90
0 1 0
0 0 1
0
o
o
o
(5-21)
0 0 0
dQ -ct1 -d2
1
0
1
and T is arbitrary but nonsingular.
It is not difficult to show that the eigenvalues of the matrix
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) = aj_
(5-22)
where and a2 ace constants. The sampled signals are
(5-23)
where sampling occurs at every t = kT seconds. Letting X (z) denote the