Control Systems Flashcards

The steady-state error of a Type-1 system to a unit ramp input is:

Answer: 1/Kv

For a Type-1 system, the velocity error constant Kv is finite, so the steady-state error to a ramp is 1/Kv.

Which of the following is the correct expression for the Gain Margin (GM) of a system?

Answer: GM = -20 log|G(jω_pc)H(jω_pc)|

Gain margin in dB is -20 log|G(jω)H(jω)| evaluated at the phase crossover frequency where the phase is -180°.

For a second-order underdamped system, the peak overshoot depends on:

Answer: Damping ratio only

Peak overshoot Mp = exp(-πζ/√(1-ζ²)) × 100%, which is a function of the damping ratio ζ only.

A system has poles at s = -1 ± j2 and a zero at s = -3. The damped natural frequency is:

Answer: 2 rad/s

The damped natural frequency ωd is the imaginary part of the complex poles, which equals 2 rad/s.

In a Bode plot, a pure integrator (1/s) contributes a slope of:

Answer: -20 dB/decade and -90° phase

A pure integrator 1/s has a gain of -20 dB/decade and a constant phase of -90° across all frequencies.

The number of asymptotes in the root locus of a system with 4 poles and 1 zero is:

Answer: 3

The number of asymptotes equals P - Z = 4 - 1 = 3, where P is the number of poles and Z is the number of zeros.

The transfer function of an ideal proportional-integral (PI) controller is:

Answer: Kp(1 + 1/(Tis))

A PI controller adds an integrator to eliminate steady-state error, with transfer function Kp(1 + 1/(Ti·s)).