GATE 2007 ECE Control Systems - Complete Video Solutions with Answers | GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems

GATE 2007

1. If the closed loop transfer function of a control system is given as T(s) = (s – 5)/[(s + 2)(s + 3)], then it is

a) an unstable system

b) an uncontrollable system

c) a minimum phase system

d) a non-minimum phase system

Solution : https://www.youtube.com/watch?v=4soEmuGvfcI

2. If the Laplace Transform of a signal y(t) is Y(s) = 1/[s(s – 1)], then its final value is:

a) – 1

b) 0

c) 1

d) unbounded

Solution : https://www.youtube.com/watch?v=cvCDerivzj0

3. A control system with a PD controller is shown in the figure.

If the velocity error constant K_v = 1000 and the damping ratio ξ = 0.5, then the values of K_p and K_D are

a) K_p = 100, K_D = 0.09

b) K_p = 100, K_D = 0.9

c) K_p = 10, K_D = 0.09

d) K_p = 10, K_D = 0.9

Solution : https://www.youtube.com/watch?v=vxHx4zTs5vg

4. The transfer function of a plant is T(s) = 5/[(s + 5)(s² + s + 1)]. The second order approximation of T(s) using dominant pole concept is

Solution : https://www.youtube.com/watch?v=y1BxLLTHJOI

5. The open loop transfer function of a plant is given as G(s) = 1/(s² – 1). If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

Solution : https://www.youtube.com/watch?v=HJ09FtxcO-I

6. A unity feedback control system has an open loop transfer function G(s) = – K/[s(s² + 7s + 12)]. The gain k for which s = –1+j1 will lie on the root locus of this system is

a) 4

b) 5.5

c) 6.5

d) 10

Solution : https://www.youtube.com/watch?v=ppJqQhOp_xk

7. The asymptotic Bode plot of a transfer function is as shown in figure. The transfer function G(s) corresponding to this Bode plot is