National Instruments 370753C-01 Manual De Usuario

To illustrate how you can examine the stability and dynamic response of a 
system using Xmath, start with the open-loop transfer function system

You close a unity feedback loop around this system, as shown in Figure 4-1.

Figure 4-1.  Constructing the Closed-Loop System G

(s) from the Open-Loop System 

G(s), with Input U(s) and Output Y(s)

You can derive the expression for the closed-loop transfer function G

(s):

Calculate the closed-loop transfer function. 

You convert the state-space system returned by 

feedback( )

 to a transfer function 

using 

check( )

.

sys = polynomial(-0.5)/polynomial([0,0,-2,-10]);

syscl=feedback(sys);

[,syscl] = check(syscl,{tf, convert})

syscl (a transfer function) =

(s + 0.5)

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

 2 

(s + 1.95266)(s + 10.0118)(s + 0.0354992s + 0.02...

initial integrator outputs

0

0

( )

s 0.5

+

(

)

2

s 2

+

(

) s 10

+

(

)

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

=

V(s)

u(s)

Y(s)

G(s)

G

cl

(s)

+

–

( ) U s

( ) Y s

( )

–

=

( ) G s

( )V s

( )

=

( )

( )

( )

-----------

( )

1 G s

( )

+

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

=

=

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