omega)Evaluate a transfer function at a single angular frequency.
feedback
([other, sign])Feedback interconnection between two LTI objects.
freqresp
(omega)Evaluate the transfer function at a list of angular frequencies.
horner
(s)Evaluate the systems’s transfer function for a complex variable
returns True if and only if all of the numerator and denominator polynomials of the (possibly MIMO) transfer function are zeroth order, that is, if the system has no dynamics.
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
minreal
([tol])Remove cancelling pole/zero pairs from a transfer function
pole
()Compute the poles of a transfer function.
Return a list of a list of
scipy.signal.lti
objects.sample
(Ts[, method, alpha, prewarp_frequency])Convert a continuoustime system to discrete time
zero
()Compute the zeros of a transfer function.
Attributes
s
z

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 (or DC) gain
For a continoustime transfer function G(s), the DC gain is G(0) For a discretetime transfer function G(z), the DC gain is G(1)
 Returns
gain – The zerofrequency gain
 Return type
ndarray

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

feedback
(other=1, sign= 1)¶ Feedback interconnection between two LTI objects.

freqresp
(omega)¶ Evaluate the transfer function at a list of angular 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 or list or tuple) – 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.

is_static_gain
()¶ returns True if and only if all of the numerator and denominator polynomials of the (possibly MIMO) transfer function are zeroth order, that is, if the system has no dynamics.

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

minreal
(tol=None)¶ Remove cancelling pole/zero pairs from a transfer function

pole
()¶ Compute the poles of a transfer function.

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

sample
(Ts, method='zoh', alpha=None, prewarp_frequency=None)¶ Convert a continuoustime 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”, “matched”} Method to use for sampling:
gbt: generalized bilinear transformation
bilinear: Tustin’s approximation (“gbt” with alpha=0.5)
euler: Euler (or forward difference) method (“gbt” with alpha=0)
backward_diff: Backwards difference (“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
StateSpace system
Notes
Available only for SISO systems
Examples
>>> sys = TransferFunction(1, [1,1]) >>> sysd = sys.sample(0.5, method='bilinear')

zero
()¶ Compute the zeros of a transfer function.
