Control System Principles Flashcards

In a feedback control system, what is the effect of increasing proportional gain Kp on steady-state error for a step input in a Type 0 system?

Answer: Decreases but does not eliminate steady-state error

For a Type 0 system, steady-state error = 1/(1+Kp), so increasing Kp reduces error but it approaches zero only as Kp → ∞.

Which condition must be satisfied for a system to be both controllable and observable?

Answer: The controllability matrix and observability matrix must both have full rank

Controllability requires rank(C) = n and observability requires rank(O) = n, where n is the system order.

If a system's Bode phase plot crosses -180° at 10 rad/s and the magnitude at that frequency is -10 dB, what is the gain margin?

Answer: 10 dB

Gain margin is the negative of the magnitude at the phase crossover frequency: GM = 0 - (-10 dB) = +10 dB.

In discrete-time control systems, what is the z-transform equivalent of an integrator (1/s)?

Answer: z/(z-1)

The bilinear or exact z-domain equivalent of 1/s using the forward Euler method maps to z/(z-1), while Tustin's method gives (z+1)T/[2(z-1)].

What is the percent overshoot for a second-order system with damping ratio ζ = 0.5?

Answer: 16.3%

Percent overshoot = exp(-πζ/√(1-ζ²)) × 100 = exp(-π×0.5/√0.75) × 100 ≈ 16.3%.

A lag compensator is typically used to:

Answer: Increase the low-frequency gain to reduce steady-state error

Lag compensators boost low-frequency gain (improving steady-state accuracy) while minimally affecting phase near crossover.

When applying the final value theorem to find steady-state output, which condition must hold?

Answer: All poles of sY(s) must be in the open left-half plane

The final value theorem lim(t→∞) y(t) = lim(s→0) sY(s) is valid only if all poles of sY(s) are in the open left-half plane (system is stable and converges).