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 ω_{c}) between the above two frequency ranges, and below the crossover frequency ω_{c}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 < ω_{c}).

Other considerations that might affect your choice of `Gd`

are
the right-half-plane poles and zeros of the plant `G`

,
which impose ffundamental
limits on your 0 dB crossover frequency ω_{c} [12]. For instance,
your 0 dB crossover ω_{c} must be greater
than the magnitude of any plant right-half-plane poles and less than
the magnitude of any right-half-plane zeros.

$$\underset{\mathrm{Re}\left({p}_{i}\right)>0}{\mathrm{max}}\left|{p}_{i}\right|<{\omega}_{c}<\underset{\mathrm{Re}\left({z}_{i}\right)>0}{\mathrm{min}}\left|{z}_{i}\right|.$$

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.

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