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Transcript of EC6405-Control Systems Engineering
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7/24/2019 EC6405-Control Systems Engineering
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EC6405-CSE_IVSem_ ECE_ACY2015-16(Even)_Prepared by Mercy Subaraman
,Thrilogasundari.V , C.Sumitha
VALLIAMMAI ENGINEERING COLLEGESRM 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
6. Give Masons gain formula of Signal flow graph. BTL 2 Understandin
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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 Understandin
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 Understandin
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 Understandin
PART B
1. i. Determine the Transfer Function of the system Shown in the fig. (8M)
ii. Determine the Transfer function of the electrical network shown in the
fig. (8M)
BTL 5 Evaluating
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BTL 5 Evaluating
2. (i) Modify the Block diagram to its Canonical form and obtain
C(s)/R(s). (10M)
ii. Comparison between block diagram and Signal flow graph methods.(6M)
BTL 6
BTL4
Creating
Analyzing
3. Solve C/R for the signal flow graph shown below. (16M) BTL 3 Applying
4. i. Consider the Mechanical system shown below and write the
Differential equation. (8M)
BTL1 Remembering
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ii. Draw the torque-voltage electrical analogous circuit for the mechanicalsystem shown below. (8M)
BTL1 Remembering
5. i. For the Signal flow graph shown below find C/R, using Masons
gain formula. (8M)
ii. Find the Transfer Function C(S)/R(S) of block diagram shown
below. (8M)
BTL 1
BTL 1
Remembering
Remembering
6. i. Construct the Equivalent signal flow graph and obtain C/R using
masons gain formula for the block diagram show below.(8M)
BTL6 Creating
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ii. For the block diagram shown below, Calculate the output C/R (8M)
BTL3 Applying
7. Using SFG, Analyze the overall Transfer function for the system shown in
the fig. (16M)
BTL4 Analyzing
8. Give the differential equations governing the mechanical rotational system
shown in Fig. and estimate the T-V and T-I electrical analogous circuits .
(16M)
BTL2 Understandin
9. Write the differential Equations governing the mechanical system shown in
the fig. and determine the transfer function. (16M)
BTL1 Remembering
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10. Estimate the overall transfer function of the system shown in the fig.
(8M)
Fig(i)
Fig(ii) (8M)
BTL2 Understandin
UNIT II TIME RESPONSE ANALYSIS
Time response analysis - First Order Systems - Impulse and Step Response analysis of second order systems - Steady st
errors P, PI, PD and PID Compensation, Analysis using MATLABPART A
Q.No Questions BT
Level
Domain
1. Illustrate how a Control system is classified depending on the value of BTL 3 Applying
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damping ratio?
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 Understandin
5. Determine the Damping ratio and natural frequency of oscillation for the
closed loop transfer function of a second order system is givenby .
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 Understandin
12. Give the units of kp, kv, ka . BTL 2 Understandin
13. Outline the response of the second order under damped system. BTL 2 Understandin
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. With the Suitable block diagrams and Equations, Explain the following type
of controllers employed in Control Systems.
i. Proportional controller
ii. Proportional plus integral controller
iii. PID controller
BTL 4 Analyzing
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iv. Integral controller (16M)2. The Unity feedback system is characterized by the open loop transfer
function G . Estimate the gain K, so that the system will havethe 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. (16M)
BTL2 Understandin
3. Evaluate the Expression for Rise time, fall time, settling time, peak
overshoot. (16M)
BTL 5 Evaluating
4. The open loop transfer function of a unity feedback control system is given
by where K and T are positive constants. Illustrate by whatfactor the amplifier gain should be reduced so that the peak overshoot of
unit step response of the system is reduced from 75% to 25%. (16M)
BTL3 Applying
5.Consider a Second order model
; 0 1. Find the
response y (t) to a unit step input. (16M)
BTL 1 Remembering
6. (i)Analyze the response of Second order under damped system. (8M)
(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) where R(s) 2 33 2 1
3s s s= + . (8M)
BTL 4
BTL3
Analyzing
Applying
7. Derive an Expression to find steady state error of closed loop system.
(16M)
BTL 6 Creating
8. A unit ramp input is applied to a unity feedback system whose transfer
function is C(s)= 100/(s2+5s+100).Find the time response and steady state
error (8M)
BTL1 Remembering
9. i. A unity feedback system with unit step input for which open loop
transfer function G(s) =16/s(s+8).Find the transfer function, the naturalFrequency, the damping ratio and the damped frequency of oscillation.
