valliammai engineering college - Vidyarthiplus

VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur – 603 203.

DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING

QUESTION BANK

SUBJECT : EC6405 – CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year B.E.

EC6405 CONTROL SYSTEM ENGINEERING

UNIT I – CONTROL SYSTEM MODELLING

Basic Elements of Control System – Open loop and Closed loop systems - Differential equation - Transfer

function, Modeling of Electric systems, Translational and rotational mechanical systems - Block diagram

reduction Techniques - Signal flow graph PART A

Q.No Questions BT

Level

Domain

1. Compare the Open loop System with Closed loop System. BTL 4 Analyzing

2. Design the Electrical analogous network for the mechanical

system shown in the fig. using Force-Voltage Analogy.

BTL 6 Creating

3. Mention the transfer Function of the System. BTL 1 Remembering

4. List the advantages of Closed loop System? BTL 1 Remembering

5. What are the Properties of Signal flow graphs? BTL 1 Remembering

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6. Give Mason’s gain formula of Signal flow graph. BTL 2 Understanding

7. Explain any two dynamic models to represent control system. BTL5 Evaluating

8. Discuss about the block diagram and its components of a

control system.

BTL 2 Understanding

9. Demonstrate the basic elements used for modelling a

mechanical rotational system.

BTL 3 Applying

10. Assess feedback and its types employed in Control system. BTL 4 Analyzing

11. Negative feedback is preferred in control system. Justify BTL 5 Evaluating

12. Write F-V Analogy for the elements of mechanical rotational

system?

BTL 1 Remembering

13. Illustrate any two rules to be followed in block diagram reduction

techniques.

BTL 3 Applying

14. Define Control System BTL 1 Remembering

15. Analyze non-touching loops. BTL 4 Analyzing

16. Interpret signal flow graph BTL 2 Understanding

17. Name the two types of electrical analogous for mechanical

system.

BTL 1 Remembering

18. Formulate force balance equation of ideal spring, ideal mass. BTL 6 Creating

19. Calculate transfer function of the network

BTL3 Applying

20. Describe mathematical model of a system. BTL 2 Understanding

PART –B

1. (i) How could you determine the Transfer Function of the

system Shown in the fig. (7)



(ii) Estimate the Transfer function of the electrical network

shown in the fig. (6)

BTL 5

Evaluating

2. (i) Design the Block diagram to its Canonical form and obtain

C(s)/R(s). (8)

(ii) Compile the differences between block diagram and Signal

flow graph methods. (5)

BTL 6

Creating

3. Solve C/R for the signal flow graph shown below. (13)

BTL 3

Applying

4. (i) Consider the Mechanical system shown below and write

the Differential equation. (7)

BTL1

Remembering



(ii) Draw the torque-voltage electrical analogous circuit for the

mechanical system shown below. (6)

5. (i) State any five block diagram reduction rules with example.

(8)

(ii) Mention in detail about any five terminologies used in

signal flow graph. (5)

BTL1

Remembering

6. (i) Can you discover the Equivalent signal flow graph and

obtain C/R using mason’s gain formula for the block diagram

show below. (6)

(ii) For the block diagram shown below, inspect the output

C/R. (7)

BTL4

Analyzing



7. Using SFG, Analyze the overall Transfer function for the

system shown in the fig. (13)

BTL4

Analyzing

8. How can you explain the differential equations governing the

mechanical rotational system shown in Fig. and estimate the T-

V and T-I electrical analogous circuits. (13)

BTL 1 Remembering

9. Demonstrate the differential Equations governing the

mechanical system shown in the fig. and determine the transfer

function. (13)

BTL2

Understanding

10. Estimate the overall transfer function of the system shown in

the fig.

BTL2

Understanding



Fig(i) (7)

(8)

(ii)Estimate the overall transfer function of the system shown

in the fig.

