The sensitivity function,
also referred to simply as sensitivity, measures
how sensitive a signal is to an added disturbance. Sensitivity is
a closedloop measure. Feedback reduces the sensitivity in the frequency
band where the openloop gain is greater than 1
.
To compute the sensitivity at an analysis point, x
,
the software injects a disturbance signal, dx
,
at the point. Then, the software computes the transfer function from dx
to x
,
which is equal to the sensitivity function at x
.
Analysis Point in Simulink Model  How getSensitivity Interprets the Analysis Point  Sensitivity Function 

 Transfer function from dx to x 
For example, consider the following model where you compute
the sensitivity function at u
:
Here, the software injects a disturbance signal (du
)
at u
. The sensitivity at u
, S_{u}
,
is the transfer function from du
to u
.
The software calculates S_{u}
as
follows:
$$\begin{array}{l}u=duKGu\\ \to (I+KG)u=du\\ \to u=\underset{{S}_{u}}{\underbrace{{(I+KG)}^{1}}}du.\end{array}$$
Here, I is an identity matrix of the same
size as KG.
Similarly, to compute the sensitivity at y
,
the software injects a disturbance signal (dy
)
at y
. The software computes the sensitivity function
as the transfer function from dy
to y
.
This transfer function is equal to (I+GK)^{1},
where I is an identity matrix of the same size
as GK.
The software does not modify the Simulink model when it
computes the sensitivity transfer function.
Analysis points, used
by the slLinearizer
and slTuner
interfaces,
identify locations within a model that are relevant for linear analysis
and control system tuning. You use analysis points as inputs to the
linearization commands, such as getIOTransfer
, getLoopTransfer
, getSensitivity
, and getCompSensitivity
. As inputs to the
linearization commands, analysis points can specify any open or closedloop
transfer function in a model. You can also use analysis points to
specify design requirements when tuning control systems using commands
such as systune
(requires
a Robust Control Toolbox™ license).
Location refers to a specific block output
port within a model. For convenience, you can use the name of the
signal that originates from this port to refer to an analysis point.
You can add analysis points to an slLinearizer
or slTuner
interface, s
,
when you create the interface. For example:
Alternatively, you can use the addPoint
command.
To view all the analysis points of s
, type s
at
the command prompt to display the interface contents. For each analysis
point of s
, the display includes the block name
and port number and the name of the signal that originates at this
point. You can also use getPoints
to
programmatically obtain a list of all the analysis points.
For more information about how you can use analysis points,
see Marking Signals of Interest for Control System Analysis and
Design.
Permanent openings,
used by the slLinearizer
and slTuner
interfaces,
identify locations within a model where the software breaks the signal
flow. The software enforces these openings for linearization and tuning.
Use permanent openings to isolate a specific model component. Suppose
you have a largescale model capturing aircraft dynamics and you want
to perform linear analysis on the airframe only. You can use permanent
openings to exclude all other components of the model. Another example
is when you have cascaded loops within your model and you want to
analyze a specific loop.
Location refers to a specific block output
port within a model. For convenience, you can use the name of the
signal that originates from this port to refer to an opening.
You can add permanent openings to an slLinearizer
or slTuner
interface, s
,
when you create the interface or by using the addOpening
command. To remove a location
from the list of permanent openings, use the removeOpening
command.
To view all the openings of s
, type s
at
the command prompt to display the interface contents. For each permanent
opening of s
, the display includes the block name
and port number and the name of the signal that originates at this
location. You can also use getOpenings
to
programmatically obtain a list of all the permanent openings.