Example 4.1
Consider again the system of Example 2.2
(t) = 3x(t) + x2(t) + (2x2(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 a, and frequency w
1. Thus
r (t) = alsint
w (t) = a2 (4-29)
It was found in Example 2.2 that the input u* (t) and state x* (t) satisfy the differential equation
d5 d3 d
(. 5 + 5 3 .) + 4 C.) 0 0
dt5 + dt3
(4-30)
The internal model system is thus
0
0 0
(t) : 0
0
0 0 0 0 I 0 TI(t)
0 1
-5 0
01
0
+ 0 e(t)
10
L' 1i
For the nonlinear system (4-28) we have
(4-31)