Categories: Fourth Year Second Semester (4-2)

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

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

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

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

*****

[3]

b)Obtain the Z-transform of

[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]

sketch?

[8]

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

continuous signals?

[8]

3. a)Given the z transform

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 .

[8]

4.

Consider the discrete control system represented by the following transfer

function

the observable canonical form. Also find its state transition matrix.

[16]

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

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

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

*****

[3]

b)Obtain the Z-transform of

[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]

sketch?

[8]

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

continuous signals?

[8]

3. a)Given the z transform

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 .

[8]

4.

Consider the discrete control system represented by the following transfer

function

the observable canonical form. Also find its state transition matrix.

[16]

b) Construct the Jury stability table for the following characteristic equation

Where a

0

>0. Write the stability

conditions.

[10]

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

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

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

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

*****

[3]

b)Obtain the Z-transform of

[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]

sketch?

[8]

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

continuous signals?

[8]

3. a)Given the z transform

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 .

[8]

4.

Consider the discrete control system represented by the following transfer

function

the observable canonical form. Also find its state transition matrix.

[16]

b) Construct the Jury stability table for the following characteristic equation

Where a

0

>0. Write the stability

conditions.

[10]

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

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

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

*****

b) Obtain the Z-transform of

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]

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]

b) Investigate the controllability and observability of the following system.

[10]

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

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

*****

[3]

b)Obtain the Z-transform of

[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]

sketch?

[8]

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

continuous signals?

[8]

3. a)Given the z transform

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 .

[8]

4.

Consider the discrete control system represented by the following transfer

function

the observable canonical form. Also find its state transition matrix.

[16]

b) Construct the Jury stability table for the following characteristic equation

Where a

0

>0. Write the stability

conditions.

[10]

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

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

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

*****

b) Obtain the Z-transform of

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]

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]

b) Investigate the controllability and observability of the following system.

[10]

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

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

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

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

*****

[3]

b)Obtain the Z-transform of

[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]

sketch?

[8]

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

continuous signals?

[8]

3. a)Given the z transform

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 .

[8]

4.

Consider the discrete control system represented by the following transfer

function

the observable canonical form. Also find its state transition matrix.

[16]

b) Construct the Jury stability table for the following characteristic equation

Where a

0

>0. Write the stability

conditions.

[10]

Set No. 1

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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

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

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

*****

b) Obtain the Z-transform of

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]

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]

b) Investigate the controllability and observability of the following system.

[10]

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

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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

closed loop characteristic root at .

[16]

Set No. 2

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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

*****

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]

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

[8]

Code No: RT42021

Set No. 3

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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

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