(a) The block diagram of a position control system is shown in the figure. Determine the sensitivity of the closed loop transfer function T(s) with respect to G(s) and H(s) for 1 rad/sec. 10 marks

(b) The disc in a single-phase energy meter rotates

Question

(a) The block diagram of a position control system is shown in the figure. Determine the sensitivity of the closed loop transfer function T(s) with respect to G(s) and H(s) for 1 rad/sec. 10 marks

(b) The disc in a single-phase energy meter rotates 1320 times when monitoring a 110 V, 3 A load at unity power factor over a period of 8 hours. Calculate the meter constant. If the meter makes 750 revolutions when measuring the energy supplied to a 110 V, 5 A load for 3 hours, determine the load power factor. 5+5=10 marks

(c) Write the bus admittance matrix for the network shown in the figure. 10 marks

(d) A single core cable without grading operates at 14 kV. The conductor radius is 1·12 cm and insulation radius is 2·75 cm. If cable is with inter-sheath grading at suitable radius, then calculate the maximum operating voltage of the cable. 10 marks

(e) How does information get passed from one layer to the next in the Internet model? How do the layers of the Internet model correlate to the layers of the OSI model? 6+4=10 marks

UPSC Answer Check · Accepted Answer

This is a solve-type question requiring systematic treatment of five distinct technical problems. Allocate approximately 25-30% time to part (a) due to its analytical complexity involving sensitivity functions; 20% each to parts (b) and (d) for their numerical calculations; 15% to part (c) for matrix construction; and 15% to part (e) for conceptual explanation. Begin each sub-part with the relevant governing equation, show complete working, and conclude with the final numerical answer or clear conceptual summary.
- Part (a): Derive sensitivity S_G^T = 1/(1+GH) and S_H^T = -GH/(1+GH), then evaluate at ω=1 rad/sec with proper substitution of G(jω) and H(jω) from the block diagram
- Part (b): Calculate meter constant K = 1320/(110×3×8×1) = 0.5 rev/kWh, then use 750 = K×110×5×3×cosφ to find power factor cosφ = 0.909 lagging
- Part (c): Construct Y_bus by inspection method: diagonal elements Y_ii = sum of admittances connected to bus i, off-diagonal Y_ij = -y_ij, showing the n×n symmetric matrix
- Part (d): Calculate ungraded cable stress ratio, determine optimal inter-sheath radius r1 = √(r×R) = 1.756 cm, then find new maximum voltage V_max = E_max×r×ln(r1/r) + E_max×r1×ln(R/r1) ≈ 19.8 kV
- Part (e): Explain encapsulation/decapsulation with headers added/removed at each layer; map Internet model (Application, Transport, Internet, Network Access) to OSI layers 5-7, 4, 3, and 1-2 respectively

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly applies sensitivity definition S = (∂T/T)/(∂G/G) for (a); understands energy meter theory including creeping and friction compensation for (b); applies proper Y_bus formation rules for (c); uses inter-sheath grading potential distribution for (d); accurately describes TCP/IP encapsulation and OSI correlation for (e)	Minor errors in sensitivity formula or partial understanding of grading; correct meter constant but wrong power factor calculation; Y_bus with sign errors or missing elements; vague OSI mapping	Confuses open-loop and closed-loop sensitivity; fundamental misunderstanding of energy meter operation; incorrect Y_bus construction method; no concept of grading or layer encapsulation
Numerical accuracy	20%	10	All calculations precise: sensitivity values at 1 rad/sec correct to 3 decimal places; meter constant 0.5 rev/kWh and power factor 0.909; Y_bus numerical values match network; inter-sheath voltage ≥19 kV with proper intermediate steps	Correct method but arithmetic errors in 1-2 parts; wrong unit conversions (hours to seconds); approximate values without proper rounding	Major calculation errors in multiple parts; incorrect formula substitution; order-of-magnitude errors; missing units throughout
Diagram quality	20%	10	Reproduces block diagram for (a) with clear G(s), H(s), summing point; sketches network topology for (c) showing all buses, lines with impedances; draws cable cross-section for (d) showing conductor, inter-sheath, outer insulation with radii labeled; clear layer diagrams for (e)	Diagrams present but missing labels or unclear signal flow; network diagram without proper bus numbering; cable diagram without radii marked	No diagrams despite figure references; completely wrong block diagram; missing network topology; no visual representation for layer models
Step-by-step derivation	20%	10	Shows T(s) = G/(1+GH) derivation before sensitivity; explicit partial differentiation steps; clear energy calculation E = VItcosφ progression; systematic Y_bus building from element admittances; graded cable potential equations derived from equal stress criterion	Jumps from formula to answer without intermediate steps; missing sensitivity derivation; direct substitution without showing equation rearrangement	No derivations, only final answers; incorrect starting equations; logical gaps between steps; no justification for inter-sheath radius selection
Practical interpretation	20%	10	Interprets sensitivity results for controller design robustness; discusses meter accuracy class and load power factor significance; explains Y_bus application in load flow studies for Indian power grids; justifies grading for EHV cables used in NTPC/State utilities; relates TCP/IP to modern internet infrastructure	Brief mention of practical relevance without elaboration; generic statements about 'useful in industry'	No practical context; purely mathematical treatment; no connection to real-world electrical engineering applications or Indian power sector relevance

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