Question 1

Difference equation model results in:
A)sampled-data systems
B)numerical analysis of continuous time systems
C)continuous time feedback systems
D)both a & b

Accepted Answer

Difference equations are used to model sampled-data systems, which are inherently discrete in nature, and they are also fundamental in the numerical analysis of continuous-time systems, where the continuous system is approximated by a discrete model for computational purposes. Continuous time feedback systems are typically modeled by differential equations rather than difference equations.

Question 2

Which of the following is an advantage of Laplace transform method
A)it gives solution in frequency domain only
B)it gives total solution more systematically
C)initial conditions are incorporated in the very first step
D)both b & c

Accepted Answer

The Laplace transform method is advantageous because it provides a more systematic approach to finding the total solution of differential equations, and it incorporates initial conditions from the very beginning, simplifying the process of solving complex problems.

Question 3

Analysis of control system by Laplace transform technique is not possible for
A)discrete time systems
B)linear systems
C)time invarient systems
D)unstable continuous time systems

Accepted Answer

The Laplace transform technique is primarily used for continuous time systems, making it unsuitable for analyzing discrete time systems.

Question 4

Z-transform is used in:
A)continuous optimal control problem
B)discrete optimal problem
C)control systems
D)none of the mentione

Accepted Answer

Z-transform is primarily used in the analysis and design of discrete-time control systems and signal processing, making it relevant for discrete optimal problems.

Question 5

Unit step response of the system described by the equation y(n) +y(n-1) =x(n) is: A)z²/(z+1)(z-1) B)z/(z+1)(z-1) C)z+1/z-1 D)z(z-1)/z+1

Accepted Answer

The unit step response is the inverse z-transform of the system function H(z) = 1/(z+1)(z-1). Using partial fraction expansion, we get H(z) = 1/(z+1) - 1/(z-1). Taking the inverse z-transform of each term, we get h(n) = (1/2)^n u(n) - (-1/2)^n u(n) = (1/2)^n u(n), where u(n) is the unit step function.

Quiz 1: Control Systems, Sampling, and Transform Techniques

Difference equation model results in:

Which of the following is an advantage of Laplace transform method

Analysis of control system by Laplace transform technique is not possible for

Z-transform is used in:

Unit step response of the system described by the equation y(n) +y(n-1) =x(n) is: