Worst-case disk-based stability margins of uncertain feedback loops

The worst-case disk margin is the smallest disk margin that occurs within a
specified uncertainty range. It is also the minimum guaranteed margin over the uncertainty
range. `wcdiskmargin`

estimates the worst-case disk margins and
corresponding worst-case gain and phase margins for both loop-at-a-time and multiloop
variations. The function also returns the worst-case perturbation, the combination of
uncertain elements that yields the weakest margins.

`[`

estimates the worst-case loop-at-a-time disk-based stability margins for the uncertain
negative feedback loop `wcDM`

,`wcu`

] = wcdiskmargin(`L`

,'siso')`feedback(L,eye(N))`

, where `N`

is
the number of inputs and outputs in `L`

.

While `diskmargin`

computes stability margins for a nominal model, `wcdiskmargin`

computes
the worst-case (smallest) disk margin over the modeled uncertainty in
`L`

. Disk-based margin analysis provides a stronger guarantee of robust
stability than the classical gain and phase margins. For general information about disk
margins, see Stability Analysis Using Disk Margins.

`___ = wcdiskmargin(___,`

specifies an additional eccentricity parameter that biases the modeled gain and phase
variation toward gain increase (positive `E`

)`E`

) or gain decrease (negative
`E`

). You can use this argument to test the relative sensitivity of
stability margins to gain increases versus decreases. You can use this argument with any of
the previous syntaxes.

`[___,`

returns a structure with additional information about the worst-case margins and the
perturbations that generate them. You can use this output argument with any of the previous
syntaxes.`info`

] = wcdiskmargin(___)

`wcdiskmargin`

assumes negative feedback. To compute the worst-case disk margins of a positive feedback system, use`wcdiskmargin(-L)`

or`wcdiskmargin(P,-C)`

.You can visualize worst-case disk margins with

`wcdiskmarginplot`

.

`wcdiskmargin`

models gain (and phase) variation as
`umargin`

uncertainty, combines it with the specified plant uncertainty,
and uses `mussv`

to compute the worst-case disk margins and perturbation.
This generalizes the `diskmargin`

algorithm to feedback loops with
uncertainty. For more information about disk-margin computation and interpretation, see Stability Analysis Using Disk Margins.