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Chapter 4 System Analysis
© National Instruments Corporation 4-17 Xmath Control Design Module
The simulation performed in initial( ) uses an input of zero for each
point in the time vector. The output
Y is a PDM where domain is the time
vector.
By varying the initial values of the states individually, you can determine
which is the most sensitive. For an example using
initial( ) to
determine the sensitivity of the states, refer to Example 4-8.
Example 4-8 Using initial( ) to Determine the Sensitivity of the States
Sys = system([-2.3,0.01,5.1;0,-0.35,-2;0,2,-.35],
[1,.25,.25]',[1.34,0,0],0);
ic1 = initial(Sys, 0:.1:15, {X0 = [1,0,0]});
ic2 = initial(Sys, 0:.1:15, {X0 = [0,1,0]});
ic3 = initial(Sys, 0:.1:15, {X0 = [0,0,1]});
plot ([ic1,ic2,ic3], {xlab = "Time (sec)",
legend = ["State 1", "State 2", "State 3"],
ylab = "Amplitude"})
Figure 4-5. 15-Second System Response to Unity Nonzero Conditions
at Each of the States
In Figure 4-5, notice that the value of the second state has the highest
maximum value and takes the longest to “zero out.”