Electrical Engineering 2021 Paper II 50 marks Compulsory Solve

Q1

(a) A system is described by the following state equations : $$\dot{x}_1 = x_1 + x_2 + 3x_3$$ $$\dot{x}_2 = 2x_1 + 3x_2 + u_1$$ $$\dot{x}_3 = 2x_2 + x_3 + u_2$$ Check the controllability of the system. (10 marks) (b) A single phase, single line diagram of a power system is shown in figure. Find the sending end voltage and the value of load resistance in p.u. referred to sending end if the voltage across load resistance is 9·8 KV. (10 marks) (c) Explain the following related to computer programming : (i) Machine Language (ii) Assembly Language (iii) Compiler (iv) Interpreter (v) ASCII (10 marks) (d) A current of (0·5 + 0·3 sinωt – 0·2 sin 2ωt) amps is passed through the circuit shown in figure. Determine the reading of each instrument if ω = 10⁶ rad/sec. (10 marks) (e) A DPCM system uses a linear predictor with a single tap. The normalized autocorrelation function of the input signal for a lag of one sampling interval is 0·75. The predictor is designed to minimize the prediction error variance. Determine the processing gain attained by the use of this predictor. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक तंत्र को निम्नलिखित अवस्था समीकरणों द्वारा वर्णित किया गया है : $$\dot{x}_1 = x_1 + x_2 + 3x_3$$ $$\dot{x}_2 = 2x_1 + 3x_2 + u_1$$ $$\dot{x}_3 = 2x_2 + x_3 + u_2$$ तंत्र की नियंत्रणीयता की जाँच करें । (10 अंक) (b) एक एकल कला विद्युत शक्ति प्रणाली को एकल रेखीय आरेख द्वारा चित्र में दर्शाया गया है । यदि भार प्रतिरोध पर वोल्टता 9·8 KV हो तो प्रेषण सिरे की वोल्टता व प्रेषण सिरे के संदर्भ में भार प्रतिरोध का मान प्रति इकाई में ज्ञात करें । (10 अंक) (c) अभिकलित्र प्रक्रमण के संदर्भ में निम्नलिखित की व्याख्या करें : (i) मशीन भाषा (ii) समन्वयोजन (असेंबली) भाषा (iii) संकलक (कम्पाइलर) (iv) भाषांतरक (v) ASCII (10 अंक) (d) चित्र में दर्शाये गये परिपथ में (0·5 + 0·3 sinωt – 0·2 sin 2ωt) Amp विद्युत धारा का प्रवाह हो रहा है । यदि ω = 10⁶ rad/sec हो तो प्रत्येक मापन के पठन (रीडिंग) का निर्धारण करें । (10 अंक) (e) एक DPCM तंत्र एक रैखिक प्राक्सूचक को एकल टैप के साथ प्रयोग करता है । एक प्रतिचयन अंतराल पश्चता के लिए सामान्यीकृत स्वतः सह संबंध फलन के निवेश का मान 0·75 है । प्राक्सूचक को, पूर्वानुमान त्रुटि के प्रसरण को निम्नतम करने के लिए अभिकल्प किया गया है । इस प्राक्सूचक के प्रयोग करने से प्राप्त संसाधन लब्धि का निर्धारण करें । (10 अंक)

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How this answer will be evaluated

Approach

This is a multi-part technical question requiring precise problem-solving across five distinct domains: control systems, power systems, computer programming, measurements, and communication systems. Allocate approximately 20% time each to parts (a), (b), (d), and (e) which involve numerical calculations, and 20% to part (c) which is descriptive. Begin each part with the relevant governing equations, show systematic derivations, and conclude with boxed final answers for numerical parts.

Key points expected

  • Part (a): Form correct A and B matrices from state equations, construct controllability matrix Qc = [B AB A²B], compute rank and conclude controllability status
  • Part (b): Draw equivalent circuit with sending end, line impedance and load; apply KVL/KCL to find sending end voltage and load resistance in p.u. given load voltage of 9.8 kV
  • Part (c): Define machine language (binary, processor-specific), assembly language (mnemonic-based, one-to-one with machine code), compiler (full translation to object code), interpreter (line-by-line execution), and ASCII (7-bit character encoding standard)
  • Part (d): Analyze circuit with given current components; calculate instrument readings considering frequency response at ω = 10⁶ rad/sec (ammeter reads RMS, voltmeter responds to specific frequency component)
  • Part (e): Apply linear prediction theory with single tap; use normalized autocorrelation R(1) = 0.75 to find optimal predictor coefficient, then compute prediction gain as ratio of input variance to prediction error variance

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies controllability condition (rank test) for (a); applies per-unit system and transmission line model for (b); accurately distinguishes all five programming concepts in (c); uses proper instrument response theory for (d); applies Wiener-Hopf equation for optimal prediction in (e)Minor errors in one or two parts such as wrong controllability test, confused compiler/interpreter distinction, or incorrect prediction coefficient formulaFundamental conceptual errors like using observability instead of controllability, treating all programming levels as identical, or completely wrong prediction theory application
Numerical accuracy20%10Precise calculations: correct rank determination for (a); accurate sending end voltage and p.u. resistance for (b); correct instrument readings considering frequency-dependent impedance for (d); exact processing gain of 2.29 dB or 1.78 in linear scale for (e)Correct method but arithmetic errors leading to slightly wrong final values, or unit conversion mistakes in p.u. calculationsMajor calculation errors, wrong order of magnitude, or missing numerical answers entirely for computational parts
Diagram quality15%7.5Clear circuit diagram for (b) showing source, line impedance (R+jX), and load with voltage markings; properly labeled block diagram for DPCM encoder in (e) showing quantizer, predictor, and feedback loopRough sketches without proper labeling or missing one diagram where requiredNo diagrams where essential, or completely incorrect circuit representations
Step-by-step derivation25%12.5Systematic derivations: explicit A, B matrices and Qc construction for (a); clear KVL application with impedance calculation for (b); logical progression from low-level to high-level languages in (c); component-wise current analysis for (d); complete Wiener-Hopf solution with variance derivation for (e)Some steps skipped or condensed excessively, making verification difficult; missing intermediate resultsNo derivations shown, only final answers stated, or logically disconnected steps without justification
Practical interpretation20%10Interprets controllability result for controller design implications; discusses practical significance of p.u. system in Indian grid operations; relates programming concepts to modern software development workflow; explains why different instruments respond differently to harmonic content; connects prediction gain to bit rate reduction in speech coding (e.g., Indian telecom standards)Brief mention of practical relevance without elaboration, or generic statements not tied to specific contextNo practical interpretation provided, or completely irrelevant applications cited

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