VINAYAKA MISSIONS UNIVERSITYVMKV ENGINEERING COLLEGE, SALEM

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

( COMMON TO EEE,ECE,EIE,ETCE,MECHTRANOICS)

COURSE : BE / EEE YEAR /SEM : III / V

CONTROL SYSTEMSQUESTION BANK

UNIT IPART A

1. What is a control system?2. Define Transfer function.3. What is a state variable model?4. What are the advantages and disadvantages of open loop system?5. What are the advantages and disadvantages of closed loop system?6. What are the components of feedback control system?7. What is a summing point?8. Write the rule for elimination of a feedback loop in a block diagram.9. Give three examples of open loop systems10.define loop gain11.what is sink and source?12.write the force balance equation of ideal mass element.13.functionally ,how do closed loop systems differ from open loop

systems?14.What are the advantages and disadvantages of transfer function?15.Write the Mason’s Gain formula.16.what are the characteristics of negative feedback?17.Define neumatic resistance18.write the torque balance equation of ideal rotational spring19.what is inertance?20.what are the basic elements of hydraulic system?21.define non touching loop 22.name the two types of electrical analogous for mechanical system23.What is signal flow graph?24.Define thermal capacitance25.What is a mixed node? How can it be eliminated?

PART B

1. The block diagram of a closed loop system is shown in the figure using the block reduction technique determine the closed loop transfer function C(s)/R(s).

2. Convert the block diagram to signal flow graph and determine the transfer function using mason’s gain formula.

C(S)+

+ -

+

-

G1(S) G2(S)

H2(S)

H1(S)

R(S)

10

6 + + C(S)

7 8 9

+ 5

4 -

+

3 -

+

2 -

R(S) 1

G1

G4

G2 G3

H1

H1

3. Derive the transfer function of an armature controlled dc motor and hence develop its block diagram.

4. Consider the mechanical translation system shown in the figure ,draw (a) force voltage and force –current analogous circuits

5. Write the differential equation governing the rotational systems shown in the figure and determine the transfer function

6. Convert the block diagram to signal flow graph and determine the transfer function using mason’s gain formula.

B3 V1

K

V3

V2

BB2

F (t)

B1

M1

M2 M3

T (t)

ω1 ω2 ω3

k2k1

B3B2B1

J1 J2 J3

C(S)+

+ -

+

-

G1(S) G2(S)

H2(S)

H1(S)

R(S)

7. The block diagram of a closed loop system is shown in the figure. Using the block reduction technique determine the closed loop transfer function C(s)/R(s).

8. Write the differential equation governing the translational systems shown in the figure and determine the transfer function

9. Consider the mechanical rotational system shown in the figure; draw (a) force voltage and force –current analogous circuits

10

6 + + C(S)

7 8 9

+ 5

4 -

+

3 -

+

2 -

R(S) 1

G1

G4

G2 G3

H1

H1

B3 V1

K

V3

V2

BB2

F (t)

B1

M1

M2 M3

T (t)

ω1 ω2 ω3

k2k1

B3B2B1

J1 J2 J3

10. Write the rules for Block diagram reduction techniques.

UNIT – II

PART – A

1. Define Peak Time2. Define Peak Over Shoot.3. Define Settling Time.4. What is the order of a system?5. Write the second order systems response.6. How the system is classified depending on the value of damping?7. what is transient and steady state response?8. Name the test signal used in control system.9. What is the type of damping in the system?10.define pole.11.what is damped frequency of oscillation12.define rise time13.distinguish between order and type of the system.14.What is steady state error?15.what is time response?16.What is a PID controller?17.What are generalized error coefficients?18.Mention two advantages of generalized error constants over static

error constants.19.Define velocity error constant20.what is the effect of P controller on the system performance?21.why derivative controller is not used in the control systems?22.A unity feedback system has a open loop transfer function of G(s)=10 /(s+1)(s+2) .determine the steady state error for unit step input.23.what is an impulse signal?24.what are static error constants?25.The closed loop transfer function of second order system is

C(s) = 10______ R(s) s2 + 6s + 10 Determine the damping ratio and the natural frequency of oscillations.

