BMS

BMS – Verified PYQ Authority Guide

BMS is an exam authority hub based on SRO’s verified mapped PYQs. It helps students see the papers/years and technical areas represented in the current corpus and move directly into solved exam questions. Every factual learning cue below is drawn from the existing verified, published and approved English PYQ corpus or from its Knowledge Graph relationships; the hub does not invent unsupported technical claims.

PYQ evidence snapshot

196 verified PYQs are currently mapped to this Exam hub. The represented years include 2024. Exam coverage currently includes BMS. Subject context includes Electrical Engineering. These values come from live mappings and can expand automatically when new verified PYQs are added.

Most useful verified PYQs to solve first

Start with the actual questions rather than memorising a generic note. The links below are ranked from the mapped corpus using repeat history and editorial quality, while the complete explanation stays on the individual question page.

1. Given the Laplace transform of a signal as Y(s) = 6e−2s/(s + 4), what will be the initial value in time domain y(0)?
   BMS · 2024 · Initial Value of a Time-Delayed Signal
   The factor e−2s is a 2 s transport delay. Therefore y(t)=6e−4(t−2)u(t−2), which is zero for t<2 s. Hence y(0)=0.
2. If the gain of an open-loop system is doubled, then the gain margin
   BMS · 2024 · Effect of Open-Loop Gain Scaling on Gain Margin
   Linear gain margin is the reciprocal of the open-loop magnitude at the phase-crossover frequency: GM = 1/|L(jωpc)|. Doubling the loop gain doubles that magnitude,…
3. A certain system has a state space model as[Ẋ1 ; Ẋ2] = [−2 −3 ; 4 2][X1 ; X2] + [3 ; 5]UY = [1 1][X1 ; X2], D = 0What will…
   BMS · 2024 · Transfer Function from State-Space Model
   Use G(s)=C(sI−A)−1B+D. Here det(sI−A)=s2+8. Multiplying C·adj(sI−A)·B gives 8s+1; therefore G(s)=(8s+1)/(s2+8).
4. Read the following statements:Statement 1: A system is said to be completely controllable if it is possible to transfer the system state from an initial state X(t0) to any desired state X(t)…
   BMS · 2024 · Complete Controllability and Observability
   Statement 1 gives the standard meaning of complete controllability: the input can drive the state to any desired state in finite time. Statement 2…
5. Read the following statements in the context of a PI controller used to control a first order LTI system.Statement 1: The order of overall closed loop system becomes higher than the open…
   BMS · 2024 · PI Controller Effect on Order and Damping
   A PI controller introduces an integrator 1/s, so a first-order plant normally produces a second-order closed-loop characteristic equation: Statement 1 is true. For a…
6. Read the following statements in the context of negative feedback system.Statement 1: Negative feedback always makes the overall system response stable.Statement 2: Negative feedback system may improve the system’s robustness towards parametric…
   BMS · 2024 · Negative Feedback Stability and Robustness
   Statement 1 is false because negative feedback does not always guarantee stable closed-loop poles. Statement 2 is true because negative feedback can reduce parameter…
7. Which of the following condition should be satisfied for ensuring stability of an LTI system?
   BMS · 2024 · Positive Gain Margin and Phase Margin
   In the standard negative-feedback frequency-response stability test used in this question, both margins must be positive: GM > 0 dB and PM > 0°.…
8. An LTI system has a unit step response y(t) = (2 − e−t)u(t). What is the transfer function of this system?
   BMS · 2024 · Transfer Function from Unit-Step Response
   For a unit-step input, U(s) = 1/s and G(s) = Y(s)/U(s) = sY(s). Transforming the given response gives Y(s) = (s + 2)/[s(s +…

Formula & key-relationship bank from verified solutions

• ℒ−1{6/(s + 4)} = 6e−4tu(t)e−asF(s) ↔ f(t − a)u(t − a)y(t) = 6e−4(t−2)u(t − 2)y(0) = 0
• GM = 1/|L(jωpc)|Lnew(s) = 2Lold(s)GMnew = GMold/220log10(2) = 6.02 dB
• G(s) = C(sI − A)−1B + DsI − A = [s + 2 3 ; −4 s − 2]det(sI − A) = (s + 2)(s − 2) − 3(−4) =…
• 𝒞 = [ B AB A²B … An−1B ]Complete controllability: rank(𝒞) = n𝒪 = [ C ; CA ; CA² ; … ; CAn−1 ]Complete observability: rank(𝒪) = n
• C(s) = Kp + Ki/s = (Kps + Ki)/sG(s) = K/(τs + 1)Characteristic equation: τs² + (1 + KKp)s + KKi = 0ζ = (1 + KKp)/(2√(τKKi))
• T(s) = G(s)/[1 + G(s)H(s)]Characteristic equation: 1 + G(s)H(s) = 0Sensitivity: S = 1/[1 + G(s)H(s)]

