Main Content

Compute linear response characteristics

`lsiminfo`

lets you compute linear response characteristics
from an array of response data `[y,t]`

. For a linear response
*y*(*t*), `lsiminfo`

computes
characteristics relative to *y _{init}* and

`lsiminfo`

uses *y _{init}* = 0 and

The function returns the characteristics in a structure containing the fields:

`TransientTime`

— The first time*T*such that the error |*y*(*t*) –*y*| ≤_{final}*SettlingTimeThreshold*×*e*for_{max}*t*≥*T*, where*e*is the maximum error |_{max}*y*(*t*) –*y*| for_{final}*t*≥ 0.By default,

*SettlingTimeThreshold*= 0.02 (2% of the peak error). Transient time measures how quickly the transient dynamics die off.`SettlingTime`

— The first time*T*such that |*y*(*t*) –*y*| ≤_{final}*SettlingTimeThreshold*× |*y*–_{final}*y*| for_{init}*t*≥*T*.By default, settling time measures the time it takes for the error to stay below 2% of |

*y*–_{final}*y*|._{init}`Min`

— Minimum value of*y*(*t*).`MinTime`

— Time the response takes to reach the minimum value.`Max`

— Maximum value of*y*(*t*).`MaxTime`

— Time the response takes to reach the maximum value.

computes linear response characteristics from an array of response data
`S`

= lsiminfo(`y`

,`t`

)`y`

and corresponding time vector `t`

. This syntax
uses *y _{init}* = 0 and the last value in

`y`

(or the last value in each channel's corresponding response data)
as For SISO system responses, `y`

is a vector with the same number of
entries as `t`

. For MIMO response data, `y`

is an
array containing the responses of each I/O channel.

computes linear response characteristics relative to the steady-state value
`S`

= lsiminfo(`y`

,`t`

,`yfinal`

)`yfinal`

. This syntax is useful when you know that the expected
steady-state system response differs from the last value in y for reasons such as
measurement noise. This syntax uses *y _{init}* =
0.

For SISO responses, `t`

and `y`

are vectors with the
same length `NS`

. For systems with `NY`

outputs, you can
specify `y`

as an `NS`

-by-`NY`

array
and `yfinal`

as an `NY`

-by-`1`

array.
`lsiminfo`

then returns a `NY`

-by-`1`

structure array `S`

of response characteristics corresponding to each
output channel.

computes response characteristics relative to the response initial value
`S`

= lsiminfo(`y`

,`t`

,`yfinal`

,`yinit`

)`yinit`

. This syntax is useful when your `y`

data
has an initial offset, that is, `y`

is nonzero before the input is
applied.

For SISO responses, `t`

and `y`

are vectors with the
same length `NS`

. For systems with `NY`

outputs, you can
specify `y`

as an `NS`

-by-`NY`

array
and `yfinal`

and `yinit`

as an
`NY`

-by-`1`

arrays. `lsiminfo`

then
returns a `NY`

-by-`1`

structure array
`S`

of response characteristics corresponding to each output
channel.

`S = lsiminfo(___,'SettlingTimeThreshold',`

lets you specify the threshold `ST`

)`ST`

used in definition of settling and
transient times. The default value is `ST = 0.02`

(2%). You can use this
syntax with any of the previous input-argument combinations.