Chapter 4 System Analysis
© National Instruments Corporation 4-7 Xmath Control Design Module
0
0
Input Names
-----------
Input 1
Output Names
------------
Output 1
System is continuous
You can examine the stability of G
cl
(s) by representing it as a sum of partial
fractions, using the
residue( ) function.
residue(syscl)
ans (a pdm) =
Poles |
-------------------------+-----------------------
-0.0177496 - 0.158936 j | Order 1 0.0180045 + ...
-0.0177496 + 0.158936 j | Order 1 0.0180045 -...
-1.95266 | Order 1 -0.0478224
-10.0118 | Order 1 0.0118134
residue( )
returns a PDM with the poles as the domain elements, and the
associated dependent matrices being the residue at each pole. It also can be
expressed in the following form:
Using a table of inverse Laplace transforms to convert this expression to the
transient time response rather than a complex frequency response, you can
rewrite the time response G(t) as:
Notice from this example that because all the poles are in the left half plane,
the response each contributes is an exponential which decays with time, so
this closed-loop system is stable.
G
cl
s()
0.0478–
s 1.95+()
------------------------
0.0118
s 10.012+()
------------------------------++=
0.036 s 0.01775+()0.16065 0.1589()+
s 0.01775+()
2
0.1589()
2
+
----------------------------------------------------------------------------------------------
e
0.018t–
0.036 cos(0.1589t) 0.160 sin(0.1589t)+()
Gt() 0.0478e–
1.95t–
0.0118e
10.012t–
+=+