PART – B

1. Derive the expression for unit step response of a second order critically damped system

G(s) =Wn2/s2+2ζWnS+Wn2.2. Find the unit impulse response of the second order system whose

transfer function G(S) = 9/s2+4s+9.3. Derive the expression for steady state error of the closed loop system

in terms of generalized error coefficients.4. A unity feedback control system has an open loop transfer function G(S)= 10 /s(s+2) .find the rise time ,percentage overshoot,peak time,and settling time for a step input of 12 units5. Obtain the response of unity feed back system whose open loop

transfer function is G(s) = 4/s(s+5) and when the input is unit step.

6. obtain the response of velocity feedback system whose closed loop transfer function is c(s)/r(s) =100/ (s2+12s+100) and when the input is unit step

7. Explain PI, PD and PID controllers.

8. Explain the time domain specifications of control system

9. Derive the expression for response of first order for unit step input. 10. For a Unity feedback system, the open loop transfer function .

G(s)= 10(s+2)/ s2(s+1) .Find (a) the position,velocity,and acceleration error constants, (b)the steady state error when the input is R(s)= 3/s -2/s2 +1/3s3

+

-

C(S)G(S)R(S)

UNIT-III

PART-A1. What is frequency response?2. What are the frequency domain specifications?3. How to find the order of the system and give one example?4. Define resonant peak.5. What is resonance frequency? 6. Define gain margin7. Define phase margin8. What is Nichols chart.9. What are the advantages of Nichols chart?10. Define polar plot11.Define bode plot12.What are the advantages of polar plot13.What is cut off rate?14.What is gain cross over frequency?15.What is phase cross over frequency?16.Define corner frequency17.What are M& N circles?18.Define bandwidth19.Enumerate the advantages of frequency response?20. Write the circle equation of M circle?21.Differentiate bode and polar plot22.Write the formula for gain margin and phase margin23.Write the expression for resonant peak and resonant frequency.24.What is All-pass systems?25.What is non-minimum phase transfer function?

PART-B

1. Draw the bode plot for the following transfer function and obtain gain cross-over frequency. G(S) = 20/S(1+3s)(1+4s).

2. Write the procedure for bode plot.3. Consider a unity feed back system having open loop transfer function

G(S) = 1/S2(1+S)(1+2S) using polar plot find the gain and phase margin

4. Derive the expression for M circle.5. Derive the expression for N circle.6. Write the procedure for polar plot.

7. Consider a unity feed back system having open loop transfer function G(S) = 75(1+0.2S)/S(S+5). sketch bode plot

8. The open loop transfer function of a unity feedback system is given by G(S)=1/S(1+S)(1+2S). Sketch the polar plot and determine the gain margin and phase margin.

9. Write the procedure for Nichols chart.10.Plot the Bode diagram for the following transfer function and obtain the

gain and phase cross over frequency. G(S)=10/S(1+0.4S)(1+0.1S).

UNIT –IV PART-A

1. Define BIBO stability.2. What is the requirement for BIBO stability?3. Write the boundary condition of BIBO4. What is characteristics equation?5. Define impulse response6. Enumerate the characteristic equation of Routh stability criterion.7. Write the polynomial expression for Nyquist stability criterion8. How the roots of characteristics equation are related stability?9. What is the relation between stability and coefficient of characteristics

polynomiyal?10.What is the necessary condition for stability?11.What is Routh stability criterion?12.What is Nyquist stability criterion?13.What will be the nature of impulse response when the roots of

characteristic equation are lying on imaginary axis?14.What is auxiliary polynomial?15.What is limitedly stable system?16.Define gain margin.17.Define phase margin.18.For the system represented by the following characteristics equation

say whether the necessary condition for stability is satisfied or not.(i) S4+3S3+4S2+5S+10=0 (ii) S3-8S2+7S+6=0.

19.Write the transfer function of Nyquist stability criterion?20.Distinguish between the concept of encircled and enclosed of Nquist

stability criterion?21.What will be the nature of impulse response if the roots of

characteristic equation are lying on right half of s-plane?

