# JNTU Kakinada B-Tech 4-2 DIGITAL CONTROL SYSTEMS R13 April 2018 Question Paper

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2
6. The closed loop transfer function for the digital control system is given as

Find the steady state errors and error constants due to step input.



7.
Control a system, defined by

, It is desired to have eigen
values at -3.0 and -5.0 by using a state feedback control u = – KX. Determine
the necessary feedback gain matrix k and the control signal u.



2 of 2
Code No: RT42021
Set No. 1
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2
6. The closed loop transfer function for the digital control system is given as

Find the steady state errors and error constants due to step input.



7.
Control a system, defined by

, It is desired to have eigen
values at -3.0 and -5.0 by using a state feedback control u = – KX. Determine
the necessary feedback gain matrix k and the control signal u.



2 of 2
Code No: RT42021
Set No. 1
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) What are the advantages offered by digital control? 
b) Obtain the Z-transform of

where ?a? is constant. 
c) Write about the observable canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.

e) Write brief note on design procedure in the w-plane. 
f) Write the sufficient condition for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) State and explain the theorem required to satisfy to recover the signal e(t) from
the samples e*(t).

b) Explain how the reconstructing the input signal by hold circuits. 

3.
Obtain the inverse Z-transform of the following in the closed form. (i)

(ii)

(iii)



4. a) Explain any one method of evaluation of state transition matrix. 
b) Investigate the controllability and observability of the following system.



5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.

b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)



Code No: RT42021
Set No. 2
R13
1 of 2

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2
6. The closed loop transfer function for the digital control system is given as

Find the steady state errors and error constants due to step input.



7.
Control a system, defined by

, It is desired to have eigen
values at -3.0 and -5.0 by using a state feedback control u = – KX. Determine
the necessary feedback gain matrix k and the control signal u.



2 of 2
Code No: RT42021
Set No. 1
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) What are the advantages offered by digital control? 
b) Obtain the Z-transform of

where ?a? is constant. 
c) Write about the observable canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.

e) Write brief note on design procedure in the w-plane. 
f) Write the sufficient condition for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) State and explain the theorem required to satisfy to recover the signal e(t) from
the samples e*(t).

b) Explain how the reconstructing the input signal by hold circuits. 

3.
Obtain the inverse Z-transform of the following in the closed form. (i)

(ii)

(iii)



4. a) Explain any one method of evaluation of state transition matrix. 
b) Investigate the controllability and observability of the following system.



5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.

b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)



Code No: RT42021
Set No. 2
R13
1 of 2

6. a) Consider the transfer function system shown in figure 6(a). The sampling
period T is assumed to be 0.1 sec. obtain G(w).
Figure 6 (a)


b) List out the transient response specifications and explain in brief. 

7. A discrete time regulator system has the plant equation

Design a state feedback control algorithm with u(k)=-KX(k) which places the
closed loop characteristic root at .



Code No: RT42021
Set No. 2
R13
2 of 2

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2
6. The closed loop transfer function for the digital control system is given as

Find the steady state errors and error constants due to step input.



7.
Control a system, defined by

, It is desired to have eigen
values at -3.0 and -5.0 by using a state feedback control u = – KX. Determine
the necessary feedback gain matrix k and the control signal u.



2 of 2
Code No: RT42021
Set No. 1
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) What are the advantages offered by digital control? 
b) Obtain the Z-transform of

where ?a? is constant. 
c) Write about the observable canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.

e) Write brief note on design procedure in the w-plane. 
f) Write the sufficient condition for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) State and explain the theorem required to satisfy to recover the signal e(t) from
the samples e*(t).

b) Explain how the reconstructing the input signal by hold circuits. 

3.
Obtain the inverse Z-transform of the following in the closed form. (i)

(ii)

(iii)



4. a) Explain any one method of evaluation of state transition matrix. 
b) Investigate the controllability and observability of the following system.



5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.

b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)



Code No: RT42021
Set No. 2
R13
1 of 2

6. a) Consider the transfer function system shown in figure 6(a). The sampling
period T is assumed to be 0.1 sec. obtain G(w).
Figure 6 (a)


b) List out the transient response specifications and explain in brief. 

7. A discrete time regulator system has the plant equation

Design a state feedback control algorithm with u(k)=-KX(k) which places the
closed loop characteristic root at .



Code No: RT42021
Set No. 2
R13
2 of 2
IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Illustrate the step motor control system examples of discrete data control
systems.

b) Find the z-transforms of f(t) = t sin(?t). 
c) State the state transition matrix. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
4
-1.7z
3
+1.04z
2
-0.268z + 0.024 = 0.

e) Write the design procedure of lag compensator in w-plane. 
f) What do you mean by state feedback controller? 

