control.StateSpace

class control.StateSpace(*args)

A class for representing state-space models

The StateSpace class is used to represent state-space realizations of linear time-invariant (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).

Discrete-time 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__(*args)

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 call the copy constructor, call StateSpace(sys), where sys is a StateSpace object.

Methods

__init__(*args) Construct a state space object.
append(other) Append a second model to the present model.
damp()
dcgain() Return the zero-frequency 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 continuous-time system
isdtime([strict]) Check to see if a system is a discrete-time 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 state-space if necessary, inputs and outputs are appended and their order is preserved

dcgain()

Return the zero-frequency gain

The zero-frequency gain of a continuous-time state-space system is given by:

and of a discrete-time state-space system by:

Returns:

gain : ndarray

An array of shape (outputs,inputs); the array will either be the zero-frequency (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 ang. frequencies.

mag, phase, omega = self.freqresp(omega)

reports the value of the magnitude, phase, and angular frequency of the system’s 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 continuous-time 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 discrete-time 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 discrete-time system from a continuous-time 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: zero-order 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.