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QUESTION: 1

Non-minimum phase transfer function is defined as the transfer function

Solution:

The non-minimum phase transfer function is defined as the transfer function is defined as the transfer function which has zeros (or) poles in right side of s-plane

QUESTION: 2

The type and order of the system described by the open loop transfer function are respectively

Solution:

There is no open loop pole at origin. Hence, type of system = 0.

Highest power of s of the characteristic equation 1+ G(s) = 0 will be 2.

Hence, order of given System = 2.

QUESTION: 3

Assertion (A): If the number of zeros are less than the number of poles (i.e. Z < P), we say that there are zeros at infinity and the order of such zeros is P-Z

Reason (R): The value of the transfer function becomes zero for s tends to zero.

Solution:

For Z < P,

∴ Here, number of zeros = 1 and no. of poles = 2

∴ P - Z = 1

When s →∞, transfer function becomes zero. Thus, there is one zero (P - Z = 1) at infinity. Thus, assertion is true.

Since value of transfer function becomes zero as s →∞ therefore, reason is false.

QUESTION: 4

The transfer function ofthe network shown below is

Solution:

Let i be the current in the given circuit.

QUESTION: 5

Consider the following statements regarding the properties of transfer function:

1. The transfer function is independent of the input of the system.

2. The transfer function is defined for linear time- variant system.

3. The transfer function of a continuous-data system is expressed only as a function of the complex variable s.

4. All the initial conditions are not necessarily set to zero for finding the transfer function of a given system.

Q. Which of the above statements is/are not true?

Solution:

**Correct Answer :- D**

**Explanation : **The properties of transfer function are given below:

1) The ratio of Laplace transform of output to Laplace transform of input assuming all initial conditions to be zero.

2) The transfer function of a system is the Laplace transform of its impulse response under assumption of zero initial conditions.

3) Replacing ‘s’ variable with linear operation D = d/dt in transfer function of a system, the differential equation of the system can be obtained.

4) The transfer function of a system does not depend on the inputs to the system.

5) The system poles and zeros can be determined from its transfer function.

QUESTION: 6

The differential equation of a control system having input x(t) and output y(t) is given as

The output response of the system for unit step input is given by

Solution:

Given differential equation is

QUESTION: 7

The step response of a system is given by

c(t) = 1 + 0.25 e^{-50t} - 1.25e^{-10t}

The steady state gain of the transfer function in time constant form will be

Solution:

Given, c(t) = 1 + 0.25 e^{-50t} - 1.25e^{-10t}

Thus,C(s)/R(s) is in time constant form having steady state gain = 1.

QUESTION: 8

The poles and zeros of the transfer function for the network shown below are located at

Solution:

For given network, total input impedance is

QUESTION: 9

The pole-zero configuration of a transfer function is shown below:

If the value of the transfer function at s = 1 is 3.2, the gain factor K is

Solution:

From given pole-zero plot, transfer function is

So, gain factor K =12

QUESTION: 10

The type of a system denotes the number of

Solution:

The type of a system denotes the no. of poles of origin.

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