57
Example 4.1
Consider again the system of Example 2.2
x(t) = 3x(t) + x^(t) + (2x^(t) + 4)w(t) + u(t)
y(t) = x(t) (4-28)
Assume that the disturbance is a constant with a value of a2 and
that the reference is a sinusoid with amplitude and frequency u> =
1. Thus
r*(t) = ajsint
w*(t) = a2 (4-29)
Vf 'if
It was found in Example 2.2 that the input u (t) and state x (t) satisfy
the differential equation
5 3
d_ (.) + 51_ (.) + 4d_ (.} = o (4-30)
dt dt
The internal model system is thus
n(t)
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
n(t) +
0
0
0
0
0
1
0
0
-4
0
-5
0
1
e(t)
(4-31)
For the nonlinear system (4-28) we have