### GATE 2005 ECE Control Systems - Complete Video Solutions with Answers

GATE 2005

1. A linear system is equivalently represented by two sets of state equations
Ẋ = AX + BU   and   Ẇ = CW + DU.
The eigen values of the representations are also computed as |λ| and |μ|. Which one of the following statements is TRUE?

Solution :

2. Which one of the following polar diagrams corresponds to a lag network?

3. Despite the percentage of negative feedback, control systems still have problems of Instability because the
a) components used have non-linearity
b) dynamic equations of the sub-systems are not know exactly
c) mathematical analysis involves approximations
d) system has large negative phase angle at high frequencies

4. The polar diagram of a conditionally stable system for open loop gain K = 1 is shown in figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

5. In the derivation of expression for peak percent overshoot, which one of the following conditions is NOT required?
a) system is linear and time invariant
b) system transfer function has a pair of complex conjugate poles and no zeros
c) there is no transportation delay in the system
d) the system has zero initial conditions

6. A ramp input applied to an unity feedback system results in 5% steady state error. The Type number and zero frequency gain of the system are respectively
a) 1 and 20
b) 0 and 20
c) 0 and 1/20
d) 1 and 1/20

7. A double integrator plant, G(s) = K/S2, H(s) = 1 is to be compensated to achieve the damping ratio ξ = 0.5, and an undamped natural frequency ωn = 5 rad/sec. Which one of the following compensator Gc(s) will be suitable?

8. A unity feedback system is given as G(s) = k(1 – s) / [s(s + 3)]. Indicate the correct root locus diagram.

The open loop transfer function of a unity feedback is given by G(s) = 3e–2s / [s(s + 2)].
9. The Gain and Phase cross over frequencies in rad/sec are, respectively
a) 0.932 and 1.26
b) 0.632 and 0.485
c) 0.485 and 0.632
d) 1.26 and 0.632

10. based on the above results, the Gain and Phase Margins of the system will be
a) –7.09 dB and 87.5o
b) 7.09 dB and 87.5o
c) 7.09 dB and –87.5o
d) –7.09 dB and –87.5o