Free Printable CA - 3 (STATE VARIABLE MODELLING & ANALYSIS)

1.

For an $n^{th}$ order SISO system, the system matrix $'A'$ is of the order of

a)

$n\times n$

b)

$n\times1$

c)

$1\times n$

d)

None of the above

2.

State space approach of the system analysis is a frequency domain analysis

a)

True

b)

False

3.

For an $n^{th}$ order control system, minimum number of state variables which can completely describe the system behaviour are

a)

$n$

b)

$1$

c)

$2n$

d)

$\frac{n}{2}$

4.

For a single input, $4$ state & $2$ output system, the dimension of $A$ matrix is

a)

$4\times2$

b)

$2\times4$

c)

$4\times1$

d)

$4\times4$

5.

For a $4^{th}$ order SISO system the dimension of $C$ matrix is

a)

$4\times1$

b)

$1\times4$

c)

$4\times4$

d)

$4\times2$

6.

In series $RLC$ circuit, the number of the state variables are

a)

3

b)

2

c)

1

d)

None of these

7.

The state variable technique is suitable for

a)

Only

LTI

systems

b)

Only time varying system

c)

Linear as well as non-linear system

d)

All type of system

8.

Under similarity transformation

x=P\overline{x}

, the

B

matrix is related by

a)

$\overline{B}=P^{-1}B$

b)

$\overline{B}=PB$

c)

$\overline{B}=BP^{-1}$

d)

$\overline{B}=BP$

9.

Resolvent matrix $\theta\left(s\right)$ is defined as

a)

$\left[sI-A\right]$

b)

$\left|sI-A\right|$

c)

$\left[sI-A\right]^{-1}$

d)

$\frac{1}{\left|sI-A\right|}$

10.

A set of state variable for a system is always unique

a)

True

b)

False

11.

Which of the following is not a property of the $State\ Transition\ Matrix,\ \theta\left(t\right)$

a)

$\left[\theta\left(t\right)\right]^{-1}=\theta\left(t\right)$

b)

$\theta\left(-t\right)=-\theta\left(t\right)$

c)

$\theta\left(t_1+t_2\right)=\theta\left(t_2\right).\theta\left(t_1\right)$

d)

$\left[\theta\left(t\right)\right]^n=n\theta\left(t\right)$

12.

Eigen values of a matrix are unique

a)

True

b)

False

13.

All the Eigen values of the system matrix $A$ always indicates the open loop poles of the system

a)

True

b)

Flase

14.

For the $State\ Transition\ Matrix,\ \left[\theta\left(t\right)\right]^n=n\theta\left(t\right)$

a)

True

b)

False

15.

Cayley - Hamilton theorem is applicable for any matrix

a)

True

b)

False

16.

$x\left(t\right)=\int_0^te^{A\left(t-\tau\right)}.Bu\left(\tau\right)d\tau$ , indicates the $Zero\ Input\ Response\ \left(ZIR\right)$

a)

True

b)

False

17.

The Transfer Function of a State Model is given by

a)

$B\left[sI-A\right]^{-1}C$

b)

$B^{-1}\left[sI-A\right]C$

c)

$C\left[sI-A\right]^{-1}B$

d)

$C^{-1}\left[sI-A\right]B$

18.

The matrix formed by placing the Eigen vectors together is called

a)

State Transition Matrix

b)

Modal Matrix

c)

Resolvent Matrix

d)

Transfer Matrix

19.

The free response of a system is the system with

a)

Step input

b)

Any input

c)

No input

d)

A bounded input

20.

The concept of Controllability & Observability were introduced by

a)

Gilbert

b)

Newton

c)

Kalman

d)

Gibson

CA - 3 (STATE VARIABLE MODELLING & ANALYSIS)

Total questions: 20

Worksheet time: 20mins

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