MU Principles of Control Systems - December 2015 Exam Question Paper

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

Answer the following:

1 (a) Define relative and absolute stability. State its significance.

5 M

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

5 M

1 (c) Differentiate open and closed system.

5 M

1 (d) Explain different types of models used in applications.

5 M

2 (a) Obtain the transfer function of the following mechanical system.

10 M

2 (b) Using Mason's gain formula, find C(s)/R(s)

10 M

3 (a) Construct root locus for the following transfer function. Find range of K for system to be stable

G (s) H (s) = \frac{K (S + 13)}{S (S + 3) (S + 8)}

$G(s)H(s)= \dfrac {K(S+13)}{S(S+3)(S+8)}$

10 M

3 (b) Check controllability and observability for the system

$x= \begin{bmatrix} 1 &2 &1 \\0 &1 &3 \\1 &1 &1 \end{bmatrix}x+\begin{bmatrix} 1\\2 \\0 \end{bmatrix} \\ y= \begin{bmatrix} 1&3&1\end{bmatrix}$

10 M

4 (a) Sketch the bode plot for the system described by following transfer function. Also comment on stability

$G(s)H(s)= \dfrac {0.4 (1+ 6S)}{S^2 (1+0.5S)}$

10 M

4 (b) Find the solution of following state equation

$x= \begin{bmatrix} -5 &-6 \\1 &0 \end{bmatrix} x+ \begin{bmatrix} 1\\0\end{bmatrix} u \\ y=\begin{bmatrix} 1&1 \end{bmatrix}$

10 M

5 (a) State and prove properties of state transition matrix.

7 M

5 (b) The characteristics equations for certain feedback systems are given below. Determine range of k for the system to be stable
i) S⁴+20KS²+5S²+10S+15=0
ii) S²+2KS²+(K+2)+4=0

8 M

5 (c) Explain what is robust control system. Also explain the need of robust control.

5 M

6 (a) Explain the effects of P, I and D actions.

6 M

6 (b) Explain the effect of addition off poles and zeros to the system.

7 M

6 (c) Explain different time domain specifications.

7 M

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