To achieve stable tuning, the controller gain at the critical frequency should be set to what value relative to 1?

• A. Greater than 1
• B. Equal to 1
• C. Less than 1
• D. Undefined

Answer: (C)

Stability hinges on the loop gain magnitude at the frequency where the phase lag hits -180 degrees. At that point the feedback effectively becomes positive, and if the loop gain is 1 or greater, the system can meet the Barkhausen criterion and become unstable or oscillate. Keeping the controller gain at that critical frequency below 1 ensures the loop gain is less than unity there, providing a safety margin and promoting stable operation. If the gain were equal to 1, you’d be at the stability boundary and anything could push you into instability; greater than 1 increases that risk.