## Control Systems - Dec 2014

### Electronics & Telecom Engineering (Semester 4)

TOTAL MARKS: 100

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

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

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.

### Answer any one question from Q1 and Q2

**1 (a)** Explain open loop and closed loop systems with real time example.(6 marks)
**1 (b)** A unity feedback system has open loop transfer function: $$ G(s) = \dfrac {K} {s(s+10)} $$ Determine 'K' so that damping factor is 0.5. For this value of 'K' determine:

(1) Location of closed loop poles,

(2) Peak overshoot, and

(3) Peak time. Assume input is unit step(6 marks)
**2 (a)** Find closed loop transfer function $$ \dfrac {y(s)}{x(s)} \ if \ G_1 = G_2 = \dfrac {1}{s+1} \ and \ G_3=G_4=s+1, \ H_1=1 $$ for system shown in Fig Q2 (a) using block diagram reduction technique.
(6 marks)
**2 (b)** If open loop transfer function is $$ G(s) = \dfrac {1}{s+1} $$, obtain unit step response. Also find output at time t=0,1,2,3,4,5. Assume unity feedback and G(s) is in closed loop.(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Comment on stability using Routh criteria if characteristic equation is:

Q(s) = s^{5}+2s^{4}+3s^{3}+4s^{2}+5s+6=0

How many poles lie in right half of s-plane?(4 marks)
**3 (b)** Construct Nyquist plot and find phase frequency and gain margin if: $$ G(s)\cdot H(s) = \dfrac {1} {s(s+1)(s+2)} $$ Also comment on stability.(8 marks)
**4 (a)** $$ If \ G(s) \ H(s)= \dfrac {k(s+2)}{s(s+1)(s+3)}. $$ construct root locus and comment on stability of system.(7 marks)
**4 (b)** Obtain resonance peak and resonance frequency if: $$ G(s)\cdot H(s)= \dfrac {21} {s(s+5)} \ with \ H(s) =1$$(4 marks)
**5 (a)** Obtain controllable and observable canonical state model if: $$ G(s) = \dfrac {y(s)}{u(s)} = \dfrac {s^3 + 2s^2 + 5s +1}{s^4 = 4s^3 + 4s^2 + 7s +2} $$(6 marks)

### Answer any one question from Q5 and Q6

**5 (b)** Find controllability and observability if: $$ A=\begin{bmatrix}
-2 &1 &0 \\1
&-3 &2 \\10
&0 &-8
\end{bmatrix}, \ B=\begin{bmatrix}
0\\0.1
\\1
\end{bmatrix}, \ C=\begin{bmatrix}
1 &0 &1
\end{bmatrix}, \ D=[0] $$(7 marks)
**6 (a)** List advantages of state space over transfer function.(6 marks)
**6 (b)** Obtain state transition matrix if: $$ x= \begin{bmatrix}
0 &-3 \\1
&-4
\end{bmatrix} x(t) $$(7 marks)

### Answer any one question from Q7 and Q8

**7 (a)** Explain Ladder concept in PLC. Draw and explain different symbols used to construct ladder.(6 marks)
**7 (b)** Find pulse transfer function and impulse response for the system shown in Fig. Q. 7(b).
(7 marks)
**8 (a)** Write PID equation. For unit step input sketch the response of P, I, D action of PID.(6 marks)
**8 (b)** Write a note on digital control system with help of suitable block diagram.(7 marks)