Chapter 6 State-Space Design
© National Instruments Corporation 6-39 Xmath Control Design Module
the derivative of x2 is set to zero, resulting in reduced-order state equations
of the form:
In the discrete case, x2k + 1 is taken to be equal to x2k so that the state
equations become:
When using mreduce( ), remember to remove states corresponding to
complex conjugate poles. Not doing so—that is, eliminating only one pole
in a pair—will produce a meaningless system.
More complex model reduction algorithms, which are intended to model
complete system dynamics in the absence of one of more states, are
available with the Xmath Model Reduction Module, as shown in Figure 6-8
and in Example 6-13.
Example 6-13 Model Reduction Module
A= [0.37,0.26,0.22,0.67;
0,0.52,0.63,0.20;
0,0,0.76,0.39;
0,0,0.04,0.83]
B = [0,1.7e-5,0,0.0004]'
C = [1,0,1,0]
D = 0
Sys = system(A,B,C,D,{dt = 0.2});
[SysM, T] = modal(Sys)
SysM (a state space system) =
A
0.37 0 0 0
0 0.52 0 0
0 0 0.665289 0
x
·1A11 A12A22
1–A21
–()x1B1A12A22
1–B2
–()u+=
yC
1C2
–A22
1–A21
()x1DC
2A22
1–B2
–()u+=
x1k1+A11 A12 A22 I–()
1–
–A21
[]x1k+=
yC
1C2
–A22 I–()
1��A21
[]x1k+=
B1A12 A22 I–()
1–B2
–[]uk
DC
2A22 I–()
1–B2
–[]uk