User`s guide

5 ODE P ara meter Estimation (Grey-Box Modeling)
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= .
. For more information about this example, see the section
on state-space models in System Identification: Theory for the User ,Second
Edition, by Lennart Ljung, Prentice 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 prepare this model for identification:
1 Create the following M-file to represent the model structure in this example:
function [A,B, C,D, K,x0] = myfunc(par,T,aux)
A = [0 1; 0 par(1)];
B = [0;par(2)];
C = eye(2);
D = zeros(2,1);
K = zeros(2,2);
x0 =[par(3);0];
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