PART ?B (3×16 = 48 Marks)2. a) Explain the examples of data control systems of the following (i) Microprocessor controlled system (ii) A digital computer controlled rolling mill regulating system.


b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.


3. a) Obtain the inverse z-transform of the following


b)Write the difference equation governing the system for

as shown
in figure.3 (b)Figure.3 (b)



4. a) Obtain the Jordan canonical form realization for the following transfer function

.


b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?

Code No: RT42021
Set No. 3
R13
1 of 2

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2
6. The closed loop transfer function for the digital control system is given as

Find the steady state errors and error constants due to step input.



7.
Control a system, defined by

, It is desired to have eigen
values at -3.0 and -5.0 by using a state feedback control u = – KX. Determine
the necessary feedback gain matrix k and the control signal u.



2 of 2
Code No: RT42021
Set No. 1
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) What are the advantages offered by digital control? 
b) Obtain the Z-transform of

where ?a? is constant. 
c) Write about the observable canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.

e) Write brief note on design procedure in the w-plane. 
f) Write the sufficient condition for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) State and explain the theorem required to satisfy to recover the signal e(t) from
the samples e*(t).

b) Explain how the reconstructing the input signal by hold circuits. 

3.
Obtain the inverse Z-transform of the following in the closed form. (i)

(ii)

(iii)



4. a) Explain any one method of evaluation of state transition matrix. 
b) Investigate the controllability and observability of the following system.



5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.

b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)



Code No: RT42021
Set No. 2
R13
1 of 2

6. a) Consider the transfer function system shown in figure 6(a). The sampling
period T is assumed to be 0.1 sec. obtain G(w).
Figure 6 (a)


b) List out the transient response specifications and explain in brief. 

7. A discrete time regulator system has the plant equation

Design a state feedback control algorithm with u(k)=-KX(k) which places the
closed loop characteristic root at .



Code No: RT42021
Set No. 2
R13
2 of 2
IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Illustrate the step motor control system examples of discrete data control
systems.

b) Find the z-transforms of f(t) = t sin(?t). 
c) State the state transition matrix. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
4
-1.7z
3
+1.04z
2
-0.268z + 0.024 = 0.

e) Write the design procedure of lag compensator in w-plane. 
f) What do you mean by state feedback controller? 

PART ?B (3×16 = 48 Marks)2. a) Explain the examples of data control systems of the following (i) Microprocessor controlled system (ii) A digital computer controlled rolling mill regulating system.


b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.


3. a) Obtain the inverse z-transform of the following


b)Write the difference equation governing the system for

as shown
in figure.3 (b)Figure.3 (b)



4. a) Obtain the Jordan canonical form realization for the following transfer function

.


b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?

Code No: RT42021
Set No. 3
R13
1 of 2

5. Consider the sample-data system shown in Figure.5 and assume its sampling
period is 0.4 Sec. Find the range of K, so that the closed – loop system for which
stable.
Figure.5



6. The open loop transfer function of a unity – feedback digital control system is
given as

. Sketch the root loci of the system for 0 Indicate all important information on the root loci.



7.
Consider the system defined by

by using the state feedback control u = -Kx, it is desired to have the closed loop
poles at s = -2 ? j 4 and s= -10. Determine the state feedback gain matrix K.



2 of 2
Code No: RT42021
Set No. 3
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2
6. The closed loop transfer function for the digital control system is given as

Find the steady state errors and error constants due to step input.



7.
Control a system, defined by

, It is desired to have eigen
values at -3.0 and -5.0 by using a state feedback control u = – KX. Determine
the necessary feedback gain matrix k and the control signal u.



2 of 2
Code No: RT42021
Set No. 1
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) What are the advantages offered by digital control? 
b) Obtain the Z-transform of

where ?a? is constant. 
c) Write about the observable canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.

e) Write brief note on design procedure in the w-plane. 
f) Write the sufficient condition for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) State and explain the theorem required to satisfy to recover the signal e(t) from
the samples e*(t).

b) Explain how the reconstructing the input signal by hold circuits. 

3.
Obtain the inverse Z-transform of the following in the closed form. (i)

(ii)

(iii)



4. a) Explain any one method of evaluation of state transition matrix. 
b) Investigate the controllability and observability of the following system.



5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.

b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)



Code No: RT42021
Set No. 2
R13
1 of 2

6. a) Consider the transfer function system shown in figure 6(a). The sampling
period T is assumed to be 0.1 sec. obtain G(w).
Figure 6 (a)


b) List out the transient response specifications and explain in brief. 

7. A discrete time regulator system has the plant equation

Design a state feedback control algorithm with u(k)=-KX(k) which places the
closed loop characteristic root at .



