LECTURE ROOM/16 — LOOP TRADEOFFS
CHAPTER 16 / LOOP TRADEOFFS

Tracking, disturbance and sensitivity

A target, a load and sensor noise do not enter the feedback loop at the same place.

01 / THE INTUITION

First, picture it

A motor can follow a new speed quickly but still dip when a load arrives. Looking only at the target-step plot hides the second task. Write down where each signal enters before deciding which curve matters.

02 / THE IDEA

What the model says

For a linear unity-feedback loop L=CG, S=1/(1+L) and T=L/(1+L). Reference tracking uses T; a plant-output disturbance is shaped by S, while an input torque disturbance follows the plant and controller's injection path. Measurement noise can pass through T into output. At each frequency S+T=1, so making one small everywhere is impossible. The motor load is an input torque, not an output disturbance; never substitute one transfer path for the other. Saturation breaks the linear relations during a limited run.

RELATIONL=CG, S=1/(1+L), T=L/(1+L), S+T=1

These are linear loop functions; a disturbance's exact transfer also depends on where it enters.

03 / IN PRACTICE

Make it concrete

Pin the unloaded target response, then add a step load at 4 s without changing the controller. Compare speed error and applied voltage. Repeat with I enabled, checking for saturation.

Compare tracking and load rejection
BE CAREFUL

A good target response is not proof of disturbance rejection or noise tolerance; test all three with the same stated model and constraints.

Check your understanding+

Why can a target-step test miss a load-rejection problem?

The reference and input-load disturbance enter at different points and follow different transfer paths.