Chapter 6 State-Space Design
Xmath Control Design Module 6-4 ni.com
X0
0
Input Names
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Input 1
Output Names
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Output 1
System is continuous
T (a square matrix) =
2.22045e-16 0 -1
0 1 0
-1 0 2.22045e-16
nuc (a scalar) = 2
These results indicate that only the first state of the system corresponds to
a controllable mode, and the remaining two are uncontrollable.
Similarly, if you form the controllability matrix for this system,
[,states] = size(A);
Con = B;
For i = 1:states-1;
Con = [B, A*Con];
endFor
det(Con)
ans (a scalar) = 0
you see that the controllability matrix is singular (its determinant is zero),
confirming the results from controllable( ).
Observability and Estimation
As described in the Controllability section, the term controllability
describes whether or not a system’s states can be affected, and the system
eigenvalues relocated, by changes to the system input. The analogous
concept of observability describes whether it is possible to determine the
value of an individual state at a particular time by observing the system
outputs for a finite amount of time. In essence, an observable system is one
for which you can “observe” state values by knowing the output of the
system.