National Instruments 370753C-01

Chapter 4 System Analysis

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.”