IV B.Tech II Semester Supplimentry Examinations,May 2010 DIGITAL CONTROL SYSTEMS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Discuss the Liapunov stability criterion for discrete time systems.
ld .
(b) Consider the system defined by the equations: x1 (k + 1) = 2x1 (k) + 0.5x2 (k)-5 x2 (k + 1) = 0.8x2 (k)+2 Using direct method of Liapunov determine the stability of the equilibrium state. [8+8]
or
2. The open loop transfer function of a unity - feedback digital control system is given K(z+0.5)(z+0.2) Sketch the root loci of the system for 0< K < ∞. as G(z) = (z−1)(z 2 −z+0.5) . Indicate all important information on the root loci. [16]
uW
3. A block diagram of a digital control system is shown in Figure 8. Design a PID controller D(z), to eliminate the steady-state error due to a step input and simultaneously realizing a good transient response, and the ramp-error constant Kv should equal 5. [16]
nt
Figure 8
4. The closed loop transfer function for the digital control system is given as C(z) 0.5z = z2 −z+0.5 . Find the maximum overshoot and the normalized peak time R(z) Tmax /T of the step response. [16]
Aj
5. A discrete system is described by the difference equation y(k + 2) + 3y(k + 1) + 2y(k) = r(k) y(0) = y(1) = 0, T = 1 Sec. (a) Determine a state variable model for the system. Draw the state diagram.
(b) Find the state transition matrix.
6. The block diagram of a digital control system is shown in Figure 1, where K Gp (s) = s(s+5) .
1
[8+8]
RR
Code No: RR420201
Set No. 2
7. (a) Find the z-transform of the following function x(k) k P x(k) = ak h=0
ld .
where a is a constant.
in
Figure 1 Determine the range of K for the system to be asymptotically stable.
(b) Find the inverse z-transform of the following functions: i. X(z) = ii. X(z) =
z −1 (1−z −2 ) (1+z −2 )2 z−0.4 z 2 +z+2
and
[8+8]
or
8. (a) What are the different types of sampling operations? Explain each of them. (b) What do you mean by the problem of aliasing? How to overcome this?
(c) Explain the advantages and disadvantages of digital control systems.[6+5+5]
Aj
nt
uW
?????
2
RR
Code No: RR420201
Set No. 4
in
IV B.Tech II Semester Supplimentry Examinations,May 2010 DIGITAL CONTROL SYSTEMS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Discuss the Liapunov stability criterion for discrete time systems.
ld .
(b) Consider the system defined by the equations: x1 (k + 1) = 2x1 (k) + 0.5x2 (k)-5 x2 (k + 1) = 0.8x2 (k)+2 Using direct method of Liapunov determine the stability of the equilibrium state. [8+8]
h=0
where a is a constant.
or
2. (a) Find the z-transform of the following function x(k) k P x(k) = ak
(b) Find the inverse z-transform of the following functions: z −1 (1−z −2 ) (1+z −2 )2 z−0.4 z 2 +z+2
and
uW
i. X(z) = ii. X(z) =
[8+8]
3. A discrete system is described by the difference equation y(k + 2) + 3y(k + 1) + 2y(k) = r(k) y(0) = y(1) = 0, T = 1 Sec. (a) Determine a state variable model for the system. Draw the state diagram.
nt
(b) Find the state transition matrix.
[8+8]
4. The open loop transfer function of a unity - feedback digital control system is given K(z+0.5)(z+0.2) as G(z) = (z−1)(z Sketch the root loci of the system for 0< K < ∞. 2 −z+0.5) . Indicate all important information on the root loci. [16]
Aj
5. The block diagram of a digital control system is shown in Figure 1, where K Gp (s) = s(s+5) .
Figure 1 Determine the range of K for the system to be asymptotically stable. 3
Code No: RR420201
RR
Set No. 4
6. (a) What are the different types of sampling operations? Explain each of them. (b) What do you mean by the problem of aliasing? How to overcome this? (c) Explain the advantages and disadvantages of digital control systems.[6+5+5]
Figure 8
ld .
in
7. A block diagram of a digital control system is shown in Figure 8. Design a PID controller D(z), to eliminate the steady-state error due to a step input and simultaneously realizing a good transient response, and the ramp-error constant Kv should equal 5. [16]
or
8. The closed loop transfer function for the digital control system is given as C(z) 0.5z = z2 −z+0.5 . Find the maximum overshoot and the normalized peak time R(z) Tmax /T of the step response. [16]
Aj
nt
uW
?????
