HEI control systems 2008 tc tronc commun

Description

HEI 43 TC 2007-2008 Control of Temperature. The controlled temperature θ of indirect heating is represented by the following figure: u Exchanger θ 1 Plate q valve θ pomp u(t) represents the voltage control of valve, q(t )the inlet flow in exchanger and θ the output 1temperature of exchanger. t⎧ ...

Informations

• Publié par: aiolos
• Nombre de lectures: 245
• Langue: Français

Extrait

HEI 43 TC 2007-2008

Control of Temperature

.

The controlled temperature

θ

of indirect heating is represented by the following figure:

u(t) represents the voltage control of valve,

q(t )

the

inlet flow in exchanger and

θ

1

the output

temperature of exchanger.

Let the following relations:

(t)

k

=

dt

(t)

d

+

(t)

q(t)

k

=

dt

(t)

d

+

(t)

).d

u(

k

=

q(t)

1

2

2

1

1

1

1

t

0

o

⎪

⎪

⎩

⎪

⎪

⎨

⎧

⋅

⋅

⋅

⋅

⋅

∫

θ

θ

τ

θ

θ

τ

θ

τ

τ

We assume that all initial conditions are null. Numerical applications

:

τ

1

=600s,

τ

2

=6000s,

k

2

=1, k

1

=20 S.I., k

o

=2.10

-4

S.I.

We take:

λ

= k

o.

k

1

.k

2

.

1

. Give the box diagram of the system and deduce the transfer function of the exchanger H(p)

(input u and

θ

).

2. Proportional Controller

u(t) =G

r

ε

(t)= G

r

.(

θ

ref

(t) -

θ

(t)) where

θ

ref

(t) is the setpoint or reference.

2.1

Give the box diagram of the closed loop system

2.2

To determine k, we neglect a pole of the system.

2.2.1

From the numerical values, which is the pole to be neglected?

2.2.2

Give the expression of the approximated open loop transfer noted W

Oa

.

2.2.3

Compute from W

Oa

the approximated closed loop transfer W

Fa

.

2.3.4

W

Fa

will be written as normalized second order:

1

2

1

1

0

2

2

0

+

+

p

p

ω

ξ

ω

. Give

ξ

and

ω

0

.

2.2.5

Compute the proportional gain G

r

in order to obtain a damping coefficient un coefficient

2

2

=

ξ

.Numerical Application..

2.2.6

Determine the settling time (5%) of the controlled system . Numerical Application.

θ

1

q

u

θ

Exchanger

pomp

Plate

valve