Code No: RT42021
Set No. 2
R13
2 of 2
IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Illustrate the step motor control system examples of discrete data control
systems.

b) Find the z-transforms of f(t) = t sin(?t). 
c) State the state transition matrix. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
4
-1.7z
3
+1.04z
2
-0.268z + 0.024 = 0.

e) Write the design procedure of lag compensator in w-plane. 
f) What do you mean by state feedback controller? 

PART ?B (3×16 = 48 Marks)2. a) Explain the examples of data control systems of the following (i) Microprocessor controlled system (ii) A digital computer controlled rolling mill regulating system.


b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.


3. a) Obtain the inverse z-transform of the following


b)Write the difference equation governing the system for

as shown
in figure.3 (b)Figure.3 (b)



4. a) Obtain the Jordan canonical form realization for the following transfer function

.


b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?

Code No: RT42021
Set No. 3
R13
1 of 2

5. Consider the sample-data system shown in Figure.5 and assume its sampling
period is 0.4 Sec. Find the range of K, so that the closed – loop system for which
stable.
Figure.5



6. The open loop transfer function of a unity – feedback digital control system is
given as

. Sketch the root loci of the system for 0 Indicate all important information on the root loci.



7.
Consider the system defined by

by using the state feedback control u = -Kx, it is desired to have the closed loop
poles at s = -2 ? j 4 and s= -10. Determine the state feedback gain matrix K.



2 of 2
Code No: RT42021
Set No. 3
R13
IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Explain the digital controller for a turbine and generator examples of discrete
data control systems.

b)Find the z transform of

where ?a? is a constant.

c) Write about the controllable canonical form. 
d) Enumerate the conclusions from the general mapping between the s and z
planes by the z transform.

e) Write the design procedure of lead compensator in w-plane. 
f) Write the necessary conditions for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Draw the magnitude and phase curves of the zero order hold and compare these
curves with those of the ideal low pass filter?

b) Explain the problems encountered in reconstructing e(t) from its samples. 

3. a) By using the inversion integral method, obtain the inverse z transform of


b)Write the difference equation governing the system for

as shown in
figure.3 (b).
Figure.3(b)



4. a) Write the following state space representation of discrete time systems (i) Observable canonical form (ii) Jordan canonical form

b) Obtain the state transition matrix of the following discrete time system

Where

Then obtain the state x(k) and output y(k) when the input u(k)=1 for
k=0,1,2,?..


Code No: RT42021
Set No. 4
R13
1 of 2

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Define the following fundamental parameters of an sample and hold element (i) Acquisition time (ii) Aperture time (iii) Droop rate

b)Obtain the Z-transform of

, where ?a? is a constant

c) Write about the Jordan canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.

e) What do understand by primary strip and complimentary strips? 
f) Enumerate the design steps for pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?

b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?


3. a)Given the z transform

Where a is a constant and T is the
sampling period, determine the inverse z transform x(kT) by use of the partial
fraction expansion method.


b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .



4.
Consider the discrete control system represented by the following transfer
function

. Obtain the state representation of the system in
the observable canonical form. Also find its state transition matrix.



5. a) How do you map constant damping loci from s-plane to z-plane? 
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.



Code No: RT42021
Set No. 1
R13
1 of 2
6. The closed loop transfer function for the digital control system is given as

Find the steady state errors and error constants due to step input.



7.
Control a system, defined by

, It is desired to have eigen
values at -3.0 and -5.0 by using a state feedback control u = – KX. Determine
the necessary feedback gain matrix k and the control signal u.



2 of 2
Code No: RT42021
Set No. 1
R13

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) What are the advantages offered by digital control? 
b) Obtain the Z-transform of

where ?a? is constant. 
c) Write about the observable canonical form. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.

e) Write brief note on design procedure in the w-plane. 
f) Write the sufficient condition for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) State and explain the theorem required to satisfy to recover the signal e(t) from
the samples e*(t).

b) Explain how the reconstructing the input signal by hold circuits. 

3.
Obtain the inverse Z-transform of the following in the closed form. (i)

(ii)

(iii)



4. a) Explain any one method of evaluation of state transition matrix. 
b) Investigate the controllability and observability of the following system.



5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.

b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)



Code No: RT42021
Set No. 2
R13
1 of 2

6. a) Consider the transfer function system shown in figure 6(a). The sampling
period T is assumed to be 0.1 sec. obtain G(w).
Figure 6 (a)


b) List out the transient response specifications and explain in brief. 

7. A discrete time regulator system has the plant equation

Design a state feedback control algorithm with u(k)=-KX(k) which places the
closed loop characteristic root at .



Code No: RT42021
Set No. 2
R13
2 of 2
IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Illustrate the step motor control system examples of discrete data control
systems.

b) Find the z-transforms of f(t) = t sin(?t). 
c) State the state transition matrix. 
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
4
-1.7z
3
+1.04z
2
-0.268z + 0.024 = 0.

e) Write the design procedure of lag compensator in w-plane. 
f) What do you mean by state feedback controller? 

