c2d (Function Reference)

Discretize continuous-time systems

Syntax

sysd = c2d(sys,Ts)
sysd = c2d(sys,Ts,method)
[sysd,G] = c2d(sys,Ts,method)

Description

sysd = c2d(sys,Ts) discretizes the continuous-time LTI model sys using zero-order hold on the inputs and a sample time of Ts seconds.

sysd = c2d(sys,Ts,method) gives access to alternative discretization schemes. The string method selects the discretization method among the following:

'zoh'
Zero-order hold. The control inputs are assumed piecewise constant over the sampling period Ts.

'foh'
Triangle approximation (modified first-order hold, see [1], p. 151). The control inputs are assumed piecewise linear over the sampling period Ts.

'tustin'
Bilinear (Tustin) approximation.

'prewarp'
Tustin approximation with frequency prewarping.

'matched'
Matched pole-zero method. See [1], p. 147.

`'zoh'`	Zero-order hold. The control inputs are assumed piecewise constant over the sampling period `Ts`.
`'foh'`	Triangle approximation (modified first-order hold, see [1], p. 151). The control inputs are assumed piecewise linear over the sampling period `Ts`.
`'tustin'`	Bilinear (Tustin) approximation.
`'prewarp'`	Tustin approximation with frequency prewarping.
`'matched'`	Matched pole-zero method. See [1], p. 147.

Refer to "Continuous/Discrete Conversions of LTI Models" for more detail on these discretization methods.

c2d supports MIMO systems (except for the 'matched' method) as well as LTI models with delays with some restrictions for 'matched' and 'tustin' methods.

[sysd,G] = c2d(sys,Ts,method) returns a matrix G that maps the continuous 
initial conditions  and  to their discrete counterparts  and  
according to

Example

Consider the system

with input delay second. To discretize this system using the triangle approximation with sample time second, type

H = tf([1 -1],[1 4 5],'inputdelay',0.35)
Transfer function:
                   s - 1
exp(-0.35*s) * -------------
               s^2 + 4 s + 5
Hd = c2d(H,0.1,'foh')
Transfer function:
0.0115 z^3 + 0.0456 z^2 - 0.0562 z - 0.009104
---------------------------------------------
        z^6 - 1.629 z^5 + 0.6703 z^4

Sampling time: 0.1

The next command compares the continuous and discretized step responses.

```
step(H,'-',Hd,'--')
```

See Also
d2c Discrete to continuous conversion

d2d Resampling of discrete systems-

References

[1] Franklin, G.F., J.D. Powell, and M.L. Workman, Digital Control of Dynamic Systems, Second Edition, Addison-Wesley, 1990.

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