Actuator Limits Break the Ideal Loop - Electronic Circuits IX: Feedback Control and Stability Margins Step by Step

Rails and actuator limits are separate checked contracts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The upper rail clips the command

A 7 volt command cannot exceed the 5 volt upper rail, so the actual output is 5 volts.

\min(7,5)=5\ \text{V}

The lower rail is checked too

A command of negative 2 volts clips at the 0 volt lower rail.

\max(-2,0)=0\ \text{V}