Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 6th Sem 2161707 Control System Design Previous Question Paper

Seat No.: ________

Enrolment No.___________

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**BE - SEMESTER? VI EXAMINATION ? SUMMER 2020**

**Subject Code: 2161707**

**Date:27/10/2020**

**Subject Name: Control System Design**

**Time: 10:30 AM TO 01:00 PM Total Marks: 70**

**Instructions:**

**1. Attempt all questions.**

**2. Make suitable assumptions wherever necessary.**

**3. Figures to the right indicate full marks.**

**MARKS**

**Q.1 (a)**Explain state, state variable and state vector with reference to

**03**

state space.

**(b)**Compare lead and lag compensation techniques in frequency

**04**

domain.

**(c)**Find state space model for RLC series circuit. Consider voltage

**07**

across capacitor as an output with R = 1K, C=5F and L=2H.

**Q.2 (a)**Explain diagonal canonical form in state space.

**03**

**(b)**Find controllable and observable canonical form for the system

**04**

with transfer function 2 .

(+1)

**(c)**Derive condition for complete state controllability of the system.

**07**

Also find controllability for the system x = Ax + Bu and y =

0

1

0

cx with A=[

], B=[ ] and C = [0 1].

-1 -2

1

**OR**

**(c)**Derive condition for complete state observability of the system.

**07**

Also find observability for the system x = Ax + Bu and y =

0

1

1

Cx with A=[

] , B=[ ] and C=[0 1].

-2 -3

0

**Q.3 (a)**Find Eigen value for the system x = Ax + Bu and y = cx with

**03**

A= 0 1

[

].

2

4

**(b)**Compare conventional and modern control theory.

**04**

**(c)**Explain dead beat response with suitable example.

**07**

**OR**

**Q.3 (a)**Explain linear dependence and independence of vectors.

**03**

**(b)**Explain lag compensation using root locus technique.

**04**

**(c)**Design a suitable compensator for the unity feedback system

**07**

with open loop transfer function

K

G(s) =

, to meet the

S(S+1)(S+3)

following specifications:

a. Phase margin at least 52 degree

b. Gain margin at least 8 db

c. Velocity error constant at least 6 sec-1

**Q.4 (a)**Explain need of linear quadratic regulator.

**03**

**(b)**Explain lead compensation using root locus technique.

**04**

**(c)**Find transfer function of system with following state space

**07**

representation. Also comment on stability of the system.

0

1

0

*A*

*B*

*C*0

1

*D*.

1 2

0

1

1

**OR**

**Q.4 (a)**Explain optimal control system.

**03**

**(b)**Explain Lyapunov stability criteria.

**04**

**(c)**Discuss about the design of state observer with diagram and

**07**

equations.

**Q.5 (a)**Explain the need of robust PID controller.

**03**

**(b)**Discuss factors to be considered while designing robust control

**04**

system.

**(c)**Find state transition matrix of system with following state space

**07**

representation. Also state property of state transition matrix.

0

1

0

*A*

*B*

*C*0

1

*D*.

4

6

0

1

**OR**

**Q.5 (a)**Explain Riccatti Equation.

**03**

**(b)**Discuss Lag-Lead Compensator design in frequency domain.

**04**

**(c)**Discuss design steps for pole placement using Ackerman's

**07**

formula.

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2

This post was last modified on 04 March 2021