MU Principles of Control Systems - May 2015 Exam Question Paper

MU Electronics Engineering (Semester 4)
Principles of Control Systems
May 2015

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Attempt any four:

1 (a) Explain the effect of addition of pole and zero to the system.

5 M

1 (b) Define gain margin and phase margin. Explain how these margins are used for stability analysis.

5 M

1 (c) Difference open-loop and closed-loop systems.

5 M

1 (d) Explain need of compensator.

5 M

1 (e) State and prove properties of state transition matrix.

5 M

2 (a) obtain the transfer function of the following electrical system.

10 M

2 (b) Find the transfer function

\frac{c (s)}{R (s)}

$\dfrac {c(s)}{R(s)}$ for the following system using block diagram reduction technique.

10 M

3 (a) Obtain the state space model for the following mechanical system.

10 M

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 M

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 M

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 M

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 M

5 (b) Derive the relationship between time and frequency domain specification of the system.

10 M

6 (a) Write a short note on model predictive control.

5 M

6 (b) Explain the features of P, I and D control actions

5 M

6 (c) Find the range of K for the system to be stable
s⁴+7s³+10s²+2ks + k =0

5 M

6 (d) Describe the Mason's gain formula with an example.

5 M

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