Question Paper: Principles of Control Systems : Question Paper May 2015 - Electronics Engineering (Semester 4) | Mumbai University (MU)
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## Principles of Control Systems - May 2015

### 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:

1 (a) Explain the effect of addition of pole and zero to the system.(5 marks) 1 (b) Define gain margin and phase margin. Explain how these margins are used for stability analysis.(5 marks) 1 (c) Difference open-loop and closed-loop systems.(5 marks) 1 (d) Explain need of compensator.(5 marks) 1 (e) State and prove properties of state transition matrix.(5 marks) 2 (a) obtain the transfer function of the following electrical system. (10 marks) 2 (b) Find the transfer function $$\dfrac {c(s)}{R(s)}$$ for the following system using block diagram reduction technique. (10 marks) 3 (a) Obtain the state space model for the following mechanical system. (10 marks) 3 (b) Obtain the solution of the system described by $$x= \begin{bmatrix} 0 &1 \\ -2 & -4 \end{bmatrix} x + \begin{bmatrix}0\\2 \end{bmatrix} u$$(10 marks) 4 (a) The open-loop transfer function of a unity feedback system is given by $$G(s) = \dfrac {K}{(s+3)(s+5)(s^2+2s+2)}$$ Plot the root loci. Find the points where the root loci cross the imaginary axis.(10 marks) 4 (b) Construct the bode plot for the following transfer function. Comment on stability $$G(s)= \dfrac {100}{s^2 (1+0.005s)(1+0.08s)(1+0.5s)}$$(10 marks) 5 (a) Check controllability and observability for the system described by $$x= \begin{bmatrix}0 &6 &-5 \\1 &0 &2 \\3 &2 &4 \end{bmatrix} x+ \begin{bmatrix}0\\1 \\2 \end{bmatrix} u \\ y = \begin{bmatrix} 1 &2 &3 \end{bmatrix}x$$(10 marks) 5 (b) Derive the relationship between time and frequency domain specification of the system.(10 marks) 6 (a) Write a short note on model predictive control.(5 marks) 6 (b) Explain the features of P, I and D control actions(5 marks) 6 (c) Find the range of K for the system to be stable
s4+7s3+10s2+2ks + k =0
(5 marks)
6 (d) Describe the Mason's gain formula with an example.(5 marks)

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