Electrical Engineering 2025 Paper II 50 marks Solve

Q4

(a) (i) Consider a second-order type-1 system with no zeros. The system under unity feedback admits a resonant peak of 1·36 at resonant frequency 8·2 rad/s. Compute the transfer function G(s), and its steady-state error due to input signal x(t) = 2u(t) + 3t·u(t) under unity feedback. 10 (ii) For the system shown in the figure below the unit step response is given by $$y(t) = 1 - 1.15 e^{-2t} \sin\left(3.464t + \frac{\pi}{3}\right)$$ Obtain the state-space representation of the system in observable canonical form. 10 (b) (i) For 8085 microprocessor, write a program to do the following : 1. Clear the accumulator 2. Add 47H (using ADI instruction) 3. Subtract 92H 4. Add 64H 5. Display the results after subtracting 92H and after adding 64H Specify the answer you would expect at the output port. Also give the reason for clearing the accumulator before adding the number 47H directly to the accumulator. (ii) Write the instruction to clear the CY flag to load FFH in register B and increment (B). If the CY flag is set, display 1 at the output port; otherwise, display the contents of register B. Explain your result. (c) A quartz piezoelectric transducer having a capacitance of 3000 pF and voltage sensitivity of 0.06 V-m/N has a resistance of 10^7 MΩ. The impedance of the measuring system has a capacitance of 300 pF in parallel with a 1 MΩ resistance. A force as shown in the figure is applied across the transducer : Find the voltages just before and after t = 4 ms. [Permittivity of quartz is 40.6×10^-12 F/m]

हिंदी में प्रश्न पढ़ें

(a) (i) एक द्वितीय क्रम (ऑर्डर) प्रकार-1 (टाइप-1) तंत्र जिसमें कोई शून्य नहीं है, दिया गया है। यह तंत्र इकाई पुनर्निवेश के तहत 8·2 rad/s की अनुनाद आवृत्ति पर अनुनाद शिखर का मान 1·36 देता है। तंत्र के अंतरण फलन G(s) की गणना कीजिये, एवं इकाई पुनर्निवेश के तहत निवेश (इनपुट) सिग्नल x(t) = 2u(t) + 3t·u(t) के लिये इसकी स्थायी-दशा त्रुटि की गणना कीजिये। 10 (ii) नीचे चित्र में दर्शाये गये तंत्र के लिये इकाई पद अनुक्रिया (रेस्पांस) $$y(t) = 1 - 1.15 e^{-2t} \sin\left(3.464t + \frac{\pi}{3}\right)$$ द्वारा दी गई है। तंत्र का अवस्था-समीकरण (स्टेट-स्पेस) निरूपण, प्रेक्षणीय (आब्जर्वेबल) विहित (कैनोनिकल) रूप में प्राप्त कीजिये। 10 (b) (i) 8085 सूक्ष्म-संसाधित्र (माइक्रोप्रोसेसर) में निम्नलिखित कार्य करने के लिये एक प्रोग्राम लिखिये : 1. संचायक (एक्युमुलेटर) को खाली (क्लियर) कीजिये 2. 47H को जोड़िये (ADI निर्देश का उपयोग करते हुए) 3. 92H को घटाइये 4. 64H को जोड़िये 5. 92H को घटाने और 64H को जोड़ने के पश्चात् परिणाम प्रदर्शित कीजिये आप जिस उत्तर की आशा करते हैं उसे निर्गत पोर्ट पर निर्दिष्ट कीजिये। संचायक में सीधे अंक 47H जोड़ने के पहले संचायक को खाली करने का कारण भी बताइये। (ii) CY फ्लैग को खाली (क्लियर) करने और FFH को पंजी (रजिस्टर) B में भरने तथा पंजी B में वृद्धि के लिये निर्देश लिखिये। यदि CY फ्लैग सेट है, तो निर्गत पोर्ट पर 1 प्रदर्शित कीजिये अन्यथा पंजी B की अंतर्वस्तुओं (कांटेंट) को प्रदर्शित कीजिये। अपने परिणाम की व्याख्या कीजिये। (c) एक क्वार्ट्ज दाब-विद्युत (पीजोइलेक्ट्रिक) परिवर्तक (ट्रांसड्यूसर) की संधारिता 3000 pF, वोल्टेज संवेदनशीलता (सुग्राहिता) 0.06 V-m/N तथा प्रतिरोध 10^7 MΩ है। मापन तंत्र (प्रणाली) की प्रतिबाधा में संधारिता 300 pF तथा इसके समानांतर में 1 MΩ का प्रतिरोध संयोजित है। एक बल, जैसा चित्र में दर्शाया गया है, ट्रांसड्यूसर के आर-पार आरोपित किया जाता है : t = 4 ms के तुरंत पहले एवं बाद में वोल्टता ज्ञात कीजिये। [क्वार्ट्ज की पारगम्यता (परमिटिविटी) 40.6×10^-12 F/m है]

