scipy.signal.cont2discrete¶

scipy.signal.cont2discrete(system, dt, method='zoh', alpha=None)[source]¶

Transform a continuous to a discrete state-space system.

Parameters:

Parameters:	system : a tuple describing the system or an instance of `lti` The following gives the number of elements in the tuple and the interpretation: 1: (instance of `lti`) 2: (num, den) 3: (zeros, poles, gain) 4: (A, B, C, D) dt : float The discretization time step. method : {“gbt”, “bilinear”, “euler”, “backward_diff”, “zoh”}, optional 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], optional The generalized bilinear transformation weighting parameter, which should only be specified with method=”gbt”, and is ignored otherwise
Returns:	sysd : tuple containing the discrete system Based on the input type, the output will be of the form (num, den, dt) for transfer function input (zeros, poles, gain, dt) for zeros-poles-gain input (A, B, C, D, dt) for state-space system input

system : a tuple describing the system or an instance of lti

The following gives the number of elements in the tuple and the interpretation:

1: (instance of lti)

2: (num, den)

3: (zeros, poles, gain)

4: (A, B, C, D)

dt : float

The discretization time step.

method : {“gbt”, “bilinear”, “euler”, “backward_diff”, “zoh”}, optional

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], optional

The generalized bilinear transformation weighting parameter, which should only be specified with method=”gbt”, and is ignored otherwise

Returns:

sysd : tuple containing the discrete system

Based on the input type, the output will be of the form

(num, den, dt) for transfer function input

(zeros, poles, gain, dt) for zeros-poles-gain input

(A, B, C, D, dt) for state-space system input

Notes

By default, the routine uses a Zero-Order Hold (zoh) method to perform the transformation. Alternatively, a generalized bilinear transformation may be used, which includes the common Tustin’s bilinear approximation, an Euler’s method technique, or a backwards differencing technique.

The Zero-Order Hold (zoh) method is based on [R193], the generalized bilinear approximation is based on [R194] and [R195].

References

[R193]

(1, 2) http://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models

[R194]

(1, 2) http://techteach.no/publications/discretetime_signals_systems/discrete.pdf

[R195]

(1, 2) G. Zhang, X. Chen, and T. Chen, Digital redesign via the generalized bilinear transformation, Int. J. Control, vol. 82, no. 4, pp. 741-754, 2009. (http://www.ece.ualberta.ca/~gfzhang/research/ZCC07_preprint.pdf)