National Instruments 370753C-01

Chapter 4 System Analysis

Input Names

-----------

Input 1

Output Names

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

Output 1

System is continuous

You can examine the stability of Gcl(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.

Gcl s() 0.0478–

s1.95+()

------------------------0.0118

s10.012+()

------------------------------++=

0.036 s0.01775+()0.16065 0.15 89()+

s0.01775+()

20.1589()

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

e0.018t–0.036 cos(0.1589t) 0.160 sin(0.1589t)+()

Gt() 0.0478 e–1.95t–0.0118e10.012t–

+=+