## Mechanical Measurement And Control - Jun 19

### Mechanical Engineering (Semester 5)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**1.a.**Determine the stability using Routh Hurwitz Criterion of the following characteristic equation:

$S^{5}+S^{4}+2 S^{3}+2 S^{2}+3 S+15=0$

**1.b.**Differentiate between open and closed loop systems with their respective block diagrams and examples

**1.c.**Explain the following terms with respect to static characteristics of the measuring instruments:

i. Hysteresis

ii. Accuracy and Precision

iii. Resolution

iv. Drift

**1.d.**Explain the principle of LVDT with a neat sketch

**2.a.**Convert the following state space system into a transfer function

$X(t)=\left(\begin{array}{ccc}{0} & {1} & {0} \\ {0} & {0} & {1} \\ {-3} & {-2} & {-5}\end{array}\right) x(t)+\begin{array}{c}{0} \\ {0} \\ {10}\end{array} u(t)$

$\mathbf{Y}(t)=\left[\begin{array}{lll}{1} & {0} & {0}\end{array}\right] \mathbf{x}(t)$

**2.b.**Explain the construction and working of an Optical Pyrometer with a neat sketch

**3.a.**A rectangular steel rod of width ‘b’ and depth‘d’ is supported at its end and is loaded at its center by load ‘W’. If the length of the rod between supports is ‘l’ and ‘$\mathrm{d}_{\mathrm{m}}$’ where -

$\mathrm{d}_{\mathrm{m}}=\frac{\mathrm{Wl}^{2}}{4 \mathrm{Ebd}^{3}}$

Where; $\mathrm{b}=4.942 \pm 0.42 \mathrm{cm}$

$\mathrm{d}=5.25 \pm 0.25 \mathrm{cm}$

$I=1000 \pm 0.5 \mathrm{cm}$

$\mathrm{d}_{\mathrm{m}}=2.622 \pm 2.25 \%$

$\mathrm{W}=1500 \mathrm{N}$

Find value of modulus of elasticity, % of uncertainty in various quantities, % of uncertainty in various quantities.

**3.b.**For a unity feedback system having open loop transfer function,

$G(s)=\frac{14(s+3)}{s(s+5)\left(S^{2}+2 s+2\right)}$

Determine

i. Type and order of the system

ii. All error coefficients

iii. Steady state error for input $1+4 t+\frac{t^{2}}{2}$

**4.a.**Prove Gauge factor, $\mathbf{K}=\frac{\Delta \rho / \boldsymbol{\rho}}{\Delta \boldsymbol{L} / \mathbf{L}}+\mathbf{1}+2 \mathbf{v}$

**4.b.**Enumerate the types of pressure measurement devices w.r.t. to pressure levels. Explain the construction and working of Bourdon tube with a neat sketch

**5.a.**Obtain transfer function C(s) / R(s) using block diagram reduction technique.

**5.b.**A feedback system has $\mathrm{G}(\mathrm{s}) .\mathrm{H}(\mathrm{s})=242(\mathrm{s}+5) / \mathrm{s}\left(\mathrm{s}^{2}+5 \mathrm{s}+121\right)(\mathrm{s}+1)$. Draw Bode plot and comment on its stability.

**6.a.**Sketch the Root Locus for the given system having $\mathrm{G}(\mathrm{s}) . \mathrm{H}(\mathrm{s})=\mathrm{K}(\mathrm{s}+5) /\left(\mathrm{s}^{2}+4 \mathrm{s}+20\right)$. Comment on its stability.

**6.b.**Explain the construction and working of non contact type of speed measurement system with a neat sketch