Guidelines
Based on the preceding
discussion, we can give some guidelines for the loop-shaping design.
qThe loop transfer function
should be shaped in such a way that it has low gain around the frequency of
the modulus of any right-half plane zero z. Typically, it requires that the
crossover frequency be much smaller than the modulus of the right-half plane zero;
say, wc<|z|/2 for any real zero and wc <|z| for any complex zero with a much
larger imaginary part than the real part (see Figure 16.6).
qThe loop transfer function
should have a large gain around the frequency of the modulus of any
right-half plane pole.
qThe loop transfer function
should not have a large slope near the
crossover frequencies.
These
guidelines are consistent with the rules used in classical control theory (see Bode[1945] and
Horowitz[1963]).
