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UPSC ESE E&T Control Systems Flashcards
51 question-and-answer cards covering Control Systems as it is examined in UPSC ESE E&T. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Control Systems deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the formula for the centroid of root locus asymptotes?
σ = (Σ poles − Σ zeros) / (P − Z), located on the real axis.
What is the rule for which segments of the real axis are part of the root locus?
A real-axis point lies on the root locus if the total number of real poles and zeros to its right is odd.
What are the angle and magnitude conditions for a point to be on the root locus?
Angle condition: ∠G(s)H(s) = ±180°(2q+1). Magnitude condition: |G(s)H(s)| = 1, used to find the gain K at that point.
What is a Bode plot?
A pair of plots versus frequency (log scale): magnitude in decibels (20·log10|G(jω)|) and phase in degrees, used for frequency-response analysis.
What is the slope contribution of a simple pole and a simple zero on a Bode magnitude plot?
A simple pole contributes −20 dB/decade; a simple zero contributes +20 dB/decade (beyond their corner frequencies).
Define gain margin from a Bode plot.
Gain margin = the amount (in dB) by which the magnitude is below 0 dB at the phase crossover frequency (where phase = −180°). GM = −20log10|G(jω)| at that frequency.
Define phase margin from a Bode plot.
Phase margin = 180° + ∠G(jω) measured at the gain crossover frequency (where |G(jω)| = 1, i.e., 0 dB).
What is the gain crossover frequency and the phase crossover frequency?
Gain crossover frequency: where magnitude = 0 dB (|G|=1). Phase crossover frequency: where phase = −180°.
For stability via Bode plots, what must be true of gain margin and phase margin?
For a stable system both the gain margin and phase margin must be positive.
On a Bode magnitude plot, what is the slope at low frequency for a Type-N system?
The initial slope is −20N dB/decade, where N is the system type (number of poles at the origin).
What does the Nyquist plot represent?
A polar plot of the open-loop frequency response G(jω)H(jω) as ω varies from −∞ to +∞, in the complex plane.
State the Nyquist stability criterion.
N = P − Z, where N = number of clockwise encirclements of the point (−1+j0) by the G(jω)H(jω) plot, P = open-loop poles in the right-half plane, and Z = closed-loop poles in the right-half plane. For stability Z = 0.
In the Nyquist criterion, what is the critical point?
The point (−1 + j0) in the complex plane; encirclements of this point determine closed-loop stability.
For an open-loop stable system (P = 0), what does the Nyquist criterion require for closed-loop stability?
The Nyquist plot must not encircle the (−1+j0) point (N = 0).
What is the state-space (state-variable) representation of an LTI system?
ẋ = Ax + Bu (state equation) and y = Cx + Du (output equation), where x is the state vector, u input, y output, and A,B,C,D constant matrices.
In state-space, what do matrices A, B, C, and D represent?
A = system (state) matrix, B = input matrix, C = output matrix, D = direct (feedforward) transmission matrix.
How do you obtain the transfer function from a state-space model?
G(s) = C(sI − A)^(-1) B + D.
How are the eigenvalues of the system matrix A related to system poles?
The eigenvalues of A (roots of det(sI − A) = 0) are the poles of the system; they determine stability.
What is the state transition matrix φ(t)?
φ(t) = e^(At), the matrix that maps the initial state to the state at time t for the unforced system: x(t) = φ(t)x(0).
How can the state transition matrix be computed using Laplace transforms?
φ(t) = L^(-1){ (sI − A)^(-1) }.
State two key properties of the state transition matrix φ(t).
φ(0) = I (identity); φ(t1+t2) = φ(t1)φ(t2); and φ^(-1)(t) = φ(−t).
State the condition for complete controllability of an LTI system.
The controllability matrix Qc = [B AB A²B ... A^(n−1)B] must have full rank n (be nonsingular for single-input systems).
State the condition for complete observability of an LTI system.
The observability matrix Qo = [C; CA; CA²; ...; CA^(n−1)] must have full rank n.
What is the difference between controllability and observability?
Controllability concerns whether the input can drive the state to any desired value in finite time; observability concerns whether the state can be determined from the output over finite time. They are dual properties.
What this deck covers
The Control Systems deck follows the UPSC ESE E&T Control Systems syllabus — 3 chapters and 10 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 17.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 108 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Control Systems flashcards FAQ
How many Control Systems flashcards are in this UPSC ESE E&T deck?
51 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these UPSC ESE E&T flashcards free?
Yes. The preview here is free to read with no signup, and the full 51-card deck is free inside the Examius app.
What do the Control Systems cards cover?
They follow the UPSC ESE E&T Control Systems syllabus — 3 chapters and 10 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.