### Control Systems - GATE Paper 2015 ECE Video Solutions

2015

1. The polar plot of the transfer function G(s) = 10(s+1)/(s+10) for 0 < ω < will be in the

2. A unity negative feedback system has the open loop transfer function
the value of the gain K (>0) at which the root locus crosses the imaginary axis is __________________

3. A lead compensator network includes a parallel combination fo R and C in the feed-forward path. If the transfer function of the compensator is GC(s) = (s+2)/(s+4) , the value of RC is ___________

4. A plant transfer function is given as
When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
a) KP > KI/2 > 0
b) 2KI > KP > 0
c) 2KI < KP
d) 2KI > KP

5. The open loop transfer function of a unity feedback configuration is given as
The value of a gain K( >0 ) for which -1+j2 lies on the root locus is _________.

6. A unity negative feedback system has an open loop transfer function G(s) = K / S(S+10), the gain K for the system to have a damping ratio of 0.25 is _____________

7. For the signal flow graph shown in the figure, the value of C(s)/R(s) is

8. By performing cascading and/or summing/differencing operations using transfer function blocks G1(s) and G2(s), one CANNOT realize a transfer function of the form

9. The transfer function of a mass-spring-damper system is given by
the frequency response data for the system are given in the following table.
The unit step response of the system approaches a steady state value of _____________

10. The state variable representation of a system is given as
The response y(t) is
a) sin (t)
b) 1 et
c) 1 – cos (t)
d) 0

11. The output of a standard second order system for a unit step input is given as
The transfer function of the system is

12. Consider the differential equation dx/dt = 10 – 0.2x with initial condition x(0) = 1. The response x(t) for t > 0 is
a) 2 – e-0.2t
b) 2 – e0.2t
c) 50 – 49e-0.2t
d) 50 – 49e0.2t

13. The transfer function of a first order controller is given as Gc(s) = K(s+a) / (s+b), where K, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is
a) a < b
b) a > b
c) K < ab
d) K > ab

14. Consider the Bode plot shown in figure.
Assume that all the poles and zeros are real valued. The value of fHfL (in Hertz) is ____________________

15. The phase margin (in degrees ) of the system G(s) = 10 /s(s+10) is _____________

16. The characteristic equation of an LTI system is given by F(s) = s5 + 2s4 + 3s3 + 6s2 – 4s – 8 = 0. The number of roots that lie strictly in the left half S – plane is __________.

17. A network is described by the state model as
then the transfer function H(s) = (Y(s)/U(s)) is

18. For the system shown in figure, s = - 2.75 lies on the root locus if K is ____________

19. The position control of a DC servo-motor is given in the figure. The values of the parameters are KT = 1 N-mA, Ra = 1 ohm, La = 0.1 H, J = 5 kg-m2, B = 1 N-m/(rad/sec) and Kb = 1 volt/(rad/sec). The steady state position response(in radians) due to unit impulse disturbance torque Td is _______.