Fig(i) (6)

(5)

11. (i) Recall the functional blocks of closed loop feedback control

system. (6)

(ii) Give the step by step procedure of determining the transfer

function from the signal flow graph. (7)

BTL1

Remembering

12. (i)A certain system is described by the differential

equation𝑑2𝑦

𝑑𝑡2+

14𝑑𝑦

𝑑𝑡+ 40𝑦 = 5 . What is the relationship to

y(t), assuming initial conditions to be zero. (6)

(ii) Analyze the transfer function of the electric circuit shown

in figure (7)

BTL 4 Analyzing



13. Identify the transfer function of the system shown in figure

using block diagram reduction technique and signal flow

graph technique. (13)

BTL 3 Applying

14. (i) Explain with a neat block diagram explain the working of

Armature controlled DC motor as a control system. (5)

(ii) Translate to the signal flow graph for the following system

and obtain the transfer function using mason gain formula. (8)

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3322221122

xaxax

xaxaxax

xaxax

xaxaxax

BTL 2 Understanding

PART –C

1. Deduce the transfer function of system shown in figure (15)

BTL 6 Creating



2. Solve X2/X1 using state Mason’s gain formula and state it. (15)

BTL 5 Evaluating

3. (i) Can you predict the C/R for the Signal flow graph shown

below using Mason’s gain formula. (8)

(ii) Compile the Transfer Function C(S)/R(S) of block

diagram shown below. (7)

BTL 6

Creating

4. Estimate the transfer function for the following electrical

network. (7)

(ii) Inspect the signal flow graph for the following set of

simultaneous equations and obtain the overall transfer function

using Mason Gain formula. (8)

BTL 5 Evaluating



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3332321313

3231212

XAXAX

XAXAXAX

XAXAX

UNIT II TIME RESPONSE ANALYSIS

Time response analysis - First Order Systems - Impulse and Step Response analysis of second order

systems - Steady state errors – P, PI, PD and PID Compensation, Analysis using MATLAB PART A

Q.No Questions BT

Level

Domain

1. Illustrate how a Control system is classified depending on

the value of damping ratio?

BTL 3 Applying

2. List the advantages of generalized error coefficients. BTL 1 Remembering

3. Generalize why derivative controller is not used in Control

systems.

BTL 6 Creating

4. Give steady state errors to a various standard inputs for type

2 systems.

BTL 2 Understanding

5. Determine the Damping ratio and natural frequency of

oscillation for the closed loop transfer function of a second

order system is given by 40022

400

SS

BTL 5 Evaluating

6. What is meant by peak overshoot? BTL 1 Remembering

7. Mention steady state error. BTL 1 Remembering

8. Define rise time. BTL 1 Remembering

9. The damping ratio and natural frequency of a second order

system are 0.5 and 8 rad/sec respectively. Calculate resonant

peak and resonant frequency.

BTL 3 Applying

10. With reference to time response, Examine peak time. BTL 4 Analyzing



11. Describe the transient and steady state response of control

system?

BTL 2 Understanding

12. Give the units of kp, kv, ka . BTL 2 Understanding

13. Outline the response of the second order under damped

system.

BTL 2 Understanding

14. Point out the time domain specifications. BTL 4 Analyzing

15. Summarize the generalized error and static error constants. BTL 5 Evaluating

16. Compare position, velocity error constants. BTL 4 Analyzing

17. Define damping ratio. BTL 1 Remembering

18. Demonstrate the test signals used in time response analysis. BTL 3 Applying

19. Label a step signal. BTL 1 Remembering

20. Formulate ramp, parabolic and impulse signal. BTL 6 Creating

PART –B

1. Explain how PI, PD and PID compensation will improve the

time response of a system with a neat block diagram and

derivation. (13)

BTL 1 Remembering

2. The Unity feedback system is characterized by the open loop

transfer function G(𝑆) =𝑘

𝑠(𝑠+10) . Estimate the gain K, so

that the system will have the damping ratio of 0.5. For this

value of K, Determine the settling times, peak overshoot, and

time to peak overshoot for a unit step input. (7)

ii) The open loop transfer function of a servo system with

unity feedback is G(s) =10

s(0.1s+1). Determine the static

error constants of the system. Obtain the steady state error of

the system, when subjected to an input given by

r(t) = 2 + 4t + (t2

6) (6)

BTL2

Understanding

3. How will you explain the meaning of for Rise time, fall

time, settling time, peak overshoot with expressions. (13) BTL 2 Understanding

4. The open loop transfer function of a unity feedback control

system is given by 𝐺(𝑆) = 𝑘

𝑠(𝑠𝑇+1) where K and T are

positive constants. Illustrate by what factor the amplifier

Applying



gain should be reduced so that the peak overshoot of unit

step response of the system is reduced from 75% to 25%.(7)

ii) A certain unity negative feedback control system has the

following forward path transfer function

G(s) =K(s+2)

s(s+5)(4s+1). The input applied is r(t) = 1 + 3t.

