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State Space Analysis MCQs for Electrical Engineering (EE) Exam
It covers all Important Questions with answers on State Space Analysis for the Electrical Engineering (EE) exam. The questions are based on important topics. Details about the questions:- Topic: State Space Analysis
- Type of Questions: MCQs with solutions
- Number of Questions: 41
- You can attempt them on EduRev to score high in Electrical Engineering (EE) exam.
For a linear time invariant system, an optimal controller can be designed if- a)the system is unstable but observable
- b)the system is controllable and observable
- c)the system is stable and unobservable
- d)the system is uncontrollable but stable
Correct answer is option 'B'. Can you explain this answer?
For a linear time invariant system, an optimal controller can be designed if
a)
the system is unstable but observable
b)
the system is controllable and observable
c)
the system is stable and unobservable
d)
the system is uncontrollable but stable
 | Ishani Iyer answered |
An optimal controller for an LTI system can be designed provided the system is both controllable and observable
The eigen values of linear system are the location of- a)zeros of the system
- b)poles of the system
- c)both (a) and (b)
- d)finite poles and zeros
Correct answer is option 'B'. Can you explain this answer?
The eigen values of linear system are the location of
a)
zeros of the system
b)
poles of the system
c)
both (a) and (b)
d)
finite poles and zeros
 | Avik Saha answered |
Eigen value are given by | sI- A I = 0, which is the location of poles.
Consider the following statements related to state space analysis of control systems:
1. The zeros of the system can be obtained from eigen value of the system matrix.
2. A system is said to be observable if every state x0 can be exactly determined from the measurement of the output ‘y’ over a finite interval of time 0 ≤ t ≤ tf.
3. The process by which transfer function changes to state diagram or state equations is called decomposition of the transfer function.
4. The state space techniques can be applied to linear and time invariant systems only.Which of the above statements are correct?- a)1, 3 and 4
- b)1, 2 and 3
- c)2 and 3
- d)2, 3 and 4
Correct answer is option 'C'. Can you explain this answer?
Consider the following statements related to state space analysis of control systems:
1. The zeros of the system can be obtained from eigen value of the system matrix.
2. A system is said to be observable if every state x0 can be exactly determined from the measurement of the output ‘y’ over a finite interval of time 0 ≤ t ≤ tf.
3. The process by which transfer function changes to state diagram or state equations is called decomposition of the transfer function.
4. The state space techniques can be applied to linear and time invariant systems only.
1. The zeros of the system can be obtained from eigen value of the system matrix.
2. A system is said to be observable if every state x0 can be exactly determined from the measurement of the output ‘y’ over a finite interval of time 0 ≤ t ≤ tf.
3. The process by which transfer function changes to state diagram or state equations is called decomposition of the transfer function.
4. The state space techniques can be applied to linear and time invariant systems only.
Which of the above statements are correct?
a)
1, 3 and 4
b)
1, 2 and 3
c)
2 and 3
d)
2, 3 and 4
 | Rajesh Verma answered |
The poles of the system can be obtained from eigen values of the system matrix. Hence, statement-1 is false.
State space techniques can be applied to linear or non-linear, time variant or time invariant systems.
Hence, statement-4 is false.
State space techniques can be applied to linear or non-linear, time variant or time invariant systems.
Hence, statement-4 is false.
Consider the system shown in fig.
Q. The system is- a)Controllable and observable
- b)Controllable only
- c)Observable only
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
Consider the system shown in fig.
Q. The system is
a)
Controllable and observable
b)
Controllable only
c)
Observable only
d)
None of the above
 | Bijoy Mehra answered |
Since the determinant is not zero, the 3 x 3 matrix is nonsingular and system is controllable
The rank of OM is 3. Hence system is observable.
