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Example 4 -- Controllability and Observability
The linearized equations of motion for a satellite are
<![CDATA[
.
X = AX + BU
Y = CX + DU
]]>
where
<![CDATA[
[0 1 0 0 ] [0 0]
A =[0 0 0 0.0024], B = [1 0], C = [1 0 0 0], D = 0
[0 0 0 1 ] [0 0] [0 0 1 0]
[0 0.0024 0 0 ] [0 1]
]]>
determine the controllability and observability of the system.
Answer:
The controllability matrix is
[0 0 1 0 0 0.002400 -0.000006 0 ]
co = [1 0 0 0.002400 -0.000006 0 0 0 ]
[0 0 0 1 -0.002400 0 0 -0.000006]
[0 1 -0.002400 0 0 -0.000006 0 0 ]
The observability matrix is
[1 0 0 0 ]
[0 0 1 0 ]
[0 1 0 0 ]
ob = [0 0 0 1 ]
[0 0 0 0.002400 ]
[0 -0.002400 0 0 ]
[0 -0.000006 0 0 ]
[0 0 0 -0.000006]
Program in Ch
Output in Ch
Program in MATLAB
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