## Principles of Control Systems - Dec 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.

### Answer the following:

**1 (a)** Define relative and absolute stability. State its significance.(5 marks)
**1 (b)** Derive relationship between time and frequency domain specification of system.(5 marks)
**1 (c)** Differentiate open and closed system.(5 marks)
**1 (d)** Explain different types of models used in applications.(5 marks)
**2 (a)** Obtain the transfer function of the following mechanical system.
(10 marks)
**2 (b)** Using Mason's gain formula, find C(s)/R(s)
(10 marks)
**3 (a)** Construct root locus for the following transfer function. Find range of K for system to be stable $ G(s)H(s)= \dfrac {K(S+13)}{S(S+3)(S+8)} $(10 marks)
**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 marks)
**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 marks)
**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 marks)
**5 (a)** State and prove properties of state transition matrix.(7 marks)
**5 (b)** The characteristics equations for certain feedback systems are given below. Determine range of k for the system to be stable

i) S^{4}+20KS^{2}+5S^{2}+10S+15=0

ii) S^{2}+2KS^{2}+(K+2)+4=0(8 marks)
**5 (c)** Explain what is robust control system. Also explain the need of robust control.(5 marks)
**6 (a)** Explain the effects of P, I and D actions.(6 marks)
**6 (b)** Explain the effect of addition off poles and zeros to the system.(7 marks)
**6 (c)** Explain different time domain specifications.(7 marks)