Modeling, Identification and Control of Irrigation Station with Sprinkling: Takagi-Sugeno Approach - Complex System Modelling and Control Through Intelligent Soft Computations - page 477

P

c

1 l lik

ð xk ðÞ Þ y i k ð þ 1 Þ

i¼

ð þ Þ ¼ ð Þ

yk 1 23

P

c
i¼1 l lik

ð xk ðÞ Þ

Then the global rule of the pressure output is as follow:

R PG : y PG k ðÞ ¼ 1 : 0851y p k ð 1 Þ 0 : 1745y p k ð 2 Þ

ð 24 Þ

þ 0 : 0563uk ð 1 Þþ 0 : 0317uk ð 2 Þ

and the global rule of fl flow output is as follow:

R QG : y QG k ðÞ ¼ 1 : 0851y Q k ð 1 Þ 0 : 1745y Q k ð 2 Þ

ð 25 Þ

þ 1 : 4116uk ð 1 Þ 1 : 32uk ð 2 Þ

thus, the open loop transfer functions are:

8
<

0 : 05632z þ 0 : 0317

H BOP ¼

z 2 1 : 0851z þ 0 : 1745

ð 26 Þ

1 : 4116z 1 : 32

:

H BOQ ¼

z 2 1 : 0851z þ 0 : 1745

The discrete state representation associated with system 26 :

8
<

P k
Q k

þ

u k

P k þ 1
Q k þ 1

0 : 1422 0 : 4403 0 : 0917

¼

0 : 0917 0 : 9428 0 : 0119

ð 27 Þ

þ

u k

: 0 4 : 7235 P k

Q k

0
0

y k ¼

14 : 7535 4 : 9165

5 s into the model obtained, The system sampling
period is chosen T e = 0.2 s then the delay

We introduce the delay s ¼

s ¼ 5 s is calculated at field discrete time

by z T e

5
0 : 2

z z 25 . The system 26 becomes:

¼ ¼

<

0 : 05632z þ 0 : 0317

z 25

H BOP ¼

z 2 1 : 0851z þ 0 : 1745

ð 28 Þ

1 : 4116z 1 : 32

:

z 25

H BOQ ¼

z 2 1 : 0851z þ 0 : 1745

3.5 Validation Tests of T-S Model

Therefore, to ensure that the model obtained from the estimation it is compatible
with other forms of inputs to represent correctly system functioning to identify. In