Simulink Control Design™ - MathWorks

Here, the software adds a linearization output at y, followed by a linearization input, dy.
The complementary sensitivity function at y, T, is the transfer function from dy to y. T is
calculated as follows:

y=−GK(y+dy)

y=−GKy−GKdy

(I+GK)y=−GKdy

y=−︸(I+GK)−^1 GK

T

dy.

Here I is an identity matrix of the same size as GK. The complementary sensitivity
transfer function at y is equal to -1 times the closed-loop transfer function from r to y.

Generally, the complementary sensitivity function, T, computed from reference signals to
plant outputs, is equal to I–S. Here S is the sensitivity function at the point, and I is the
identity matrix of commensurate size. However, because getCompSensitivity adds the
linearization output and input at the same point, T, as returned by
getCompSensitivity, is equal to S–I.

The software does not modify the Simulink model when it computes the complementary
sensitivity function.

Analysis Point

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-loop or closed-loop transfer
function in a model. You can also use analysis points to specify design requirements when
tuning control systems using commands such as systune.

Location refers to a specific block output port within a model or to a bus element in such
an output port. 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:

s = slLinearizer('scdcascade',{'u1','y1'});

getCompSensitivity