User`s guide

3 Linear Model Identification
This equation represents an electrical motor, where
yt xt
11
() ()=
is the
angular position of the motor shaft, and
yt xt
22
() ()=
is the angular velocity.
The parameter
−θ
1
is the inverse time constant of the motor, and
−
θ
θ
2
1
is th e
static gain from the input to the angular velocity.
The motor is at rest at t=0, but its angular position
θ
3
is unknown. Suppose
that the approximate nominal values of the unknown parameters are
θ
1
1=−
and
θ
2
025= .
. The variance of the errors in the position measurement is
0.01, and the variance in the angular velocity measurements is 0.1.For
more information about this example, s ee the section on state-space m odels
in System Identification: Theory for the User, Second E dition, by Lennart
Ljung, P rentice Hall PTR, 1999.
The continuous-time state-space model structure is defined by the following
equation:


xt Fxt Gut Kwt
yt Hxt Dut wt
xx
() () () ()
() () () ()
()
=++
=++
=00
To construct and estimate the parameters of this continuous-time state-space
model:
1 Construct the parameter matrices and initia li ze the pa r ameter values
using the nominal parameter values:
Note The following matrices correspond to continuous-time
representation. However, to be consistent with the
idss object property
name, this example uses
A, B,andC instead of F, G,andH.
A = [0 1;0 -1];
B = [0;0.25];
C = eye(2);
D = [0;0];
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