Use these as revision triggers and open the linked PYQ before applying a formula numerically; variable definitions and assumptions belong to the exact solved question.

Core ideas repeatedly reinforced by the solved corpus

• The factor e−2s is a 2 s transport delay. Therefore y(t)=6e−4(t−2)u(t−2), which is zero for t<2 s. Hence y(0)=0.
• Linear gain margin is the reciprocal of the open-loop magnitude at the phase-crossover frequency: GM = 1/|L(jωpc)|. Doubling the loop gain doubles that magnitude, so GMnew = GMold/2. Thus it decreases by a factor of 2.
• Use G(s)=C(sI−A)−1B+D. Here det(sI−A)=s2+8. Multiplying C·adj(sI−A)·B gives 8s+1; therefore G(s)=(8s+1)/(s2+8).
• Statement 1 gives the standard meaning of complete controllability: the input can drive the state to any desired state in finite time. Statement 2 gives the observability idea: the initial state can be reconstructed from output measurements. For…
• A PI controller introduces an integrator 1/s, so a first-order plant normally produces a second-order closed-loop characteristic equation: Statement 1 is true. For a standard plant K/(τs+1) with fixed Kp, ζ = (1 + KKp)/(2√(τKKi)); increasing Ki reduces…

Exam tips already validated in SRO solutions

• e⁻ᵃˢ means a-second delay; a causal delayed signal is zero for 0 ≤ t < a.
• Gain ×2 shifts the Bode magnitude up by 6.02 dB and reduces gain margin by the same 6.02 dB.
• For a 2×2 realization, write sI−A and its determinant explicitly before any multiplication.
• Input → state = controllability; state → output = observability.
• PI adds an integrator. For a first-order plant, expect a second-order characteristic equation unless cancellation is explicitly present.

Common mistakes to avoid

• Ignoring the delay factor e⁻²ˢ and directly taking the undelayed initial value 6.
• Assuming loop gain and gain margin are directly proportional. Gain margin is the remaining reserve, so it changes inversely.
• Writing sI + A instead of sI − A, or changing the off-diagonal signs incorrectly while forming the adjugate.
• Interchanging the matrix tests: B generates the controllability matrix, while C generates the observability matrix.
• Assuming that increasing integral gain automatically improves damping because it improves steady-state accuracy.

Topic and concept coverage

Mapped topic labels include HVDC Transmission, AC Circuits, Frequency Response, Induction Motors, Power Semiconductor Devices, Transformers, DC Motors. The concept trail includes Characteristic Harmonics, 30° Phase Shift, 8051 Machine Cycle, Alternator Synchronizing Conditions, Angular Displacement Sensor, Angular Region in a Plane, Armature Current vs Field Current, Assembler Directives. Use these labels as a revision map: move from the broad area to the narrow concept, solve a verified PYQ, inspect the detailed reasoning, and then attempt another question from the same cluster.

Knowledge Graph navigation

Continue with Not stated in supplied question paper, Technical Examination, Electrical Engineering, Power Systems, Control Systems, Digital Electronics, Electrical Machines, Electrical Engineering. These are canonical SRO entity links based on the Knowledge Graph and shared question mappings, not keyword-stuffed tag pages.

How to revise this authority page efficiently

1. Solve before reading: answer a mapped PYQ first.
2. Read the exact explanation: verify the correct principle, formula, distractor logic and common mistake on that question page.
3. Move one level in the graph: use the closest concept/sub-topic/topic link rather than opening unrelated content.
4. Reattempt: solve another verified PYQ from this hub and check whether the same error repeats.

Quality scope: this page is automatically maintained from SRO’s verified mapped corpus. It enriches one canonical authority URL instead of generating multiple near-duplicate pages for keyword variants. Manual authority articles are never overwritten by the automated engine.