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Visualize worst-case disk-based stability margins

`wcdiskmarginplot(`

plots the nominal and
worst-case disk-based gain and phase margins for the SISO or MIMO negative feedback loop
`Lunc`

)`feedback(Lunc,eye(N))`

, where `N`

is the number of
inputs and outputs in the uncertain open-loop response `Lunc`

.

For MIMO responses, `diskmarginplot`

uses multiloop disk margins.
(For details about disk-based gain and phase margins, see `diskmargin`

.)
The plot includes:

Nominal — Nominal gain and phase margins of

`Lunc`

. The disk-based gain margin at each frequency is ±*GM*, where*GM*is the value shown in the plot in dB. Similarly, the disk-based phase margin is ±*PM*degrees, where*PM*is the value shown on the plot.Worst perturbation — The disk-based gain and phase margins for the worst perturbation within the uncertainty range

`Lunc.Uncertainty`

. The worst perturbation corresponds to the`wcu`

output argument of`wcdiskmargin`

. It is the perturbation that yields the smallest disk margin.Worst-case margin (lower bound) — Lower bound on the worst-case margins at each frequency. This curve represents the envelope produced by finding the smallest disk margin possible at each frequency, within the uncertainty of

`Lunc`

.Worst-case margin (upper bound) — Upper bound on the worst-case margins at each frequency.

Sampled Uncertainty — Margins of responses randomly sampled from

`Lunc`

.

`wcdiskmarginplot(`

plots the disk-based gain and phase margins computed using the skew
`Lunc`

,`sigma`

)`sigma`

to bias the gain variation toward gain increase
(`sigma`

> 0) or gain decrease (`sigma`

< 0). If
you have used `wc`

to obtain worst-case disk-based margins with some
particular `sigma`

, you can use this syntax to see the frequency
dependence of the margins at that `sigma`

value. For
`sigma`

≠ 0, the plotted value is ```
GM =
min(gmax,1/max(0,gmin))
```

. In other words, the plot shows the largest amount of
gain change `[1/GM,GM]`

that fits within the disk-based gain margin
`[gmin,gmax]`

of the system at the specified `sigma`

.

`wcdiskmarginplot(___,`

plots the
worst-case margins at the frequencies specified by `w`

)`w`

.

If

`w`

is a cell array of the form`{wmin,wmax}`

, then the plot shows the margins at frequencies ranging between`wmin`

and`wmax`

.If

`w`

is a vector of frequencies, then the plot shows the margins at each specified frequency.

`wcdiskmarginplot(___,`

uses
specified options to customize plot elements, aspects of the worst-case margin computation,
or both. Use `opts`

)`diskmarginoptions`

to specify customizations for the plot.
Use `wcOptions`

to specify customizations for the computation. You can
use this argument with any of the previous syntaxes.

`diskmargin`

| `diskmarginoptions`

| `diskmarginplot`

| `wcdiskmargin`

| `wcOptions`