kKs( ) ( ) T (s) = F(s) ( ) ( )
When a = 0, TR(s) corresponds to a Type l system and when a ≠ O TR(s) corresponds to a Type 0 system. Assuming this is acceptable an Lo(s) is synthesized, as shown in Fig. F.2, and results in
In order to achieve the desired specification e(∞) = r(∞) − c(∞) = 0, for r(t) = u-1(t), then the compensator G(s) must be a Type 1 transfer function in order to yield a Type 1 system for a ≠ O and a Type 2 system for a = 0. The synthesized loop transmission function is
) ( ) (s
) ( ) kK( = L 2o3
for which three points (denoted by X) are shown in Fig. F.2. It is left to the reader to complete the synthesis of a Lo(s).