3. Case of study: EDF-1000 distillation pilot plant

As a case of study, an EDF-1000 distillation pilot plant is used (Figure 2), consisting of 11 perforated plates, having 7 RTD (PT100) temperature sensors

Eq. (19) shows the mathematical model of a batch-type 11-plate EDF-1000 distillation pilot plant for an ethanol-water mixture, considering the compositions in each plate ð Þ x1; x2; ⋯ x10; x<sup>11</sup> , where the condenser composition is x<sup>1</sup> and the boiler composition is x11; in addition, the control inputs are the heating power Qf

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation…

x1 x2 ⋮

1

CCCCCCCCCA

x1 x2 ⋮

x<sup>10</sup>

x<sup>11</sup>

V · G xð Þ <sup>2</sup>α<sup>2</sup> M<sup>1</sup>

⋮

� <sup>V</sup> · G xð Þ� <sup>10</sup>α<sup>10</sup> <sup>L</sup> M<sup>10</sup>

> L M<sup>11</sup>

> > 0

0 ⋮ 0 x11ð Þ 1 � G xð Þ <sup>11</sup>α<sup>11</sup>

<sup>H</sup>20ð Þ <sup>1</sup> � <sup>x</sup><sup>11</sup> <sup>M</sup><sup>11</sup> � �

� <sup>V</sup> · G xð Þ� <sup>3</sup>α<sup>3</sup> <sup>L</sup> M<sup>2</sup>

<sup>þ</sup> <sup>B</sup> Rf Qb !

1

(19)

CCCCCCCCCA

⋯ 0 0

⋯ 0 0

⋮

1

CCCCCCCCCCCCCCCCCA

(20)

V · G xð Þ <sup>11</sup>α<sup>11</sup> M<sup>10</sup>

> � <sup>L</sup> M<sup>11</sup>

> > 1

CCCCCCCCCCCA

0

BBBBBBBBB@

x<sup>10</sup>

x<sup>11</sup>

0

BBBBBBBBB@

y ¼ C

x\_ ¼ A

� ð Þ <sup>V</sup> <sup>þ</sup> <sup>D</sup> M<sup>1</sup>

L M<sup>2</sup>

⋯

⋯

⋯

Lx<sup>1</sup> M<sup>1</sup>

> 0 ⋮ 0

> 0

C ¼

Hvap

0 ⋮

0

BBBB@

1

⋮

Ethx<sup>11</sup> <sup>þ</sup> <sup>H</sup>vap

where the output matrix is defined by an 11 � 11 identity matrix as shown in

1 0 ⋯ 0 0

⋯

⋮

0 ⋮

1

CCCCA

⋮

⋱

0 0 ⋯ 0 1

where A and B matrixes are defined by

A ¼

Eq. (20).

17

⋮

BBBBBBBBBBBBBBBBB@

0

⋮

0

0

0

BBBBBBBBBBB@

0

0

B ¼

and the reflux Rf :

DOI: http://dx.doi.org/10.5772/intechopen.83479
