## Control Systems - May 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 the rules of block diagram reduction techniques.(6 marks)
**1 (b)** f peak overshoot is 16.3% and peak time is 0.3023 seconds. Determine:

(1) damping factor,

(2) undamped natural frequency and <br? (3)="" settling="" time="" (for="" 2%="" tolerance)="" of="" the="" system.<="" a="">

</br?>(6 marks)
**2 (a)** Find the closed loop transfer function $$ \dfrac {C(s)} {R(s)} $$ of system shown in Fig. 1 using block diagram reduction technique.

(6 marks)
**2 (b)** $$ If G(s) \ H(s) = \dfrac {25}{s(s+5)},$$ obtain damping factor, un-damped and damped natural frequency, rise time, peak time, and settling time.(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Comment on the stability of a system using Routh's stability criteria whose characteristic equation is:

s^{4}+2s^{3}+4s^{2}+6s+8=0.

How many poles of systems lie in right half of s-plane?(4 marks)
**3 (b)** $$ If G(s) \ H(s) = \dfrac {24} {s(s+2)(s+12)}, $$ construct the Bode plot and calculate gain crossover frequency, phase crossover frequency, gain margin, phase margin and comment on stability.(8 marks)
**4 (a)** Open loop transfer function of unity feedback system is $$ G(s) = \dfrac {K}{s(s+3)(s+5)} $$ Sketch the complete root locus and find marginal gain.(8 marks)
**4 (b)** $$ If G(s) \ H(s) = \dfrac {1} {s(s+1)}, $$ determine the value of:

i) Resonance Peak and

ii) Resonance frequency.(4 marks)

### Answer any one question from Q5 and Q6

**5 (a)** State any three advantages of state space approach over classical approach. Derive an expression to obtain transfer function from state model.(7 marks)
**5 (b)** Find Controllability and Observability of the system given by
state model: $$ A= \begin{bmatrix}
1 &1 &5 \\1
&-2 &2 \\5
&2 &-8
\end{bmatrix}, \ B=\begin{bmatrix}
5 \\ 1\\10
\end{bmatrix}, \ C=\begin{bmatrix}
10 &15 &11
\end{bmatrix}, \ D=[0] $$(6 marks)
**6 (a)** Explain canonical controllable and observable state model with any example/transfer function.(6 marks)
**6 (b)** Obtain the state transition matrix for the system with state equation: $$ [x]= \begin{bmatrix}
0 &1 \\-8
&-9
\end{bmatrix} $$ using Laplace transformation.(7 marks)

### Answer any one question from Q7 and Q8

**7 (a)** Explain application of programmable logic controller for elevator system with ladder diagram.(6 marks)
**7 (b)** Find the pulse transfer function and impulse response of the system shown in Fig. 2.

(7 marks)
**8 (a)** Write the equation of PID controller and explain role of each action in short.(6 marks)
**8 (b)** Obtain pulse transfer function of the system shown in Fig. 3 using first (Starred Laplace) principle.

(7 marks)