qA typical design works as follows: the designer
inspects the open-loop singular values of the nominal plant, and shapes these by pre- and/or postcompensation until
nominal performance (and possibly robust stability) specifications are met. (Recall that the
open-loop shape is related to closed-loop objectives.) A feedback controller K¥ with associated stability margin (for the
shaped plant) e £ bopt(Ps) is then synthesized. If bopt(Ps) is small, then the specified loop
shape is incompatible with robust stability requirements, and should be adjusted
accordingly, then K¥ is
reevaluated.
qNote that the final controller is K=W1K¥W2 , so it is necessary to check if the loop
properties are significantly changed. It is helpful to choose W1 and W2 with
small condition numbers.
qOnly W1 or W2 is needed if P is SISO.
