### GATE 2008 ECE Control Systems - Complete Video Solutions with Answers

GATE 2008

1. The pole-zero plot given below corresponds to a

a) Low pass filter
b) High pass filter
c) band pass filter
d) Notch filter

2. Step response of a set of three second order under damped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

3. Group – I lists a set of four transfer functions. Group – II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions.
a) P - 3, Q - 1, R - 4, S - 2
b) P - 3, Q - 2, R - 4, S - 1
c) P - 2, Q - 1, R - 4, S - 3
d) P - 3, Q - 4, R - 1, S – 2

4. A certain system has transfer function G(s) = (s + 8)/(s2 + αs – 4 ), where α is a parameter. Consider the standard negative unity feedback configuration shown below.

Which of the following statements is true?
a) The closed loop system is never stable for any value of α
b) For some positive values of α, the closed loop system is stable, but not for all positive values
c) For all positive values of α, the closed loop system is stable
d) The closed loop system is stable for all values of α, both positive and negative

5. A signal flow graph of a system is given below.

The set of equations that correspond to this signal flow graph is

6. The number of open right half plane poles of G(s) = 10 / (s5 + 2s4 + 3s3 + 6s2 + 5s + 3) is
a) 0
b) 1
c) 2
d) 3

7. The magnitude of frequency response of an under damped second order system is 5 at 0 rad/sec and peaks to 10/√3 at 5√2 rad/sec. The transfer function of the system is

8. Group – I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition R2C2>R1C1. The transfer function Vo/V1 represents a kind of controller. Match the impedance's in Group – I with the types of controllers in Group – II.

a) Q – 1, R – 2
b) Q – 1, R – 3
c) Q – 2, R – 3
d) Q – 3, R – 2