Evaluate your answer to this question → See all 2025 Electrical Engineering questions

Directive word: Solve

This question asks you to solve. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Solve all four sub-parts systematically, allocating approximately 35% time to (a)(i) control system analysis with resonant peak and steady-state error calculations, 25% to (a)(ii) state-space derivation from given response, 25% to (b) 8085 assembly programming with proper instruction sequences and flag handling, and 15% to (c) piezoelectric transducer voltage calculations at specific time instants. Present derivations step-by-step with clear final answers for each sub-part.

Key points expected

  • For (a)(i): Derive damping ratio ξ=0.5 from resonant peak Mr=1.36, compute natural frequency ωn=9.43 rad/s, obtain G(s)=ωn²/[s(s+2ξωn)], and calculate steady-state error ess=0.636 for the given input
  • For (a)(ii): Extract poles at -2±j3.464 from the response, determine ωn=4 rad/s and ξ=0.5, construct observable canonical form with appropriate A, B, C matrices
  • For (b)(i): Write correct 8085 program using MVI A,00H; ADI 47H; SUI 92H; OUT PORT1; ADI 64H; OUT PORT2; explain accumulator clearing prevents garbage value accumulation
  • For (b)(ii): Use STC/CMC instructions for CY flag manipulation, demonstrate conditional branching with JC/JNC, show FFH+1=00H with CY=1 causing output 01H at port
  • For (c): Calculate transducer voltage V=0.06×F/Cp, determine time constant τ=RC=3.3ms, compute voltages at t=4ms⁻ and t=4ms⁺ considering charge redistribution between transducer and measuring capacitance

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%2Correctly identifies type-1 system characteristics for (a)(i), recognizes observable canonical form structure for (a)(ii), understands 8085 flag operations and addressing modes for (b), and applies piezoelectric equivalent circuit model with charge conservation for (c)Identifies some correct concepts but confuses system type, canonical forms, or microprocessor flag logic; partial understanding of transducer equivalent circuitFundamental misconceptions about resonant peak formula, state-space forms, 8085 instruction set, or piezoelectric charge-voltage relationship
Numerical accuracy20%2Precise calculations: ξ=0.5, ωn=9.43 rad/s, ess=0.636 for (a)(i); correct matrix elements for (a)(ii); correct hex arithmetic results 0BH and 6FH for (b)(i); voltages ~4.8V and ~4.36V for (c)Correct approach with minor calculation errors in arithmetic, matrix elements, or time constant; correct final answers with wrong intermediate stepsMajor numerical errors, wrong formulas applied, or missing calculations; incorrect hex results or voltage values orders of magnitude wrong
Diagram quality20%2Clear block diagram for unity feedback system in (a), labeled 8085 program flowchart or register diagrams for (b), and accurate equivalent circuit diagram showing transducer capacitance, resistance, and measuring system impedance for (c)Basic diagrams present but missing labels, or rough sketches without proper notation; diagrams support answer but lack clarityMissing essential diagrams, incorrect circuit representations, or no visual aids where required for problem understanding
Step-by-step derivation20%2Systematic derivation: Mr=1/(2ξ√(1-ξ²)) solved for ξ, ωn=ωr/√(1-2ξ²), ess=1/(1+Kp)+1/Kv; clear Laplace transform steps for state-space; commented assembly code; charge conservation equations for transducerSome steps shown but jumps in logic, missing intermediate derivations, or insufficient comments in code; final answers without proper justificationOnly final answers with no working, disorganized presentation, or incorrect logical flow between steps
Practical interpretation20%2Explains why ξ=0.5 gives acceptable overshoot in control systems, discusses accumulator clearing necessity for deterministic initialization in embedded systems, and interprets voltage drop at t=4ms due to charge sharing in piezoelectric measurement systemsBrief mention of practical relevance without elaboration; standard explanations without connecting to real-world implicationsNo practical context provided, purely mathematical treatment without physical interpretation of results

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Electrical Engineering 2025 Paper II