Question

Consider a type 2, unity feedback system. The intersection of the initial -40 dB/dec segment of its Bode plot with the zero dB line occurs at a frequency of 2 rad/s. The acceleration error constant of the system \(K_a\) is \(\underline{\hspace{2cm}}\).

Hint:

For type 2 systems, the acceleration error constant is the square of the frequency where the -40 dB/dec slope intersects the zero dB line.

Answer 1

Correct Answer: 4

For a type 2 system, the acceleration error constant \(K_a\) is related to the frequency of intersection: \[ K_a = \omega^2 \] Substitute \( \omega = 2 \): \[ K_a = 2^2 = 4 \] Thus, \[ \boxed{4} \]