Fit an uncertain model to set of LTI responses

returns an uncertain model `usys`

= ucover(`Parray`

,`Pnom`

,`ord`

)`usys`

with nominal value
`Pnom`

and whose range of behaviors includes all responses in the LTI
array `Parray`

. The uncertain model structure is of the form $$usys=Pnom\left(I+W(s)\Delta (s)\right)$$, where

Δ is a

`ultidyn`

object that represents uncertain dynamics with unit peak gain.*W*is a stable, minimum-phase shaping filter of order`ord`

that adjusts the amount of uncertainty at each frequency. For MIMO`Pnom`

,*W*is diagonal, with orders of the diagonal elements given by`ord`

.

returns an uncertain model with the structure specified by
`usys`

= ucover(`Parray`

,`Pnom`

,`ord`

1,`ord`

2,`utype`

)`utype`

.

`utype`

=`'InputMult'`

— Input multiplicative form, in which`usys = Pnom*(I + W1*Delta*W2)`

`utype`

=`'OutputMult'`

— Output multiplicative form, in which`usys = (I + W1*Delta*W2)*Pnom`

`utype`

=`'Additive'`

— Additive form, in which`usys = Pnom + W1*Delta*W2`

`Delta`

represents uncertain dynamics with unit peak gain, and
`W1`

and `W2`

are diagonal, stable, minimum-phase
shaping filters with orders specified by `ord`

`1`

and
`ord`

`2`

, respectively.

`[`

improves the fit using initial filter values in the `usys`

,`info`

] = ucover(`Pnom`

,`info_in`

,`ord`

1,`ord`

2)`info`

result. Supply
new orders `ord`

1 and `ord`

2 for `W1`

and `W2`

. When you are trying different filter orders to improve the
result, this syntax speeds up iteration by letting you reuse previously computed
information.

`ucover`

fits the responses of LTI models in
`Parray`

by modeling the gaps between `Parray`

and the
nominal response `Pnom`

as uncertainty on the system dynamics. To model the
frequency distribution of these unmodeled dynamics, `ucover`

measures the
gap between `Pnom`

and `Parray`

at each frequency on a
grid, and selects shaping filters whose magnitude approximates the maximum gap.

To design the minimum-phase shaping filters `W1`

and
`W2`

, the `ucover`

command performs two steps:

Computes the optimal values of

`W1`

and`W2`

on a frequency grid.Fits

`W1`

and`W2`

values with the dynamic filters of the specified orders using`fitmagfrd`

.

The model structure $$usys=Pnom\left(I+W(s)\Delta (s)\right)$$ that you obtain using `usys = ucover(Parray,Pnom,ord)`

,
corresponds to `W1`

= `W`

and `W2`

=
1.

For instance, the following figure shows the relative gap between the nominal response and six LTI responses, enveloped using a second-order shaping filter and a fourth-order filter.

If you use the single-filter syntax `usys = ucover(Parray,Pnom,ord)`

, the
software sets the uncertainty to `W*Delta`

, where `Delta`

is
a `ultidyn`

object that represents unit-gain uncertain dynamics. This ensures
that the amount of uncertainty at each frequency is specified by the magnitude of
`W`

and therefore closely tracks the gap between `Pnom`

and `Parray`

. In the above figure, the fourth-order filter tracks the maximum
gap more closely and therefore yields a less conservative estimate of uncertainty.