Find the minimum value of K so that the steady state error is

less than 1. (6)

BTL3

5.

Consider a Second order model 222

2

)(

)(

ns

ns

n

SR

SY

0 < 𝜀 < 1. Determine the response y (t) to a unit step input.

(13)

BTL 5

Evaluating

6. (i) A unit ramp input is applied to a unity feedback system

whose output response is𝐂(𝐬) =𝟏𝟎𝟎

𝐬𝟐+𝟓𝐬+𝟏𝟎𝟎. Analyze the

time response and steady state error. (6)

(ii) For a unity feedback control system the open loop transfer

function

𝐆(𝐬) =𝟏𝟎(𝐬+𝟐)

𝐬𝟐(𝐬+𝟏).Calculate Kp, KV, Ka and the steady state

error when the input is R(s) where𝐑(𝐬)2 3

3 2 1

3s s s . (7)

BTL 4

Analyzing

7. (i)Develop an Expression to find steady state error of closed

loop system. (6)

(ii) A unity feedback system has the forward transfer function

2)1(

.)(

S

SKSG

for the input r(t) = 1 + 5t, formulate the

minimum value of K so that the steady state error is < 0.1.

(Use final value theorem). (7)

BTL 6 Creating

8. Derive the time response analysis of a first order system for

step and ramp input. (13)

BTL1 Remembering

9. With a neat diagram explain the function of PID

compensation in detail. (13)

BTL1 Remembering



10. (i) What inference can you make about the unit step response

of the control system shown in the fig. (6)

(ii) The open loop transfer function of a unity feedback

system is given by )2(

20)(

SSSG .The input function

is r(t) = 2 + 3t + t2 . Examine the generalized error

coefficient and steady state error. (7)

BTL 4 analyzing

11. (i) A unity feedback system with unit step input for which

open loop transfer 𝐺(s) =16

s(s+8).Solve for the transfer

function, the natural Frequency, the damping ratio and the

damped frequency of oscillation. (7)

(ii) Calculate the delay time, rise time and peak overshoot

for the system whose natural frequency of oscillation is

10rad/s and damping factor 0.707. (6)

BTL 3 Applying

12. The unity feedback system is characterized by an open loop

transfer function 2)1)(15(

)12()(

sss

sKSG

with

r(t) = (1 + 6t). Estimate the minimum value of K if the

steady error is to be less than 0.1. (13)

BTL2 Understanding

13. Analyze the steady state errors for unit step, unit ramp and

unit acceleration input. For a unity feedback system

characterized by the open loop transfer function

G(s) =1

s(0.5s+1)(0.2s+1). Also determine the damping

ratio and natural frequency of dominant errors. (13)

BTL 4 Analyzing

14. 12

(i) What are the various standard test signals? Draw the

characteristics diagram and obtain the mathematical

representation of all. (7)

(ii). Write the response of undamped second order system for

unit step input. (6)

BTL 1 Remembering



PART –C

1. Determine the open loop transfer function for a unit feedback

control system with unit impulse response given by

c(t) = −te−t + 2e−t for (t>0). (15)

BTL 5 Evaluating

2. (i)A certain unity negative feedback control system has the

following open loop transfer function

G(s) =10(s+10)

s(s+2). Derive an expression for the output

variable as a function of time when the input applied is unit

step. What is the percentage overshoot, peak time and rise

time? (7)

(ii)For unity feedback system having

)10)(3(

)1(5)(

2

sss

ssG . Determine the type of system, error

coefficients and the steady state error, r (t) = 1 + 3t + (t2

2).