(8M)
ii.Writetheresponseofundampedsecondordersystemforunitstepinput.(8M)
BTL1
BTL 1
Remembering
Remembering
10. The unity feedback system is characterized by an open loop transfer
function G(s) = K(2s+1)/ s(5s+1)(1+s)2with r(t) = (1+6t). Estimate the
BTL2 Understandin
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minimum value of K if the steady error is to be less than 0.1. (16M)
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 Understandin
6. Sketch shape of polar plot for the open loop transfer function
G(s)H(s) =
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 Understandin
9.Mention gain crossover Frequency.
BTL 1 Remembering
10. Express M and N circles in detail BTL2 Understandin
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 Nichols chart BTL 1 Remembering
15. Estimate the corner frequency in frequency response analysis? BTL2 Understandin
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
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18. Compare series compensator and feedback compensator BTL 4 Analyzing
19. Determine the Phase angle of the given transfer function
G(S) = 10 / S (1+0.4S) (1+0.1S)
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)=
BTL 5 Evaluating
PART B
1.
Given G(s) = ./28Draw the Bode plot and find K for the following two cases:(i) Gain margin equal to 6db
(ii) Phase margin equal to 45. (16M)
BTL 1 Remembering
2. An UFB system has G(s) =
. Design a Lead Compensator for thefollowing specification ess= 20sec, Phase Margin = 50 deg. and Gain Margin
10dB (16M)
BTL6 Creating
3. The open loop transfer function of a unity feedback control system is
G(s) = .Illustrate a suitable lag-lead compensator so as to meet thefollowing specifications static energy velocity error constant Kv =10 sec
-1, phase
margin =50 and gain margin 10db. (16M)
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 300. (16M)
BTL2 Understandin
5.A unity feedback control system has G(s) = .._ Draw the Bodeplot. Find K when GCOF = 5rad/sec. (16M)
BTL 1 Remembering
6. Sketch the polar plot and find the gain and phase margin of a control system
has G(s) =
with unity feedback. (16M)BTL 1 Remembering
7. Discuss a suitable lead compensator for a system with G(S) =
to meet
the specifications.(i) Kv = 20 sec
-1
(ii) Phase Margin = +50
(iii) Gain margin +10db (16M)
BTL2 Understandin
( )(1 0.5 )(1 4 )
KG S
S S S=
+ +
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8. A Unity feedback system has an open loop transfer function, G(s) =. Select a suitable lag compensator so that phase margin is 40 andthe steady state error for ramp input is less than or equal to 0.2. (16M)
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. (16M)
BTL 5 Evaluating
10. Explain in detail the procedure for Nichols chart with M and N circles.
(16M)
BTL4 Analyzing
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 Routhscriterion.
BTL 3 Applying
3. Explain stability of a system. BTL 4 Analyzing
4. State Nyquist stability criterion. BTL2 Understandin
5. Assess Routh Hurwitz stability criterion. BTL 5 Evaluating
6. What is the advantage of using root locus for design? BTL 1 Rememberin
7. Express the rules to obtain the breakaway point in root locus. BTL 2 Understandin
8. Describe BIBO stability Criterion. BTL 2 Understandin
9. What is Centroid? BTL1 Rememberin
10. Quote Root locus BTL 1 Rememberin
11. Associate the necessary and sufficient condition for stability. BTL2 Understandin
12. Name the effects of addition of open loop poles? BTL 1 Rememberin
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13. Elaborate the Parameters which constitute frequency domainSpecifications
BTL 6 Creating
14. Define characteristic equation. BTL1 Rememberin
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 Rememberin
20. Using Routh Criterion, design the stability of the system represented by thecharacteristic equation s
4+8s
3+18s
2+16s+5=0.
BTL 6 Creating
PART B
1. Using Routh criterion,
(i) Investigate the stability of a unity feedback control system whoseopen-loop transfer function is given by
G(s) =
(8M)(ii) Investigate the stability Closed loop control system has the
characteristics equation
S3+4.5S
2+3.5S+1.5 = 0. (8M)
BTL 6 Creating
2. (i) Discuss the stability of a system with characteristics equationS
4+S
3+20S
2+9S+100 = 0 using Routh Hurwitz criterion. (8M)
(ii)Explain the rules to construct a root locus . (8M)
BTL 2
BTL 4
Understandin
Analyzing
3. Determine the range of K for stability of unity feedback system whoseOLTF is
G(s) =
(16M)Using RH criterion.
