## Principles of Control Systems - May 2015

### Electronics Engineering (Semester 4)

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.

### Attempt any four:

**1 (a)** Explain the effect of addition of pole and zero to the system.(5 marks)
**1 (b)** Define gain margin and phase margin. Explain how these margins are used for stability analysis.(5 marks)
**1 (c)** Difference open-loop and closed-loop systems.(5 marks)
**1 (d)** Explain need of compensator.(5 marks)
**1 (e)** State and prove properties of state transition matrix.(5 marks)
**2 (a)** obtain the transfer function of the following electrical system.
(10 marks)
**2 (b)** Find the transfer function $$ \dfrac {c(s)}{R(s)} $$ for the following system using block diagram reduction technique.
(10 marks)
**3 (a)** Obtain the state space model for the following mechanical system.
(10 marks)
**3 (b)** Obtain the solution of the system described by $$ x= \begin{bmatrix} 0 &1 \\ -2 & -4 \end{bmatrix} x + \begin{bmatrix}0\\2 \end{bmatrix} u $$(10 marks)
**4 (a)** The open-loop transfer function of a unity feedback system is given by $$ G(s) = \dfrac {K}{(s+3)(s+5)(s^2+2s+2)} $$ Plot the root loci. Find the points where the root loci cross the imaginary axis.(10 marks)
**4 (b)** Construct the bode plot for the following transfer function. Comment on stability $$ G(s)= \dfrac {100}{s^2 (1+0.005s)(1+0.08s)(1+0.5s)} $$(10 marks)
**5 (a)** Check controllability and observability for the system described by $$ x= \begin{bmatrix}0 &6 &-5 \\1 &0 &2 \\3 &2 &4 \end{bmatrix} x+ \begin{bmatrix}0\\1 \\2
\end{bmatrix} u \\ y = \begin{bmatrix} 1 &2 &3
\end{bmatrix}x $$(10 marks)
**5 (b)** Derive the relationship between time and frequency domain specification of the system.(10 marks)
**6 (a)** Write a short note on model predictive control.(5 marks)
**6 (b)** Explain the features of P, I and D control actions(5 marks)
**6 (c)** Find the range of K for the system to be stable

s^{4}+7s^{3}+10s^{2}+2ks + k =0(5 marks)
**6 (d)** Describe the Mason's gain formula with an example.(5 marks)