National Instruments 370753C-01 Manual De Usuario

Many of the discretization techniques discussed in the 

 section can be easily reversed to 

obtain a continuous equivalent to a discrete system. The 

makecontinuous( )

 function implements these reverse algorithms 

based on the keyword you specify as shown in Example 2-10. Although 

makecontinuous( )

 accepts an input system in any form, it returns the 

continuous-time system as a state-space system.

The forward, backward, and Tustin methods for mapping from the s-plane 
to the z-plane can be easily reversed using the equivalencies shown in 
Table 2-3.

Discrete-to-continuous algorithms using matrix logarithms (to reverse the 
exponential operations involved in doing the z-transform for the impulse 
invariant zero-order hold) are available for the 

exponential

 

(step-invariant) transformation and the 

ztransform

(impulse-invariant) 

methods. A limitation of these methods, however, is that they will not return 
a meaningful continuous equivalent to a discrete system that has pure 
delays (1/z terms), because the logarithm of zero is infinite. 

Create a system:

H = 0.5*polynomial([-0.36])/...

polynomial([-1,-1,-0.395+0.06305*jay,

-0.395-0.06305*jay]);

Form the discrete equivalent using the forward approximation:

Hd_f = discretize(H,0.1, {forward});

Table 2-3.  Mapping Methods for makecontinuous( )

Forward rectangular rule:
Keyword: 

forward

Backward rectangular rule:
Keyword: 

backward

Tustin’s rule:
Keyword: 

tustins

1 s dt

( )

+

→

1

1 s dt

( )

–

---------------------

→

1 s dt

( )

+

2

⁄

1 s dt

( )

–

2

⁄

----------------------------

→