Question Paper: Control Systems : Question Paper Jun 2013 - Electronics & Communication (Semester 4) | Visveswaraya Technological University (VTU)
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## 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 tr=? and Mp=? 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
S2+2S5+8S4+12S3+20S2+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 e1(t), e2(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)