### GATE 2007 ECE Control Systems - Complete Video Solutions with Answers

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

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

3. A control system with a PD controller is shown in the figure.
If the velocity error constant Kv = 1000 and the damping ratio ξ = 0.5, then the values of Kp and KD are
a) Kp = 100, KD = 0.09
b) Kp = 100, KD = 0.9
c) Kp = 10, KD = 0.09
d) Kp = 10, KD = 0.9

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

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

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

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

8. The state space representation of a separately excited DC servo motor dynamics is given as
where ω is the speed of the motor, ia is the armature current and u is the armature voltage. The transfer function of the motor is

9. The eigen value and eigen vector pairs (λi, vi) for the system are

Solution :

10. The system matrix A is

Solution :