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.

### Answer the following

**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.

**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) s

^{6}+ 4s

^{5}+ 3s

^{4}+ 16s

^{2}- 64s - 48 =0

(ii) s

^{6}+ 2s

^{5}+ 8s

^{4}+ 12s

^{3}+ 20s

^{2}+ 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 W

_{gc}, W

_{pc}, 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)