Chapter 6 State-Space Design
© National Instruments Corporation 6-3 Xmath Control Design Module
Figure 6-1. Full-State Feedback Being Used to Relocate the Eigenvalues
of a Controllable System Based on the Value of the Gain K
controllable( )[SysC,T,nuc]=controllable(Sys,{tol})
The question that naturally arises is, “How do you know which states are
controllable in a given system?” The controllable( ) function returns
the controllable partition of a state-space system, the number of
uncontrollable states in the original system, and a linear transformation
matrix which can be used to partition the states into controllable and
uncontrollable sets. For an example of how this is done, refer to
Example 6-1.
controllable( ) uses the staircase algorithm, which is discussed in
more detail in the stair( ) section.
Example 6-1 Controllability of a System
Perform controllable( ) on a system is described by:
A = [1,0,0.01;0,1,0;0,0,1];
B = [1,0,0]'; C = [0.6,0.8,0];D = 0;
Sys = system(A,B,C,D);
[SysC,T,nuc] = controllable(Sys)
The system has 2 uncontrollable states
SysC (a state space system) =
A
1
B
-1
C
-0.6
D
0
vu y
x = Ax + Bu
y = Cx + Du
K
+
–