MU Principles of Control Systems - December 2014 Exam Question Paper

MU Electronics Engineering (Semester 4)
Principles of Control Systems
December 2014

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 five

1 (a) Differentiate between open loop and closed loop control system.

4 M

1 (b) Explain the Mason's Gain formula with reference to signal Flow Graph Technique.

4 M

1 (c) Define and state the condition for controllability and observability for n^th order MIMO system.

4 M

1 (d) The characteristic equation for certain feedback control system is given below. Determine the range of value of K for the system to be stable.
S³+2ks²+ (k+2)s+4=0

4 M

1 (e) Define gain and phase margin. Draw approximate Bode plot for a stable system showing gain and phase margin.

4 M

1 (f) Compare between Lead and Lay compensator.

4 M

2 (a) Derive the output response for second order under-damped control system subjected to unit step input.

10 M

2 (b) Find the transfer function C(S)/R(S) using Block diagram reduction Technique.

10 M

3 (a) Find the Transfer function for the system show below.

4 M

3 (b) What are the properties of state transition matrix?

4 M

3 (c) For the system shown below, chose V₁(t) and V₂(t) as state variales and write down the state equations satisfied by them. Bring these equations in the vector-matrix form

12 M

4 (a) Examine the observability of the system given below using kalman's test.

⎡ ⎢ ⎣ \begin{matrix} x_{1} x_{2} x_{3} \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 0 0 & 0 & 1 0 & - 2 & - 3 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x_{1} x_{2} x_{3} \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 001 \end{matrix} ⎤ ⎥ ⎦ u = A x + B u

$\begin{bmatrix}x_1\\x_2 \\x_3 \end{bmatrix} = \begin{bmatrix}0 &1 &0 \\0 &0 &1 \\0 &-2 &-3 \end{bmatrix} \begin{bmatrix}x_1\\x_2 \\x_3 \end{bmatrix} = \begin{bmatrix}0\\0 \\1 \end{bmatrix} u = Ax+ Bu$

8 M

4 (b) Derive the expression for Peak resonant of a standard second order control system.

8 M

4 (c) Explain the concept of ON/OFF controller.

4 M

5 (a) For a unit feedback system the open loop transfer function is given by

$G(S) = \dfrac {K}{S(S+2) (S^2+6S+25)}$ Sketch the root locus and find the value of K at which the system becomes unstable.

10 M

5 (b) Explain Robust control and Adaptive control system.

10 M

6 (a) Find polar plot for the transfer function given below

$G(S) = \dfrac {1}{(1+S)(1+4S)}$

5 M

6 (b) Write a short note on PID controller.

5 M

6 (c) Determine the stability of a system shown by following open loop transfer function using Nyquist criterion

$G(s) \ H(s) = \dfrac {(4s+1)} {s^2 (s+1) (2s+1)}$

10 M

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