(8)

BTL 6 Creating

3. (i) Discuss the effect of derivative control on the

performance of a second order system. (8)

(ii) Figure shows PD controller used for a system

What would happen to the value of Td so when the system

will be critically damped. Calculate it’s settling time. (7)

BTL 6 Creating

4. An unity feedback control system is show in the fig. By using

derivative control the damping ration is to be made 0.8.

Evaluate the value of Td with and without derivative control

(15)

BTL 5 Evaluating



UNIT III FREQUENCY RESPONSE ANALYSIS

Frequency Response - Bode Plot, Polar Plot, Nyquist Plot - Frequency Domain specifications

from the plots - Constant M and N Circles - Nichol‟s Chart - Use of Nichol‟s Chart in Control

System Analysis. Series, Parallel, series-parallel Compensators - Lead, Lag, and Lead Lag

Compensators, Analysis using MATLAB. PART A

Q.No Questions BT

Level

Domain

1. Derive the transfer function of a lead compensator network. BTL 6 Creating

2. Define Phase margin & gain margin. BTL 1 Remembering

3. Illustrate the need for compensation. BTL3 Applying

4. What is Nyquist plot? BTL 1 Remembering

5. Describe Lag-Lead compensation. BTL2 Understanding

6. Sketch shape of polar plot for the open loop transfer function

G(s)H(s) = 1

𝑠(1+𝑇𝑠)

BTL 1 Remembering

7. Analyze the effects of addition of open loop poles. BTL 4 Analyzing

8. Summarize the advantages of Frequency Response

Analysis.

BTL2 Understanding

9. Mention gain crossover Frequency. BTL 1 Remembering

10. Express M and N circles in detail BTL2 Understanding

11. Demonstrate the MATLAB Command for Plotting Bode

Diagram.Y(S)

U(S)= 4S +

6

S3 + 3S2 + 8S + 6

BTL3 Applying

12. Explain compensators and list types of compensators. BTL 4 Analyzing

13. Formulate the transfer function of a lead compensator network. BTL 6 Creating

14. List the advantages of Nichol’s chart BTL 1 Remembering

15. Estimate the corner frequency in frequency response analysis? BTL2 Understanding

16. Draw the circuit of lead compensator and draw its pole zero

diagram.

BTL 1 Remembering

17. Frame the specifications required for frequency domain

analysis?

BTL3 Applying

18. Compare series compensator and feedback compensator BTL 4 Analyzing



19. Determine the Phase angle of the given transfer function

)1.01)(4.01(

10)(

SSSsG

BTL 5 Evaluating

20. Evaluate the frequency domain specification of a second order

system when closed loop transfer function is given by

C(S)/R(S) =164

𝑠2+10𝑠+64

BTL 5 Evaluating

PART –B

1. Given G(s) =

𝑘𝑒−0.2𝑠

𝑠(𝑠+2)(𝑠+8)

Draw the Bode plot and find K for the following two cases:

(i) Gain margin equal to 6db

(ii) Phase margin equal to 45°. (13)

BTL 1 Remembering

2. An UFB system has G(s)=

10

𝑠(𝑠+1). Design a Lead

Compensator for the following specification ess= 20sec,

Phase Margin = 50 deg. and Gain Margin ≥ 10dB

(13)

BTL6

Creating

3. The open loop transfer function of a unity feedback control

system is G(s) = 𝑘

𝑠(𝑠+1)(𝑠+2).Illustrate a suitable lag-

lead compensator so as to meet the following specifications

static energy velocity error constant Kv =10 sec-1, phase

margin =50 and gain margin ≥10db. (13)

BTL3 Applying

4. Consider a unity feedback system having an open loop

transfer function

Outline the polar plot and determine the value of K so that

(i) Gain margin is 20db

(ii) phase margin is 30°. (13)

BTL2 Understanding

5. A unity feedback control system has G(s) =

𝑘𝑠2

(1+0.2𝑠)(1+0.02𝑠) Draw the Bode plot.

