Time Response Analysis MCQ

21. The overall transfer function of a second-order control system is given by,

$\frac{C(s)}{R(s)}=\frac{2}{s^2+3s+2}$

The time response of this system, when subjected to a unit step response is

1. 1 – e^-2t + 2e^-t
2. 1 + e^-2t + 2e^-t
3. 1 – 2e^-t + e^-2t
4. 1 + e^-2t

22.  Fora unity feedback control with $G(s)=\frac{9}{s(s+3)}$

the damping ratio is

1. 1
2. 0.5
3. 0.33
4. 0.707

23. The dominant poles of a servo-system are located at s = (-2 ± j2). The damping ratio of the system is

1. 0.8
2. 1
3. 0.707
4. 0.6

24. Unit impulse response of a given system is c(t) = -4e^-t + 6e^-2t. The step response for t ≥ 0 is

1. -3e^-2t + 4e^-t – 1
2. 3e^2t + 4e^-t + 1
3. -3e^-2t – 4e^-t + 1
4. 3e^-2t + 4e^-t – 1

25. The working of a PMMC (Permanent magnet moving coil) meter is described by a second-order differential equation

$J\frac{\mathrm{d^2}\theta}{\mathrm{d} t^2}+D\frac{\mathrm{d} \theta }{\mathrm{d} t}+S\theta = T$

where,

J = Moment of inertia of the system

D = Damping coefficient

S = Spring constant

θ = Angular deflection and

T= Activating torque.

Assuming D = 0, an undamped natural angular frequency is

1. $\sqrt{\frac{S}{J}}$
2. $\sqrt{\frac{J}{S}}$
3. $\sqrt{\frac{1}{JS}}$
4. $\sqrt{\frac{1}{4JS}}$

26. A unit impulse response of a second-order system is $\frac{1}{6}e^{-0.8t}\sin (0.6t)$. Then natural frequency and damping ratio of the system are respectively

1. 1 and 0.6
2. 1 and 0.8
3. 2 and 0.4
4. 2 and 0.3

27. For a critically damped second order system, if gain constant (K) is increased, the system behaviour

1. becomes oscillatory
2. becomes underdamped
3. becomes overdamped
4. shows no change

28. The transfer function of a system is $\frac{1}{1+sT}$. The input to this system is the ramp function, tu(t). The output would track this system with an error given by

1. zero
2. $\frac{T}{2}$
3. T
4. $\frac{T^2}{2}$

29. Damping ratio ξ and peak overshoot M_p, are measures of

1. relative stability
2. absolute stability
3. speed of response
4. steady-state error

30. A second-order system is described by

$2\frac{\mathrm{d^2}y }{\mathrm{d} t^2}+4\frac{\mathrm{d} y}{\mathrm{d} t}+8y = 8x$

The damping ratio of the system is

1. 0.1
2. 0.25
3. 0.333
4. 0.5