Question Paper: Control Systems : Question Paper May 2016 - Electronics & Telecomm (Semester 4) | Mumbai University (MU)
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## Control Systems - May 2016

### 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) Explain the concept of relative stability.(5 marks) 1(b) What do you mean by frequency domain analysis and explain the frequency domain performance indices.(5 marks) 1(c) Find out the t.F. of the given network.

(5 marks) 1(d) The forward path gain of a system is 2.5 and pole-zero configuration of the system is shown below, find the overall transfer function and type of the system for system for unity feedback. (5 marks) 2(a) Reduce the block diagram and obtain its transfer function.

(10 marks)
2(b) Draw the corresponding signal flow graph of given block diagram and find $\dfrac{C(s)}{R(s)}$

(10 marks)
3(a) State and prove properties of state transition matrix and check controllability and observability for the system. $$\dot{x}=\begin{bmatrix} 0 & 6 & 5\\ 1 & 0 & 2\\ 3 & 2 & 4 \end{bmatrix}x-\begin{bmatrix} 0\\ 1\\ 2 \end{bmatrix}u$$ $$y=[1\ \ \ 3 \ \ \ 0]x$$(10 marks) 3(b) A unity feedback system has $$G(s)=\dfrac{40(s-2)}{s(s-1)(s-4)}$$
Determine : (i) Type of the system
(ii) All error coefficients
(iii) Error for ramp Input with magnitude 4.
(10 marks)
4(a) Discuss the stability of the following systems for given characteristics equation using Routh-Hurwitz criterion.
(i) s6 + 4s5 + 3s4 + 16s2 - 64s - 48 =0
(ii) s6 + 2s5 + 8s4 + 12s3 + 20s2 + 16s + 16 = 0
(10 marks)
4(b) A feedback system has an open-loop transfer function. $$G(S)=\dfrac{K}{S(S+3)(S^2+2S+2)}$$
Find the root-locus as k &rarr
(10 marks)
5(a) For a particular unity feedback system, $$G(s)=\dfrac{242(s-5)}{s(s-1)(s^2-5x-121)}$$
Sketch the Bode plot and find Wgc, Wpc, G.M.., p.M. and comment on stability.
(10 marks)
5(b) For a certain control system $$G(s).H(s)=\dfrac{K}{s(s+2)(s-10)}$$
Sketch the nyquist plot and hence calculate the range of K for stability.
(10 marks)
6(a) Explain the frequency domain specifications.(7 marks) 6(b) Explain the concept of Neuro-Fuzzy adaptive control system.(7 marks) 6(c) Write short note on : Steady state errors in feed back control system and their types.(7 marks)