Find K when GCOF = 5rad/sec. (13)

BTL 1

Remembering

6. Sketch the polar plot and find the gain and phase margin

of a control system has G(s) = 1

𝑠2(𝑠+1)(1+2𝑠) with unity

feedback. (13)

BTL 1

Remembering

( )(1 0.5 )(1 4 )

KG S

S S S



7. Discuss a suitable lead compensator for a system with

G(S) = 𝑘

𝑠(𝑠+2)to meet the specifications.

(i) Kv = 20 sec -1

(ii) Phase Margin = +50°

(iii) Gain margin ≥ +10db (13)

BTL2 Understanding

8. A Unity feedback system has an open loop transfer

function, G(s) = 𝑘

𝑠(1+2𝑠) . Select a suitable lag compensator

so that phase margin is 40° and the steady state error for

ramp input is less than or equal to 0.2. (13)

BTL4 Analyzing

9. Recommend a Lead Compensator for a Unity feedback

System with Open loop transfer function

G(S) =K

S(S+1)(S+3) to Satisfy the following

Specifications.

i) Velocity error Constant, Kv ≥50

ii) Phase Margin is ≥ 20 degrees. (13)

BTL 5 Evaluating

10. Analyse and explain in detail the procedure for Nichol’s

chart with M and N circles. (13)

BTL4 Analyzing

11. (i) Frequency domain specification. (3)

(ii) Derive any two frequency domain

specification parameters. (10)

BTL3 Applying

12. For the 𝐺(S) =

5(1+2S)

(1+4S)(1+0.25S), Estimate the value of

phase and gain margin using bode plot. (13)

BTL2 Understanding

13. Report the value of gain and phase cross over frequencies

for the following function using bode plot.

G(S) =10

S(1+0.4S)(1+0.1S) (13)

BTL4 Analyzing

14. (i) Write short notes on series compensation. (3)

(ii) Write down the procedure for designing lead

compensator using bode plot. (10) BTL 1

Remembering

PART-C

1. Consider a Unity feedback system has an open loop

transfer function, G(s) =K

s(1+0.2s)(1+0.05s).Apply the

polar plot and determine the value of k so that

(i)gain margin is 18db (7)

(ii)phase margin is 60 degrees. (8)

BTL5 Evaluating



2. Unity feedback control system having

G(S) =15

S(S+1). Design a lead compensator such that the

closed loop system will satisfy the following specification

(i)Phase margin of the system ≥45 degrees (7)

(ii) Steady state error of unit ramp input≤ 1/15

(iii)Gain cross over frequency of the system must be less

than 7.5 rad/sec . (8)

BTL6

Creating

3. (i)Apply the Bode magnitude plot for the transfer function

G(S) =100(1+0.1S)

(1+0.01S)(1+S)find phase and gain margin. (7)

(ii) Polar plot for G(S) =10(S+2)

S(S+1)(S+3) (8)

BTL6 Creating

4. Evaluate the stability of the unity feedback system

G(S) =100

S(1+0.1S)(1+0.2S) using bode plot. (15)

BTL 5 Evaluating

UNIT-4 STABILITY ANALYSIS

Stability, Routh-Hurwitz Criterion, Root Locus Technique, Construction of Root Locus, Stability,

Dominant Poles, Application of Root Locus Diagram - Nyquist Stability Criterion - Relative Stability,

Analysis using MATLAB

PART A

Q.No Questions BT Level Domain

1. Illustrate any two limitations of Routh-stability criterion. BTL 3 Applying

2. Report the advantages of Nyquist stability criterion over

that of Routh’s criterion.

BTL 3 Applying

3. Explain stability of a system. BTL 4 Analyzing

4. State Nyquist stability criterion. BTL2 Understanding

5. Assess Routh Hurwitz stability criterion. BTL 5 Evaluating

6. What is the advantage of using root locus for design? BTL 1 Remembering

7. Express the rules to obtain the breakaway point in root

locus.

BTL 2 Understanding

8. Describe BIBO stability Criterion. BTL 2 Understanding

9. What is Centroid? BTL1 Remembering

10. Quote Root locus BTL 1 Remembering

11. Associate the necessary and sufficient condition for

stability.

