MU Control Systems - December 2015 Exam Question Paper

MU Electronics and Telecom Engineering (Semester 4)
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

1 (a) Define rise time.

5 M

1 (b) Define gain margin and phase margin.

5 M

1 (c) What are the difficulties encountered in applying Routh stability criterion?

5 M

1 (d) Find out response of give system for a unit step I/P.

5 M

2 (a) Obtain the transfer function of the mechanical system shown in Fig. 11A (i).

10 M

2 (b) Draw a signal flow graph for the system shown in fig 11a (ii) and hence obtain the transfer function using Mason's gain formula.

10 M

3 (a) Derive the expression for step response of second-order under damped system.

10 M

3 (b) Find the impulse response of the second order system whose transfer function

G (s) = \frac{9}{(s^{2} + 4 s + 9)}

$G(s) = \dfrac {9}{(s^2 + 4s+ 9)}$

10 M

4 (a) A unity feedback system is characterized by an open loop transfer function

G (s) = \frac{K}{s (s + 10)} .

$G(s) = \dfrac {K} {s(s+10)}.$ Determine the gain K so that the system will have a damping ratio of 0.5. For this values of K determine settling time peak over shoot and time to peak over shoot for a unit step input.

10 M

4 (b) An unity feedback system is given as

G (s) = \frac{1}{s (s + 1)} .

$G(s) = \dfrac {1} {s(s+1)}.$ The input to the system is described by r(t)=4+6t+2t². Find the generalized error coefficients and the steady state error.

10 M

5 (a) Sketch the Bedplate showing the magnitude in dB and phase angle in degree as a function of log frequency for the transfer function given by

G (s) = \frac{10}{s (1 + 0.5 s) (1 + 0.1 s)}

$G(s) = \dfrac {10} {s(1+0.5s) (1+0.1s)}$ and hence determine the gain margin and the phase margin of the system.

10 M

5 (b) Sketch the root locus for n unity feedback system with open loop transfer function

G (s) = \frac{K}{s (s^{2} + 8 s + 32)} .

$G(s) = \dfrac {K}{s(s^2 + 8s + 32)}.$

10 M

6 (a) Using Routh Hurwitz criterion for the unity feedback system with open loop transfer function

G (s) = \frac{K}{s (s + 1) (s + 2) (s + 5)}

$G(s) = \dfrac {K}{s(s+1) (s+2) (s+5)}$ find
i) the range of k for stability
ii) the value of k for marginally stable
iii) the actual location of the closed loop poles when the system is marginally stable.

10 M

6 (b) Explain controllably and observably.

10 M

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