22.What is the necessary and sufficient condition for stability?23.What is quadrantal symmetry?24.In routh array what conclusion you can make when thare is a row of

all zeros? 25.For the system represented by the following characteristics equation

say whether the necessary condition for stability is satisfied or not.(i) S6-2S5+S3+S2+S+6=0 (ii) S5+4S4-5S3-4S2+2S+1=0

PART-B

1. Using Routh criterion, determine the stability of the system represented by the characteristics equation, s4+8s3+18s2+16s+5 = 0. Comment on the location of the roots of the roots of characteristics equation.

2. Construct Routh array and determine the stability of the system represented by the characteristics equation s5+s4+2s3+2s2+3s+5 = 0. Comment on the location of the roots of characteristics equation.

3. Construct Routh array and determine the stability of the system whose characteristics equation, s6+2s5+8s4+12s3+20s2+16s+16 = 0. Also determine the number of roots lying on the half of s-plane and on imaginary axis.

4. What are the necessary condition for stability? Explain briefly5. Write the procedure for investigating the stability using Nyquist

criterion.6. Determine the Gain cross over frequency, phase cross over frequency,

phase margin and gain margin of a system with open loop transfer function,G(S) = 1/S(1+2S)(1+S).

7. Draw 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 closed loop system is stable.

8. Construct the Nyquist plot for a system whose open loop transfer

function is G(S)H(S)=K(1+S)2/S3. Find the range of K for stability

9. The characteristic polynomial of a system is S7+9S6+24S5+24S4+24S3+24S2+23S+15=0

10. The open loop transfer function of a unity feedback system is given

by G(s) = K/s(1+sT1)(1+sT2).Determine an expression for gain K in

terms T1, T2 and specified gain margin, Kg.

UNIT –VPART-A

1. What is meant by compensator? 2. List out the different types of compensator?3. Draw the electric lag network4. When the lag/lead compensation is employed?5. State the property of lag compensator6. Write the transfer function of a lag compensator.7. Write the transfer function of a lead compensator8. Draw the pole zero plot for the lead compensator9. What is difference between root locus and frequency response of a

compensator?10. What is meant by lag compensator? 11. What are the characteristics of lag compensation? 12. Explain how band width is affected by the introduction of lag

compensator in a system13. What is meant by lead compensator? 14. What are the characteristics of lag compensation? 15. Explain how band width is affected by the introduction of lead

compensator in a system16. Draw the electric lead network 17. What is relation between фm and β in lag and lead compensator?18. What is series compensation? 19. What is the need for compensator?20. What is feedback compensation? 21. Draw the bode plot of lag compensator.22. Draw the bode plot of lead compensator.23. When maximum phase lag occurs in lag compensator.24. List out the advantages in frequency domain design.25. Draw the pole zero plot for the lag compensator.

PART-B1. Explain the frequency response of lag compensator.2. Write the frequency response of lead compensator.3. The open loop transfer function of certain unity feedback control

system is given by G(s) = K/s (0.1s+1) (0.2s+1). It is designed to have the phase margin to be at least 30°. Design a suitable lead series compensator.

4. Consider a type 1 unity feedback system with an open loop transfer

function G(S) =K/S (S+1) (S+4). The system is to be compensated to

meet the following specifications Kv > 5sec and Phase Margin > 43

deg. Design suitable lag compensators.

5. i)What are the limitation of lead compensatorii)Drive the equation of phase angle of lag compensator

6. Design a lead compensator for a unity feedback system with open

loop transfer function G(S) = K/ S(S+1) (S+5) to satisfy the

following specifications (i) Kv >50 (ii) Phase Margin is > 20 .

7. Write the procedure of lead compensator on root locus method

8. Describe the different types of compensation schemes.

9. The controlled plant of a unity feedback system is G(s) = K/s(s+5). It

is specified that velocity error constant of the system be equal to 15, while

the damping ratio is 0.6 and velocity error is less than 0.25 rad per unit ramp

input. Design a suitable lag compensator?

10. A unity feedback system has an open loop transfer function,

G(s) = K/s(1+2s). Design 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.