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Summary: 1104 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. AC-23,NO. 6, DECEMBER 1978
111. AN ExAhrpLE
To itlustratethepreceding let us consider the following example
which is given in [2, Sec.7.31: In particular, suppose
We note that R(s) and P(s) are relatively right prime and that P(s) is
column proper. Furthermore, since T,(s) is strictly proper, R(s) is of
lower column degree than P(s). As is shown in [2], if
then IP(s)-F(s)l=(s+l)(s2+2s+2); i.e., all 3 (controllableand observ-
able) poles of the system can be arbitrarily positioned in Re(s)
s= - 1 and -1+j, by employment of the Luenberger observer given in
[2] with (see Theorem 1)
and
K(s)=[ - 5-1 010 .
In viewof Theorem 2, therefore, ifwe employ the proper feedfonvard
compensator
r 3s2+6s 0 1
Tg(s)=[Q(s)-K(s)]-'H(s)=
L2s2+12s+102s2+14s+20]
s2+7s+ 10
in series with T,(s) in the e t y feedback configuration of Fig. 2, the
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