For a control system having fourteen poles and two zeros, the slope in its magnitude plot for high frequency asymptote will be :

Explanation:

To determine the slope in the magnitude plot for the high frequency asymptote of a control system, we need to understand the relationship between the number of poles and zeros in the system.

In control systems, the Bode plot is a graphical representation of a system's frequency response. The slope of the magnitude plot in the high frequency region is influenced by the number of poles and zeros. Specifically, each pole contributes a slope of -20 dB/decade, and each zero contributes a slope of +20 dB/decade.

Given:

• Number of poles ( $P$ ) = 14
• Number of zeros ( $Z$ ) = 2

The formula to determine the overall slope in the high frequency asymptote is:

Slope (dB/decade) = -20 × (Number of poles - Number of zeros)

Substituting the given values:

Slope (dB/decade) = -20 × (14 - 2)

Slope (dB/decade) = -20 × 12

Slope (dB/decade) = -240 dB/decade

Therefore, the correct option is:

Option 2: -240 dB/decade