1.a. Derive an expression for steady state error when step and ramp input is given to the system.

1.b. Define the following terms with reference to static space modelling of the system.

1.State space

2.State variables

1.c. Explain the following terms with reference to static characteristics of the measuring instruments.

1.Hysteresis

2.Drift

2.a. What is mathematical modelling? Explain with importance of mathematical modelling in controls systems.

2.b. Explain the construction, working and theory of thermal conductivity gauges for measurement of vacuum.Explain how radiation effects are minimized

2.c. Obtain the state-space equation and output equation for the system defined by the equation ,

$\frac{Y(s)}{U(s)}=\frac{2 s^{3}+s^{2}+s+2}{s^{3}+4 s^{2}+5 s+2}$

3.a. Explain the construction and working of a d.c. tachogenerator. Explain its advantages and disadvantages.

3.b. For a system having $G(s)=\frac{15}{(s+1)(s+3)}$, H(s)=1,determine

(i) Characteristics equation

(ii) ω_n and damping ratio (ξ)

(iii) Time at which I^st overshoot will occur

(iv) Time period of oscillations

(v) No. of cycles output will perform before settling down

4.a. What are different temperature compensation techniques used in the measurement of strain using strain gauges ? Explain any two methods in detail.

4.b. Construct the block diagram that combines the following set of equations expressed in the "s" notations (Laplace notation). (1)W = X - Y, (2) V = W - Z , (3) 7(S + 6) = V(S + 2), (4) Y(S² + 6S + 8) = Z, Given X is the input to the system and Y is the output from the block diagram. Find the transfer function.

5.a. For a certain feedback system having, $G(s) H(s)=\frac{3(s+1)(s+6)}{s^{2}\left(s^{2}+18 s+400\right)}$,Sketch Bode plot and comment on G.M,P.M and stability.

5.b.i. With a neat sketch explain the constructional feature and working of

Piezo-electric accelerometer

5.b.ii. Pyrometers.

6.a. For a unity feedback system having $G(s)=\frac{100(s+1)}{s^{2}(s+2)(s+10)}$ ,determine (i) Type of system (ii) Error coefficients (iii) Steady state error for input $1 + 4t + \frac{t^2}{2}$.

6.b. With neat sketches discuss significance of followings aspects of signal conditioning for any one of the sensor: amplification, conversion filtering , modulation/demodulation and grounding.