Simulink Control Design™ - MathWorks

Analysis Point Description

Complementary

sensitivity

function

Specifies an output measurement followed by an input perturbation.

The complementary sensitivity function at a point is the transfer

function from an additive disturbance at the point to a measurement at

the same point. In contrast to the sensitivity function, the disturbance

is added after the measurement. Use this analysis point to compute the

closed-loop transfer function around the loop.

For example, to compute the closed-loop transfer function for the

example system, add a complementary sensitivity function analysis

point as shown. The software adds an output measurement u followed

by and input perturbation du. The closed-loop transfer function from

du to u is -KG/(1+KG).

K G

r e y

du

u

Opening Feedback Loops

If your model contains one or more feedback loops, you can choose to linearize an open-
loop or a closed-loop system.

To remove the effects of a feedback loop, using analysis points lets you insert a loop
opening without manually breaking the signal line. Manually removing the feedback
signal from a nonlinear model changes the model operating point and produces a
different linearized model. For more information, see “How the Software Treats Loop
Openings” on page 2-44.

Proper placement of the loop opening is important for obtaining the linear model that you
want. To understand the difference between open-loop and closed-loop analysis, consider
the following single-loop control system.

Specify Portion of Model to Linearize