Corrige HEI Control systems 2008 TC

Description

iFEEDBACK CONTROL SYSTEMS: TD n°2 CORRECTION 1. Step Responsek From: U(1) u(p) 212 k k θ (p) 10 1 + τ p2 101 + τ p p 18 6 θ (p) λH (p) = = 4u(p) p(1 + τ ...

Informations

• Publié par: shin
• Nombre de lectures: 230
• Langue: Français

Extrait

Abdel AITOUCHE, 2007-2008, FEEDBACK CONTROL SYSTEMS

FEEDBACK

CONTROL SYSTEMS: TD n°2 CORRECTION

1.

)

1

)(

1

(

)

(

)

(

)

(

2

1

p

p

p

p

u

p

p

H

τ

τ

λ

θ

+

+

=

=

2.1

2.2.1

We neglect

the pole

1

1

τ

−

.

2.2.2

)

1

(

2

p

p

k

H

BOa

τ

λ

+

=

2.2.3

1

1

1

2

2

+

+

=

p

k

p

k

H

BFa

λ

λ

τ

2.2.4

2

τ

λ

ω

k

n

=

2

2

1

λτ

ξ

k

=

2.2.5

0208

,

0

:

2

1

2

=

⇒

=

k

AN

k

λτ

2.2.6

heures

t

t

r

n

r

10

3

=

⇒

=

ξω

2.2.7

C

D

e

D

°

=

∞

=

⇒

=

−

−

10

)

(

%

33

,

4

%

%

2

1

θ

ξ

ξπ

2.4.1

dB

MG

MG

k

MG

2

,

27

9

,

22

2

1

2

1

≈

⇒

≈

⇒

+

=

τ

λτ

τ

τ

3.1

3.2

)

1

(

1

p

p

k

H

BO

τ

λ

+

=

⇒

1

1

1

2

1

+

+

=

p

k

p

k

H

BF

λ

λ

τ

3.3

208

,

0

:

2

1

1

=

⇒

=

k

AN

k

λτ

3.4

heure

t

t

r

n

r

1

3

=

⇒

=

ξω

3.5

C

D

e

D

°

=

∞

=

⇒

=

−

−

10

)

(

%

33

,

4

%

%

2

1

θ

ξ

ξπ

3.6 Controller PD allows accelerating the dynamic of system 10

times faster than the controller P for a same accuracy and a same

overshoot.

4.1

4.2

1

1

1

)

(

)

(

1

+

=

⇒

=

⇒

=

p

p

H

p

p

H

T

BF

BO

d

λ

λ

τ

4.3

25

,

1

:

3

3

1

1

0

1

=

⇒

=

⇒

=

=

k

AN

k

k

k

t

r

τ

τ

λ

4.4.1

4.4.2

4.4.3

1

1

1

1

)

(

2

2

2

+

+

=

p

k

k

p

k

k

p

H

i

i

BF

λ

4.4.4

1

2

2

3

τ

k

k

i

=

0025

,

0

=

⇒

i

k

4.4.5

mn

t

t

r

n

r

20

3

=

⇒

=

ξω

C

D

e

D

°

=

∞

=

⇒

=

−

−

10

)

(

%

33

,

4

%

%

2

1

θ

ξ

ξπ

4.5

Cascade Control allows obtaining a step time response three

times less than a controller PD, thirty time less than a

controller P with the same accuracy and the same overshoot.

.

2

1

τ

−

1

1

τ

−

0

Tim e (s ec .)

Amplitude

S tep Response

0

1400

2800

4200

5600

7000

0

2

4

6

8

10

12

From: U(1)

To: Y(1)

Amplitude

S tep Res pons e

0

500

1000

1500

2000

2500

3000

0

0.005

0.01

0.015

0.02

0.025

0.03

From: U(1)

To: Y(1)

u(p)

)

(

p

θ

p

k

0

p

k

1

1

1

τ

+

p

k

2

2

1

τ

+

ref

θ

)

(

p

θ

)

(

p

H

k

ref

θ

)

(

p

θ

)

1

1

(

2

+

p

p

k

k

i

λ

ref

θ

)

(

p

θ

1

ϑ

BF

H

p

p

T

k

i

i

)

1

(

+

p

k

2

2

1

τ

+

ref

1

θ

)

(

1

p

θ

)

1

(

1

1

0

p

p

k

k

τ

+

k

)

1

(

p

T

d

+

ref

θ

)

(

p

θ

)

(

p

H

)

1

(

p

T

k

d

+