Question 1

The transfer function of a LTI system is given as 1/(s+1). What is the steady-state value of the unit-impulse response?
A)0
B)1
C)2
D)infinite

Accepted Answer

The steady-state value of the unit-impulse response of a stable LTI system is always zero because the impulse response is a transient response.

Question 2

The values of the characteristic equation is given by:
A)eigen values
B)state matrix
C)eigen vector
D)none of the mentioned

Accepted Answer

The values of the characteristic equation are known as eigenvalues. These are the values for which the characteristic equation (determined from the state matrix of a system) equals zero, indicating the system's natural frequencies or modes.

Question 3

The state variable representation is preferred
A)to increase the sensitivity to the plant parameter variations
B)to reduce the sensitivity to the plant parameter variations
C)to make a plant simple and to control the transient response
D)none of the above

Accepted Answer

C

Question 4

With the knowledge of state space representation the transfer function of the system
A)can be determined partly
B)can be determined completely
C)cannot be determined
D)none of the above

Accepted Answer

The transfer function of a system can be determined completely from its state space representation by using the formula $H(s) = C(sI - A)^{-1}B + D$, where $H(s)$ is the transfer function, $A$, $B$, $C$, and $D$ are matrices that define the state space model, and $s$ is the complex frequency variable.

Question 5

Which among the following are the interconnected units of state diagram representation?
A)scalars
B)adders
C)integrators
D)all of the above

Accepted Answer

In state diagram representation, interconnected units can include scalars, adders, and integrators, as they all play roles in defining the system's behavior over time.

Question 6

Which among the following controls the speed of D.C. motor?
A)galvanometer
B)gauss meter
C)potentiometer
D)tachometer

Accepted Answer

A tachometer is a device that measures the speed of a rotating shaft. It is used to control the speed of a DC motor by measuring the speed of the motor's armature and adjusting the voltage applied to the motor to maintain the desired speed.

Question 7

State model representation is possible using _________
A)physical variables
B)phase variables
C)canonical state variables
D)all of the above

Accepted Answer

State model representation can be achieved using physical variables, phase variables, or canonical state variables. Each approach offers a different perspective or method for representing the system's state, making all of the above correct choices for state model representation.

Question 8

Which among the following constitute the state model of a system in addition to state equations?
A)input equations
B)output equations
C)state trajectory
D)state vector

Accepted Answer

The state model of a system consists of state equations and output equations. The output equations relate the state variables to the outputs of the system.

Question 9

Which among the following plays a crucial role in determining the state of dynamic system?
A)state variables
B)state vector
C)state space
D)state scalar

Accepted Answer

State variables are the variables that describe the state of a dynamic system. They are used to determine the state vector, which is a vector of all the state variables. The state space is the space of all possible values of the state vector. The state scalar is a single variable that represents the state of the system.

Question 10

What is Eigen value?
A)a vector obtained from the coordinates
B)a matrix determined from the algebraic equations
C)a scalar associated with a given linear transformation
D)it is the inverse of the transform

Accepted Answer

Eigenvalues are scalars associated with a linear transformation that, when multiplied by a given vector, do not change the direction of that vector, only its magnitude.

Question 11

Let us consider a 3×3 matrix A with Eigen values of ?1, ?2, ?3 and the Eigen values of A-1 are?
A)?1, ?2, ?3
B)1/?1,1/?2,1/?3
C)-?1, -?2, -?3
D)?1, 0, 0

Accepted Answer

The eigenvalues of the inverse of a matrix A (denoted as A^-1) are the reciprocals of the eigenvalues of A. Therefore, if A has eigenvalues λ1, λ2, λ3, then A^-1 will have eigenvalues 1/λ1, 1/λ2, 1/λ3.

Question 12

The Eigen values of a 3×3 matrix are ?1, ?2, ?3 then the Eigen values of a matrix A3 are __________
A)?1, ?2, ?3
B)1/?1,1/?2,1/?3
C)?31,?32,?33
D)1, 1, 1

Accepted Answer

If $\lambda$ is an eigenvalue of a matrix $A$, then $\lambda^n$ is an eigenvalue of $A^n$. Therefore, the eigenvalues of $A^3$ are $\lambda_1^3$, $\lambda_2^3$, and $\lambda_3^3$.

