Code.No: 27021

SET-1

RR

or ld

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD IV.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOV/DEC, 2009 ADVANCED CONTROL SYSTEMS (ELECTRICAL & ELECTRONICS ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1.a) State and explain controllability and observability applied to continuous time invariant systems. b) Consider the system ⎛ −1 0 1 ⎞ ⎛0⎞ ⎜ ⎟ ⎜ ⎟ X = ⎜ 1 −2 0 ⎟ × + ⎜ 1 ⎟ u and output y = [1 1 1] X ⎜ 0 0 −3 ⎟ ⎜1⎟ ⎝ ⎠ ⎝ ⎠

Transform the system into observable canonical form.

b)

Define i) Positive definiteness iii) Positive semi definiteness

ii) Negative definiteness iv) negative semi definiteness of a scalar function [4+4+4+4] A linear autonomous system is described by the state equation X =AX ⎡ −4k 4k ⎤ Where A= ⎢ ⎥ Use the direct method of Lyapunou, find restrictions on the parameter ⎣ 2k −6k ⎦ K to guarantee the stability of the system.

uW

2.a)

[8+8]

Draw the block diagram of reduced-order observer and explain each block. Write short notes on dead beat observers. [8+8]

4.

For the block diagram shown in Figure below, G(s)=

nt

3.a) b)

values of parameters K1 and K2 such that ∞

J = ∫ ⎡⎣e 2 ( t ) + 0.25u 2 ( t ) ⎤⎦ dt is minimum

Aj

0

100 1 and R(s)= . Determine the optimal 2 S S [16]

What is non-linearity of a control system? Explain different types of non- linearities? Obtain the describing function of Dead zone non-linearity. [8+8]

6.

A linear second-order servo is described by the equation e + 2ξ wn e + wn 2 e = 0 Where ξ = 0.15 ; wn = 1 e(0) = 1.5 , e (0) = 0 Determine the singular points. Construct the phase trajectory, using the method of isoclines. [16]

7.

Use the minimum principles to find the input voltage u(t) that changes the capacitors, in figure below, from x(0) = 2V, at t = 0 to x(10) = 12V while minimizing the energy dissipated in the resistor. There are no constraints on u(t). Note that, by KVL, Ri(t) + x(t) = u(t) dx (t ) Where i(t) = C and the energy dissipated is [16] dt

8.

Use dynamic programming to find u(0) and u(1) that minimizing

uW

or ld

.in

5.a) b)

1

J = ( x(2) − 2 ) + ∑ u 2 ( K ) 2

K =0

Aj

nt

subjected to x(K+1) = x(K) + u(K), x(0) = 1.

********************

[16]

Code.No: 27021

SET-2

RR

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD IV.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOV/DEC, 2009 ADVANCED CONTROL SYSTEMS (ELECTRICAL & ELECTRONICS ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

Draw the block diagram of reduced-order observer and explain each block. Write short notes on dead beat observers. [8+8]

2.

For the block diagram shown in Figure below, G(s)=

or ld

values of parameters K1 and K2 such that ∞

100 1 and R(s)= . Determine the optimal 2 S S [16]

J = ∫ ⎡⎣e 2 ( t ) + 0.25u 2 ( t ) ⎤⎦ dt is minimum

uW

0

What is non-linearity of a control system? Explain different types of non- linearities? Obtain the describing function of Dead zone non-linearity. [8+8]

4.

A linear second-order servo is described by the equation e + 2ξ wn e + wn 2 e = 0 Where ξ = 0.15 ; wn = 1 e(0) = 1.5 , e (0) = 0 Determine the singular points. Construct the phase trajectory, using the method of isoclines. [16]

Aj

nt

3.a) b)

5.

Use the minimum principles to find the input voltage u(t) that changes the capacitors, in figure below, from x(0) = 2V, at t = 0 to x(10) = 12V while minimizing the energy dissipated in the resistor. There are no constraints on u(t). Note that, by KVL, Ri(t) + x(t) = u(t) dx (t ) Where i(t) = C and the energy dissipated is [16] dt

Use dynamic programming to find u(0) and u(1) that minimizing 1

J = ( x(2) − 2 ) + ∑ u 2 ( K ) 2

K =0

b)

8.a)

Define i) Positive definiteness iii) Positive semi definiteness

ii) Negative definiteness iv) negative semi definiteness of a scalar function [4+4+4+4] A linear autonomous system is described by the state equation X =AX ⎡ −4k 4k ⎤ Where A= ⎢ ⎥ Use the direct method of Lyapunou, find restrictions on the parameter ⎣ 2k −6k ⎦ K to guarantee the stability of the system.

Aj

nt

b)

State and explain controllability and observability applied to continuous time invariant systems. Consider the system ⎛ −1 0 1 ⎞ ⎛ 0⎞ ⎜ ⎟ ⎜ ⎟ X = ⎜ 1 −2 0 ⎟ × + ⎜ 1 ⎟ u and output y = [1 1 1] X ⎜ 0 0 −3 ⎟ ⎜1⎟ ⎝ ⎠ ⎝ ⎠ Transform the system into observable canonical form. [8+8]

uW

7.a)

[16]

or ld

subjected to x(K+1) = x(K) + u(K), x(0) = 1.

.in

6.