BTL2 Understanding

12. Name the effects of addition of open loop poles? BTL 1 Remembering

13. Elaborate the Parameters which constitute frequency

domain Specifications

BTL 6 Creating



14. Define characteristic equation. BTL1 Remembering

15. In routh array what conclusion you can make when there

is a row of all zeros

BTL 5 Evaluating

16. Relate roots of characteristic equation to stability. BTL 3 Applying

17. Infer on dominant pole. BTL 4 Analyzing

18. Compare the regions of root locations for stable, unstable

and limitedly stable systems.

BTL 4 Analyzing

19. Mention asymptotes. How will you find the angle of

asymptotes?

BTL1 Remembering

20. Using Routh Criterion, design the stability of the system

represented by the characteristic equation

s4+8s3+18s2+16s+5=0.

BTL 6 Creating

PART –B

1. Using Routh criterion,

(i) Investigate the stability of a unity feedback control system

whose open-loop transfer function is given by

G(s) = 𝑒−𝑠𝑡

𝑠(𝑠+2) (7)

(ii) Investigate the stability Closed loop control system

has the characteristics equation

S3 + 4.5S2 + 3.5S + 1.5 = 0.

(6)

BTL 6 Creating

2. (i) Discuss the stability of a system with characteristics

equation S4 + S3 + 20S2 + 9S + 100 = 0 using Routh

Hurwitz criterion. (10)

(ii)Explain the rules to construct a root locus . (3)

BTL 2

Understanding

3. Determine the range of K for stability of unity feedback system

whose OLTF is

G(s) = 𝑘

𝑠(𝑠+1)(𝑠+2) using RH criterion. (13)

BTL 5

Evaluating

4.

(i) Draw the root locus of the G(s)=G(s) =

2

k s 2

s 2s 3

whose

H(s) = 1. Determine open loop gain k at = 0.7. (8)

(ii) Determine the range of K for which system is stable using

RH Criterion S4 + 3 S3 + 3 S2 + S + k = 0. (5)

BTL 1

Remembering

5. (i)Sketch the root locus of the system whose open loop

transfer function is K

S(S+2)(S+4). Find the value of K so

that the damping ratio of the Closed loop system is 0.5.

(7)

BTL1 Remembering



(ii) Determine the range of values of K for which the unity

feedback system, whose G(S) =K

S(S2+S +1)(S+4)Is

stable and determine the frequency of sustained

oscillations.

(6)

6. (i) Express the mathematical preliminaries for nyquist

stability criterion. (5)

(ii) Explain the procedure for Nyquist Stability Criterion

(8)

BTL4

Analyzing

7. (i) Interpret Routh array and determine the stability of the

system whose characteristic equation is

S5 + S4 + 2S3 + 2S2 + 3S + 5 = 0. Comment on the

location of the roots of Characteristic equation. (7)

(ii) Summarize the rules used for construction of the Root

Locus of a feedback system. (6)

BTL2

Understanding

8. Label the Root Locus of the System whose open loop

transfer function is G(S) = K

S(S+1)(S+3) Determine the

Value of K for Damping Ratio equal to 0.5. (13)

BTL 1 Remembering

9. Demonstrate the Nyquist plot for a system, whose

O.L.T.F is given by G(S) H(S) = K(1+S)2

S3 Find the range

of K for stability. (13)

BTL3 Applying

10. Analyze the Nyquist plot for the System whose open loop

transfer function is G(s) H(s) = K

S(S+2)(S+10) Determine

the range of K for which the closed loop System is

Stable. (13)

BTL4

Analyzing

11. (i)Using RH criterion determine the stability of a system

representing the characteristic equation

S6 + 2S5 + 8S4 + 12S3 + 20S2 + 16S + 16 = 0.and

comment on location of the roots of the characteristic

equation. (8)

(ii)Describe about nyquist contour and its various

segments. (5)

BTL3

Applying

12. (i)Analyze the open loop gain for a specified damping of

the dominant roots. (9)

(ii)Point out the concepts BIBO stability. (4)

BTL 4 Analyzing



13. (i)Compare relative stability with absolute stability. (3)

(ii)Discuss the procedure for construction of root locus.

