Break-in points occur:

• A. Between two poles
• B. Between two zeros
• C. At the centroid
• D. At the origin

Answer: (B)

Break-in points refer to certain critical points in a control system where the system transitions from one behavior to another, often identified in root locus analysis. These points are significant because they indicate changes in the system's dynamics as various parameters, such as gain, are varied.

The correct understanding of break-in points is that they occur between two zeros in the transfer function of the system. In the context of control systems, zeros are the values of s (complex frequency) that make the numerator of the transfer function equal to zero and are therefore pivotal in determining the nature of the system's response. As the system's performance is analyzed, particularly in root locus approaches, identifying these break-in points is crucial for assessing system stability and performance.

In contrast, choices like the one suggesting break-in points occur at the centroid or the origin do not align with the established definitions within control system theory. These terms refer to other specific criteria in analysis but do not relate directly to the behavior characterized by break-in points.