## Mechanical Measurement and Control - May 2016

### 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)** What is mathematical modeling? Write significance of mathematical modeling in control systems.(5 marks)
**1(c)** Write short note on PID controller.(5 marks)
**1(d)** Write the working principle of piezoelectric accelerometer(5 marks)
**2(a)** Explain the following terms with respect to measurement system: (i) Span and Range (ii) Drift(5 marks)
**2(b)** Illustrate the working principle of 'Nozzle flapper' for displacement measurement.(5 marks)
**2(c)** Convert the following state-space system of a single input single output system into a transfer function: $$\begin{Bmatrix} x_1\\ x_2 \end{Bmatrix}=\begin{bmatrix} -3 & 2\\ 1 & 1 \end{bmatrix}\begin{Bmatrix} x_1\\ x_2 \end{Bmatrix}+\begin{Bmatrix} 0\\ 2 \end{Bmatrix}u(t)\\\\y(t)=\begin{bmatrix}1 &0\end{bmatrix} \begin{Bmatrix} x_1\\ x_2 \end{Bmatrix}$$

Here x_{1} and x_{2} are state variable u(t) is a force vector and y(t) being the system response.(10 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)** For a unity feedback system having $ G(s)=\dfrac{10(s+1)}{s^2(s+2)(s+10)}$ determine (i) error coefficients (ii) Steady State error for input as $1+4t+\dfrac{t^2}{2} $(10 marks)
**4(a)** What are the different elastic transducers used for the pressure measurement. Illustrate the working principle of any one in detail.(10 marks)
**4(b)** A system is represented by the equation S^{B}+5S^{6}+2S^{4}+3S^{2}+1=0. Examine the stability of the system by using Routh's criterion.(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 a neat sketch explain the constructional feature and working of (i) Ionization Gauge, (ii) Thermocouples(10 marks)
**6(a)** Draw the root-locus of the control system whose open-loop transfer option is given by $$G(S)H(S)=\dfrac{K}{S^2(S+1)}$$(10 marks)
**6(b)** With a neat sketch explain the constructional feature and working of (i) digital tachometer, (ii) Rota-meter.(10 marks)