Question Paper: Principles of Control Systems : Question Paper May 2014 - Electronics Engineering (Semester 4) | Mumbai University (MU)
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## Principles of Control Systems - May 2014

### 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.

### Attempt any four:-

1 (a) Differentiate between feedback and feed forward control system.(5 marks) 1 (b) What is a compensator? Why is it required?(5 marks) 1 (c) What are the properties of state transition matrix?(5 marks) 1 (d) Explain the concept of absolute, relative and robust stability.(5 marks) 1 (e) Find the transfer function for following network. (5 marks) 2 (a) Obtain the transfer function of the mechanical system. (10 marks) 2 (b) Consider unity feedback control system with an open loop transfer function of - $$G(s) =\dfrac {k(s+1)(s+2)}{(S+0.1)(s-1)}$$
i) Plot the root loci showing asymptotes, centroid break away point, the gain at which root locus crosses jw axis.

ii) Find value of gain for which a closed system is critically damped.
(10 marks)
3 (a) A unity feedback control system is characterized by the open loop transfer function $$G(s) = \dfrac {k(s+13)}{s(s+3)(s+7)}$$ using the Routh criterion, calculate the range of values of k for system to be stable.(10 marks) 3 (b) Write a note on advances in control systems.(10 marks) 4 (a) Obtain the state variable model of the transfer function- $$\dfrac {Y(s)}{U(s)} = \dfrac {s^2 + 3s+3}{s^2 + 2^2s+3s+1}$$(10 marks) 4 (b) Sketch the Bode plot for the open loop transfer function given by - $$G(s) \ H(s) = \dfrac {0.5 (1+5s)}{s^2 (1+0.5s)}$$(10 marks) 5 (a) Find rise time, setting time and peak overshoot for the system given by transfer function - $$G(s) = \dfrac {25}{(s^2 + 8s +25)}$$(5 marks) 5 (b) Using Nyquist criterion, determine the closed loop system having following open loop transfer function is stable or not. If not, find the number of poles in right half of s plane- $$G(s) \ H(s) = \dfrac {1+4s}{s^2 (1+s)(1+2s)}$$(5 marks) 5 (c) Check controllability and observability for the system- $$x= \begin{bmatrix}1 &2 &1 \\0 &1 &3 \\1 &1 &1 \end{bmatrix} x+ \begin{bmatrix} 1\\0 \\2 \end{bmatrix} u \\ y = \begin{bmatrix}1 &3 &0 \end{bmatrix} x$$(10 marks) 6 (a) Explain the concept of on-off controller using example.(5 marks) 6 (b) Compare lead-lag compensator.(5 marks) 6 (c) Obtain the overall transfer function from signal flow graph. (10 marks)