Virtual Labs

a:

\zeta > 0

and

\omega_n > 0

Explanation

b:

\zeta < 0

and

\omega_n > 0

Explanation

c: Only

\omega_n > 0

matters Explanation

Explanation

d: Only

\zeta > 0

matters Explanation

Explanation

a: Only the real part of

(a + ib)

Explanation

b: Only the imaginary part of

(a + ib)

Explanation

c: The magnitude

|a + ib|

must be less than 1 Explanation

Explanation

d: The phase angle of

(a + ib)

Explanation

a: No effect if PID gains are properly tuned Explanation

Explanation

b: Only affects the proportional term Explanation

Explanation

c: Can cause oscillations and impact derivative control significantly Explanation

Explanation

d: Only affects the integral term Explanation

Explanation

a: Proportional term (

K_p

) Explanation

Explanation

b: Integral term (

K_i

) Explanation

Explanation

c: Derivative term (

K_d

) Explanation

Explanation

d: All terms equally Explanation

Explanation

System Stability