National Instruments 370753C-01 Discretizing a System

Chapter 2 Linear System Representation

check(sys, {stable})

ans (a scalar) = 0

check(sys, {discrete, ss})

ans (a scalar) = 1

[, tfsys] = check(sys, {tf, convert})

tfsys (a transfer function) =

(z + 0.26)

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

(z + 0.26)(z - 1.875)

initial delay outputs

System is discrete, sampling at 0.001 seconds.

Discretizing a System

Many systems where behavior derives from physical equations of motion

can be modeled most naturally as continuous processes, using differential

equations. Therefore, you often choose to discretize these models for use

with a digital controller. A number of mathematical methods have been

developed to approximate the behavior of a continuous system in a

discrete-time representation with an appropriately fast sampling rate.

Xmath provides two functions, discretize( ) and

makecontinuous( ), which encompass a range of these techniques.

discretize( ) converts a system from its representation as a continuous

function in the s-domain to a discrete-time z-domain function.

makecontinuous( ) does the reverse, transforming a discrete system to

its continuous form.

SysD = discretize(Sys,{dt,exponential,forward,backward,

tustins,ztransform,polezero,firstorder})

The discretize( ) function has a number of keywords that correspond

to the different methods of continuous-to-discrete conversion that are

implemented within Xmath. The sampling interval (in seconds) for the

discrete system should be set equal to the keyword dt. If no value for dt

is specified, a default of 0.5 seconds is used. The default discretization

method used is the exponential (step-invariant) transform. The different