Question Paper: Control Systems : Question Paper May 2013 - Electronics & Telecomm. (Semester 4) | Mumbai University (MU)
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## Control Systems - May 2013

### Electronics & Telecomm. (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.
1 (a) What is damping ratio? Show the location of roots in s-plane for different values of damping ratio.(5 marks) 1 (b) From the pole-zero plot given below obtain:
(i) Transfer function.
(ii) Order of the system.
(iii) Characteristic equation.
(iv) DC gain of the system.
(5 marks)
1 (c) Find the transfer functions from the signal flow graph given below:
(5 marks)
1 (d) Define the following terms related to second order system subjected to unit step input.
(i) Rise time
(ii) Peak time.
(iii) Peak overshoot
(iv) Delay time.
(v) Settling time.
(5 marks)
2 (a) Find C using block diagram reduction rules.
(10 marks)
2 (b) Sketch the root locus for a unity feedback control system with
G(s) = K/[s(s+3)(s+5)] and determine -
(i) K for marginal stability.
(ii) Frequency of oscillation for marginal stability.
(iii) K for damping ratio of 0.5.
(10 marks)
3 (a) Derive the time response expression for a second order control system subjected to unit step input.(10 marks) 3 (b) What is stepper motor? Mention its types. Explain one type of stepper motor with neat diagrams.(10 marks) 4 (a) Define sensitivity of a control system. Derive the sensitivities SH<supt&lt; sup=""> and SG<supt&lt; sup=""> of a feedback control system where T is closed loop gain, H is the feedback gain and G is the open loop gain of the system.</supt&lt;&gt;<>(10 marks) 4 (b) For the transfer function given below:
G(s)H(s) = 48(s+10)/[(s(s+20)(s2+2-4s+16)]. Find
(i) Static position error co-efficient.
(ii) Static velocity error co-efficient.
(iii) Static acceleration error co-efficient.
(iv) Steady state error if the input to the system is unit step.
(10 marks)
5 (a) Sketch the bode plot for a system with open loop transfer function:
G(s)H(s) = 30/[s(1+0.5s)(1+0.8s)] and comment on stability.
(10 marks)
6 (b) Find the overall transmittance using Masons gain Formula.
(10 marks)

### Write short notes on:-

7 (a) Nyquist stability criteria.(10 marks) 7 (b) Error compensation techniques.(10 marks)