**B.Tech.** **(EE-2011 Batch)**

## LINEAR CONTROL SYSTEMS

### Subject Code : BTEE-402Â Â Â Â Â Paper ID : [ A1188]

### Time : 3 Hrs.Â Â Â Â Â Â Â Â Â Â Â Â Â Max. Marks : 60

#### INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.

2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.

3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions

## Linear Control Systems 4th Sem BTEE-402 B.Tech EE PTU Nov 2016 Paper

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SECTION-A**

**Q1. Write Short Notes on :**

#### a What do you mean by servo mechanism? Explain.

b Write down the analogies of electrical and mechanical systems.

c What do you mean by the term relative stability? Explain.

d Define poles and zeros of a system.

e Discuss (in brief) various test signals used for time domain analysis.

f Why sinusoidal input signal alone is used for the analysis in frequency domain?

g Define Transfer Function.

h What do you mean by steady state error? Explain.

i List the advantages of frequency domain analysis.

j What is the need of compensator? Discuss.

## Â **Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SECTION-B**

**Q2. Attempt any FOUR questions.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5×4=20**

#### 2. Discuss the field control DC motor. Also find the transfer function relating angular velocity and the input voltage applied to the field winding.

#### 3. Discuss the correlation between time and frequency domain specifications for second order systems.

#### 4. Determine theÂ stabilityÂ ofÂ theÂ systemÂ whoseÂ characteristicsÂ equationÂ isÂ givenÂ byÂ Â s^{5} + s^{4} + 2 s^{3} + 2 s^{2} + 11s + 10 = 0

#### 5. Represent the following set of equations by a signal flow graph and determine the overall gain relating *x*_{5} and *x*_{1 .Â Â }*x*_{2} = 2*x*_{1} + 6*x*_{2}Â Â ; *x*_{3} = *x*_{2} + 7*x*_{4} ;Â Â Â Â Â Â *x*_{4} = 5*x*_{3} + 3*x*_{5};Â Â Â Â Â *x*_{5} = 3*x*_{4} + 8*x*_{2}

#### 6. Sketch the Bode plot for the open loop transfer function for the unity feedback system

#### G(s) = 50/(s + 2)(s +1)

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SECTION-C**

**Q3. Attempt any TWO questions.****Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2×10=20**

**Â 1.**Discuss :a) Linear and non-linear systems

#### b). Open and closed loop systems

#### c). Time variant and time invariant systems

#### d) Transfer function

#### 4. Sketch the root locus plot and determine the value of K if damping ratio is 707, for the system whose open loop transfer function is given by G(s) H(s) = K/s(s + 4)

#### 5. Design a phase lead, compensation network having open loop transfer function given below such that the system will have acceleration error coefficient =100 sec^{â€“2} and suitable phase margin for stable operation

#### G(s) =K/s2Â (1 + 0.05s)

Servo mechanism.Explain.

Analogies of electrical and mechanical systems.

Explain the term relative stability

Poles and zeros of a system.

Various test signals used for time domain analysis.

Explain Why sinusoidal input signal alone is used for the analysis in frequency domain.

Transfer Function.

Explain Steady state error.

Advantages of frequency domain analysis.

Need of compensator.

###### Linear Control Systems 4th Sem BTEE-402 B.Tech PTU NOVÂ PaperÂ

#### Field control DC motor.Â

#### Transfer function relating angular velocity and the input voltage applied to the field winding.

#### Â

#### Correlation between time and frequency domain specifications for second order systems.

#### Â

#### StabilityÂ ofÂ theÂ systemÂ whoseÂ characteristicsÂ equationÂ isÂ givenÂ byÂ Â s^{5} + s^{4} + 2 s^{3} + 2 s^{2} + 11s + 10 = 0

#### Â

#### Following set of equations by a signal flow graph and determine the overall gain relating *x*_{5} and *x*_{1 .Â Â }*x*_{2} = 2*x*_{1} + 6*x*_{2}Â Â ; *x*_{3} = *x*_{2} + 7*x*_{4} ;Â Â Â Â Â Â *x*_{4} = 5*x*_{3} + 3*x*_{5};Â Â Â Â Â *x*_{5} = 3*x*_{4} + 8*x*_{2}

#### Â

#### Bode plot for the open loop transfer function for the unity feedback system

#### G(s) = 50/(s + 2)(s +1)

##### Linear Control Systems 4th Sem BTEE-402 B.Tech PTU NOV 2016 PaperÂ

#### a) Linear and non-linear systems

#### Â

#### b) Open and closed loop systems

#### Â

#### c) Time variant and time invariant systems

#### Â

#### d) Transfer function

#### Â

#### Root locus plot and determine the value of K if damping ratio is 707, for the system whose open loop transfer function is given by G(s) H(s) = K/s(s + 4)

#### Â

#### Phase lead, compensation network having open loop transfer function given below such that the system will have acceleration error coefficient =100 sec^{â€“2} and suitable phase margin for stable operation

#### G(s) =K/s2Â (1 + 0.05s)

##### Linear Control Systems 4th Sem BTEE-402 B.Tech PTU Nov 2016 Paper

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