Question Paper: Principles of Control Systems : Question Paper May 2016 - Electronics Engineering (Semester 4) | Mumbai University (MU)
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## Principles of Control Systems - May 2016

### Electronics Engineering (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.

### Attempt any Four questions

1(a) Explain Adaptive control system.(5 marks) 1(b) Explain lead and lag compensator(5 marks) 1(c) Explain Controllability and Observability with its necessity for stability.(5 marks) 1(d) Determine whether the following systems are stable, marginally stable, and unstable
(i) -2,0; (ii) -2+j, -2-j; (iii) -2+j4, -2-j4, -2; (iv) x(t) = cosωt; (v) x(t) = e-t sin4t.
(5 marks)
1(e) Examine the stability of s5+2s4+2s3+4s2+4s+8=0 using Routh's method.(5 marks) 2(a) Obtain the overall transfer function from block diagram.

(10 marks) 2(b) Sketch the complete root locus for the system
G(s)H(s) = [K (s+1)(s+2)] / [(s+0.1)(s-1)], where K>0.
(10 marks)
3(a) Obtain the state variable model of the parallel RLC network.

(10 marks)
3(b) Explain P, PI and PID controller.(10 marks) 4(a) The state equation of a linear time-invariant system is given below: $$\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 1 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 0\\ 1 \end{bmatrix}u$$
Where u>0.
Determine the following:
(i) The state transition matrix.
(ii) Controllability of the system.
(10 marks)
4(b) Sketch the bode plot for the open loop transfer function given by:
G(s) = [288(s+4)] / [s(s+1) (s2+4.8s+144)] and H(s) = 1.
(10 marks)
5(a) Derive the expression of Peak Overshoot when step input applied to the system.(5 marks) 5(b) Sketch the polar plot of G(s) = 12 / [s(s+1)].(5 marks) 5(c) For G(s)H(s) = 1+4s / [s2+(1+s)(1+2s)], draw the Nyquist plot examine the stability of the system.(10 marks)

### Attempt any two

6(a) Write a short note on Robust control system.(10 marks) 6(b) Construct the signal flow graphs for the following set of equations:
Y2 = G1Y1 - G2Y4
Y3 = G3Y2 + G4Y3
Y4 = G5Y1 + G6Y3
Where Y4 is the output.
(10 marks)
6(c) Explain the Correlations between time and frequency domain specifications of the system.(10 marks)