# 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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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.

[16]

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.

[16]

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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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.

[16]

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.

[16]

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? [4]
b) Obtain the Z-transform of

where ?a? is constant. [4]
c) Write about the observable canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.
[4]
e) Write brief note on design procedure in the w-plane. [5]
f) Write the sufficient condition for arbitrary pole placement. [2]

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).
[8]
b) Explain how the reconstructing the input signal by hold circuits. [8]

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

(ii)

(iii)

[16]

4. a) Explain any one method of evaluation of state transition matrix. [6]
b) Investigate the controllability and observability of the following system.

[10]

5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.
[8]
b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)

[8]

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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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.

[16]

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.

[16]

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? [4]
b) Obtain the Z-transform of

where ?a? is constant. [4]
c) Write about the observable canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.
[4]
e) Write brief note on design procedure in the w-plane. [5]
f) Write the sufficient condition for arbitrary pole placement. [2]

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).
[8]
b) Explain how the reconstructing the input signal by hold circuits. [8]

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

(ii)

(iii)

[16]

4. a) Explain any one method of evaluation of state transition matrix. [6]
b) Investigate the controllability and observability of the following system.

[10]

5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.
[8]
b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)

[8]

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)

[8]
b) List out the transient response specifications and explain in brief. [8]

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 .

[16]

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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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.

[16]

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.

[16]

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? [4]
b) Obtain the Z-transform of

where ?a? is constant. [4]
c) Write about the observable canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.
[4]
e) Write brief note on design procedure in the w-plane. [5]
f) Write the sufficient condition for arbitrary pole placement. [2]

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).
[8]
b) Explain how the reconstructing the input signal by hold circuits. [8]

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

(ii)

(iii)

[16]

4. a) Explain any one method of evaluation of state transition matrix. [6]
b) Investigate the controllability and observability of the following system.

[10]

5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.
[8]
b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)

[8]

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)

[8]
b) List out the transient response specifications and explain in brief. [8]

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 .

[16]

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.
[4]
b) Find the z-transforms of f(t) = t sin(?t). [4]
c) State the state transition matrix. [3]
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.
[4]
e) Write the design procedure of lag compensator in w-plane. [4]
f) What do you mean by state feedback controller? [3]

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.

[8]
b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.
[8]

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

[8]
b)Write the difference equation governing the system for

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

[8]

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

.

[8]
b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?
[8]
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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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.

[16]

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.

[16]

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? [4]
b) Obtain the Z-transform of

where ?a? is constant. [4]
c) Write about the observable canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.
[4]
e) Write brief note on design procedure in the w-plane. [5]
f) Write the sufficient condition for arbitrary pole placement. [2]

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).
[8]
b) Explain how the reconstructing the input signal by hold circuits. [8]

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

(ii)

(iii)

[16]

4. a) Explain any one method of evaluation of state transition matrix. [6]
b) Investigate the controllability and observability of the following system.

[10]

5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.
[8]
b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)

[8]

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)

[8]
b) List out the transient response specifications and explain in brief. [8]

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 .

[16]

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.
[4]
b) Find the z-transforms of f(t) = t sin(?t). [4]
c) State the state transition matrix. [3]
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.
[4]
e) Write the design procedure of lag compensator in w-plane. [4]
f) What do you mean by state feedback controller? [3]

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.

[8]
b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.
[8]

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

[8]
b)Write the difference equation governing the system for

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

[8]

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

.

[8]
b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?
[8]
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

[16]

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.

[16]

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.

[16]

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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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.

[16]

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.

[16]

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? [4]
b) Obtain the Z-transform of

where ?a? is constant. [4]
c) Write about the observable canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.
[4]
e) Write brief note on design procedure in the w-plane. [5]
f) Write the sufficient condition for arbitrary pole placement. [2]

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).
[8]
b) Explain how the reconstructing the input signal by hold circuits. [8]

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

(ii)

(iii)

[16]

4. a) Explain any one method of evaluation of state transition matrix. [6]
b) Investigate the controllability and observability of the following system.

[10]

5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.
[8]
b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)

[8]

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)

[8]
b) List out the transient response specifications and explain in brief. [8]

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 .

