Chapter 4 System Analysis
Xmath Control Design Module 4-6 ni.com
Example 4-3 Dynamic Response through Partial Fraction Expansion
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
cl
(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
cl
(s):
Calculate the closed-loop transfer function.
Note 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
Gs()
s 0.5+()
s
2
s 2+()s 10+()
-----------------------------------------=
V(s)u(s) Y(s)
G(s)
G
cl
(s)
+
–
Vs() Us() Ys()–=
Ys() Gs()Vs()= G
cl
s()
Ys()
Us()
-----------
Gs()
1 Gs()+
---------------------==
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