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In the specific industry of sensitive control systems, it is essential to ensure that the amplification is appropriately set to maintain stability in the control circuit. This involves considering the average slope or gradient of the sensor. However, it is also crucial to be mindful of any variations that may occur in this slope.

If there are instances where the gradient becomes significantly steeper than the mean gradient, it can result in a higher closed-loop gain in that particular position. This, in turn, can lead to feedback oscillation, which can disrupt the system's stability. On the other hand, if the gradient is less steep than the mean gradient at certain points, it can reduce repeatability and compromise control accuracy.

To address this issue, we can assess the local gradient variation (gl) by comparing it to the mean gradient (go) of the potentiometer. This criterion allows for a direct comparison between different potentiometers, regardless of their length. By considering and managing these factors, the control system can be optimized for optimal performance and accuracy.