SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
QUESTION BANK
UNIT-I
1. “The sensitivity of a closed-loop system with respect to variation of a closed
loop system with
respect to variation in G is reduced by a factor (1+GH) as compared to that of
an open-loop
system”. Prove the statement.
2. 1.Write the differential equations governing the Mechanical system shown
in fig
3. Determine the transfer function Y2(S)/F(S) of the system shown in fig.
(a).List out the comparison between open loop and closed loop control
systems.
(b). Write down the system equations representing given
mechanical network:Find X0(s)/Xi(s)
(c).Write Mason’s Gain formula with explanation of every parameter involved.
(d).Define State, State variable, State space, State Vector.
(e)The transfer function relating X(s) and U(s) for equation:
M.d2x/dt +F.dx/dt +Kx =u(t) is…..
Q(1).Reduce the system block diagram shown in figure :
Q(2).Obtain the transfer function
:
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
for the electrical network drawn below
Q(3). Explain in brief State-Transition Matrix, its properties and state
transition equation.
Q(4).Discuss in brief, the utility of potentiometer as a sensor and encoder
element in feedback control system.
5. For the system whose signal flow graph is shown by Fig.1, find Y(s)/R(s).
6.For the block diagram system shown in figure ,find out the overall transfer
function by block diagram reduction technique:
7.(i).Drawing free body diagram obtain system equations ,transfer function
X2(s)/F(s).
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
Also draw equivalent electrical network. (ii).Describe effect of feedback on
sensitivity and hence stability with suitable expression for a feedback control
system
8. Write Mason’s gain formula.
9. What is mathematical model of a system?
10. What do you mean by sensitivity of the control system?
11. What is a system?
12. What is control system?
13. What are the two major types of control systems?
14. Define open loop and closed loop systems.
15. What is feedback? What type of feed back is employed in control system?
16. Why negative feedback is preferred in control systems?
17. Distinguish between open loop and closed loop systems.
18. State principle of superposition theorem.
19. What is time variant and Time invariant?
20. Define transfer function.
21. Write force balance equation of ideal spring, ideal mass.
22. Name the two types of electrical analogous for mechanical system.
23. What is signal flow graph? Define non-touching loop.
24. Write the differential equations governing the Mechanical system
25. Write the differential equations governing the Mechanical rotational system. Give the
Torque-voltage and Torque-current electrical analogous conversions.
26. Determine the overall transfer function C(S)/R(S) for the system shown in fig.(16)
27. Obtain the closed loop transfer function C(S)/R(S) of the system whose block diagram is
shown in fig.(16)6. For the system represented by the block diagram shown in fig.
DetermineC1/R1
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
28. Obtain the closed loop transfer function C(S)/R(S_ of the system whose block diagram is
shown
29. Draw a signal flow graph and evaluate the closed loop transfer function of a system
whose
block
i
30. Derive the transfer function for Armature controlled DC servo motor..
31. Derive the transfer function for Field controlled DC servo motor.
UNIT –III
1. What is time response?
2. What is transient and steady state response?
3. Name the test signals used in time response analysis.
4. Define step signal.
5. Define Ramp signal and parabolic signal.
6. What is an impulse signal?
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
7. How is system classified depending on the value of damping?
8. Sketch the response of a second order under damped system.
9. What is damped frequency of oscillation?
10. The closed-loop transfer function of second order system is C(S)/R(S) =10/ S2+6S +10.
What is the type of damping?
11. List the time domain specifications.
12. Define rise time, delay time, peak time.
13. What is steady state error?
14. What are static error constants?
15. Define position, velocity error constants.
16. What are generalized error constants?
17. List the advantages of generalized error constants.
(a)Derive the expressions and draw the response of first order system for unit step input.
18) Draw the response of second order system for critically damped case and when input
is unit step.
(19). Derive the expressions for Rise time, Peak time, Peak overshoot.
20. A potential control system with velocity feedback is shown in fig. What is the response
of the system for unit step input?
21. Measurements conducted on a Servomechanism show the system response to be
c(t)=1+0.2 ê 60t-1.2 ê
–
10 t. when subjected to a unit step. Obtain an expression for closed loop transfer function.
22. A positional control system with velocity feedback is shown in fig. What is the
Response c(t) to the unit step input. Given that ς =0.5.and also calculate rise time,
Peak time, Maximum overshoot and settling time.
23. A unity feedback control system has an open loop transfer function G(S)
=10/S(S+2).Find the rise time, percentage over shoot, peak time and settling time.
24. A closed loop servo is represented by the differential equation, where c is the
displacement of the output shaft, r is the displacement of the input shaft and e= rc.Determine undamped natural frequency, damping ratio and percentage maximum
overshoot for unit step input.
25. For a unity feedback control system the open loop transfer function G(S) = 10(S+2)/
S2(S+1).Find (a) position, velocity and acceleration error constant
(b) The steady state error when the input is R(S) where R(S) =3/S –2/S2+1/3S3
26. The open loop transfer function of a servo system with unity feed back system is
G(S) = 10/ S(0.1S+1).Evaluate the static error constants of the system. Obtain the steady
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
state error of the system when subjected to an input given by the polynomial r(t) = a0+a1t
+a2 /2 t2.
27.Find the dynamic error coeffecients of the unity feedback system whose forward
transfer function is G(s)=200/S(S+5) .Find the steady state error.
28.An electronic pacemaker with G(S) H(S)=K/S(S+20) .Determine the steady state error
for unit ramp input when K=400 .Also determine the value of K for which the steady state
error to a unit ramp will be 0.02.