********************

Code.No: 27021

SET-3

RR

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD IV.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOV/DEC, 2009 ADVANCED CONTROL SYSTEMS (ELECTRICAL & ELECTRONICS ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

What is non-linearity of a control system? Explain different types of non- linearities? Obtain the describing function of Dead zone non-linearity. [8+8]

2.

A linear second-order servo is described by the equation e + 2ξ wn e + wn 2 e = 0 Where ξ = 0.15 ; wn = 1 e(0) = 1.5 , e (0) = 0 Determine the singular points. Construct the phase trajectory, using the method of isoclines. [16]

3.

Use the minimum principles to find the input voltage u(t) that changes the capacitors, in figure below, from x(0) = 2V, at t = 0 to x(10) = 12V while minimizing the energy dissipated in the resistor. There are no constraints on u(t). Note that, by KVL, Ri(t) + x(t) = u(t) dx (t ) Where i(t) = C and the energy dissipated is [16] dt

nt

uW

or ld

1.a) b)

4.

Use dynamic programming to find u(0) and u(1) that minimizing 1

J = ( x(2) − 2 ) + ∑ u 2 ( K ) 2

K =0

Aj

subjected to x(K+1) = x(K) + u(K), x(0) = 1.

5.a)

b)

[16]

State and explain controllability and observability applied to continuous time invariant systems. Consider the system

⎛ −1 0 1 ⎞ ⎛ 0⎞ ⎜ ⎟ ⎜ ⎟ X = ⎜ 1 −2 0 ⎟ × + ⎜ 1 ⎟ u and output y = [1 1 1] X ⎜ 0 0 −3 ⎟ ⎜1⎟ ⎝ ⎠ ⎝ ⎠ Transform the system into observable canonical form.

6.a)

Define i) Positive definiteness iii) Positive semi definiteness

[8+8]

or ld

.in

ii) Negative definiteness iv) negative semi definiteness of a scalar function [4+4+4+4] b) A linear autonomous system is described by the state equation X =AX ⎡ −4k 4k ⎤ Where A= ⎢ ⎥ Use the direct method of Lyapunou, find restrictions on the parameter ⎣ 2k −6k ⎦ K to guarantee the stability of the system.

7.a) b)

Draw the block diagram of reduced-order observer and explain each block. Write short notes on dead beat observers. [8+8]

8.

For the block diagram shown in Figure below, G(s)= values of parameters K1 and K2 such that ∞

100 1 and R(s)= . Determine the optimal 2 S S [16]

uW

J = ∫ ⎡⎣ e 2 ( t ) + 0.25u 2 ( t ) ⎤⎦ dt is minimum

Aj

nt

0

********************

Code.No: 27021

SET-4

RR

1.

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD IV.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOV/DEC, 2009 ADVANCED CONTROL SYSTEMS (ELECTRICAL & ELECTRONICS ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

Use dynamic programming to find u(0) and u(1) that minimizing 1

J = ( x(2) − 2 ) + ∑ u 2 ( K ) 2

K =0

subjected to x(K+1) = x(K) + u(K), x(0) = 1.

3.a)

or ld

b)

State and explain controllability and observability applied to continuous time invariant systems. Consider the system ⎛ −1 0 1 ⎞ ⎛0⎞ ⎜ ⎟ ⎜ ⎟ X = ⎜ 1 −2 0 ⎟ × + ⎜ 1 ⎟ u and output y = [1 1 1] X ⎜ 0 0 −3 ⎟ ⎜1⎟ ⎝ ⎠ ⎝ ⎠ Transform the system into observable canonical form. [8+8]

uW

2.a)

[16]

Define i) Positive definiteness iii) Positive semi definiteness

nt

ii) Negative definiteness iv) negative semi definiteness of a scalar function [4+4+4+4] b) A linear autonomous system is described by the state equation X =AX ⎡ −4k 4k ⎤ Where A= ⎢ ⎥ Use the direct method of Lyapunou, find restrictions on the parameter ⎣ 2k −6k ⎦ K to guarantee the stability of the system.

Draw the block diagram of reduced-order observer and explain each block. Write short notes on dead beat observers. [8+8]

Aj

4.a) b) 5.

100 1 and R(s)= . Determine the optimal 2 S S [16]

For the block diagram shown in Figure below, G(s)=

values of parameters K1 and K2 such that ∞

J = ∫ ⎡⎣ e 2 ( t ) + 0.25u 2 ( t ) ⎤⎦ dt is minimum 0

.in

What is non-linearity of a control system? Explain different types of non- linearities? Obtain the describing function of Dead zone non-linearity. [8+8]

7.

A linear second-order servo is described by the equation e + 2ξ wn e + wn 2 e = 0 Where ξ = 0.15 ; wn = 1 e(0) = 1.5 , e (0) = 0 Determine the singular points. Construct the phase trajectory, using the method of isoclines. [16]

8.

Use the minimum principles to find the input voltage u(t) that changes the capacitors, in figure below, from x(0) = 2V, at t = 0 to x(10) = 12V while minimizing the energy dissipated in the resistor. There are no constraints on u(t). Note that, by KVL, Ri(t) + x(t) = u(t) dx (t ) Where i(t) = C and the energy dissipated is [16] dt

Aj

nt

uW

or ld

6.a) b)

********************