Question 13

State space analysis is applicable even if the initial conditions are _____
A)zero
B)non-zero
C)equal
D)not equal

Accepted Answer

State space analysis is applicable for any initial conditions, including non-zero initial conditions, because it accounts for the system's entire state at a given time, not just its output or input.

Question 14

According to the property of state transition method, e0 is equal to _____
A)i
B)a
C)e^-at
D)-e^At

Accepted Answer

The property of the state transition method indicates that e^0 is equal to the identity matrix, which is mathematically represented as I. However, among the given options, the closest representation to the identity matrix when considering the context of state transition and time t=0 is e^(-at) where a=0, making e^0 = e^(0) = I. The correct interpretation of the identity matrix or the effect of zero state transition in the context of the given options is thus e^(-at) with a=0, leading to the identity matrix. However, it's important to clarify that the exact representation of the identity matrix is not listed among the options, but C is the closest based on the given context.

Question 15

Which mechanism in control engineering implies an ability to measure the state by taking measurements at output?
A)controllability
B)observability
C)differentiability
D)adaptability

Accepted Answer

Observability is the property of a system that allows for the determination of its internal states by observing its outputs. This concept is crucial in control engineering for designing systems that can be effectively monitored and controlled.

Question 16

State model representation is possible using _________
A)physical variables
B)phase variables
C)canonical state variables
D)all of the mentioned

Accepted Answer

State model representation can be achieved using physical variables, phase variables, and canonical state variables, making all the mentioned options correct.

Question 17

Which among the following constitute the state model of a system in addition to state equations?
A)input equations
B)output equations
C)state trajectory
D)state vector

Accepted Answer

The state model of a system consists of state equations and output equations, which together describe the system's dynamics and outputs.

Question 18

Which among the following are the interconnected units of state diagram representation?
A)scalars
B)adders
C)integrator
D)all of the mentioned

Accepted Answer

State diagram representation involves interconnected units that can include scalars, adders, and integrators, among others, to describe the behavior of dynamic systems.

Question 19

Which among the following is a unique model of a system?
A)transfer function
B)state variable
C)block diagram
D)signal flow graphs

Accepted Answer

The answer of Which among the following is a unique...

Question 20

State model is generally not suitable for measuring:
A)investigation of system properties
B)evaluation of time response
C)real variables
D)both a and b

Accepted Answer

State models are primarily used for analyzing system properties and evaluating time responses, making them suitable for these purposes. They are not inherently unsuitable for dealing with real variables, which can be represented in state models. Therefore, the statement that state models are generally not suitable for measuring both the investigation of system properties and the evaluation of time response is incorrect.

Quiz 3: State Space Analysis and Eigen Values

The transfer function of a LTI system is given as 1/(s+1) . What is the steady-state value of the unit-impulse response?

The values of the characteristic equation is given by:

The state variable representation is preferred

With the knowledge of state space representation the transfer function of the system

Which among the following are the interconnected units of state diagram representation?

Which among the following controls the speed of D.C. motor?

State model representation is possible using _________

Which among the following constitute the state model of a system in addition to state equations?

Which among the following plays a crucial role in determining the state of dynamic system?

What is Eigen value?

Let us consider a 3×3 matrix A with Eigen values of ?1, ?2, ?3 and the Eigen values of A-1 are?

The Eigen values of a 3×3 matrix are ?1, ?2, ?3 then the Eigen values of a matrix A3 are __________

State space analysis is applicable even if the initial conditions are _____

According to the property of state transition method, e0 is equal to _____

Which mechanism in control engineering implies an ability to measure the state by taking measurements at output?

State model representation is possible using _________

Which among the following constitute the state model of a system in addition to state equations?

Which among the following are the interconnected units of state diagram representation?

Which among the following is a unique model of a system?

State model is generally not suitable for measuring: