c2d

Computes a discrete-time state-space model from a continuous-time state-space model.

Syntax

SYSD = c2d(SYSC, Ts)

SYSD = c2d(SYSC, Ts, METHOD)

SYSD = c2d(SYSC, Ts, 'prewarp', W0)

Inputs

SYSC
Continuous-time state-space model.
Ts
Sampling time in seconds.
METHOD
A string to specify the method used to convert the SYSC model to the SYSD model.
zoh
Zero-Order-Hold method (default method).
prewarp
Pre-warp method. This method requires W0.
tustin
Tustin approximation method.
bilin
Bilinear transformation.
W0
The pre-warp frequency.

Outputs

SYSD
A discrete-time state-space model.

Example

Default method: 
A = [10.0  5;
        5  10 ];

 B = [0.0 -10;
      10  0.0 ];

 C = [-10  0.0;
      0.0  10 ];

 D = [10  0.0;
      0.0 -10 ];

ResSys1 = c2d (ss (A, B, C, D), 2, 'zoh')

ResSys1 = object [
Scaled: 0
TimeUnit: seconds
ts: 2
a: [Matrix] 2 x 2
5.34324e+12  5.34324e+12
5.34324e+12  5.34324e+12
b: [Matrix] 2 x 2
3.56216e+12  -3.56216e+12
3.56216e+12  -3.56216e+12
c: [Matrix] 2 x 2
-10   0
  0  10
d: [Matrix] 2 x 2
10    0
 0  -10
e: [Matrix] 0 x 0
type: StateSpaceModel
]
Using the pre-warp method: 
ResSys2 = c2d (ss (A, B, C, D), 2, 'prewarp',0.5) %For the same state space matrices given above
ResSys2 = object [
Scaled: 0
TimeUnit: seconds
ts: 2
a: [Matrix] 2 x 2
-1.28904   0.15908
 0.15908  -1.28904
b: [Matrix] 2 x 2
 1.17581   2.13639
-2.13639  -1.17581
c: [Matrix] 2 x 2
2.13639  -1.17581
1.17581  -2.13639
d: [Matrix] 2 x 2
  1.30930  -15.79057
-15.79057  -18.69070
e: [Matrix] 0 x 0
type: StateSpaceModel
]

Comments

Computes a discrete-time state-space model from a continuous-time state-space model.

SYSD = c2d(SYS, Ts, METHOD) computes the discrete-time approximation of the continuous-time systems models SYS, with sampling period T's using METHOD.

Based on the SLICOT library functions ab04md and expm.