Control Systems Flashcards

The centroid of asymptotes in the root locus is given by:

Answer: (Sum of poles - Sum of zeros) / (P - Z)

The centroid σ = (Σpoles - Σzeros) / (P - Z), giving the real-axis intersection of the asymptotes.

For a discrete-time system to be BIBO stable, the poles of its z-transfer function must lie:

Answer: Inside the unit circle

Discrete-time BIBO stability requires all poles of the z-transfer function to be strictly inside the unit circle |z| < 1.

Which of the following conditions is NECESSARY for a system to be minimum-phase?

Answer: All zeros in the left half-plane

A minimum-phase system has all its zeros (and poles for stability) in the left half-plane, giving the minimum possible phase lag.

The Mason's gain formula is used to find:

Answer: Transfer function from a signal flow graph

Mason's gain formula computes the overall transfer function of a signal flow graph using forward paths, loops, and cofactors.

In the time-domain analysis of a second-order system, the settling time (2% criterion) is approximately:

Answer: 4 / (ζωn)

The 2% settling time is approximately ts ≈ 4/(ζωn), derived from the envelope of the exponentially decaying oscillation.

The transfer function representation of a system is LESS general than the state-space representation because:

Answer: Transfer functions assume zero initial conditions

Transfer functions are defined under zero initial conditions, so they only capture the forced response, whereas state-space handles arbitrary initial conditions.

A lead compensator in frequency domain primarily improves:

Answer: Phase margin and transient response

A lead compensator adds positive phase at the gain crossover frequency, increasing phase margin and improving transient (speed and damping) response.