control.StateSpace¶

class
control.
StateSpace
(A, B, C, D[, dt])¶ A class for representing statespace models
The StateSpace class is used to represent statespace realizations of linear timeinvariant (LTI) systems:
 dx/dt = A x + B u
 y = C x + D u
where u is the input, y is the output, and x is the state.
The main data members are the A, B, C, and D matrices. The class also keeps track of the number of states (i.e., the size of A).
Discretetime state space system are implemented by using the ‘dt’ instance variable and setting it to the sampling period. If ‘dt’ is not None, then it must match whenever two state space systems are combined. Setting dt = 0 specifies a continuous system, while leaving dt = None means the system timebase is not specified. If ‘dt’ is set to True, the system will be treated as a discrete time system with unspecified sampling time.

__init__
(A, B, C, D[, dt])¶ Construct a state space object.
The default constructor is StateSpace(A, B, C, D), where A, B, C, D are matrices or equivalent objects. To create a discrete time system, use StateSpace(A, B, C, D, dt) where ‘dt’ is the sampling time (or True for unspecified sampling time). To call the copy constructor, call StateSpace(sys), where sys is a StateSpace object.
Methods
__init__
(A, B, C, D[, dt])Construct a state space object. append
(other)Append a second model to the present model. damp
()dcgain
()Return the zerofrequency gain evalfr
(omega)Evaluate a SS system’s transfer function at a single frequency. feedback
([other, sign])Feedback interconnection between two LTI systems. freqresp
(omega)Evaluate the system’s transfer func. 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])Calculate a minimal realization, removes unobservable and pole
()Compute the poles of a state space system. returnScipySignalLTI
()Return a list of a list of scipy.signal.lti objects. sample
(Ts[, method, alpha])Convert a continuous time system to discrete time 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

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 : ndarray
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.

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)¶ Feedback interconnection between two LTI systems.

freqresp
(omega)¶ Evaluate the system’s transfer func. at a list of freqs, omega.
mag, phase, omega = self.freqresp(omega)
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). omega: 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.
 mag: The magnitude (absolute value, not dB or log10) of the system
 frequency response.
 phase: The wrapped phase in radians of the system frequency
 response.
 omega: 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 (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=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.

sample
(Ts, method='zoh', alpha=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
Returns: sysd : StateSpace system
Discrete time system, with sampling rate Ts
Notes
Uses the command ‘cont2discrete’ from scipy.signal
Examples
>>> sys = StateSpace(0, 1, 1, 0) >>> sysd = sys.sample(0.5, method='bilinear')

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