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

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.

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.