(10)

BTL2 Understanding

14. (i)Write detailed notes on relative stability with its roots

of S-plane. (8)

(ii)State and explain about different cases of RH

criterion. (5)

BTL 1 Remembering

PART-C

1. A unity feedback control system has an open loop

transfer function 𝐺(𝑆) =𝐾

𝑆(𝑆2+4𝑆+13) Determine the

location of poles using root locus. (15)

BTL 5 Evaluating

2. 𝑆7 + 5𝑆6 + 9𝑆5 + 9𝑆4 + 4𝑆3 + 20𝑠2 + 36𝑆 + 36 = 0.Find the

location of roots on S-plane and hence the stability of the

system. (15)

BTL 6 Creating

3. The open loop transfer function of a unity feedback

system is given by 𝐺(𝑆) =𝐾(𝑆+9)

𝑆(𝑆2+4𝑆+11) .Sketch the root

locus of the system and the evaluate the system stabilitity

with respect to their location of poles . (15)

BTL 5 Evaluating

4. Design the system using Nyquist plot

𝐺(𝑆)𝐻(𝑆) =𝐾(1+.5𝑆)(1+𝑆)

(1+10𝑆)(𝑆−1).Determine the range of

values of K for which the system is stable. (15)

BTL 6 Creating

UNIT V STATE VARIABLE ANALYSIS

State space representation of Continuous Time systems – State equations – Transfer function

from State Variable Representation – Solutions of the state equations - Concepts of

Controllability and Observability – State space representation for Discrete time systems.

Sampled Data control systems Sampling Theorem – Sampler & Hold – Open loop & Closed

loop sampled data systems. PART - A

Q.

No

Questions BT

Level

Competence

1. Name the methods of state space representation for phase

variables. BTL 1 Remembering

2. What is meant by quantization? BTL 1 Remembering

3. Write the properties of State transition matrix? BTL 1 Remembering

4. Determine the controllability of the system described by the

state equation. BTL 5 Evaluating



5. Evaluate modal matrix . BTL5 Evaluating

6. What are the advantages of Sate Space representations? BTL 1 Remembering

7. Describe State and State Variable. BTL2 Understanding

8. Define State equation. BTL 1 Remembering

9. Explain the concept of Controllability. BTL 4 Analyzing

10. Summarize Sampled –data Control System. BTL 2 Understanding

11. Discuss the advantages of State Space approach? BTL 2 Understanding

12. Explain Alias in sampling process? BTL4 Analyzing

13. State sampling theorem. BTL 1 Remembering

14. Propose the need for State variables. BTL 6 Creating

15. Illustrate Observability of the System. BTL 3 Applying

16. Design the Nyquist contour for the Pole which lie at origin BTL 6 Creating

17. Illustrate closed loop sampled data systems. BTL3 Applying

18. Analyze the term Compensation. BTL 4 Analyzing

19. Examine Open loop sampled data systems. BTL3 Applying

20. Distinguish type and order of the system. BTL 2 Understanding

1. Explain the stability analysis of sampled data control

systems. (13) BTL 4 Analyzing

2. Mention in detail a state space representation of a

continuous time systems and discrete time systems. (13) BTL 1 Remembering

3. Determine the z-domain transfer function for the following

s-domain transfer function for the following s-domain

transfer functions.

i)𝐻(𝑠) =𝑎

(𝑠+𝑎)2 (4)

ii) 𝐻(𝑠) =5

𝑠2+𝑤2 (5)

iii)H(s) =a

s2−a2 (4)

BTL 5 Evaluating



4.

Apply the necessary equations to obtain the Z-transform of

following discrete time sequences.

i) ak(k+1)(k+2)

2! (5)

ii)ak(k+1)(k+2)(k+3)

3! (4)

iii)ak

k! (4)

BTL 3

Applying

5. A system is represented by State equation �̇�= AX+BU;

Y=CX Where

A=[0 1 00 −1 10 −1 −10

], B=[00

10] and C= [1 0 0].Inspect the

Transfer function of the System. (13)

BTL 4

Analyzing

6. A System is characterized by the Transfer function

𝒀(𝑺)

