Question Paper: Principles of Control Systems : Question Paper Dec 2015 - Electronics Engineering (Semester 4) | Mumbai University (MU)
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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.

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