# Transfer Function

1. A linear system at rest is subject to an input signal r(t)=1-e-t. The response of the system for t>0 is given by c(t)=1-e-2t. The transfer function of the system is:
a) (s+2)/(s+1)
b) (s+1)/(s+2)
c) 2(s+1)/(s+2)
d) (s+1)/2(s+2)

2. In continuous data systems:
a) Data may be continuous function of time at all points in the system
b) Data is necessarily a continuous function of time at all points in the system
c) Data is continuous at the inputs and output parts of the system but not necessarily during intermediate processing of the data
d) Only the reference signal is continuous function of time
Answer: Data is necessarily a continuous function of time at all points in the system

3. In regenerating the feedback, the transfer function is given by
a) C(s)/R(s)=G(s)/1+G(s)H(s)
b) C(s)/R(s)=G(s)H(s)/1-G(s)H(s)
c) C(s)/R(s)=G(s)/1+G(s)H(s)
d) C(s)/R(s)=G(s)/1-G(s)H(s)

4. A control system whose step response is -0.5(1+e-2t) is cascaded to another control block whose impulse response is e-t. What is the transfer function of the cascaded combination?
a) 1/(s+2)(s+1)
b) 1/(s+1)s
c) 1/(s+3)
d) 0.5/(s+1)(s+2)

5. A transfer function has two zeroes at infinity. Then the relation between the numerator(N) and the denominator degree(M) of the transfer function is:
a) N=M+2
b) N=M-2
c) N=M+1
d) N=M-1

6. The output of the feedback control system must be a function of:
a) Reference input
b) Reference output
c) Output and feedback signal
d) Input and feedback signal

7. If the initial conditions for a system are inherently zero, what does it physically mean?
a) The system is at rest but stores energy
b) The system is working but does not store energy
c) The system is at rest or no energy is stored in any of its part
d) The system is working with zero reference input
Answer: The system is at rest or no energy is stored in any of its part

8. The principle of homogeneity and superposition are applied to:
a) Linear time invariant systems
b) Nonlinear time invariant systems
c) Linear time variant systems
d) Nonlinear time invariant systems

9. When deriving the transfer function of a linear element
b) Initial conditions are taken into account but the element is assumed to be not loaded
c) Initial conditions are assumed to be zero but loading is taken into account
d) Initial conditions are assumed to be zero and the element is assumed to be not loaded

10. Which of the following is not the feature of modern control system?
a) Quick response
b) Accuracy
c) Correct power level
d) No oscillation

11. The transfer function of a system is given as 81/ (s^2 + 16s + 81). Find the undamped natural frequency, damping ratio, and peak time for a unit step input.

a) 9, 0.889, 0.762

b) 9, 0.559, 0.762

c) 9, 0.889, 0.187

d) 9, 0.667, 0.187

12. The transfer function of a compensating network is in the form of (1 +aTs) / (1 + Ts). Find the value of 'a' if the given network is the phase-lag network.

a) Between 0 and 1.

b) 0

c) 1

d) Greater than 1