The system equations are given by
y(t) = [1 0]x(t)
The transfer function of the above system is- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The system equations are given by
y(t) = [1 0]x(t)
The transfer function of the above system is
y(t) = [1 0]x(t)
The transfer function of the above system is
a)
b)
c)
d)
 | Alok Verma answered |
Given,
Transfer function of the given system is
Now,
∴
= s2 + 3s + 2
Now,
Now,
Transfer function of the given system is
Now,
∴
= s2 + 3s + 2
Now,
Now,
The transfer function of the system shown below is
- a)
- b)
- c)
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The transfer function of the system shown below is
a)
b)
c)
d)
none of these
 | Hiral Kulkarni answered |
From given block diagram, the state equations can be written as:
Also, output equation is
y = 2x1 + x2
In matrix form, we have:
and y = [2 1]x(t)
Now,
∴ Transfer function,
Also, output equation is
y = 2x1 + x2
In matrix form, we have:
and y = [2 1]x(t)
Now,
∴ Transfer function,
The state variable description of an autonomous system is, X = AX where X is a two-dimensional vector and A is a matrix given by
The eigen values of A are- a)jω and σ + jω
- b)σ + jω and σ - jω
- c)σ - jω and σ + jω
- d)σ - jω and jω
Correct answer is option 'B'. Can you explain this answer?
The state variable description of an autonomous system is, X = AX where X is a two-dimensional vector and A is a matrix given by
The eigen values of A are
The eigen values of A are
a)
jω and σ + jω
b)
σ + jω and σ - jω
c)
σ - jω and σ + jω
d)
σ - jω and jω
| | Pankaj Mehta answered |
Eigen values of A are given by
or, (s - σ)2 + ω2 = 0
or, s = σ ± jω
or, s = σ + jω and s = σ - jω
or, (s - σ)2 + ω2 = 0
or, s = σ ± jω
or, s = σ + jω and s = σ - jω
Determine the state-space representation for the transfer function given in question. Choose the state variable as follows
Q. 
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Determine the state-space representation for the transfer function given in question. Choose the state variable as follows
Q.
a)
b)
c)
d)
 | Sneha Roy answered |
(s3 + a2s2 + a1s + a0)C(s) = b0R(s)
Taking the inverse Laplace transform assuming zero initial conditions
Consider the network shown in fig.
Q. The state variable may be- a)i2 , i4
- b)i2 , i4 , vo
- c)i1 , i3
- d)i1 , i3 , i5
Correct answer is option 'B'. Can you explain this answer?
Consider the network shown in fig.
Q. The state variable may be
a)
i2 , i4
b)
i2 , i4 , vo
c)
i1 , i3
d)
i1 , i3 , i5
 | Moumita Chopra answered |
There are three energy storage elements, hence 3 variable. i2 ,i4 and vo are available in differentiated form hence these are state variable.
Consider the following matrix:
x(t) is given by - a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
Consider the following matrix:
x(t) is given by
x(t) is given by
a)
b)
c)
d)
| | Arindam Sengupta answered |
Given,
So, x(t) = ϕ(t).x(0)
= state transition equation
So, x(t) = ϕ(t).x(0)
= state transition equation
The state-variable description of a linear autonomous system is 
is a two-dimensional state vector and A is a matrix given by 
The poles of the system are located at - a)- 5 and +5
- b)- 5j and +5j
- c)-5 and -5
- d)+5 and +5
Correct answer is option 'A'. Can you explain this answer?
The state-variable description of a linear autonomous system is is a two-dimensional state vector and A is a matrix given by
is a two-dimensional state vector and A is a matrix given by The poles of the system are located at
a)
- 5 and +5
b)
- 5j and +5j
c)
-5 and -5
d)
+5 and +5
 | Prisha Sen answered |
Poles of given system are given by
A state flow graph is shown in fig.
The system is- a)Observable and controllable
- b)Controllable only
- c)Observable only
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
A state flow graph is shown in fig.
The system is
a)
Observable and controllable
b)
Controllable only
c)
Observable only
d)
None of the above
 | Diya Patel answered |
det OM = 0. Thus system is not observable
det CM = -1. Thus system is controllable.
det CM = -1. Thus system is controllable.
The state space representation of the system represented by the SFG shown below is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The state space representation of the system represented by the SFG shown below is
a)
b)
c)
d)
| | Bijoy Mehta answered |
The state equations from the given signal flow graph can be written as:
In matrix form,
Also, output is
y(t) = 6x1 + x2
In matrix form
In matrix form,
Also, output is
y(t) = 6x1 + x2
In matrix form
Complete the given series from the options given below.
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
Complete the given series from the options given below.
a)
b)
c)
d)
| | Arpeet Subudhi answered |
The answer is option 'C' because according to the given series the blue box will come after the red box.
Consider the network shown in fig. The state-space representation for this network is
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
Consider the network shown in fig. The state-space representation for this network is
a)
b)
c)
d)
 | Varun Banerjee answered |
vc and iL are state variable.
Hence equation are
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