[16]

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.
[4]
b) Find the z-transforms of f(t) = t sin(?t). [4]
c) State the state transition matrix. [3]
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.
[4]
e) Write the design procedure of lag compensator in w-plane. [4]
f) What do you mean by state feedback controller? [3]

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.

[8]
b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.
[8]

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

[8]
b)Write the difference equation governing the system for

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

[8]

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

.

[8]
b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?
[8]
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

[16]

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.

[16]

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.

[16]

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.
[4]
b)Find the z transform of

where ?a? is a constant.
[4]
c) Write about the controllable canonical form. [3]
d) Enumerate the conclusions from the general mapping between the s and z
planes by the z transform.
[4]
e) Write the design procedure of lead compensator in w-plane. [4]
f) Write the necessary conditions for arbitrary pole placement. [3]

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?
[8]
b) Explain the problems encountered in reconstructing e(t) from its samples. [8]

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

[8]
b)Write the difference equation governing the system for

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

[8]

4. a) Write the following state space representation of discrete time systems (i) Observable canonical form (ii) Jordan canonical form
[6]
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,?..

[10]
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
[3]
b)Obtain the Z-transform of

, where ?a? is a constant
[4]
c) Write about the Jordan canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests 5z
2
-2z + 2 = 0.
[4]
e) What do understand by primary strip and complimentary strips? [4]
f) Enumerate the design steps for pole placement. [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss the mathematical model of sample and hold operations with neat
sketch?
[8]
b) Explain the conditions to be satisfied for reconstruction of sampled signal into
continuous signals?
[8]

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.

[8]
b) The input output of a sampled data system is described by the difference
equation . Determine the pulse transfer
function, the initial conditions are .

[8]

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.

[16]

5. a) How do you map constant damping loci from s-plane to z-plane? [6]
b) Construct the Jury stability table for the following characteristic equation

Where a
0
>0. Write the stability
conditions.

[10]

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.

[16]

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.

[16]

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? [4]
b) Obtain the Z-transform of

where ?a? is constant. [4]
c) Write about the observable canonical form. [3]
d) Determine the stability of the characteristic equations by using Jury?s stability
tests z
3
-0.2z
2
-0.25z + 0.05 = 0.
[4]
e) Write brief note on design procedure in the w-plane. [5]
f) Write the sufficient condition for arbitrary pole placement. [2]

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).
[8]
b) Explain how the reconstructing the input signal by hold circuits. [8]

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

(ii)

(iii)

[16]

4. a) Explain any one method of evaluation of state transition matrix. [6]
b) Investigate the controllability and observability of the following system.

[10]

5. a) Discuss the stability analysis of discrete control system using modified Routh
stability.
[8]
b) Using Jury?s stability criterion, determine the stability of the following discrete
time systems (i)

(ii)

[8]

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)

[8]
b) List out the transient response specifications and explain in brief. [8]

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 .

[16]

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.
[4]
b) Find the z-transforms of f(t) = t sin(?t). [4]
c) State the state transition matrix. [3]
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.
[4]
e) Write the design procedure of lag compensator in w-plane. [4]
f) What do you mean by state feedback controller? [3]

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.

[8]
b) Draw the frequency domain characteristics of zero order hold? Explain with
necessary mathematical equations.
[8]

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

[8]
b)Write the difference equation governing the system for

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

[8]

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

.

[8]
b) Consider the following pulse transfer function

. Check this system is completely state controllable or not?
[8]
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

[16]

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.

[16]

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.

[16]

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.
[4]
b)Find the z transform of

where ?a? is a constant.
[4]
c) Write about the controllable canonical form. [3]
d) Enumerate the conclusions from the general mapping between the s and z
planes by the z transform.
[4]
e) Write the design procedure of lead compensator in w-plane. [4]
f) Write the necessary conditions for arbitrary pole placement. [3]

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?
[8]
b) Explain the problems encountered in reconstructing e(t) from its samples. [8]

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

[8]
b)Write the difference equation governing the system for

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

[8]

4. a) Write the following state space representation of discrete time systems (i) Observable canonical form (ii) Jordan canonical form
[6]
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,?..

[10]
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.
[8]
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 .

[8]

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

[16]

7. a) Discuss the necessary conditions for design of state feedback controller through
pole placement.
[9]
b) Prove Ackermann?s formula for the determination of the state feedback gain. [7]

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

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