Analysis on Data-Based Integrated Learning Control for Batch Processes - Intelligent Computing for Sustainable Energy and Environment - page 132

low up

u u

where , are the lower and upper bound of control input sequence respectively.

y

low

, u y are the lower and upper bound of end-product quality.
The predicted output of the data-based model [18] is

( ( ) ( ) ( ) ( ) ( )

ˆ

ykt , + = j M l ykt j , +− 1, ykt j , +− 2,  , ykt , + 1, ukt j , +− 1,

(3)

) ) ( ) (

kt , +− j 2 ,  , u kt , + 1

The model prediction error of end quality is written as

( ) ( ) ( )

ˆ ˆ

ekt , = ykt , − ykt ,

(4)

f f f

where

(

) ( ) ( )

 ˆ ˆ

yk + 1, t = yk + 1, t + α ekt ,

(6)

f f f

1

k

1

k

( )

( ) ( ) ( ) ( )  

ˆ ˆ ˆ

ekt , = eit , = yit , − yit ,

(5)

f f f f

k k i = 1 i = 1

where is error correction term parameter.

The batch-axis iterative learning control optimization problem can be formulated as

α

2

( ) () (

)

2

min J U = y t −  y U , t + U − U (7)

ILCk , + 1 d f ILCk , + 1 f ILCk , + 1 k

R

Q

UU U (8) Δ = −

ILC k , ILC k , + 1 k

where Q is selected as constant matrix here,

= QI , R is dynamic matrix,

T

R = k r × I

, where r is bounded and its upper bound is

M .

I

is T -dimensional

T T

matrix.
The proposed SNPC is described as

( ) ( ) ( )

u k t , = u k − 1, t +Δ u k t , (9)

SNPC SNPC SNPC

( ) ( ) ( ) ( ) ( )
( ) ( )

Δ u kt , = w ktekt , , + w kt , Δ ekt ,

SNPC 1 2

(10)

+ wkt ekt , δ ,

3

( ) ( ) ( )

Δ ekt , = ekt , − ekt , − 1 (11)

( ) ( ) ( )

δ ekt , =Δ ekt , −Δ ekt , − 1 (12)

( )( )

where is adjustable parameter. In order to apply it to practical batch

process, the following transformation is taken

i wkti

, = 1, 2, 3