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QUESTION: 1

The system shown in figure below has unit step input.

In order that the steady state error is 0.1, the value of K required should be

Solution:

Since Input is unit step, therefore steady state error is

Here,

QUESTION: 2

The steady-state error coefficients for a system are K_{p} = ∞ , K_{v} = finite constant and K_{a} = 0. The type of the system is

Solution:

We have,

= finite constant

From above values of K_{p}, K_{v} and K_{a} we conclude that the type of the system should be one.

QUESTION: 3

The steady-state error of a feedback control system with an acceleration input becomes finite in a

Solution:

Steady state error with an acceleration input having an amplitude of A is given by

where,

Hence, if the type of the system = 2, then K_{a }= some non-zero value or finite value due to which we will get some finite vaiue of K_{a}.

QUESTION: 4

Consider the unity feedback system shown below:

The settling time of the resulting second order system for 2% tolerance band will be

Solution:

The characteristic equation of the given closed loop system is

Comparing above equation with

Thus, setting time for 2% tolerance band is

or,

QUESTION: 5

For a control system, the Laplace transform of error signal e(t) is given by . The steady state value of the error will be

Solution:

Given,

(Using final value theorem)

or,

QUESTION: 6

For a type one system, the steady-state error due to step input is equal to

Solution:

where,

(Here, A = magnitude of step input)

Since system is type -1, therefore K_{p} = ∞

QUESTION: 7

For an unity feedback control system with the value of K for damping ratio of 0.5 is

Solution:

Characteristic equation is

or, K = 64

QUESTION: 8

The damping ratio of a system having the characteristic equation s^{2} + 2s + 8 = 0 is

Solution:

Given, s^{2} + 2s + 8 = 0

Here, ω_{n} = √8 rad/s = 2√2 rad/sec

system is underdamped.

QUESTION: 9

The closed-loop transfer function of a unity - feedback system is given by The steady state error to a unit ramp input is:

Solution:

Given,

(Since H(s) = 1)

For a unit ramp input,

QUESTION: 10

The peak overshoot of step-input response of an underdamped second-order system is an indication of

Solution:

If damping of system increases, peak overshoot M_{p} decreases and vice-versa.

QUESTION: 11

Consider the position control system shown below:

The value of K such that the steady state error is 20° for input θ_{r} = 300t rad/sec, is

Solution:

Input = 300t rad/sec = ramp input of magnitude A = 300.

For ramp input, steady state error is

where,

Now, from given block diagram, we have:

So, value of gain is K = 42.97

QUESTION: 12

Assertion (A): With the increase in bandwidth of the system the response of the system becomes fast.

Reason (R): Damping ratio of the system decreases with the increase in bandwidth.

Solution:

When BW is increased, the system response becomes fast due to fait in rise time (t_{r}).

With the increase in bandwidth of the system, damping ratio (ξ) decreases.

Thus, both assertion and reason are true but, reason is not the correct explanation of assertion.

QUESTION: 13

For the stable system described by the block diagram shown below, Match List - I (Static error coefficients) with List - II (Values) and select the correct answer using the codes given below the lists:

**List-I**

A. K_{a}

B. K_{v}

C. K_{p}

**List-II**

1. ∞

2. 0

3. 2

4. -1

Codes:

Solution:

We have,

Also,

and

QUESTION: 14

The unit step response of a system is given by c(t) - 1 + 0.25 e^{-50t }- 1.25 e^{-10t}

The given system is

Solution:

Given,

Since, ξ > 1, therefore given system is overdamped.

QUESTION: 15

Match List - I (Transfer function of systems) with List - II (Nature of damping) and select the correct answer using the codes given below the lists:

Codes:

Solution:

Characteristic equations are:

• s^{2} + 8s + 12 = 0

• s^{2} + 8s + 16 = 0

Here, ω_{n} = 4 and 2 ξω_{n} = 8

or, ξ = 1 (critically damped)

• s^{2} + 8s + 20 = 0

Here, ω_{n } = √20

and 2ξω_{n }= 8

or, ξ = 0.894 (ξ < 1 ∴ underdamped)

• s^{2} + 4 = 0

or, ω_{n} = 2

and ξ = 0 (∴ undamped)

QUESTION: 16

The block diagram of an electronic pacemaker is given in figure below.

What is the value of K for which the steady-state error to a unit ramp input is 0.02?

Solution:

Here,

As the input is a unit ramp function, therefore

QUESTION: 17

Which one of the following equations gives the steady-state error for a unity feedback system excited by r(t) = 2 + 5t + 2t^{2} ?

Solution:

Given, r(t) = 2 + 5t + 2t^{2}

QUESTION: 18

An unity feedback control system with closed loon transfer function is given by

The steady state error due a unit ramp input response is

Solution:

QUESTION: 19

The second order approximation using dominant pole concept for the transfer function

Solution:

Given,

In time constant form,

Using dominant pole concept, the given transfer function can be approximated to

QUESTION: 20

The unit step response of the system represented by the block diagram shown below is

Solution:

From given block diagram, we have

∴ c(t) = (4e^{-t} - 3e^{-2t} - 1)

= Required step response

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