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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) S4+20KS2+5S2+10S+15=0
ii) S2+2KS2+(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)