BTL 5 Evaluating
4.
(i) Draw the root locus of the G(s) =
( )2
k s 2
s 2s 3
+
+ + whose H(s) = 1. Determine open
loop gain k at = 0.7.(ii) Determine the range of K for which system is stable
using RH Criterion S4+ 3 S3+ 3 S 2+S +k = 0 . (16M)
BTL 1 Remembering
5. .(i)Sketch the root locus of the system whose open loop transfer function isK/S(S+2)(S+4) . Find the value of K so that the damping ratio of the Closed
loop system is 0.5. (8M)
BTL1 Remembering
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(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.
(8M)
6. (i) Estimate Routh array and determine the stability of the system whose
characteristic equation is S6+2S
5+8S
4+12S
3+20S
2+16S+16=0. Also
determine the number of roots lying on right half of S-plane, left half of S-
plane and on imaginary axis. (8M)
(ii) Explain the procedure for Nyquist Stability Criterion (8M)
BTL2
BTL4
Understandin
Analyzing
7. (i) Interpret Routh array and determine the stability of the system whose
characteristic equation is S5+S
4+2S
3+2S
2+3S+5=0. Comment on the
location of the roots of Characteristic equation. (8M)
(ii) Summarize the rules used for construction of the Root Locus of afeedback system. (8M)
BTL2
BTL2
Understandin
Understandin
8.Label the Root Locus of the System whose open loop transfer function isG(S) = K / S (S+1) (S+3). Determine the Value of K for Damping Ratioequal to 0.5. (16M)
BTL 1 Remembering
9. Demonstrate the Nyquist plot for a system, whose open loop transfer
function is given by G(S) H(S) = K(1+S)2/ S
3. Find the range of K for
stability. (16M)
BTL3 Applying
10. Demonstrate 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. (16M)
BTL3 Applying
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 Ope
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
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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 Understandin
8. Define State equation. BTL 1 Remembering
9. Explain the concept of Controllability. BTL 4 Analyzing
10. Summarize Sampled data Control System. BTL 2 Understandin
11. Discuss the advantages of State Space approach? BTL 2 Understandin
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 Understandin
PART-B
1. Determine the state Controllability and Observability of the system
described by
=3 1 11 0 1 0 0 1x +0 10 02 1u y=
0 0 11 1 0x (16M)BTL 5 Evaluating
2. i) Mention in detail a state space representation of a continuous timesystems and discrete time systems. (16M)
BTL 1 Remembering
3. Consider the system with state equation
= 0 1 00 0 16 11 6
+ 001 u(t)
BTL 3 Applying
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Illustrate the controllability of the system. (16M)
4. For a given state variable representation of a second order system given
below ,Write the state response for a unit step input and
= 0 12 3 + 02 0 0 = 01 by using discrete timeapproximation (16M)
BTL 1 Remembering
5. A system is represented by State equation= AX+BU; Y=CX WhereA=0 1 00 1 10 1 10, B= 0010and C= 1 0 0.Explain the Transfer functionof the System. (16M)
BTL 4 Analyzing
6.ASystemischaracterizedbytheTransferfunction
=
.ExpresswhetherornotthesystemiscompletelycontrollableandobservableandIdentifythefirststateasoutput. (16M)
BTL 2 Understandin
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. (8M)
ii) Find the Controllability of the System described by the following
equations
= 1 12 1 + 01u(t) (8M)
BTL 6
BTL3
Creating
Applying
8. i) Analyze the Transfer function of the matrix from the data given below
A=
3 10 1
B=
11
C=
1 1 D= 0 (8M)
ii) The Transfer function of a Control System is given by =
and plan the
controllability of the system. (8M)
BTL 4
BTL6
Analyzing
Creating
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9. Mention the Transfer Function of the system. The State Space
representation of a System is given below
= 2 1 00 3 13 4 5
+ 001 u
Y= 0 0 1 (16M)
BTL1 Remembering
10. i) Estimate the Controllability of the following state space system. (8M) 2 3 ii) Obtain the transfer function model for the following state space system.
0 16 5 10 1 00 (8M)
BTL2
BTL2
Understandin
Understandin
s
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