System Identification
of a Continuous-Time Linear System
Jan H. van Schuppen
25 October 2018
MUINI.FI
Brno, Czech Republic
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Example
Example 6.4. Case of a linear system – System specification
dx(t)
dt
= Ax(t), x(0) = x0,
y(t) = Cx(t),
A =


0.0 1.0 0.0
−0.8 −0.8 0.0
0.0 0.0 −0.9

 , x0 =


1.5
0.0
−0.8

 ,
C = 1.1 −0.8 1.2 ,
dx = 3, dy = 1, ds = 8,
t1 = 20, ∆t = 0.02, t1d = 100, tobsbegin = 13,
tpast = 12, tfuture = 20, thyfuture = 4, thxo = 4.
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Example 6.4 - Simulation system
Time step
0 10 20 30 40 50 60 70 80 90 100
y
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Time series
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Example 6.4 - Prediction of identified system
Time step
0 10 20 30 40 50 60
y
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Time series
Observer output
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Example
Example 6.4. Case of a linear system – Computed values
Observable canonical form used for observer and for system.
dxo(t)
dt
= Ao,ocf xo(t) + Ko[y(t) − Coxo(t)], xo(0) = xo,0,
yo(t) = Co,ocf xo(t),
Ao,ocf = =


0 1 0
0 0 1
−0.6070 −1.4670 −1.7104

 ,
Aocf =


0 1 0
0 0 1
−0.7200 −1.5200 −1.7000

 ,
Co,ocf = 1 0 0 = Cocf ,
Λo =


−0.4432 + i 0.7350
−0.4432 − i 0.7350
−0.8240

 , Λ =


−0.4000 + i 0.8000
−0.4000 − i 0.8000
−0.9000

 .
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