What does a transfer function represent in control systems?
A
Time-domain input/output relation
C
Laplace domain output/input ratio
D
Phase difference of a signal
Analysis & Theory
A transfer function is the Laplace transform of the output divided by the Laplace transform of the input, assuming zero initial conditions.
Which of the following conditions must be satisfied for defining a transfer function?
A
System must be time-varying
B
System must be nonlinear
C
Initial conditions must be non-zero
D
System must be linear and time-invariant
Analysis & Theory
Transfer functions are valid only for linear time-invariant (LTI) systems under zero initial conditions.
If the input of a system is X(s) and output is Y(s), then the transfer function is:
Analysis & Theory
The transfer function T(s) is defined as Y(s)/X(s) in the Laplace domain.
What is the transfer function of a system described by: d²y/dt² + 3dy/dt + 2y = x(t)?
Analysis & Theory
Taking Laplace transform with zero initial conditions gives Y(s)(s² + 3s + 2) = X(s), so T(s) = Y(s)/X(s) = 1 / (s² + 3s + 2).
In a transfer function, poles are defined as:
A
Values of s that make numerator zero
B
Values of s that make denominator zero
C
All positive real numbers
D
Imaginary part of s only
Analysis & Theory
Poles are values of 's' that make the denominator of the transfer function equal to zero.
What is the transfer function of a unity feedback system with forward path gain G(s)?
Analysis & Theory
For a unity feedback system, T(s) = G(s) / [1 + G(s)].
Which of the following is true for a transfer function?
A
It depends on input and output units
B
It is defined only in time domain
C
It relates input and output in Laplace domain
D
It cannot represent dynamic behavior
Analysis & Theory
A transfer function describes the system behavior in the Laplace domain (frequency domain), not the time domain.
What does a pole at s = 0 imply in a transfer function?
B
The system has a constant gain
C
The system has an integrator
D
The system is oscillatory
Analysis & Theory
A pole at s = 0 indicates the presence of an integrator in the system.
Which of these tools is used to analyze transfer functions graphically?
Analysis & Theory
Bode plots are used to analyze the frequency response of transfer functions graphically.
What happens if all poles of a transfer function lie in the left half of the s-plane?
B
System is marginally stable
Analysis & Theory
A system is stable if all poles lie in the left half of the s-plane (have negative real parts).