## Mechanical Measurement and Control - Dec 2015

### Mechanical Engineering (Semester 5)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

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

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1 (a)** Explain generalized measurement system elements with block diagram.(5 marks)
**1 (b)** Write the different classification of control systems.(5 marks)
**1 (c)** Write short note on PI controller.(5 marks)
**1 (d)** Write the working principle of piezoelectric accelerometer.(5 marks)
**2 (a)** Explain the following terms with respect to the measurement system: i) Span and Range ii) Hysteresis(6 marks)
**2 (b)** Illustrate the working principle of "VLDT" for displacement measurement.(6 marks)
**2 (c)** Convert the following state-space system of a single input single output system into a transfer function: $$ \begin{Bmatrix}
\cdot\\x_1
\\\cdot \\ x_2
\end{Bmatrix} = \begin{bmatrix}
-3 &2 \\
1&1
\end{bmatrix} \begin{Bmatrix}
x_1\\x_2
\end{Bmatrix}+ \begin{Bmatrix}
0\\2
\end{Bmatrix} u(t) \\
y(t) = \begin{bmatrix}
1 & 0
\end{bmatrix} \begin{Bmatrix}
x_1\\x_2
\end{Bmatrix} $$ Here x_{1} and x_{2} are state variables, u(t) is a force vector and y(t) being the system response.(8 marks)
**3 (a)** With a neat sketch explain working of an operational Amplifier (Op-amp). Enumerate limitations of the same.(5 marks)
**3 (b)** What are desired, interfering and modifying inputs w.r.t. measurement of a system?(5 marks)
**3 (c)** A unity feedback system has $ G(s) = \dfrac {k}{s(1+s)(1+0.4s)}, $

(a) If r(t)=4t and k=2, find steady state error

(b) If it is desired to have steady state error to be 0.2 find corresponding value of "k".

(c) Find steady state error if input is changed to 2+6t, and value of "k" to 10.(10 marks)
**4 (a)** What are rosettes? Explain different types and configuration of rosettes.(10 marks)
**4 (b)** The open loop T.F. of unity feedback system is $ G(s) = \dfrac {K}{S(1+TS)} $, for this system overshoot reduce form 0.6 to 0.2 due to change in 'K' only. Show that $ \dfrac {TK_1-1}{TK_2-1} =43,33 $, where K_{1} and K_{2} are values of "K" for 0.6 and 0.2 overshoot respectively.(10 marks)
**5 (a)** Sketch Bode plot and assess the stability for the control system having open loop transfer function $$ G(S)H(S) = \dfrac {120}{(S+2)(S+10)} $$(10 marks)
**5 (b)** With neat sketch explain the constructional feature and working of (i) Ionization Gauge, (ii) Thermistors(10 marks)
**6 (a)** Draw the root-locus of the control system whose open-loop transfer function is given by $$ G(S)H(S)= \dfrac {K}{S^2 (S+1} $$(10 marks)
**6 (b)** With a neat sketch explain the constructional features and working of (i) digital tachometer. (ii) Electromagnetic flow meter.(10 marks)