29.Consider a unity feedback control system with closed loop transfer function
C(S)/R(S)= KS+b/s2+as+b
Determine the open loop transfer function .Show that the steady state error in the unit
ramp input response is given by ess=a-k/b.
30.Define Kp,,Kv,Ka for type 1 system.
UNIT V FEQUENCY RESPONSE ANALAYSIS
1. What is frequency response analysis?
2. Draw the polar plot of the function G(S) =1/S(S+T1)(1+ST2)
3. Determine the Phase angle of the given transfer function G(S) = 10 / S (1+0.4S)
(1+0.1S)
4. What is polar plot?
5. Define gain cross over frequency.
6. Define Phase cross over frequency
7. Define Phase Margin
8. Define Gain Margin
9. How do you calculate the gain margin from the polar plot?
10. How do you find the stability of the system by using polar plot?
11. What are the advantages of Bode plot?
12. List the Frequency domain specifications
13. What is minimum phase system?
14. What is non-minimum transfer function?
15. What is cut off frequency?
16. Compare bode plot and Nyquist plot analysis.
17. What is Bandwidth?
18. Plot the Bode diagram for the following transfer function and obtain the gain and
phase cross over frequencies’(S) = 10/ S(1+0.4S) (1+0.1S)
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
19. The open loop transfer function of a unity feedback system is G(S) =
1/ S(1+S)(1+2S) Sketch the Polar plot and determine the Gain margin and Phase
margin.
20. Sketch the Bode plot and hence find Gain cross over frequency ,Phase cross , Gain
margin and Phase margin. G(S) = 0.75(1+0.2S)/ S(1+0.5S) (1+0.1S)
21. Sketch the Bode plot and hence find Gain cross over frequency, Phase crossover
frequency, Gain margin and Phase margin. G(S) = 10(S+3)/ S(S+2) S2+4S+100)
22. Sketch the polar plot for the following transfer function .and find Gain crossover
frequency, Phase cross over frequency, Gain margin and Phase margin.G(S) =
10(S+2)(S+4)/ S (S2-3S+10)
23.
Construct the polar plot for the function GH(S) =2(S+1)/ S2
24. . Find Gain cross over frequency, Phase cross over frequency, Gain margin and
Phase margin.
UNIT IV STABILITY ANALYSIS
–
1. What are the two methods of designing a control system?
2. What is the time domain specification needed to design a control system?
3. What is the frequency domain specification needed to design a control system?
4. State Nyquist stability Criterion.
5. What is root locus?
6. What is the necessary condition for stability?
7. What is characteristic equation?
8. How the roots of characteristic are related to stability?
9. Define stability.
10. What do you mean by dominant pole?
11. What are break away points?
12. How will you find the root locus on real axis?
13.. Using Routh criterion determine the stability of the system whose
Characteristic equation is 1. S4+8S3+18S2+16S+5 =0 .
2. F(S)=S6+S5-2S4-3S3-7S2-4S1-4 =0.
Find the number of roots falling in the RHSplaneand LHS plane.
14. Draw the Nyquist plot for the system whose open loop transfer function isG(S)H(S)
=K/S (S+2) (S+10).Determine the range of K for which closed loop system is stable.
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
15. Construct Nyquist plot for a feedback control system whose open loop transferfunction
is given by G(S)H(S) =5/ S(1-S).comment on the stability of open loop and closed loop
transfer function.
16. Sketch the Nyquist plot for a system with the open loop transfer function
G(S)H(S)=K(1+0.5S) (1+S) / (1+10S) (S-1).determine the range of values of K for which
system is stable.
17. Plot the Bode diagram for the following transfer function and obtain the gain and
phase cross over frequencies. G(S) =KS2 / (1+0.2S) (1+0.02S).
Determine the value of K for a gain cross over frequency of 20 rad/sec.
18 Sketch the Bode plot and hence find Gain cross over frequency ,Phase crossover
frequency, Gain margin and Phase margin.G(S) = 10(1+0.1S)/ S(1+0.01S) (1+S).
19. Write the short notes on correlation between the time and frequency response?
UNIT II STATE VARIABLE ANALYSIS
1. 6. What are the problems encountered in a practical hold circuits?
2. 7. What are the methods available for the stability analysis of sampled data control
system?
3. 8. What are the advantages of state space analysis?
4. 9. What are state variables?
5. 10. What are phase variables?
6. 11. Write notes on controllability and Observability
7. 12. Explain sampling theorem briefly and sample & hold operation.
8. 13. Explain stability analysis of sampled control system and Jury’s stability.
9. 14. Explain state space representation for descries time system.
10.
Explain state space representation for continues time system.
11. Explain the solution for state equation for discrete time system.
12.
Explain the solution for state equation for continues time system
13. Explain jury’s stability test.
14. Define and explain the following terms,
a) State Variable b) State Vector c) State d) State Space.
15.
Obtain eAT for the following matrices.
SUNDERDEEP GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS & COMMUNICATIONS ENGINEERING
CONTROL SYTEM EIC 501
16.
Obtain the homogeneous solution of the equation X. (t) = A X (t) where
17.
Explain the concept of State Transition Equation
18. Write a short note on advantages and limitations of State variable
approach.
19. Derive relationship between State equations and High-order differential
Equation.
20.
21.
22.
What is a homogeneous and non homogeneous state equation?
State the importance and various properties of state transition matrix.
Write all of the properties of State transition Matrix.