(a) An LTI system with the following state-space representation is given :
ẋ = [0 1] x + [0] u
[0 -0.5] [k]
y = [1 0] x
Design a phase lead compensator so that the system achieves a settling time of 2 seconds for a 2% tolerance band and has

Question

(a) An LTI system with the following state-space representation is given :
ẋ = [0  1] x + [0] u
    [0 -0.5]     [k]
y = [1  0] x
Design a phase lead compensator so that the system achieves a settling time of 2 seconds for a 2% tolerance band and has a damped natural frequency of 2 rad/s. Also realize the designed compensator using passive components. 20

(b) For 8085 microprocessor, write the instructions to perform the following :
(i) Set the zero flag when a register pair is used as a down counter
(ii) Load the accumulator with the contents of location 2050H, if memory location 2050H contains byte F8H
(iii) Load 3AH in memory location 2050H, if registers H and L contain 20H and 50H
(iv) Subtract 25H with borrow from accumulator, if the accumulator contains 37H and the borrow flag is set
(v) Complement the accumulator, which has data byte 89H 4×5=20

(c) A moving-coil instrument with a resistance of 10 Ω gives full-scale deflection for a current of 1 mA. A manganin shunt is used to extend its range to 1 A. Calculate the error caused by a 5 °C fall in temperature, when—
(i) the manganin shunt is directly connected across the moving coil;
(ii) a 90 Ω manganin resistance is used in series with the moving coil, before applying manganin shunt.
Assume temperature coefficient of copper as 0·004/°C and that of manganin as 0·00015/°C. 10

UPSC Answer Check · Accepted Answer

Begin with the directive 'design' for the compensator in part (a), which carries the highest marks (20). Structure the answer as: (a) state-space analysis → compensator design → passive realization (~40% time); (b) 8085 assembly instructions with clear mnemonics and comments (~40% time); (c) thermal error calculations with proper temperature coefficient handling (~20% time). No formal conclusion needed; ensure each sub-part is clearly labelled.
- Part (a): Derive transfer function from state-space, calculate required phase lead angle from settling time and damped natural frequency specifications, determine compensator parameters (α, T), and realize using R-C network with component values
- Part (b)(i): Correct use of DCX/DCR/DAD/DAD with conditional jump (JZ) to set zero flag for register pair down counter operation
- Part (b)(ii): Proper addressing mode using LDA 2050H or LHLD with appropriate register loading
- Part (b)(iii): Correct use of MVI M,3AH or MOV M,A with accumulator preload when HL=2050H
- Part (b)(iv): SBB instruction for subtract with borrow, showing accumulator result 11H with flag status
- Part (b)(v): CMA instruction for complement, result 76H with proper flag effects
- Part (c)(i): Calculate shunt resistance (10/999 Ω), apply temperature coefficients for copper and manganin, determine error due to 5°C fall
- Part (c)(ii): Recalculate with 90Ω series manganin resistance, show improved temperature compensation and reduced error

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	25%	12.5	Correctly identifies state-space to transfer function conversion for (a); knows 8085 instruction set including addressing modes and flag behavior for (b); understands temperature coefficient effects on instrument accuracy and swamping resistance principle for (c)	Minor errors in state-space conversion or instruction selection; partial understanding of thermal compensation but correct final approach	Fundamental misunderstanding of phase lead design, incorrect instruction mnemonics, or confusion between copper and manganin temperature coefficients
Numerical accuracy	25%	12.5	Precise calculation of compensator parameters (ζ=0.456, ωn=2.19 rad/s, φm=55°), correct 8085 results (F8H, 11H, 76H), accurate error values for both (c)(i) and (c)(ii) with proper decimal handling	Correct method but arithmetic slips in compensator angle or temperature error; correct final answers for (b) with minor hex conversion errors	Major calculation errors in pole placement, wrong accumulator results, or incorrect application of temperature coefficient formula
Diagram quality	15%	7.5	Clear Bode plot or root locus sketch for compensator design; neat R-C network realization diagram with labelled components; optional but helpful 8085 register/memory flow diagram	Basic compensator circuit diagram present but lacks component values or has labelling issues; no diagrams for other parts acceptable given question nature	Missing essential compensator realization diagram, or diagrams that mislead about circuit topology
Step-by-step derivation	20%	10	Systematic derivation: TF → characteristic equation → desired poles → angle deficiency → lead compensator design → component selection; clear stepwise 8085 code with comments; explicit error formula derivation for thermal effects	Correct sequence but skips key intermediate steps like angle calculation or assumes values; code without comments; jumps to final error formula	Disorganized working with no logical flow, missing essential steps like compensator zero/pole placement, or purely final answers without derivation
Practical interpretation	15%	7.5	Discusses practical limits of passive realization (component tolerances, loading effects); notes 8085 flag behavior in real programs; explains why swamping resistance reduces temperature error in measurement instruments	Brief mention of practical constraints without elaboration; standard comments on instrument accuracy	Purely theoretical treatment with no connection to real-world implementation issues or measurement practice

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