90
00 1 0 . 0 0
Cd T[ ] (521)
0 0 o . 6
-do -dI -d2 .-dr_11 1
and T is arbitrary but nonsingular.
It is not difficult to show that the eigenvalues of the matrix Ad will be identical to the eigenvalues obtained by discretizing the continuous-time internal model system given by equations (2-25) through (2-28). Consequently, the performance obtained using either the system of (5-18) or the direct discretization will be roughly the same. The
system of (5-18) is, however, often easier to obtain and implement.
The following example shows how to calculate the coefficients of the difference equation used to define the discrete-time internal model system.
Example 5.1
Suppose x*(t) = a1
u (t) = a2sinwt (5-22)
where a, and a2 are constants. The sampled signals are
x (k) = a1
u*(k) = a2sinwkT (5-23)
where sampling occurs at every t = kT seconds. Letting X*(z) denote the