## Saturday, April 25, 2015

### Control Systems - GATE 2014 ECE Video Solutions

2014

1. The forward path transfer function of a unity feedback system is given by
The value of K which will place both the poles of the closed loop system at the same location is
_________________

2. Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which of the following conclusions is correct?

a) G(s) is an all pass filter
b) G(s) is a strictly proper transfer function
c) G(s) is a stable and minimum phase transfer function
d) The closed loop system is unstable for sufficiently large and positive k

3. In the circuit shown, the value of capacitor C (in mF) needed to have critically damped response i(t) is ______________________

4. A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system.
When y(0) = 1 and u(t) is a unit step function, y(t) is

5. consider the state space model of a system, as given below.
The given system is
a) controllable and observable
b) uncontrollable and observable
c) uncontrollable and unobservable
d) controllable and unobservable

6. The phase margin in degrees of

calculated using the asymptotic Bode plot is ____________

7. For the following feedback system
The 2% settling time of the step response is required to be less than 2 seconds.
Which one of the following compensators C(s) achieves this?

8. The natural frequency of an undamped second order system is 40 rad/sec. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/sec is ______________

9. For the system shown,
when the X1(s) = 0, the transfer function Y(s)/X2(s) is

10. An unforced linear time invariant (LTI) system is represented by
If the initial conditions are x1(0) = 1 and x2(0) = - 1, then the solution of the state equation is

11. The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.
If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input is _____________

12. Consider the state space system expressed by the signal flow diagram shown in the figure.
The corresponding system is
a) always controllable
b) always observable
c) always stable
d) always unstable

13. Consider the following block diagram in the figure.
The transfer function C(s)/R(s) is

14. The input -3e2tu(t), where u(t) is the unit step function, is applied to a system with transfer function (S-2)/(S+3). If the initial value of the output is -2, then the value of the output at steady state is _____________

15. The steady state error of the system shown in the figure for a unit step input is ___________

16. The state equation of a second order linear system is given by

17. In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following tranfer functions has this root locus?

18. In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all pole system?

19. For the second order closed loop system shown in the figure,
the natural frequency (in rad/sec) is
a) 16
b) 4
c) 2
d) 1

20. The state transition matrix Φ(t) of a system,

21. Consider a transfer function
with p a positive real parameter. The maximum value of p until which Gp remains stable is ______________

22. The characteristic equation of a unity negative feedback system is 1+KG(s) = 0. The open loop transfer function G(s) has one pole at zero and two poles at – 1. The root locus of the system for varying K is shown in the figure.
The constant damping ratio line, for ζ = 0.5, intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of K at point A is ____________

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