4
RR
Code No: RR420201
Set No. 1
1. (a) Find the z-transform of the following function x(k) k P x(k) = ak h=0
ld .
where a is a constant.
in
IV B.Tech II Semester Supplimentry Examinations,May 2010 DIGITAL CONTROL SYSTEMS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
(b) Find the inverse z-transform of the following functions: i. X(z) = ii. X(z) =
z −1 (1−z −2 ) (1+z −2 )2 z−0.4 z 2 +z+2
and
[8+8]
or
2. The closed loop transfer function for the digital control system is given as C(z) 0.5z = z2 −z+0.5 . Find the maximum overshoot and the normalized peak time R(z) Tmax /T of the step response. [16]
nt
uW
3. A block diagram of a digital control system is shown in Figure 8. Design a PID controller D(z), to eliminate the steady-state error due to a step input and simultaneously realizing a good transient response, and the ramp-error constant Kv should equal 5. [16]
Figure 8
4. The open loop transfer function of a unity - feedback digital control system is given K(z+0.5)(z+0.2) as G(z) = (z−1)(z Sketch the root loci of the system for 0< K < ∞. 2 −z+0.5) . Indicate all important information on the root loci. [16]
Aj
5. (a) Discuss the Liapunov stability criterion for discrete time systems. (b) Consider the system defined by the equations: x1 (k + 1) = 2x1 (k) + 0.5x2 (k)-5 x2 (k + 1) = 0.8x2 (k)+2 Using direct method of Liapunov determine the stability of the equilibrium state. [8+8]
6. (a) What are the different types of sampling operations? Explain each of them. (b) What do you mean by the problem of aliasing? How to overcome this? 5
Code No: RR420201
RR
Set No. 1
(c) Explain the advantages and disadvantages of digital control systems.[6+5+5] 7. A discrete system is described by the difference equation y(k + 2) + 3y(k + 1) + 2y(k) = r(k) y(0) = y(1) = 0, T = 1 Sec. (a) Determine a state variable model for the system. Draw the state diagram. [8+8]
in
(b) Find the state transition matrix.
ld .
8. The block diagram of a digital control system is shown in Figure 1, where K . Gp (s) = s(s+5)
or
Figure 1 Determine the range of K for the system to be asymptotically stable.
Aj
nt
uW
?????
6
RR
Code No: RR420201
Set No. 3
in
IV B.Tech II Semester Supplimentry Examinations,May 2010 DIGITAL CONTROL SYSTEMS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
ld .
1. The block diagram of a digital control system is shown in Figure 1, where K . Gp (s) = s(s+5)
or
Figure 1 Determine the range of K for the system to be asymptotically stable.
2. (a) What are the different types of sampling operations? Explain each of them. (b) What do you mean by the problem of aliasing? How to overcome this?
uW
(c) Explain the advantages and disadvantages of digital control systems.[6+5+5] 3. The closed loop transfer function for the digital control system is given as C(z) 0.5z = z2 −z+0.5 . Find the maximum overshoot and the normalized peak time R(z) Tmax /T of the step response. [16] 4. (a) Find the z-transform of the following function x(k) k P x(k) = ak h=0
nt
where a is a constant.
(b) Find the inverse z-transform of the following functions: i. X(z) =
and [8+8]
Aj
ii. X(z) =
z −1 (1−z −2 ) (1+z −2 )2 z−0.4 z 2 +z+2
5. A discrete system is described by the difference equation y(k + 2) + 3y(k + 1) + 2y(k) = r(k) y(0) = y(1) = 0, T = 1 Sec. (a) Determine a state variable model for the system. Draw the state diagram.
(b) Find the state transition matrix.
[8+8]
6. The open loop transfer function of a unity - feedback digital control system is given K(z+0.5)(z+0.2) as G(z) = (z−1)(z Sketch the root loci of the system for 0< K < ∞. 2 −z+0.5) . Indicate all important information on the root loci. [16] 7
Code No: RR420201
RR
Set No. 3
7. (a) Discuss the Liapunov stability criterion for discrete time systems.
in
(b) Consider the system defined by the equations: x1 (k + 1) = 2x1 (k) + 0.5x2 (k)-5 x2 (k + 1) = 0.8x2 (k)+2 Using direct method of Liapunov determine the stability of the equilibrium state. [8+8]
or
ld .
8. A block diagram of a digital control system is shown in Figure 8. Design a PID controller D(z), to eliminate the steady-state error due to a step input and simultaneously realizing a good transient response, and the ramp-error constant Kv should equal 5. [16]
The open loop transfer function of a unity - feedback digital control system is ... neously realizing a good transient response, and the ramp-error constant Kv ...
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Code No: RR420203. RR. Set No. 2. IV B.Tech II Semester Examinations,APRIL 2011 · V L S I DESIGN · Electrical And Electronics Engineering · Time: 3 hours.
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Common to Information Technology, Electronics And Computer · Engineering ... List the blending functions suitable for cubic Bezier curves. Discuss their ...
