Control Systems and Dynamics Flashcards
7 cards from real ME or MEng Master of Engineering practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Control Systems and Dynamics flashcards as text
According to the Routh-Hurwitz stability criterion, a system is stable if and only if:
Answer: All elements in the first column of the Routh array are positive
The Routh-Hurwitz criterion requires all entries in the first column of the Routh array to be positive (same sign) for the system to be stable.
Gain margin is best defined as the additional open-loop gain that can be applied before the system becomes:
Answer: Marginally stable or unstable
Gain margin quantifies how much the loop gain can be increased beyond its current value before the closed-loop system reaches the verge of instability.
On a root locus diagram, open-loop poles and zeros are marked by convention as:
Answer: Poles as crosses (X), zeros as circles (O)
By standard convention, poles are denoted by × (crosses) and zeros by ○ (circles) on a root locus plot.
In state-space representation, the standard system matrices are labeled:
Answer: A, B, C, D
State-space equations use A (system/state matrix), B (input matrix), C (output matrix), and D (feedthrough matrix): ẋ = Ax + Bu, y = Cx + Du.
Phase margin is measured at which frequency on a Bode plot?
Answer: The gain crossover frequency where magnitude = 0 dB
Phase margin is the additional phase lag (above −180°) present at the gain crossover frequency, where the open-loop magnitude is exactly 0 dB (unity gain).
A linear system of order n is fully controllable if and only if its controllability matrix has:
Answer: Full row rank equal to n
The controllability matrix C = [B, AB, A²B, …, A^(n−1)B] must have rank n (full row rank) for the system to be completely controllable.
The Nyquist-Shannon sampling theorem requires the sampling frequency fs for a signal with highest frequency fmax to satisfy:
Answer: fs ≥ 2fmax
The theorem states fs ≥ 2fmax to avoid aliasing; this minimum rate (2fmax) is called the Nyquist rate.