Control Systems Theory Flashcards

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

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

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.

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

Answer: Overall transfer function between a source and sink node

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

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

Answer: Increases

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.

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

Answer: It has the minimum possible phase lag for its magnitude response

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.

The integral windup problem in a PID controller occurs when:

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

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.

Two systems with transfer functions G₁(s) and G₂(s) are connected in cascade (series). The overall transfer function is:

Answer: G₁(s) · G₂(s)

For cascaded (series) blocks, the overall transfer function is the product of individual transfer functions: G(s) = G₁(s)·G₂(s).

The gain crossover frequency of a system is 10 rad/s and the phase of the open-loop transfer function at that frequency is −150°. The phase margin is:

Answer: +30°

Phase margin = 180° + ∠G(jωgc) = 180° + (−150°) = +30°, indicating a stable system with 30° of margin.