## Control Systems - Jun 2013

### Electronics & Communication (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.
**1 (a)** Compare open loop and closed loop control system and give one practical example of each.(6 marks)
**1 (b)** For the system shown in below, write mechanical network and obtain its mathematical model.
(6 marks)
**1 (c)** For the system shown in below, Write its mechanical network and obtain mathematical model and electrical analogue based on force-current analogy.
(8 marks)
**2 (a)** Define transfer function and what are its properties.(5 marks)
**2 (b)** Obtain the transfer function for the block diagram shown in below, using block diagram reduction method.
(7 marks)
**2 (c)** For the block diagram, given in below, obtain overall transfer function using Mason's gain formula.
(8 marks)
**3 (a)** Draw the time response curve and define time domain specifications, for second order C.S. for unit step i/p.(6 marks)
**3 (b)** A unity feedback control system is given by an open-loop transfer function, $$ G(s)= \dfrac {K}{s(s+10)} $$ i) The value of K for ?=0.5

For this value of K t_{r}=? and M_{p}=? for unit step input.(6 marks)
**3 (c)** The open loop transfer function of servo system with unity feedback is given by $$ G(s)=\dfrac {10}{s(0.ls+1)} $$ Find out static error constant and obtain steady state error when subjected to an i/p of $$ r(t)=A_0+A_1t+\dfrac {A_2}{2}t^2 $$(8 marks)
**4 (a)** Explain RH stability criterion used for finding of stability of control systems.(6 marks)
**4 (b)** Find the range of K for the system to be stable using RH criterion $$ G(s)H(s)= \dfrac {k(1-s)}{s(s^2+5s+9)} $$(6 marks)
**4 (c)** Investigation stability of the system given by characteristics equation

S^{2}+2S^{5}+8S^{4}+12S^{3}+20S^{2}+16S+16=0.(8 marks)
**5** A feedback control system has an open loop transfer function $$ G(s)H(s)= \dfrac {K}{s(s+3)(S^2+2s+2)} $$ Draw the root locus as K varies from 0-to-?(20 marks)
**6 (a)** Define the following terms:

i) Resonant peak

ii) Resonant frequency

iii) Band width

iv) Cut off frequency(4 marks)
**6 (b)** Sketch the bode plot for the transfer function $$ \dfrac {300 (s^2+2s+4)}{s(s+10)(s+20)} $$(13 marks)
**6 (c)** Write a note about gain margin in brief.(3 marks)
**7 (a)** Plot the polar plot for the transfer function given $$ G(s)=\dfrac {1}{s(Ts+1)} $$(8 marks)
**7 (b)** State Nyquist stability criterion verify stability of the system described below:

$$ G(s)H(s) = \dfrac {5}{s(1-s)} $$(12 marks)
**8 (a)** Obtain the state model for the electrical system given below. Take e_{1}(t), e_{2}(t) as i/p variables and voltage across R as o/p variables.
(8 marks)
**8 (b)** List out the properties of STM.(5 marks)
**8 (c)** Obtain the state transition matrix for a system matrix given by $$ A=\begin{bmatrix}0 &1 \\-2 &-3 \end{bmatrix} $$(7 marks)