If your first attempt at loopsyn
design does not achieve everything you
wanted, you will need to readjust your target desired loop shape Gd
. Here are
some basic design tradeoffs to consider:
Stability Robustness. Your target loop
Gd
should have low gain (as small as possible) at high frequencies where
typically your plant model is so poor that its phase angle is completely inaccurate, with
errors approaching ±180° or more.
Performance. Your Gd
loop
should have high gain (as great as possible) at frequencies where your model is good, in order
to ensure good control accuracy and good disturbance attenuation.
Crossover and Roll-Off. Your desired loop shape Gd
should have its
0 dB crossover frequency (denoted ωc) between the above two frequency
ranges, and below the crossover frequency ωc it should roll off with a
negative slope of between –20 and –40 dB/decade, which helps to keep phase lag to less than
–180° inside the control loop bandwidth (0 < ω < ωc).
Other considerations that might affect your choice of Gd
are the
right-half-plane poles and zeros of the plant G
, which impose fundamental
limits on your 0 dB crossover frequency ωc
[12]. For instance, your 0 dB crossover
ωc must be greater than the magnitude of any plant right-half-plane poles
and less than the magnitude of any right-half-plane zeros.
If you do not take care to choose a target loop shape Gd
that conforms to
these fundamental constraints, then loopsyn
will still compute the optimal loop-shaping
controller K
for your Gd
, but you should expect that the
optimal loop L = G*K
will have a poor fit to the target loop shape
Gd
, and consequently it might be impossible to meet your performance
goals.