Simulink Control Design™ - MathWorks

You can calculate the transfer function from the reference input signal to the plant output
signal. The reference input (also referred to as setpoint), r, originates at the Reference
block, and the plant output, y, originates at the G block. This transfer function is also
called the overall closed-loop transfer function. To calculate this transfer function, the
software adds a linearization input at r, dr, and a linearization output at y.

K G

e u

y

dr

+

r

The software calculates the overall closed-loop transfer function as the transfer function
from dr to y, which is equal to (I+GK)-1GK.

Observe that the transfer function from r to y is equal to the transfer function from dr to
y.

You can calculate the plant transfer function from the plant input, u, to the plant output,
y. To isolate the plant dynamics from the effects of the feedback loop, introduce a loop
break (or opening) at y, e, or, as shown, at u.

K G

r e u

y

du

The software breaks the loop and adds a linearization input, du, at u, and a linearization
output at y. The plant transfer function is equal to the transfer function from du to y,
which is G.

Similarly, to obtain the controller transfer function, calculate the transfer function from
the controller input, e, to the controller output, u. Break the feedback loop at y, e, or u.

getIOTransfer