PART ?B (3×16 = 48 Marks)2. a) Explain the examples of data control systems of the following (i) Microprocessor controlled system (ii) A digital computer controlled rolling mill regulating system.


b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.


3. a) Obtain the inverse z-transform of the following


b)Write the difference equation governing the system for

as shown
in figure.3 (b)Figure.3 (b)



4. a) Obtain the Jordan canonical form realization for the following transfer function

.


b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?

Code No: RT42021
Set No. 3
R13
1 of 2

5. Consider the sample-data system shown in Figure.5 and assume its sampling
period is 0.4 Sec. Find the range of K, so that the closed – loop system for which
stable.
Figure.5



6. The open loop transfer function of a unity – feedback digital control system is
given as

. Sketch the root loci of the system for 0 Indicate all important information on the root loci.



7.
Consider the system defined by

by using the state feedback control u = -Kx, it is desired to have the closed loop
poles at s = -2 ? j 4 and s= -10. Determine the state feedback gain matrix K.



2 of 2
Code No: RT42021
Set No. 3
R13
IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
DIGITAL CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Explain the digital controller for a turbine and generator examples of discrete
data control systems.

b)Find the z transform of

where ?a? is a constant.

c) Write about the controllable canonical form. 
d) Enumerate the conclusions from the general mapping between the s and z
planes by the z transform.

e) Write the design procedure of lead compensator in w-plane. 
f) Write the necessary conditions for arbitrary pole placement. 

PART ?B (3×16 = 48 Marks)2. a) Draw the magnitude and phase curves of the zero order hold and compare these
curves with those of the ideal low pass filter?

b) Explain the problems encountered in reconstructing e(t) from its samples. 

3. a) By using the inversion integral method, obtain the inverse z transform of


b)Write the difference equation governing the system for

as shown in
figure.3 (b).
Figure.3(b)



4. a) Write the following state space representation of discrete time systems (i) Observable canonical form (ii) Jordan canonical form

b) Obtain the state transition matrix of the following discrete time system

Where

Then obtain the state x(k) and output y(k) when the input u(k)=1 for
k=0,1,2,?..


Code No: RT42021
Set No. 4
R13
1 of 2
5. a) Determine

in terms of F(s). Using this result, explain the
relationship between the z-plane and the s-plane.

b) Use the Routh-Hurwitz criterion to find the stable range of K for the closed loop unity
feedback system with loop gain
) 8 . 0 )( 1 . 0 (
) 1 (
) (
? ?
?
?
z z
z K
z F .



6. Consider the digital control system shown in figure 6, plot the root loci as the
gain K is varied from 0 to 8. Determine the critical value of gain K for stability.
The sampling period is 0.1 sec, or T=0.1. What value of gain K will yield a
damping ratio of the closed loop poles equal to 0.5? With gain K set to yield
=0.5, determine the damped natural frequency
and the number of samples
per cycle of damped sinusoidal oscillation.
Figure.6



7. a) Discuss the necessary conditions for design of state feedback controller through
pole placement.

b) Prove Ackermann?s formula for the determination of the state feedback gain. 

2 of 2
Code No: RT42021
Set No. 4
R13

Team FirstRanker.in

Share
Team FirstRanker.in

## MGR University BPT Fourth Year 746268 PAPER V – REHABILITATION MEDICINE INCLUDING GERIATRIC MEDICINE August 2018 Question Paper

746268 PAPER V - REHABILITATION MEDICINE INCLUDING GERIATRIC MEDICINETHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY…

4 years ago

## MGR University BPT Fourth Year 746268 PAPER V – REHABILITATION MEDICINE INCLUDING GERIATRIC MEDICINE August 2018 Question Paper

746268 PAPER V - REHABILITATION MEDICINE INCLUDING GERIATRIC MEDICINETHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY…

4 years ago

## MGR University BPT Fourth Year 746267 PAPER IV – P.T. IN ORTHOPAEDICS August 2018 Question Paper

746267 PAPER IV - P.T. IN ORTHOPAEDICSTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6267]…

4 years ago

## MGR University BPT Fourth Year 746267 PAPER IV – P.T. IN ORTHOPAEDICS August 2018 Question Paper

746267 PAPER IV - P.T. IN ORTHOPAEDICSTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6267]…

4 years ago

## MGR University BPT Fourth Year 746266 PAPER III – CLINICAL ORTHOPAEDICS August 2018 Question Paper

746266 PAPER III – CLINICAL ORTHOPAEDICSTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6266] AUGUST…

4 years ago

## MGR University BPT Fourth Year 746265 PAPER II – P.T. IN NEUROLOGY August 2018 Question Paper

746265 PAPER II – P.T. IN NEUROLOGYTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6265]…

4 years ago