BEE Control Systems Theory 4

Question 1

The Final Value Theorem states that lim(t→∞) f(t) = lim(s→0) s·F(s), provided that:

Accepted Answer

All poles of s·F(s) lie in the closed left-half s-plane

Answer

The Final Value Theorem is valid only if all poles of s·F(s) lie in the open left-half plane (stable), ensuring the time-domain limit exists.

Question 2

In signal flow graphs, Mason's gain formula is used to find the:

Accepted Answer

Overall transfer function between a source and sink node

Answer

Mason's gain formula computes the overall transfer function T = Σ(Pk·Δk)/Δ, summing contributions of all forward paths weighted by their cofactors.

Question 3

A plant with transfer function G(s) = 1/(s+1) is controlled with proportional gain K. The closed-loop bandwidth _____ as K increases.

Accepted Answer

Increases

Answer

The closed-loop transfer function is K/[(s+1)+K] = K/(s+1+K), giving a closed-loop pole at −(1+K); bandwidth increases with K.

Question 4

Which of the following is a characteristic of a minimum-phase system?

Accepted Answer

It has the minimum possible phase lag for its magnitude response

Answer

A minimum-phase system has all poles and zeros in the left-half plane and exhibits the least phase lag achievable for a given magnitude response.

Question 5

The integral windup problem in a PID controller occurs when:

Accepted Answer

The integrator accumulates a large error when the actuator saturates, causing overshoot upon recovery

Answer

Integral windup happens when actuator saturation prevents error correction, allowing the integral term to grow large and produce significant overshoot when the actuator comes out of saturation.

BEE - Bachelor of Electrical Engineering Practice Test

BEE - Bachelor of Electrical Engineering Practice Test

BEE Control Systems Theory 4