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.

__init__
(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__
(num, den[, dt])Construct a transfer function. damp
()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 a transfer function at a list of angular 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
()minreal
([tol])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. sample
(Ts[, method, alpha])Convert a continuoustime system to discrete time zero
()Compute the zeros of a transfer function. 
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 : ndarray
The zerofrequency gain

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 a transfer function at a list of angular frequencies.
mag, phase, omega = self.freqresp(omega)
reports the value of the magnitude, phase, and angular frequency of the transfer function matrix evaluated at s = i * omega, where omega is a list of angular frequencies, and is a sorted version of the input omega.

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 (default = False) :
If strict is True, make sure that timebase is not None

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

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 signal.scipy.lti object corresponding to the transfer function from the 6th input to the 4th output.

sample
(Ts, method='zoh', alpha=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”}
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
Returns: sysd : StateSpace system
Discrete time system, with sampling rate Ts
Notes
 Available only for SISO systems
 Uses the command cont2discrete from scipy.signal
Examples
>>> sys = TransferFunction(1, [1,1]) >>> sysd = sys.sample(0.5, method='bilinear')

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