𝑼(𝑺) =

𝟑

(𝒔𝟑+𝟓𝒔𝟐 +𝟏𝟏 𝒔+𝟔). Express whether or not the

system is completely controllable and observable and

Identify the first state as output . (13)

BTL 2

Understanding

7. i) The State model matrices of a system are given below

A=[0 1 00 0 10 −2 −3

] B=[001

] and C= [3 4 1]

Generalize the Observability of the System using Gilberts

test. (8)

ii) Find the Controllability of the System described by the

following equations. (5)

𝑋 ̇ =[−1 −1 2 −1

] [𝑋1

𝑋2] + [

01

]u(t)

BTL 3

Applying

8. i) Develop the Transfer function of the matrix from the data

given below

A= [−3 10 −1

] B= [11

] C=[1 1] D= 0

(5)

ii) The Transfer function of a Control System is given by 𝒀(𝑺)

𝑼(𝑺) =

(𝒔+𝟐)

(𝒔𝟑+𝟗𝒔𝟐 +𝟐𝟔 𝒔+𝟐𝟒) and plan the

controllability of the system. (8)

BTL6

Creating



9. Mention the Transfer Function of the system. The State

Space representation of a System is given below

(

�̇�1

�̇�2

�̇�3

) =(−2 1 00 −3 1

−3 −4 −5) (

𝑥1

𝑥2

𝑥3

) + (001

) u

Y= (0 0 1) (

𝑥1

𝑥2

𝑥3

) (13)

BTL1

Remembering

10. i) Interpret C(z)/R(z) for the following closed loop sampled

data control systems. Assume all the samplers to be of

impulse type. (8)

ii) Obtain the transfer function model for the following

state space system.

𝐴 = [0 1

−6 −5] 𝐵 = [

10

] 𝐶 = [1 0] 𝐷[0] (5)

BTL2

Understanding

11. Examine how controllability and observability for a system

can be tested, with an example. (13) BTL4 Analyzing

12. Write the explanatory notes on open loop and closed loop

sampled data systems. (13) BTL1 Remembering

13. i)State and explain sampling theorem (3)

ii)A discrete system is defined by the difference equation

𝑦(𝑘 + 2) + 5𝑦(𝑘 + 1) + 6𝑦(𝑘) = 𝑢(𝑘)

y(0)=y(1)=0;T=1 sec

Define the state mode in canonical form.Draw the block

diagram. (10)

BTL1 Remembering



14.

i)Obtain the state model of the system described by the

following transfer

𝑌(s)

U(s)=

5

s3+6s+7 (8)

ii)Express the state transition matrix for the state model

whose system matrix A is given by

A = 1 1

0 1 (5)

BTL2

Understanding

PART-C

1. i)Construct a state model for a system characterized by the

differential equation

(𝐝𝟑𝐲

𝐝𝐭𝟑) + 𝟔 (

𝐝𝟐𝐲

𝐝𝐭𝟐) + 𝟏𝟏 (

𝐝𝐲

𝐝𝐭) + 𝟔𝐲 + 𝐮 = 𝟎

(7)

ii)The input-output relation of a sampled data system is

described by the equation

𝒄(𝒌 + 𝟐) + 𝟑𝒄(𝒌 + 𝟏) + 𝟒𝒄(𝒌) = 𝒓(𝒌 + 𝟏) − 𝒓(𝒌).

Derive the z- transfer function. Also obtain the weighting

sequence of the system. (8)

BTL6 Creating

2. Determine the state model of field controlled dc

motor and armature controlled dc motor. (15) BTL5 Evaluating

3. Check for stability of the sampled data control systems

represented by the following characteristic equation.

(a) 5𝑍2 − 2𝑧 + 2 = 0 (5)

(b) 𝑍3 − 0.2𝑧2 − 0.25𝑧 + 0.05 = 0 (5)

(c) 𝑍4 − 1.7𝑧3 + 1.04𝑧2 − .268𝑧 + .024 = 0 (5)

BTL6 Creating

4. i) Evaluate the frequency response characteristics of zero

order holding device. (8)

ii) Estimate the analysis of systems with impulse

Sampling. (7)

BTL5 Evaluating



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